[Project] Add kann library to start torch removal

6 files changed, 3900 insertions, 0 deletions

diff --git a/contrib/kann/CMakeLists.txt b/contrib/kann/CMakeLists.txt
new file mode 100644
index 000000000..d7bd73d28
--- /dev/null
+++ b/contrib/kann/CMakeLists.txt
@@ -0,0 +1,22 @@
+SET(LIBKANNSRC	kautodiff.c kann.c)
+
+IF(ENABLE_FULL_DEBUG MATCHES "OFF")
+    if ("${CMAKE_C_COMPILER_ID}" STREQUAL "Clang" OR "${CMAKE_C_COMPILER_ID}" STREQUAL "GNU")
+        SET(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -O3")
+    endif ()
+ENDIF()
+
+ADD_LIBRARY(rspamd-kann SHARED ${LIBKANNSRC})
+
+ProcessPackage(BLAS OPTIONAL LIBRARY openblas blas
+        INCLUDE cblas.h INCLUDE_SUFFIXES include/openblas
+        include/blas
+        ROOT ${BLAS_ROOT_DIR}
+        LIB_OUTPUT BLAS_REQUIRED_LIBRARIES)
+IF(WITH_BLAS)
+    MESSAGE(STATUS "Use openblas to accelerate kann")
+    TARGET_LINK_LIBRARIES(rspamd-kann  ${BLAS_REQUIRED_LIBRARIES})
+    ADD_DEFINITIONS(-DHAVE_CBLAS)
+ENDIF(WITH_BLAS)
+
+INSTALL(TARGETS rspamd-kann LIBRARY DESTINATION ${RSPAMD_LIBDIR})
\ No newline at end of file
diff --git a/contrib/kann/LICENSE.txt b/contrib/kann/LICENSE.txt
new file mode 100644
index 000000000..8b2cf1141
--- /dev/null
+++ b/contrib/kann/LICENSE.txt
@@ -0,0 +1,24 @@
+The MIT License
+
+Copyright (c) 2018-2019 Dana-Farber Cancer Institute
+              2016-2018 Broad Institute
+
+Permission is hereby granted, free of charge, to any person obtaining
+a copy of this software and associated documentation files (the
+"Software"), to deal in the Software without restriction, including
+without limitation the rights to use, copy, modify, merge, publish,
+distribute, sublicense, and/or sell copies of the Software, and to
+permit persons to whom the Software is furnished to do so, subject to
+the following conditions:
+
+The above copyright notice and this permission notice shall be
+included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/contrib/kann/kann.c b/contrib/kann/kann.c
new file mode 100644
index 000000000..0af15fb2a
--- /dev/null
+++ b/contrib/kann/kann.c
@@ -0,0 +1,977 @@
+#include <math.h>
+#include <float.h>
+#include <string.h>
+#include <stdlib.h>
+#include <assert.h>
+#include <stdarg.h>
+#include "kann.h"
+
+int kann_verbose = 3;
+
+/******************************************
+ *** @@BASIC: fundamental KANN routines ***
+ ******************************************/
+
+static void kad_ext_collate(int n, kad_node_t **a, float **_x, float **_g, float **_c)
+{
+	int i, j, k, l, n_var;
+	float *x, *g, *c;
+	n_var = kad_size_var(n, a);
+	x = *_x = (float*)realloc(*_x, n_var * sizeof(float));
+	g = *_g = (float*)realloc(*_g, n_var * sizeof(float));
+	c = *_c = (float*)realloc(*_c, kad_size_const(n, a) * sizeof(float));
+	memset(g, 0, n_var * sizeof(float));
+	for (i = j = k = 0; i < n; ++i) {
+		kad_node_t *v = a[i];
+		if (kad_is_var(v)) {
+			l = kad_len(v);
+			memcpy(&x[j], v->x, l * sizeof(float));
+			free(v->x);
+			v->x = &x[j];
+			v->g = &g[j];
+			j += l;
+		} else if (kad_is_const(v)) {
+			l = kad_len(v);
+			memcpy(&c[k], v->x, l * sizeof(float));
+			free(v->x);
+			v->x = &c[k];
+			k += l;
+		}
+	}
+}
+
+static void kad_ext_sync(int n, kad_node_t **a, float *x, float *g, float *c)
+{
+	int i, j, k;
+	for (i = j = k = 0; i < n; ++i) {
+		kad_node_t *v = a[i];
+		if (kad_is_var(v)) {
+			v->x = &x[j];
+			v->g = &g[j];
+			j += kad_len(v);
+		} else if (kad_is_const(v)) {
+			v->x = &c[k];
+			k += kad_len(v);
+		}
+	}
+}
+
+kann_t *kann_new(kad_node_t *cost, int n_rest, ...)
+{
+	kann_t *a;
+	int i, n_roots = 1 + n_rest, has_pivot = 0, has_recur = 0;
+	kad_node_t **roots;
+	va_list ap;
+
+	if (cost->n_d != 0) return 0;
+
+	va_start(ap, n_rest);
+	roots = (kad_node_t**)malloc((n_roots + 1) * sizeof(kad_node_t*));
+	for (i = 0; i < n_rest; ++i)
+		roots[i] = va_arg(ap, kad_node_t*);
+	roots[i++] = cost;
+	va_end(ap);
+
+	cost->ext_flag |= KANN_F_COST;
+	a = (kann_t*)calloc(1, sizeof(kann_t));
+	a->v = kad_compile_array(&a->n, n_roots, roots);
+
+	for (i = 0; i < a->n; ++i) {
+		if (a->v[i]->pre) has_recur = 1;
+		if (kad_is_pivot(a->v[i])) has_pivot = 1;
+	}
+	if (has_recur && !has_pivot) { /* an RNN that doesn't have a pivot; then add a pivot on top of cost and recompile */
+		cost->ext_flag &= ~KANN_F_COST;
+		roots[n_roots-1] = cost = kad_avg(1, &cost), cost->ext_flag |= KANN_F_COST;
+		free(a->v);
+		a->v = kad_compile_array(&a->n, n_roots, roots);
+	}
+	kad_ext_collate(a->n, a->v, &a->x, &a->g, &a->c);
+	free(roots);
+	return a;
+}
+
+kann_t *kann_clone(kann_t *a, int batch_size)
+{
+	kann_t *b;
+	b = (kann_t*)calloc(1, sizeof(kann_t));
+	b->n = a->n;
+	b->v = kad_clone(a->n, a->v, batch_size);
+	kad_ext_collate(b->n, b->v, &b->x, &b->g, &b->c);
+	return b;
+}
+
+kann_t *kann_unroll_array(kann_t *a, int *len)
+{
+	kann_t *b;
+	b = (kann_t*)calloc(1, sizeof(kann_t));
+	b->x = a->x, b->g = a->g, b->c = a->c; /* these arrays are shared */
+	b->v = kad_unroll(a->n, a->v, &b->n, len);
+	return b;
+}
+
+kann_t *kann_unroll(kann_t *a, ...)
+{
+	kann_t *b;
+	va_list ap;
+	int i, n_pivots, *len;
+	n_pivots = kad_n_pivots(a->n, a->v);
+	len = (int*)calloc(n_pivots, sizeof(int));
+	va_start(ap, a);
+	for (i = 0; i < n_pivots; ++i) len[i] = va_arg(ap, int);
+	va_end(ap);
+	b = kann_unroll_array(a, len);
+	free(len);
+	return b;
+}
+
+void kann_delete_unrolled(kann_t *a)
+{
+	if (a && a->mt) kann_mt(a, 0, 0);
+	if (a && a->v) kad_delete(a->n, a->v);
+	free(a);
+}
+
+void kann_delete(kann_t *a)
+{
+	if (a == 0) return;
+	free(a->x); free(a->g); free(a->c);
+	kann_delete_unrolled(a);
+}
+
+static void kann_switch_core(kann_t *a, int is_train)
+{
+	int i;
+	for (i = 0; i < a->n; ++i)
+		if (a->v[i]->op == 12 && a->v[i]->n_child == 2)
+			*(int32_t*)a->v[i]->ptr = !!is_train;
+}
+
+#define chk_flg(flag, mask) ((mask) == 0 || ((flag) & (mask)))
+#define chk_lbl(label, query) ((query) == 0 || (label) == (query))
+
+int kann_find(const kann_t *a, uint32_t ext_flag, int32_t ext_label)
+{
+	int i, k, r = -1;
+	for (i = k = 0; i < a->n; ++i)
+		if (chk_flg(a->v[i]->ext_flag, ext_flag) && chk_lbl(a->v[i]->ext_label, ext_label))
+			++k, r = i;
+	return k == 1? r : k == 0? -1 : -2;
+}
+
+int kann_feed_bind(kann_t *a, uint32_t ext_flag, int32_t ext_label, float **x)
+{
+	int i, k;
+	if (x == 0) return 0;
+	for (i = k = 0; i < a->n; ++i)
+		if (kad_is_feed(a->v[i]) && chk_flg(a->v[i]->ext_flag, ext_flag) && chk_lbl(a->v[i]->ext_label, ext_label))
+			a->v[i]->x = x[k++];
+	return k;
+}
+
+int kann_feed_dim(const kann_t *a, uint32_t ext_flag, int32_t ext_label)
+{
+	int i, k, n = 0;
+	for (i = k = 0; i < a->n; ++i)
+		if (kad_is_feed(a->v[i]) && chk_flg(a->v[i]->ext_flag, ext_flag) && chk_lbl(a->v[i]->ext_label, ext_label))
+			++k, n = a->v[i]->n_d > 1? kad_len(a->v[i]) / a->v[i]->d[0] : a->v[i]->n_d == 1? a->v[i]->d[0] : 1;
+	return k == 1? n : k == 0? -1 : -2;
+}
+
+static float kann_cost_core(kann_t *a, int cost_label, int cal_grad)
+{
+	int i_cost;
+	float cost;
+	i_cost = kann_find(a, KANN_F_COST, cost_label);
+	assert(i_cost >= 0);
+	cost = *kad_eval_at(a->n, a->v, i_cost);
+	if (cal_grad) kad_grad(a->n, a->v, i_cost);
+	return cost;
+}
+
+int kann_eval(kann_t *a, uint32_t ext_flag, int ext_label)
+{
+	int i, k;
+	for (i = k = 0; i < a->n; ++i)
+		if (chk_flg(a->v[i]->ext_flag, ext_flag) && chk_lbl(a->v[i]->ext_label, ext_label))
+			++k, a->v[i]->tmp = 1;
+	kad_eval_marked(a->n, a->v);
+	return k;
+}
+
+void kann_rnn_start(kann_t *a)
+{
+	int i;
+	kann_set_batch_size(a, 1);
+	for (i = 0; i < a->n; ++i) {
+		kad_node_t *p = a->v[i];
+		if (p->pre) { /* NB: BE CAREFUL of the interaction between kann_rnn_start() and kann_set_batch_size() */
+			kad_node_t *q = p->pre;
+			if (q->x) memcpy(p->x, q->x, kad_len(p) * sizeof(float));
+			else memset(p->x, 0, kad_len(p) * sizeof(float));
+			if (q->n_child > 0) free(q->x);
+			q->x = p->x;
+		}
+	}
+}
+
+void kann_rnn_end(kann_t *a)
+{
+	int i;
+	kad_ext_sync(a->n, a->v, a->x, a->g, a->c);
+	for (i = 0; i < a->n; ++i)
+		if (a->v[i]->pre && a->v[i]->pre->n_child > 0)
+			a->v[i]->pre->x = (float*)calloc(kad_len(a->v[i]->pre), sizeof(float));
+}
+
+static int kann_class_error_core(const kann_t *ann, int *base)
+{
+	int i, j, k, m, n, off, n_err = 0;
+	for (i = 0, *base = 0; i < ann->n; ++i) {
+		kad_node_t *p = ann->v[i];
+		if (((p->op == 13 && (p->n_child == 2 || p->n_child == 3)) || (p->op == 22 && p->n_child == 2)) && p->n_d == 0) { /* ce_bin or ce_multi */
+			kad_node_t *x = p->child[0], *t = p->child[1];
+			n = t->d[t->n_d - 1], m = kad_len(t) / n;
+			for (j = off = 0; j < m; ++j, off += n) {
+				float t_sum = 0.0f, t_min = 1.0f, t_max = 0.0f, x_max = 0.0f, x_min = 1.0f;
+				int x_max_k = -1, t_max_k = -1;
+				for (k = 0; k < n; ++k) {
+					float xk = x->x[off+k], tk = t->x[off+k];
+					t_sum += tk;
+					t_min = t_min < tk? t_min : tk;
+					x_min = x_min < xk? x_min : xk;
+					if (t_max < tk) t_max = tk, t_max_k = k;
+					if (x_max < xk) x_max = xk, x_max_k = k;
+				}
+				if (t_sum - 1.0f == 0 && t_min >= 0.0f && x_min >= 0.0f && x_max <= 1.0f) {
+					++(*base);
+					n_err += (x_max_k != t_max_k);
+				}
+			}
+		}
+	}
+	return n_err;
+}
+
+/*************************
+ * @@MT: multi-threading *
+ *************************/
+
+#ifdef HAVE_PTHREAD
+#include <pthread.h>
+
+struct mtaux_t;
+
+typedef struct { /* per-worker data */
+	kann_t *a;
+	float cost;
+	int action;
+	pthread_t tid;
+	struct mtaux_t *g;
+} mtaux1_t;
+
+typedef struct mtaux_t { /* cross-worker data */
+	int n_threads, max_batch_size;
+	int cal_grad, cost_label, eval_out;
+	volatile int n_idle; /* we will be busy waiting on this, so volatile necessary */
+	pthread_mutex_t mtx;
+	pthread_cond_t cv;
+	mtaux1_t *mt;
+} mtaux_t;
+
+static void *mt_worker(void *data) /* pthread worker */
+{
+	mtaux1_t *mt1 = (mtaux1_t*)data;
+	mtaux_t *mt = mt1->g;
+	for (;;) {
+		int action;
+		pthread_mutex_lock(&mt->mtx);
+		mt1->action = 0;
+		++mt->n_idle;
+		while (mt1->action == 0)
+			pthread_cond_wait(&mt->cv, &mt->mtx);
+		action = mt1->action;
+		pthread_mutex_unlock(&mt->mtx);
+		if (action == -1) break;
+
+		if (mt->eval_out) kann_eval(mt1->a, KANN_F_OUT, 0);
+		else mt1->cost = kann_cost_core(mt1->a, mt->cost_label, mt->cal_grad);
+	}
+	pthread_exit(0);
+}
+
+static void mt_destroy(mtaux_t *mt) /* de-allocate an entire mtaux_t struct */
+{
+	int i;
+	pthread_mutex_lock(&mt->mtx);
+	mt->n_idle = 0;
+	for (i = 1; i < mt->n_threads; ++i) mt->mt[i].action = -1;
+	pthread_cond_broadcast(&mt->cv);
+	pthread_mutex_unlock(&mt->mtx);
+	for (i = 1; i < mt->n_threads; ++i) pthread_join(mt->mt[i].tid, 0);
+	for (i = 0; i < mt->n_threads; ++i) kann_delete(mt->mt[i].a);
+	free(mt->mt);
+	pthread_cond_destroy(&mt->cv);
+	pthread_mutex_destroy(&mt->mtx);
+	free(mt);
+}
+
+void kann_mt(kann_t *ann, int n_threads, int max_batch_size)
+{
+	mtaux_t *mt;
+	int i, k;
+
+	if (n_threads <= 1) {
+		if (ann->mt) mt_destroy((mtaux_t*)ann->mt);
+		ann->mt = 0;
+		return;
+	}
+	if (n_threads > max_batch_size) n_threads = max_batch_size;
+	if (n_threads <= 1) return;
+
+	mt = (mtaux_t*)calloc(1, sizeof(mtaux_t));
+	mt->n_threads = n_threads, mt->max_batch_size = max_batch_size;
+	pthread_mutex_init(&mt->mtx, 0);
+	pthread_cond_init(&mt->cv, 0);
+	mt->mt = (mtaux1_t*)calloc(n_threads, sizeof(mtaux1_t));
+	for (i = k = 0; i < n_threads; ++i) {
+		int size = (max_batch_size - k) / (n_threads - i);
+		mt->mt[i].a = kann_clone(ann, size);
+		mt->mt[i].g = mt;
+		k += size;
+	}
+	for (i = 1; i < n_threads; ++i)
+		pthread_create(&mt->mt[i].tid, 0, mt_worker, &mt->mt[i]);
+	while (mt->n_idle < n_threads - 1); /* busy waiting until all threads in sync */
+	ann->mt = mt;
+}
+
+static void mt_kickoff(kann_t *a, int cost_label, int cal_grad, int eval_out)
+{
+	mtaux_t *mt = (mtaux_t*)a->mt;
+	int i, j, k, B, n_var;
+
+	B = kad_sync_dim(a->n, a->v, -1); /* get the current batch size */
+	assert(B <= mt->max_batch_size); /* TODO: can be relaxed */
+	n_var = kann_size_var(a);
+
+	pthread_mutex_lock(&mt->mtx);
+	mt->cost_label = cost_label, mt->cal_grad = cal_grad, mt->eval_out = eval_out;
+	for (i = k = 0; i < mt->n_threads; ++i) {
+		int size = (B - k) / (mt->n_threads - i);
+		for (j = 0; j < a->n; ++j)
+			if (kad_is_feed(a->v[j]))
+				mt->mt[i].a->v[j]->x = &a->v[j]->x[k * kad_len(a->v[j]) / a->v[j]->d[0]];
+		kad_sync_dim(mt->mt[i].a->n, mt->mt[i].a->v, size); /* TODO: we can point ->x to internal nodes, too */
+		k += size;
+		memcpy(mt->mt[i].a->x, a->x, n_var * sizeof(float));
+		mt->mt[i].action = 1;
+	}
+	mt->n_idle = 0;
+	pthread_cond_broadcast(&mt->cv);
+	pthread_mutex_unlock(&mt->mtx);
+}
+
+float kann_cost(kann_t *a, int cost_label, int cal_grad)
+{
+	mtaux_t *mt = (mtaux_t*)a->mt;
+	int i, j, B, k, n_var;
+	float cost;
+
+	if (mt == 0) return kann_cost_core(a, cost_label, cal_grad);
+	B = kad_sync_dim(a->n, a->v, -1); /* get the current batch size */
+	n_var = kann_size_var(a);
+
+	mt_kickoff(a, cost_label, cal_grad, 0);
+	mt->mt[0].cost = kann_cost_core(mt->mt[0].a, cost_label, cal_grad);
+	while (mt->n_idle < mt->n_threads - 1); /* busy waiting until all threads in sync */
+
+	memset(a->g, 0, n_var * sizeof(float)); /* TODO: check if this is necessary when cal_grad is false */
+	for (i = k = 0, cost = 0.0f; i < mt->n_threads; ++i) {
+		int size = (B - k) / (mt->n_threads - i);
+		cost += mt->mt[i].cost * size / B;
+		kad_saxpy(n_var, (float)size / B, mt->mt[i].a->g, a->g);
+		k += size;
+	}
+	for (j = 0; j < a->n; ++j) { /* copy values back at recurrent nodes (needed by textgen; TODO: temporary solution) */
+		kad_node_t *p = a->v[j];
+		if (p->pre && p->n_d >= 2 && p->d[0] == B) {
+			for (i = k = 0; i < mt->n_threads; ++i) {
+				kad_node_t *q = mt->mt[i].a->v[j];
+				memcpy(&p->x[k], q->x, kad_len(q) * sizeof(float));
+				k += kad_len(q);
+			}
+		}
+	}
+	return cost;
+}
+
+int kann_eval_out(kann_t *a)
+{
+	mtaux_t *mt = (mtaux_t*)a->mt;
+	int j, B, n_eval;
+	if (mt == 0) return kann_eval(a, KANN_F_OUT, 0);
+	B = kad_sync_dim(a->n, a->v, -1); /* get the current batch size */
+	mt_kickoff(a, 0, 0, 1);
+	n_eval = kann_eval(mt->mt[0].a, KANN_F_OUT, 0);
+	while (mt->n_idle < mt->n_threads - 1); /* busy waiting until all threads in sync */
+	for (j = 0; j < a->n; ++j) { /* copy output values back */
+		kad_node_t *p = a->v[j];
+		if (p->ext_flag & KANN_F_OUT) {
+			int i, t, k, d0 = p->d[0] / B, d1 = 1; /* for RNN, p->d[0] may equal unroll_len * batch_size */
+			assert(p->d[0] % B == 0);
+			for (i = 1; i < p->n_d; ++i) d1 *= p->d[i];
+			for (i = 0; i < d0; ++i) {
+				for (t = k = 0; t < mt->n_threads; ++t) { /* similar to the forward pass of kad_op_concat() */
+					kad_node_t *q = mt->mt[t].a->v[j];
+					int size = q->d[0] / d0;
+					memcpy(&p->x[(i * B + k) * d1], &q->x[i * size * d1], size * d1 * sizeof(float));
+					k += size;
+				}
+			}
+		}
+	}
+	return n_eval;
+}
+
+int kann_class_error(const kann_t *ann, int *base)
+{
+	mtaux_t *mt = (mtaux_t*)ann->mt;
+	int i, n_err = 0, b = 0;
+	if (mt == 0) return kann_class_error_core(ann, base);
+	for (i = 0; i < mt->n_threads; ++i) {
+		n_err += kann_class_error_core(mt->mt[i].a, &b);
+		*base += b;
+	}
+	return n_err;
+}
+
+void kann_switch(kann_t *ann, int is_train)
+{
+	mtaux_t *mt = (mtaux_t*)ann->mt;
+	int i;
+	if (mt == 0) {
+		kann_switch_core(ann, is_train);
+		return;
+	}
+	for (i = 0; i < mt->n_threads; ++i)
+		kann_switch_core(mt->mt[i].a, is_train);
+}
+#else
+void kann_mt(kann_t *ann, int n_threads, int max_batch_size) {}
+float kann_cost(kann_t *a, int cost_label, int cal_grad) { return kann_cost_core(a, cost_label, cal_grad); }
+int kann_eval_out(kann_t *a) { return kann_eval(a, KANN_F_OUT, 0); }
+int kann_class_error(const kann_t *a, int *base) { return kann_class_error_core(a, base); }
+void kann_switch(kann_t *ann, int is_train) { return kann_switch_core(ann, is_train); }
+#endif
+
+/***********************
+ *** @@IO: model I/O ***
+ ***********************/
+
+#define KANN_MAGIC "KAN\1"
+
+void kann_save_fp(FILE *fp, kann_t *ann)
+{
+	kann_set_batch_size(ann, 1);
+	fwrite(KANN_MAGIC, 1, 4, fp);
+	kad_save(fp, ann->n, ann->v);
+	fwrite(ann->x, sizeof(float), kann_size_var(ann), fp);
+	fwrite(ann->c, sizeof(float), kann_size_const(ann), fp);
+}
+
+void kann_save(const char *fn, kann_t *ann)
+{
+	FILE *fp;
+	fp = fn && strcmp(fn, "-")? fopen(fn, "wb") : stdout;
+	kann_save_fp(fp, ann);
+	fclose(fp);
+}
+
+kann_t *kann_load_fp(FILE *fp)
+{
+	char magic[4];
+	kann_t *ann;
+	int n_var, n_const;
+
+	fread(magic, 1, 4, fp);
+	if (strncmp(magic, KANN_MAGIC, 4) != 0) {
+		fclose(fp);
+		return 0;
+	}
+	ann = (kann_t*)calloc(1, sizeof(kann_t));
+	ann->v = kad_load(fp, &ann->n);
+	n_var = kad_size_var(ann->n, ann->v);
+	n_const = kad_size_const(ann->n, ann->v);
+	ann->x = (float*)malloc(n_var * sizeof(float));
+	ann->g = (float*)calloc(n_var, sizeof(float));
+	ann->c = (float*)malloc(n_const * sizeof(float));
+	fread(ann->x, sizeof(float), n_var, fp);
+	fread(ann->c, sizeof(float), n_const, fp);
+	kad_ext_sync(ann->n, ann->v, ann->x, ann->g, ann->c);
+	return ann;
+}
+
+kann_t *kann_load(const char *fn)
+{
+	FILE *fp;
+	kann_t *ann;
+	fp = fn && strcmp(fn, "-")? fopen(fn, "rb") : stdin;
+	ann = kann_load_fp(fp);
+	fclose(fp);
+	return ann;
+}
+
+/**********************************************
+ *** @@LAYER: layers and model generation ***
+ **********************************************/
+
+/********** General but more complex APIs **********/
+
+kad_node_t *kann_new_leaf_array(int *offset, kad_node_p *par, uint8_t flag, float x0_01, int n_d, int32_t d[KAD_MAX_DIM])
+{
+	int i, len, off = offset && par? *offset : -1;
+	kad_node_t *p;
+
+	if (off >= 0 && par[off]) return par[(*offset)++];
+	p = (kad_node_t*)calloc(1, sizeof(kad_node_t));
+	p->n_d = n_d, p->flag = flag;
+	memcpy(p->d, d, n_d * sizeof(int32_t));
+	len = kad_len(p);
+	p->x = (float*)calloc(len, sizeof(float));
+	if (p->n_d <= 1) {
+		for (i = 0; i < len; ++i)
+			p->x[i] = x0_01;
+	} else {
+		double sdev_inv;
+		sdev_inv = 1.0 / sqrt((double)len / p->d[0]);
+		for (i = 0; i < len; ++i)
+			p->x[i] = (float)(kad_drand_normal(0) * sdev_inv);
+	}
+	if (off >= 0) par[off] = p, ++(*offset);
+	return p;
+}
+
+kad_node_t *kann_new_leaf2(int *offset, kad_node_p *par, uint8_t flag, float x0_01, int n_d, ...)
+{
+	int32_t i, d[KAD_MAX_DIM];
+	va_list ap;
+	va_start(ap, n_d); for (i = 0; i < n_d; ++i) d[i] = va_arg(ap, int); va_end(ap);
+	return kann_new_leaf_array(offset, par, flag, x0_01, n_d, d);
+}
+
+kad_node_t *kann_layer_dense2(int *offset, kad_node_p *par, kad_node_t *in, int n1)
+{
+	int n0;
+	kad_node_t *w, *b;
+	n0 = in->n_d >= 2? kad_len(in) / in->d[0] : kad_len(in);
+	w = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 2, n1, n0);
+	b = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 1, n1);
+	return kad_add(kad_cmul(in, w), b);
+}
+
+kad_node_t *kann_layer_dropout2(int *offset, kad_node_p *par, kad_node_t *t, float r)
+{
+	kad_node_t *x[2], *cr;
+	cr = kann_new_leaf2(offset, par, KAD_CONST, r, 0);
+	x[0] = t, x[1] = kad_dropout(t, cr);
+	return kad_switch(2, x);
+}
+
+kad_node_t *kann_layer_layernorm2(int *offset, kad_node_t **par, kad_node_t *in)
+{
+	int n0;
+	kad_node_t *alpha, *beta;
+	n0 = in->n_d >= 2? kad_len(in) / in->d[0] : kad_len(in);
+	alpha = kann_new_leaf2(offset, par, KAD_VAR, 1.0f, 1, n0);
+	beta  = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 1, n0);
+	return kad_add(kad_mul(kad_stdnorm(in), alpha), beta);
+}
+
+static inline kad_node_t *cmul_norm2(int *offset, kad_node_t **par, kad_node_t *x, kad_node_t *w, int use_norm)
+{
+	return use_norm? kann_layer_layernorm2(offset, par, kad_cmul(x, w)) : kad_cmul(x, w);
+}
+
+kad_node_t *kann_layer_rnn2(int *offset, kad_node_t **par, kad_node_t *in, kad_node_t *h0, int rnn_flag)
+{
+	int n0, n1 = h0->d[h0->n_d-1], use_norm = !!(rnn_flag & KANN_RNN_NORM);
+	kad_node_t *t, *w, *u, *b, *out;
+
+	u = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 2, n1, n1);
+	b = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 1, n1);
+	t = cmul_norm2(offset, par, h0, u, use_norm);
+	if (in) {
+		n0 = in->n_d >= 2? kad_len(in) / in->d[0] : kad_len(in);
+		w = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 2, n1, n0);
+		t = kad_add(cmul_norm2(offset, par, in, w, use_norm), t);
+	}
+	out = kad_tanh(kad_add(t, b));
+	out->pre = h0;
+	return out;
+}
+
+kad_node_t *kann_layer_gru2(int *offset, kad_node_t **par, kad_node_t *in, kad_node_t *h0, int rnn_flag)
+{
+	int n0 = 0, n1 = h0->d[h0->n_d-1], use_norm = !!(rnn_flag & KANN_RNN_NORM);
+	kad_node_t *t, *r, *z, *w, *u, *b, *s, *out;
+
+	if (in) n0 = in->n_d >= 2? kad_len(in) / in->d[0] : kad_len(in);
+	/* z = sigm(x_t * W_z + h_{t-1} * U_z + b_z) */
+	u = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 2, n1, n1);
+	b = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 1, n1);
+	t = cmul_norm2(offset, par, h0, u, use_norm);
+	if (in) {
+		w = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 2, n1, n0);
+		t = kad_add(cmul_norm2(offset, par, in, w, use_norm), t);
+	}
+	z = kad_sigm(kad_add(t, b));
+	/* r = sigm(x_t * W_r + h_{t-1} * U_r + b_r) */
+	u = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 2, n1, n1);
+	b = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 1, n1);
+	t = cmul_norm2(offset, par, h0, u, use_norm);
+	if (in) {
+		w = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 2, n1, n0);
+		t = kad_add(cmul_norm2(offset, par, in, w, use_norm), t);
+	}
+	r = kad_sigm(kad_add(t, b));
+	/* s = tanh(x_t * W_s + (h_{t-1} # r) * U_s + b_s) */
+	u = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 2, n1, n1);
+	b = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 1, n1);
+	t = cmul_norm2(offset, par, kad_mul(r, h0), u, use_norm);
+	if (in) {
+		w = kann_new_leaf2(offset, par, KAD_VAR, 0.0f, 2, n1, n0);
+		t = kad_add(cmul_norm2(offset, par, in, w, use_norm), t);
+	}
+	s = kad_tanh(kad_add(t, b));
+	/* h_t = z # h_{t-1} + (1 - z) # s */
+	out = kad_add(kad_mul(kad_1minus(z), s), kad_mul(z, h0));
+	out->pre = h0;
+	return out;
+}
+
+/********** APIs without offset & par **********/
+
+kad_node_t *kann_new_leaf(uint8_t flag, float x0_01, int n_d, ...)
+{
+	int32_t i, d[KAD_MAX_DIM];
+	va_list ap;
+	va_start(ap, n_d); for (i = 0; i < n_d; ++i) d[i] = va_arg(ap, int); va_end(ap);
+	return kann_new_leaf_array(0, 0, flag, x0_01, n_d, d);
+}
+
+kad_node_t *kann_new_scalar(uint8_t flag, float x) { return kann_new_leaf(flag, x, 0); }
+kad_node_t *kann_new_weight(int n_row, int n_col) { return kann_new_leaf(KAD_VAR, 0.0f, 2, n_row, n_col); }
+kad_node_t *kann_new_vec(int n, float x) { return kann_new_leaf(KAD_VAR, x, 1, n); }
+kad_node_t *kann_new_bias(int n) { return kann_new_vec(n, 0.0f); }
+kad_node_t *kann_new_weight_conv2d(int n_out, int n_in, int k_row, int k_col) { return kann_new_leaf(KAD_VAR, 0.0f, 4, n_out, n_in, k_row, k_col); }
+kad_node_t *kann_new_weight_conv1d(int n_out, int n_in, int kernel_len) { return kann_new_leaf(KAD_VAR, 0.0f, 3, n_out, n_in, kernel_len); }
+
+kad_node_t *kann_layer_input(int n1)
+{
+	kad_node_t *t;
+	t = kad_feed(2, 1, n1), t->ext_flag |= KANN_F_IN;
+	return t;
+}
+
+kad_node_t *kann_layer_dense(kad_node_t *in, int n1) { return kann_layer_dense2(0, 0, in, n1); }
+kad_node_t *kann_layer_dropout(kad_node_t *t, float r) { return kann_layer_dropout2(0, 0, t, r); }
+kad_node_t *kann_layer_layernorm(kad_node_t *in) { return kann_layer_layernorm2(0, 0, in); }
+
+kad_node_t *kann_layer_rnn(kad_node_t *in, int n1, int rnn_flag)
+{
+	kad_node_t *h0;
+	h0 = (rnn_flag & KANN_RNN_VAR_H0)? kad_var(0, 0, 2, 1, n1) : kad_const(0, 2, 1, n1);
+	h0->x = (float*)calloc(n1, sizeof(float));
+	return kann_layer_rnn2(0, 0, in, h0, rnn_flag);
+}
+
+kad_node_t *kann_layer_gru(kad_node_t *in, int n1, int rnn_flag)
+{
+	kad_node_t *h0;
+	h0 = (rnn_flag & KANN_RNN_VAR_H0)? kad_var(0, 0, 2, 1, n1) : kad_const(0, 2, 1, n1);
+	h0->x = (float*)calloc(n1, sizeof(float));
+	return kann_layer_gru2(0, 0, in, h0, rnn_flag);
+}
+
+static kad_node_t *kann_cmul_norm(kad_node_t *x, kad_node_t *w)
+{
+	return kann_layer_layernorm(kad_cmul(x, w));
+}
+
+kad_node_t *kann_layer_lstm(kad_node_t *in, int n1, int rnn_flag)
+{
+	int n0;
+	kad_node_t *i, *f, *o, *g, *w, *u, *b, *h0, *c0, *c, *out;
+	kad_node_t *(*cmul)(kad_node_t*, kad_node_t*) = (rnn_flag & KANN_RNN_NORM)? kann_cmul_norm : kad_cmul;
+
+	n0 = in->n_d >= 2? kad_len(in) / in->d[0] : kad_len(in);
+	h0 = (rnn_flag & KANN_RNN_VAR_H0)? kad_var(0, 0, 2, 1, n1) : kad_const(0, 2, 1, n1);
+	h0->x = (float*)calloc(n1, sizeof(float));
+	c0 = (rnn_flag & KANN_RNN_VAR_H0)? kad_var(0, 0, 2, 1, n1) : kad_const(0, 2, 1, n1);
+	c0->x = (float*)calloc(n1, sizeof(float));
+
+	/* i = sigm(x_t * W_i + h_{t-1} * U_i + b_i) */
+	w = kann_new_weight(n1, n0);
+	u = kann_new_weight(n1, n1);
+	b = kann_new_bias(n1);
+	i = kad_sigm(kad_add(kad_add(cmul(in, w), cmul(h0, u)), b));
+	/* f = sigm(x_t * W_f + h_{t-1} * U_f + b_f) */
+	w = kann_new_weight(n1, n0);
+	u = kann_new_weight(n1, n1);
+	b = kann_new_vec(n1, 1.0f); /* see Jozefowicz et al on using a large bias */
+	f = kad_sigm(kad_add(kad_add(cmul(in, w), cmul(h0, u)), b));
+	/* o = sigm(x_t * W_o + h_{t-1} * U_o + b_o) */
+	w = kann_new_weight(n1, n0);
+	u = kann_new_weight(n1, n1);
+	b = kann_new_bias(n1);
+	o = kad_sigm(kad_add(kad_add(cmul(in, w), cmul(h0, u)), b));
+	/* g = tanh(x_t * W_g + h_{t-1} * U_g + b_g) */
+	w = kann_new_weight(n1, n0);
+	u = kann_new_weight(n1, n1);
+	b = kann_new_bias(n1);
+	g = kad_tanh(kad_add(kad_add(cmul(in, w), cmul(h0, u)), b));
+	/* c_t = c_{t-1} # f + g # i */
+	c = kad_add(kad_mul(f, c0), kad_mul(g, i)); /* can't be kad_mul(c0, f)!!! */
+	c->pre = c0;
+	/* h_t = tanh(c_t) # o */
+	if (rnn_flag & KANN_RNN_NORM) c = kann_layer_layernorm(c); /* see Ba et al (2016) about how to apply layer normalization to LSTM */
+	out = kad_mul(kad_tanh(c), o);
+	out->pre = h0;
+	return out;
+}
+
+kad_node_t *kann_layer_conv2d(kad_node_t *in, int n_flt, int k_rows, int k_cols, int stride_r, int stride_c, int pad_r, int pad_c)
+{
+	kad_node_t *w;
+	w = kann_new_weight_conv2d(n_flt, in->d[1], k_rows, k_cols);
+	return kad_conv2d(in, w, stride_r, stride_c, pad_r, pad_c);
+}
+
+kad_node_t *kann_layer_conv1d(kad_node_t *in, int n_flt, int k_size, int stride, int pad)
+{
+	kad_node_t *w;
+	w = kann_new_weight_conv1d(n_flt, in->d[1], k_size);
+	return kad_conv1d(in, w, stride, pad);
+}
+
+kad_node_t *kann_layer_cost(kad_node_t *t, int n_out, int cost_type)
+{
+	kad_node_t *cost = 0, *truth = 0;
+	assert(cost_type == KANN_C_CEB || cost_type == KANN_C_CEM || cost_type == KANN_C_CEB_NEG || cost_type == KANN_C_MSE);
+	t = kann_layer_dense(t, n_out);
+	truth = kad_feed(2, 1, n_out), truth->ext_flag |= KANN_F_TRUTH;
+	if (cost_type == KANN_C_MSE) {
+		cost = kad_mse(t, truth);
+	} else if (cost_type == KANN_C_CEB) {
+		t = kad_sigm(t);
+		cost = kad_ce_bin(t, truth);
+	} else if (cost_type == KANN_C_CEB_NEG) {
+		t = kad_tanh(t);
+		cost = kad_ce_bin_neg(t, truth);
+	} else if (cost_type == KANN_C_CEM) {
+		t = kad_softmax(t);
+		cost = kad_ce_multi(t, truth);
+	}
+	t->ext_flag |= KANN_F_OUT, cost->ext_flag |= KANN_F_COST;
+	return cost;
+}
+
+void kann_shuffle(int n, int *s)
+{
+	int i, j, t;
+	for (i = 0; i < n; ++i) s[i] = i;
+	for (i = n; i > 0; --i) {
+		j = (int)(i * kad_drand(0));
+		t = s[j], s[j] = s[i-1], s[i-1] = t;
+	}
+}
+
+/***************************
+ *** @@MIN: minimization ***
+ ***************************/
+
+#ifdef __SSE__
+#include <xmmintrin.h>
+
+void kann_RMSprop(int n, float h0, const float *h, float decay, const float *g, float *t, float *r)
+{
+	int i, n4 = n>>2<<2;
+	__m128 vh, vg, vr, vt, vd, vd1, tmp, vtiny;
+	vh = _mm_set1_ps(h0);
+	vd = _mm_set1_ps(decay);
+	vd1 = _mm_set1_ps(1.0f - decay);
+	vtiny = _mm_set1_ps(1e-6f);
+	for (i = 0; i < n4; i += 4) {
+		vt = _mm_loadu_ps(&t[i]);
+		vr = _mm_loadu_ps(&r[i]);
+		vg = _mm_loadu_ps(&g[i]);
+		if (h) vh = _mm_loadu_ps(&h[i]);
+		vr = _mm_add_ps(_mm_mul_ps(vd1, _mm_mul_ps(vg, vg)), _mm_mul_ps(vd, vr));
+		_mm_storeu_ps(&r[i], vr);
+		tmp = _mm_sub_ps(vt, _mm_mul_ps(_mm_mul_ps(vh, _mm_rsqrt_ps(_mm_add_ps(vtiny, vr))), vg));
+		_mm_storeu_ps(&t[i], tmp);
+	}
+	for (; i < n; ++i) {
+		r[i] = (1. - decay) * g[i] * g[i] + decay * r[i];
+		t[i] -= (h? h[i] : h0) / sqrtf(1e-6f + r[i]) * g[i];
+	}
+}
+#else
+void kann_RMSprop(int n, float h0, const float *h, float decay, const float *g, float *t, float *r)
+{
+	int i;
+	for (i = 0; i < n; ++i) {
+		float lr = h? h[i] : h0;
+		r[i] = (1.0f - decay) * g[i] * g[i] + decay * r[i];
+		t[i] -= lr / sqrtf(1e-6f + r[i]) * g[i];
+	}
+}
+#endif
+
+float kann_grad_clip(float thres, int n, float *g)
+{
+	int i;
+	double s2 = 0.0;
+	for (i = 0; i < n; ++i)
+		s2 += g[i] * g[i];
+	s2 = sqrt(s2);
+	if (s2 > thres)
+		for (i = 0, s2 = 1.0 / s2; i < n; ++i)
+			g[i] *= (float)s2;
+	return (float)s2 / thres;
+}
+
+/****************************************************************
+ *** @@XY: simpler API for network with a single input/output ***
+ ****************************************************************/
+
+int kann_train_fnn1(kann_t *ann, float lr, int mini_size, int max_epoch, int max_drop_streak, float frac_val, int n, float **_x, float **_y)
+{
+	int i, j, *shuf, n_train, n_val, n_in, n_out, n_var, n_const, drop_streak = 0, min_set = 0;
+	float **x, **y, *x1, *y1, *r, min_val_cost = FLT_MAX, *min_x, *min_c;
+
+	n_in = kann_dim_in(ann);
+	n_out = kann_dim_out(ann);
+	if (n_in < 0 || n_out < 0) return -1;
+	n_var = kann_size_var(ann);
+	n_const = kann_size_const(ann);
+	r = (float*)calloc(n_var, sizeof(float));
+	shuf = (int*)malloc(n * sizeof(int));
+	x = (float**)malloc(n * sizeof(float*));
+	y = (float**)malloc(n * sizeof(float*));
+	kann_shuffle(n, shuf);
+	for (j = 0; j < n; ++j)
+		x[j] = _x[shuf[j]], y[j] = _y[shuf[j]];
+	n_val = (int)(n * frac_val);
+	n_train = n - n_val;
+	min_x = (float*)malloc(n_var * sizeof(float));
+	min_c = (float*)malloc(n_const * sizeof(float));
+
+	x1 = (float*)malloc(n_in  * mini_size * sizeof(float));
+	y1 = (float*)malloc(n_out * mini_size * sizeof(float));
+	kann_feed_bind(ann, KANN_F_IN,    0, &x1);
+	kann_feed_bind(ann, KANN_F_TRUTH, 0, &y1);
+
+	for (i = 0; i < max_epoch; ++i) {
+		int n_proc = 0, n_train_err = 0, n_val_err = 0, n_train_base = 0, n_val_base = 0;
+		double train_cost = 0.0, val_cost = 0.0;
+		kann_shuffle(n_train, shuf);
+		kann_switch(ann, 1);
+		while (n_proc < n_train) {
+			int b, c, ms = n_train - n_proc < mini_size? n_train - n_proc : mini_size;
+			for (b = 0; b < ms; ++b) {
+				memcpy(&x1[b*n_in],  x[shuf[n_proc+b]], n_in  * sizeof(float));
+				memcpy(&y1[b*n_out], y[shuf[n_proc+b]], n_out * sizeof(float));
+			}
+			kann_set_batch_size(ann, ms);
+			train_cost += kann_cost(ann, 0, 1) * ms;
+			c = kann_class_error(ann, &b);
+			n_train_err += c, n_train_base += b;
+			kann_RMSprop(n_var, lr, 0, 0.9f, ann->g, ann->x, r);
+			n_proc += ms;
+		}
+		train_cost /= n_train;
+		kann_switch(ann, 0);
+		n_proc = 0;
+		while (n_proc < n_val) {
+			int b, c, ms = n_val - n_proc < mini_size? n_val - n_proc : mini_size;
+			for (b = 0; b < ms; ++b) {
+				memcpy(&x1[b*n_in],  x[n_train+n_proc+b], n_in  * sizeof(float));
+				memcpy(&y1[b*n_out], y[n_train+n_proc+b], n_out * sizeof(float));
+			}
+			kann_set_batch_size(ann, ms);
+			val_cost += kann_cost(ann, 0, 0) * ms;
+			c = kann_class_error(ann, &b);
+			n_val_err += c, n_val_base += b;
+			n_proc += ms;
+		}
+		if (n_val > 0) val_cost /= n_val;
+		if (kann_verbose >= 3) {
+			fprintf(stderr, "epoch: %d; training cost: %g", i+1, train_cost);
+			if (n_train_base) fprintf(stderr, " (class error: %.2f%%)", 100.0f * n_train_err / n_train);
+			if (n_val > 0) {
+				fprintf(stderr, "; validation cost: %g", val_cost);
+				if (n_val_base) fprintf(stderr, " (class error: %.2f%%)", 100.0f * n_val_err / n_val);
+			}
+			fputc('\n', stderr);
+		}
+		if (i >= max_drop_streak && n_val > 0) {
+			if (val_cost < min_val_cost) {
+				min_set = 1;
+				memcpy(min_x, ann->x, n_var * sizeof(float));
+				memcpy(min_c, ann->c, n_const * sizeof(float));
+				drop_streak = 0;
+				min_val_cost = (float)val_cost;
+			} else if (++drop_streak >= max_drop_streak)
+				break;
+		}
+	}
+	if (min_set) {
+		memcpy(ann->x, min_x, n_var * sizeof(float));
+		memcpy(ann->c, min_c, n_const * sizeof(float));
+	}
+
+	free(min_c); free(min_x); free(y1); free(x1); free(y); free(x); free(shuf); free(r);
+	return i;
+}
+
+float kann_cost_fnn1(kann_t *ann, int n, float **x, float **y)
+{
+	int n_in, n_out, n_proc = 0, mini_size = 64 < n? 64 : n;
+	float *x1, *y1;
+	double cost = 0.0;
+
+	n_in = kann_dim_in(ann);
+	n_out = kann_dim_out(ann);
+	if (n <= 0 || n_in < 0 || n_out < 0) return 0.0;
+
+	x1 = (float*)malloc(n_in  * mini_size * sizeof(float));
+	y1 = (float*)malloc(n_out * mini_size * sizeof(float));
+	kann_feed_bind(ann, KANN_F_IN,    0, &x1);
+	kann_feed_bind(ann, KANN_F_TRUTH, 0, &y1);
+	kann_switch(ann, 0);
+	while (n_proc < n) {
+		int b, ms = n - n_proc < mini_size? n - n_proc : mini_size;
+		for (b = 0; b < ms; ++b) {
+			memcpy(&x1[b*n_in],  x[n_proc+b], n_in  * sizeof(float));
+			memcpy(&y1[b*n_out], y[n_proc+b], n_out * sizeof(float));
+		}
+		kann_set_batch_size(ann, ms);
+		cost += kann_cost(ann, 0, 0) * ms;
+		n_proc += ms;
+	}
+	free(y1); free(x1);
+	return (float)(cost / n);
+}
+
+const float *kann_apply1(kann_t *a, float *x)
+{
+	int i_out;
+	i_out = kann_find(a, KANN_F_OUT, 0);
+	if (i_out < 0) return 0;
+	kann_set_batch_size(a, 1);
+	kann_feed_bind(a, KANN_F_IN, 0, &x);
+	kad_eval_at(a->n, a->v, i_out);
+	return a->v[i_out]->x;
+}
diff --git a/contrib/kann/kann.h b/contrib/kann/kann.h
new file mode 100644
index 000000000..1605e5ea5
--- /dev/null
+++ b/contrib/kann/kann.h
@@ -0,0 +1,235 @@
+/*
+  The MIT License
+
+  Copyright (c) 2018-2019 Dana-Farber Cancer Institute
+                2016-2018 Broad Institute
+
+  Permission is hereby granted, free of charge, to any person obtaining
+  a copy of this software and associated documentation files (the
+  "Software"), to deal in the Software without restriction, including
+  without limitation the rights to use, copy, modify, merge, publish,
+  distribute, sublicense, and/or sell copies of the Software, and to
+  permit persons to whom the Software is furnished to do so, subject to
+  the following conditions:
+
+  The above copyright notice and this permission notice shall be
+  included in all copies or substantial portions of the Software.
+
+  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+  NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+  BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+  ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+  CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+  SOFTWARE.
+*/
+
+#ifndef KANN_H
+#define KANN_H
+
+#define KANN_VERSION "r536"
+
+#define KANN_F_IN       0x1   /* input */
+#define KANN_F_OUT      0x2   /* output */
+#define KANN_F_TRUTH    0x4   /* truth output */
+#define KANN_F_COST     0x8   /* final cost */
+
+#define KANN_C_CEB      1   /* binary cross-entropy cost, used with sigmoid */
+#define KANN_C_CEM      2   /* multi-class cross-entropy cost, used with softmax */
+#define KANN_C_CEB_NEG  3   /* binary cross-enytopy-like cost, used with tanh */
+#define KANN_C_MSE      4   /* mean square error */
+
+#define KANN_RNN_VAR_H0 0x1 /* take the initial hidden values as variables */
+#define KANN_RNN_NORM   0x2 /* apply layer normalization */
+
+#include "kautodiff.h"
+
+typedef struct {
+	int n;            /* number of nodes in the computational graph */
+	kad_node_t **v;   /* list of nodes */
+	float *x, *g, *c; /* collated variable values, gradients and constant values */
+	void *mt;         /* auxiliary data for multi-threading; NULL if multi-threading disabled */
+} kann_t;
+
+extern int kann_verbose;
+
+#define kann_size_var(a) kad_size_var((a)->n, (a)->v)
+#define kann_size_const(a) kad_size_const((a)->n, (a)->v)
+#define kann_dim_in(a) kann_feed_dim((a), KANN_F_IN, 0)
+#define kann_dim_out(a) kann_feed_dim((a), KANN_F_TRUTH, 0)
+#define kann_srand(seed) kad_srand(0, (seed))
+#define kann_drand() kad_drand(0)
+#define kann_set_batch_size(ann, B) kad_sync_dim((ann)->n, (ann)->v, (B))
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/**
+ * Generate a network from a computational graph
+ *
+ * A network must have at least one scalar cost node (i.e. whose n_d==0). It
+ * may optionally contain other cost nodes or output nodes not leading to the
+ * primary cost node.
+ *
+ * @param cost    cost node (must be a scalar, i.e. cost->n_d==0)
+ * @param n_rest  number of other nodes without predecessors
+ * @param ...     other nodes (of type kad_node_t*) without predecessors
+ *
+ * @return network on success, or NULL otherwise
+ */
+kann_t *kann_new(kad_node_t *cost, int n_rest, ...);
+
+/**
+ * Unroll an RNN
+ *
+ * @param a       network
+ * @param len     number of unrolls
+ *
+ * @return an unrolled network, or NULL if the network is not an RNN
+ */
+kann_t *kann_unroll(kann_t *a, ...);
+
+kann_t *kann_unroll_array(kann_t *a, int *len);
+kann_t *kann_clone(kann_t *a, int batch_size);
+void kann_delete(kann_t *a);          /* delete a network generated by kann_new() or kann_layer_final() */
+void kann_delete_unrolled(kann_t *a); /* delete a network generated by kann_unroll() */
+
+/**
+ * Enable/disable multi-threading (requiring pthread)
+ *
+ * KANN splits a mini-batch to $n_threads mini-mini-batches and puts each of
+ * them on one thread. So far, only kann_cost() takes the advantage of
+ * multi-threading.
+ *
+ * @param ann             network
+ * @param n_threads       number of threads; <=1 to completely disable multi-threading
+ * @param max_batch_size  max mini-batch size; shall no smaller than n_threads
+ */
+void kann_mt(kann_t *ann, int n_threads, int max_batch_size);
+
+/**
+ * Bind float arrays to feed nodes
+ *
+ * @param a         network
+ * @param ext_flag  required external flags
+ * @param ext_label required external label
+ * @param x         pointers (size equal to the number of matching feed nodes)
+ *
+ * @return number of matching feed nodes
+ */
+int kann_feed_bind(kann_t *a, uint32_t ext_flag, int32_t ext_label, float **x);
+
+/**
+ * Compute the cost and optionally gradients
+ *
+ * @param a          network
+ * @param cost_label required external label
+ * @param cal_grad   whether to compute gradients
+ *
+ * @return cost
+ */
+float kann_cost(kann_t *a, int cost_label, int cal_grad);
+
+int kann_eval(kann_t *a, uint32_t ext_flag, int ext_label);
+int kann_eval_out(kann_t *a);
+int kann_class_error(const kann_t *ann, int *base);
+
+/**
+ * Find a node
+ *
+ * @param a         network
+ * @param ext_flag  required external flags; set to 0 to match all flags
+ * @param ext_label required external label
+ *
+ * @return >=0 if found; -1 if not found; -2 if found multiple
+ */
+int kann_find(const kann_t *a, uint32_t ext_flag, int32_t ext_label);
+
+/**
+ * Get the size of a feed node, assuming mini-batch size 1
+ *
+ * @param a         network
+ * @param ext_flag  required external flags
+ * @param ext_label required external label
+ *
+ * @return size>=0; -1 if not found; -2 if found multiple
+ */
+int kann_feed_dim(const kann_t *a, uint32_t ext_flag, int32_t ext_label);
+
+/**
+ * Get an RNN ready for continuous feeding
+ *
+ * @param a         network
+ */
+void kann_rnn_start(kann_t *a);
+
+void kann_rnn_end(kann_t *a);
+
+/**
+ * Switch between training and prediction networks (effective only when there are switch nodes)
+ *
+ * @param a         network
+ * @param is_train  0 for prediction network and non-zero for training net
+ */
+void kann_switch(kann_t *a, int is_train);
+
+/**
+ * RMSprop update
+ *
+ * @param n      number of variables
+ * @param h0     learning rate
+ * @param h      per-variable learning rate; NULL if not applicable
+ * @param decay  RMSprop decay; use 0.9 if unsure
+ * @param g      gradient, of size n
+ * @param t      variables to change
+ * @param r      memory, of size n
+ */
+void kann_RMSprop(int n, float h0, const float *h, float decay, const float *g, float *t, float *r);
+
+void kann_shuffle(int n, int *s);
+float kann_grad_clip(float thres, int n, float *g);
+
+/* common layers */
+kad_node_t *kann_layer_input(int n1);
+kad_node_t *kann_layer_dense(kad_node_t *in, int n1);
+kad_node_t *kann_layer_dropout(kad_node_t *t, float r);
+kad_node_t *kann_layer_layernorm(kad_node_t *in);
+kad_node_t *kann_layer_rnn(kad_node_t *in, int n1, int rnn_flag);
+kad_node_t *kann_layer_lstm(kad_node_t *in, int n1, int rnn_flag);
+kad_node_t *kann_layer_gru(kad_node_t *in, int n1, int rnn_flag);
+kad_node_t *kann_layer_conv2d(kad_node_t *in, int n_flt, int k_rows, int k_cols, int stride_r, int stride_c, int pad_r, int pad_c);
+kad_node_t *kann_layer_conv1d(kad_node_t *in, int n_flt, int k_size, int stride, int pad);
+kad_node_t *kann_layer_cost(kad_node_t *t, int n_out, int cost_type);
+
+kad_node_t *kann_new_leaf(uint8_t flag, float x0_01, int n_d, ...); /* flag can be KAD_CONST or KAD_VAR */
+kad_node_t *kann_new_scalar(uint8_t flag, float x);
+kad_node_t *kann_new_weight(int n_row, int n_col);
+kad_node_t *kann_new_bias(int n);
+kad_node_t *kann_new_weight_conv2d(int n_out, int n_in, int k_row, int k_col);
+kad_node_t *kann_new_weight_conv1d(int n_out, int n_in, int kernel_len);
+
+kad_node_t *kann_new_leaf2(int *offset, kad_node_p *par, uint8_t flag, float x0_01, int n_d, ...);
+kad_node_t *kann_layer_dense2(int *offset, kad_node_p *par, kad_node_t *in, int n1);
+kad_node_t *kann_layer_dropout2(int *offset, kad_node_p *par, kad_node_t *t, float r);
+kad_node_t *kann_layer_layernorm2(int *offset, kad_node_t **par, kad_node_t *in);
+kad_node_t *kann_layer_rnn2(int *offset, kad_node_t **par, kad_node_t *in, kad_node_t *h0, int rnn_flag);
+kad_node_t *kann_layer_gru2(int *offset, kad_node_t **par, kad_node_t *in, kad_node_t *h0, int rnn_flag);
+
+/* operations on network with a single input node and a single output node */
+int kann_train_fnn1(kann_t *ann, float lr, int mini_size, int max_epoch, int max_drop_streak, float frac_val, int n, float **_x, float **_y);
+float kann_cost_fnn1(kann_t *a, int n, float **x, float **y);
+const float *kann_apply1(kann_t *a, float *x);
+
+/* model I/O */
+void kann_save_fp(FILE *fp, kann_t *ann);
+void kann_save(const char *fn, kann_t *ann);
+kann_t *kann_load_fp(FILE *fp);
+kann_t *kann_load(const char *fn);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/contrib/kann/kautodiff.c b/contrib/kann/kautodiff.c
new file mode 100644
index 000000000..f303a723f
--- /dev/null
+++ b/contrib/kann/kautodiff.c
@@ -0,0 +1,2396 @@
+#include <stdlib.h>
+#include <assert.h>
+#include <stdarg.h>
+#include <string.h>
+#include <float.h>
+#include <math.h>
+#include "kautodiff.h"
+
+typedef struct {
+	uint64_t s[2];
+	double n_gset;
+	int n_iset;
+	volatile int lock;
+} kad_rng_t;
+
+/**********************
+ * Graph construction *
+ **********************/
+
+static inline kad_node_t *kad_new_core(int n_d, int op, int n_child)
+{
+	kad_node_t *s;
+	if (n_d >= KAD_MAX_DIM) return 0;
+	s = (kad_node_t*)calloc(1, sizeof(kad_node_t));
+	s->n_d = n_d, s->op = op, s->n_child = n_child;
+	if (s->n_child) s->child = (kad_node_t**)calloc(s->n_child, sizeof(kad_node_t*));
+	return s;
+}
+
+static inline kad_node_t *kad_vleaf(uint8_t flag, float *x, float *g, int n_d, va_list ap)
+{
+	int i;
+	kad_node_t *p;
+	if (n_d > KAD_MAX_DIM) return 0;
+	p = (kad_node_t*)calloc(1, sizeof(kad_node_t));
+	p->n_d = n_d;
+	for (i = 0; i < n_d; ++i)
+		p->d[i] = va_arg(ap, int32_t);
+	p->x = x, p->g = g, p->flag = flag;
+	return p;
+}
+
+kad_node_t *kad_const(float *x, int n_d, ...)
+{
+	kad_node_t *p;
+	va_list ap;
+	va_start(ap, n_d); p = kad_vleaf(KAD_CONST, x, 0, n_d, ap); va_end(ap);
+	return p;
+}
+
+kad_node_t *kad_feed(int n_d, ...)
+{
+	kad_node_t *p;
+	va_list ap;
+	va_start(ap, n_d); p = kad_vleaf(0, 0, 0, n_d, ap); va_end(ap);
+	return p;
+}
+
+kad_node_t *kad_var(float *x, float *g, int n_d, ...)
+{
+	kad_node_t *p;
+	va_list ap;
+	va_start(ap, n_d); p = kad_vleaf(KAD_VAR, x, g, n_d, ap); va_end(ap);
+	return p;
+}
+
+static inline kad_node_t *kad_finalize_node(kad_node_t *s) /* a helper function */
+{
+	int i;
+	if (kad_op_list[s->op](s, KAD_SYNC_DIM) < 0) { /* check dimension */
+		if (s->ptr) free(s->ptr);
+		free(s->child); free(s);
+		return 0;
+	}
+	for (i = 0; i < s->n_child; ++i)
+		if (kad_is_back(s->child[i]))
+			break;
+	if (i < s->n_child) s->flag |= KAD_VAR;
+	return s;
+}
+
+/********** Simple arithmetic **********/
+
+static inline kad_node_t *kad_op2_core(int op, kad_node_t *x, kad_node_t *y)
+{
+	kad_node_t *s;
+	s = kad_new_core(0, op, 2);
+	s->child[0] = x, s->child[1] = y;
+	return kad_finalize_node(s);
+}
+
+static inline kad_node_t *kad_op1_core(int op, kad_node_t *x)
+{
+	kad_node_t *s;
+	s = kad_new_core(0, op, 1);
+	s->child[0] = x;
+	return kad_finalize_node(s);
+}
+
+#define KAD_FUNC_OP2(fname, op) kad_node_t *fname(kad_node_t *x, kad_node_t *y) { return kad_op2_core((op), x, y); }
+
+KAD_FUNC_OP2(kad_add, 1)
+KAD_FUNC_OP2(kad_sub, 23)
+KAD_FUNC_OP2(kad_mul, 2)
+KAD_FUNC_OP2(kad_cmul, 3)
+KAD_FUNC_OP2(kad_matmul, 9)
+KAD_FUNC_OP2(kad_ce_multi, 13)
+KAD_FUNC_OP2(kad_ce_bin, 22)
+KAD_FUNC_OP2(kad_ce_bin_neg, 4)
+KAD_FUNC_OP2(kad_mse, 29)
+
+#define KAD_FUNC_OP1(fname, op) kad_node_t *fname(kad_node_t *x) { return kad_op1_core((op), x); }
+
+KAD_FUNC_OP1(kad_log, 27)
+KAD_FUNC_OP1(kad_exp, 33)
+KAD_FUNC_OP1(kad_sin, 34)
+KAD_FUNC_OP1(kad_square, 5)
+KAD_FUNC_OP1(kad_sigm, 6)
+KAD_FUNC_OP1(kad_tanh, 7)
+KAD_FUNC_OP1(kad_relu, 8)
+KAD_FUNC_OP1(kad_1minus, 11)
+KAD_FUNC_OP1(kad_softmax, 14)
+KAD_FUNC_OP1(kad_stdnorm, 32)
+
+kad_node_t *kad_ce_multi_weighted(kad_node_t *pred, kad_node_t *truth, kad_node_t *weight)
+{
+	kad_node_t *s;
+	s = kad_new_core(0, 13, 3);
+	s->child[0] = pred, s->child[1] = truth, s->child[2] = weight;
+	return kad_finalize_node(s);
+}
+
+/********** Convolution **********/
+
+/* compute output dimension and padding sizes on both sides */
+static inline int conv_find_par(int in_size, int kernel_size, int stride, int pad0, int *new_pad0, int *new_pad1)
+{
+	int out_size, pad_both;
+	/* key equation: out_size = (in_size - kernel_size + pad_both) / stride + 1 */
+	if (pad0 == KAD_PAD_SAME && stride == 1) out_size = in_size;
+	else out_size = (in_size - kernel_size + (pad0 > 0? pad0 : 0) + stride - 1) / stride + 1;
+	pad_both = (out_size - 1) * stride + kernel_size - in_size;
+	*new_pad0 = pad_both / 2;
+	*new_pad1 = pad_both - *new_pad0;
+	return out_size;
+}
+
+typedef struct {
+	int kernel_size, stride, pad[2];
+} conv_conf_t;
+
+static inline conv_conf_t *conv2d_gen_aux(int in_row, int in_col, int kernel_r, int kernel_c, int stride_r, int stride_c, int top_pad, int left_pad)
+{
+	conv_conf_t *cnn;
+	cnn = (conv_conf_t*)calloc(2, sizeof(conv_conf_t));
+	cnn[0].kernel_size = kernel_r, cnn[0].stride = stride_r;
+	cnn[1].kernel_size = kernel_c, cnn[1].stride = stride_c;
+	conv_find_par(in_row, kernel_r, stride_r, top_pad,  &cnn[0].pad[0], &cnn[0].pad[1]);
+	conv_find_par(in_col, kernel_c, stride_c, left_pad, &cnn[1].pad[0], &cnn[1].pad[1]);
+	return cnn;
+}
+
+kad_node_t *kad_conv2d(kad_node_t *x, kad_node_t *w, int stride_r, int stride_c, int top_pad, int left_pad)
+{
+	kad_node_t *s;
+	if (x->n_d != 4 || w->n_d != 4) return 0;
+	s = kad_new_core(0, 16, 2);
+	s->child[0] = x, s->child[1] = w;
+	s->ptr = conv2d_gen_aux(x->d[2], x->d[3], w->d[2], w->d[3], stride_r, stride_c, top_pad, left_pad);
+	s->ptr_size = sizeof(conv_conf_t) * 2;
+	return kad_finalize_node(s);
+}
+
+kad_node_t *kad_max2d(kad_node_t *x, int kernel_r, int kernel_c, int stride_r, int stride_c, int top_pad, int left_pad)
+{
+	kad_node_t *s;
+	if (x->n_d != 4) return 0;
+	s = kad_new_core(0, 17, 1);
+	s->child[0] = x;
+	s->ptr = conv2d_gen_aux(x->d[2], x->d[3], kernel_r, kernel_c, stride_r, stride_c, top_pad, left_pad);
+	s->ptr_size = sizeof(conv_conf_t) * 2;
+	return kad_finalize_node(s);
+}
+
+static inline conv_conf_t *conv1d_gen_aux(int in_col, int kernel_c, int stride_c, int left_pad)
+{
+	conv_conf_t *cnn;
+	cnn = (conv_conf_t*)calloc(1, sizeof(conv_conf_t));
+	cnn->kernel_size = kernel_c, cnn->stride = stride_c;
+	conv_find_par(in_col, kernel_c, stride_c, left_pad, &cnn->pad[0], &cnn->pad[1]);
+	return cnn;
+}
+
+kad_node_t *kad_conv1d(kad_node_t *x, kad_node_t *w, int stride, int left_pad)
+{
+	kad_node_t *s;
+	if (x->n_d != 3 || w->n_d != 3) return 0;
+	s = kad_new_core(0, 18, 2);
+	s->child[0] = x, s->child[1] = w;
+	s->ptr = conv1d_gen_aux(x->d[2], w->d[2], stride, left_pad);
+	s->ptr_size = sizeof(conv_conf_t);
+	return kad_finalize_node(s);
+}
+
+kad_node_t *kad_max1d(kad_node_t *x, int kernel_size, int stride, int left_pad)
+{
+	kad_node_t *s;
+	if (x->n_d != 3) return 0;
+	s = kad_new_core(0, 19, 1);
+	s->child[0] = x;
+	s->ptr = conv1d_gen_aux(x->d[2], kernel_size, stride, left_pad);
+	s->ptr_size = sizeof(conv_conf_t);
+	return kad_finalize_node(s);
+}
+
+kad_node_t *kad_avg1d(kad_node_t *x, int kernel_size, int stride, int left_pad)
+{
+	kad_node_t *s;
+	if (x->n_d != 3) return 0;
+	s = kad_new_core(0, 28, 1);
+	s->child[0] = x;
+	s->ptr = conv1d_gen_aux(x->d[2], kernel_size, stride, left_pad);
+	s->ptr_size = sizeof(conv_conf_t);
+	return kad_finalize_node(s);
+}
+
+/********** Multi-node pooling **********/
+
+static kad_node_t *kad_pooling_general(int op, int n, kad_node_t **x)
+{
+	int i;
+	kad_node_t *s;
+	s = kad_new_core(0, op, n);
+	s->flag |= KAD_POOL;
+	for (i = 0; i < n; ++i)
+		s->child[i] = x[i];
+	return kad_finalize_node(s);
+}
+
+kad_node_t *kad_avg(int n, kad_node_t **x)   { return kad_pooling_general(10, n, x); }
+kad_node_t *kad_max(int n, kad_node_t **x)   { return kad_pooling_general(21, n, x); }
+kad_node_t *kad_stack(int n, kad_node_t **x) { return kad_pooling_general(35, n, x); }
+
+kad_node_t *kad_select(int n, kad_node_t **x, int which)
+{
+	kad_node_t *s;
+	int32_t i, *aux;
+	aux = (int32_t*)calloc(1, 4);
+	*aux = which;
+	s = kad_new_core(0, 12, n);
+	for (i = 0; i < n; ++i) s->child[i] = x[i];
+	s->flag |= KAD_POOL, s->ptr = aux, s->ptr_size = 4;
+	return kad_finalize_node(s);
+}
+
+/********** Dimension reduction **********/
+
+static kad_node_t *kad_reduce_general(int op, kad_node_t *x, int axis)
+{
+	kad_node_t *s;
+	int32_t *aux;
+	aux = (int32_t*)malloc(4);
+	aux[0] = axis;
+	s = kad_new_core(0, op, 1);
+	s->child[0] = x;
+	s->ptr = aux, s->ptr_size = 4;
+	return kad_finalize_node(s);
+}
+
+kad_node_t *kad_reduce_sum(kad_node_t *x, int axis)  { return kad_reduce_general(25, x, axis); }
+kad_node_t *kad_reduce_mean(kad_node_t *x, int axis) { return kad_reduce_general(26, x, axis); }
+
+/********** Sampling related **********/
+
+kad_node_t *kad_dropout(kad_node_t *x, kad_node_t *y)
+{
+	kad_node_t *z;
+	z = kad_op2_core(15, x, y);
+	z->ptr = kad_rng(), z->ptr_size = sizeof(kad_rng_t);
+	return z;
+}
+
+kad_node_t *kad_sample_normal(kad_node_t *x)
+{
+	kad_node_t *z;
+	z = kad_op1_core(24, x);
+	z->ptr = kad_rng(), z->ptr_size = sizeof(kad_rng_t);
+	return z;
+}
+
+/********** Miscellaneous **********/
+
+kad_node_t *kad_slice(kad_node_t *x, int axis, int start, int end)
+{
+	kad_node_t *s;
+	int32_t *aux;
+	if (end < start || start < 0) return 0;
+	aux = (int32_t*)malloc(3 * 4);
+	aux[0] = axis, aux[1] = start, aux[2] = end;
+	s = kad_new_core(0, 20, 1);
+	s->child[0] = x;
+	s->ptr = aux, s->ptr_size = 3 * 4;
+	return kad_finalize_node(s);
+}
+
+kad_node_t *kad_concat_array(int axis, int n, kad_node_t **p)
+{
+	kad_node_t *s;
+	int32_t i, *aux;
+	aux = (int32_t*)malloc(4);
+	aux[0] = axis;
+	s = kad_new_core(0, 31, n);
+	for (i = 0; i < n; ++i)
+		s->child[i] = p[i];
+	s->ptr = aux, s->ptr_size = 4;
+	return kad_finalize_node(s);
+}
+
+kad_node_t *kad_concat(int axis, int n, ...)
+{
+	int i;
+	kad_node_t **p, *s;
+	va_list ap;
+	p = (kad_node_t**)malloc(n * sizeof(kad_node_t*));
+	va_start(ap, n);
+	for (i = 0; i < n; ++i) p[i] = va_arg(ap, kad_node_p);
+	va_end(ap);
+	s = kad_concat_array(axis, n, p);
+	free(p);
+	return s;
+}
+
+kad_node_t *kad_reshape(kad_node_t *x, int n_d, int *d)
+{
+	kad_node_t *s;
+	int32_t i, *aux = 0;
+	if (n_d > 0) {
+		aux = (int32_t*)malloc(n_d * 4);
+		for (i = 0; i < n_d; ++i) aux[i] = d? d[i] : -1;
+	}
+	s = kad_new_core(0, 30, 1);
+	s->child[0] = x, s->ptr = aux, s->ptr_size = n_d * 4;
+	return kad_finalize_node(s);
+}
+
+kad_node_t *kad_reverse(kad_node_t *x, int axis)
+{
+	kad_node_t *s;
+	int32_t *aux;
+	aux = (int32_t*)malloc(4);
+	*aux = axis;
+	s = kad_new_core(0, 36, 1);
+	s->child[0] = x, s->ptr = aux, s->ptr_size = 4;
+	return kad_finalize_node(s);
+}
+
+kad_node_t *kad_switch(int n, kad_node_t **p)
+{
+	kad_node_t *s;
+	int32_t i, *aux;
+	aux = (int32_t*)calloc(1, 4);
+	s = kad_new_core(0, 12, n);
+	for (i = 0; i < n; ++i)
+		s->child[i] = p[i];
+	s->ptr = aux, s->ptr_size = 4;
+	return kad_finalize_node(s);
+}
+
+/***********************
+ * Graph linearization *
+ ***********************/
+
+static void kad_mark_back(int n, kad_node_t **v)
+{
+	int i, j;
+	for (i = 0; i < n; ++i) {
+		if (v[i]->n_child == 0) continue;
+		for (j = 0; j < v[i]->n_child; ++j)
+			if (kad_is_back(v[i]->child[j]))
+				break;
+		if (j < v[i]->n_child) v[i]->flag |= KAD_VAR;
+		else v[i]->flag &= ~KAD_VAR;
+	}
+}
+
+static void kad_allocate_internal(int n, kad_node_t **v)
+{
+	int i;
+	kad_mark_back(n, v);
+	for (i = 0; i < n; ++i) {
+		kad_node_t *p = v[i];
+		if (p->n_child == 0) continue;
+		p->x = (float*)realloc(p->x, kad_len(p) * sizeof(float));
+		if (kad_is_back(p)) {
+			p->g = (float*)realloc(p->g, kad_len(p) * sizeof(float));
+			kad_op_list[p->op](p, KAD_ALLOC);
+		}
+	}
+}
+
+int kad_sync_dim(int n, kad_node_t **v, int batch_size)
+{
+	int i, req_alloc = 0, req_sync = 0, old_size = 0;
+	for (i = 0; i < n; ++i) {
+		if (kad_is_feed(v[i])) {
+			old_size = v[i]->d[0]; /* TODO: check if all feeds have the same batch size */
+			if (batch_size > 0 && v[i]->d[0] != batch_size)
+				v[i]->d[0] = batch_size, req_sync = 1;
+		} else if (v[i]->n_child > 0 && req_sync)
+			kad_op_list[v[i]->op](v[i], KAD_SYNC_DIM);
+	}
+	if (old_size < batch_size) req_alloc = 1;
+	for (i = 0; i < n; ++i)
+		if (v[i]->n_child > 0 && v[i]->x == 0) req_alloc = 1;
+	if (req_alloc) kad_allocate_internal(n, v);
+	return batch_size > 0? batch_size : old_size;
+}
+
+#define kvec_t(type) struct { size_t n, m; type *a; }
+
+#define kv_pop(v) ((v).a[--(v).n])
+
+#define kv_push(type, v, x) do { \
+		if ((v).n == (v).m) { \
+			(v).m = (v).m? (v).m<<1 : 2; \
+			(v).a = (type*)realloc((v).a, sizeof(type) * (v).m); \
+		} \
+		(v).a[(v).n++] = (x); \
+	} while (0)
+
+/* IMPORTANT: kad_node_t::tmp MUST BE set to zero before calling this function */
+kad_node_t **kad_compile_array(int *n_node, int n_roots, kad_node_t **roots)
+{
+	int i;
+	kvec_t(kad_node_p) stack = {0,0,0}, a = {0,0,0};
+
+	/* generate kad_node_t::tmp, the count of the parent nodes; shifted by 1; lowest bit to detect fake roots */
+	for (i = 0; i < n_roots; ++i) {
+		roots[i]->tmp = 1; /* mark the root */
+		kv_push(kad_node_p, stack, roots[i]);
+	}
+	while (stack.n) {
+		kad_node_t *p = kv_pop(stack);
+		for (i = 0; i < p->n_child; ++i) {
+			kad_node_t *q = p->child[i];
+			if (q->tmp == 0) kv_push(kad_node_p, stack, q);
+			q->tmp += 1<<1;
+		}
+	}
+
+	/* topological sorting (Kahn's algorithm) */
+	for (i = 0; i < n_roots; ++i)
+		if (roots[i]->tmp>>1 == 0) /* if roots[i]->tmp>>1 != 0, it is not a real root */
+			kv_push(kad_node_p, stack, roots[i]);
+	while (stack.n) {
+		kad_node_t *p = kv_pop(stack);
+		kv_push(kad_node_p, a, p);
+		for (i = 0; i < p->n_child; ++i) {
+			p->child[i]->tmp -= 1<<1;
+			if (p->child[i]->tmp>>1 == 0)
+				kv_push(kad_node_p, stack, p->child[i]);
+		}
+	}
+	free(stack.a);
+	for (i = 0; i < (int)a.n; ++i) { /* check cycles; no cycles if constructed with kad_add() etc */
+		assert(a.a[i]->tmp>>1 == 0);
+		a.a[i]->tmp = 0;
+	}
+
+	/* reverse */
+	for (i = 0; i < (int)a.n>>1; ++i) { /* reverse a.a[] */
+		kad_node_p t;
+		t = a.a[i], a.a[i] = a.a[a.n-1-i], a.a[a.n-1-i] = t;
+	}
+	kad_allocate_internal(a.n, a.a);
+
+	*n_node = a.n;
+	return a.a;
+}
+
+kad_node_t **kad_compile(int *n_node, int n_roots, ...)
+{
+	int i;
+	kad_node_t **roots, **ret;
+	va_list ap;
+
+	roots = (kad_node_t**)malloc(n_roots * sizeof(kad_node_t*));
+	va_start(ap, n_roots);
+	for (i = 0; i < n_roots; ++i) roots[i] = va_arg(ap, kad_node_p);
+	va_end(ap);
+	ret = kad_compile_array(n_node, n_roots, roots);
+	free(roots);
+	return ret;
+}
+
+/************************************
+ * Miscellaneous on compiled graphs *
+ ************************************/
+
+void kad_delete(int n, kad_node_t **a)
+{
+	int i;
+	for (i = 0; i < n; ++i) {
+		kad_node_t *p = a[i];
+		if (p->n_child) {
+			free(p->x); free(p->g);
+		}
+		free(p->child); free(p->ptr); free(p->gtmp); free(p);
+	}
+	free(a);
+}
+
+int kad_size_var(int n, kad_node_t *const* v)
+{
+	int c, i;
+	for (i = c = 0; i < n; ++i)
+		if (kad_is_var(v[i]))
+			c += kad_len(v[i]);
+	return c;
+}
+
+int kad_size_const(int n, kad_node_t *const* v)
+{
+	int c, i;
+	for (i = c = 0; i < n; ++i)
+		if (kad_is_const(v[i]))
+			c += kad_len(v[i]);
+	return c;
+}
+
+/**********************************
+ * Computate values and gradients *
+ **********************************/
+
+static void kad_propagate_marks(int n, kad_node_t **a)
+{
+	int i, j;
+	for (i = n - 1; i >= 0; --i) {
+		kad_node_t *p = a[i];
+		if (p->tmp > 0) {
+			if (kad_is_switch(p)) {
+				int32_t *aux = (int32_t*)p->ptr;
+				if (p->child[*aux]->tmp == 0)
+					p->child[*aux]->tmp = 1;
+			} else {
+				for (j = 0; j < p->n_child; ++j)
+					if (p->child[j]->tmp == 0)
+						p->child[j]->tmp = 1;
+			}
+		}
+	}
+}
+
+void kad_eval_marked(int n, kad_node_t **a)
+{
+	int i;
+	kad_propagate_marks(n, a);
+	for (i = 0; i < n; ++i)
+		if (a[i]->n_child && a[i]->tmp > 0)
+			kad_op_list[a[i]->op](a[i], KAD_FORWARD);
+	for (i = 0; i < n; ++i) a[i]->tmp = 0;
+}
+
+const float *kad_eval_at(int n, kad_node_t **a, int from)
+{
+	int i;
+	if (from < 0 || from >= n) from = n - 1;
+	for (i = 0; i < n; ++i) a[i]->tmp = (i == from);
+	kad_eval_marked(n, a);
+	return a[from]->x;
+}
+
+void kad_grad(int n, kad_node_t **a, int from)
+{
+	int i;
+	if (from < 0 || from >= n) from = n - 1;
+	assert(a[from]->n_d == 0);
+	for (i = 0; i < n; ++i) a[i]->tmp = (i == from);
+	kad_propagate_marks(n, a);
+	for (i = 0; i <= from; ++i) /* set all grandients to zero */
+		if (a[i]->g && a[i]->tmp > 0)
+			memset(a[i]->g, 0, kad_len(a[i]) * sizeof(float));
+	for (i = from, a[i]->g[0] = 1.0f; i >= 0; --i) /* backprop */
+		if (a[i]->n_child && a[i]->tmp > 0)
+			kad_op_list[a[i]->op](a[i], KAD_BACKWARD);
+	for (i = 0; i <= from; ++i) a[i]->tmp = 0;
+}
+
+/***********************
+ * Load and save graph *
+ ***********************/
+
+static void kad_save1(FILE *fp, const kad_node_t *p)
+{
+	fwrite(&p->ext_label, 4, 1, fp);
+	fwrite(&p->ext_flag, 4, 1, fp);
+	fwrite(&p->flag, 1, 1, fp);
+	fwrite(&p->n_child, 4, 1, fp);
+	if (p->n_child) {
+		int32_t j, pre = p->pre? p->pre->tmp : -1;
+		fwrite(&p->op, 2, 1, fp);
+		for (j = 0; j < p->n_child; ++j)
+			fwrite(&p->child[j]->tmp, 4, 1, fp);
+		fwrite(&pre, 4, 1, fp);
+		fwrite(&p->ptr_size, 4, 1, fp);
+		if (p->ptr_size > 0 && p->ptr)
+			fwrite(p->ptr, p->ptr_size, 1, fp);
+	} else {
+		fwrite(&p->n_d, 1, 1, fp);
+		if (p->n_d) fwrite(p->d, 4, p->n_d, fp);
+	}
+}
+
+static kad_node_t *kad_load1(FILE *fp, kad_node_t **node)
+{
+	kad_node_t *p;
+	p = (kad_node_t*)calloc(1, sizeof(kad_node_t));
+	fread(&p->ext_label, 4, 1, fp);
+	fread(&p->ext_flag, 4, 1, fp);
+	fread(&p->flag, 1, 1, fp);
+	fread(&p->n_child, 4, 1, fp);
+	if (p->n_child) {
+		int32_t j, k;
+		p->child = (kad_node_t**)calloc(p->n_child, sizeof(kad_node_t*));
+		fread(&p->op, 2, 1, fp);
+		for (j = 0; j < p->n_child; ++j) {
+			fread(&k, 4, 1, fp);
+			p->child[j] = node? node[k] : 0;
+		}
+		fread(&k, 4, 1, fp);
+		if (k >= 0) p->pre = node[k];
+		fread(&p->ptr_size, 4, 1, fp);
+		if (p->ptr_size > 0) {
+			p->ptr = malloc(p->ptr_size);
+			fread(p->ptr, p->ptr_size, 1, fp);
+		}
+	} else {
+		fread(&p->n_d, 1, 1, fp);
+		if (p->n_d) fread(p->d, 4, p->n_d, fp);
+	}
+	return p;
+}
+
+int kad_save(FILE *fp, int n_node, kad_node_t **node)
+{
+	int32_t i, k = n_node;
+	fwrite(&k, 4, 1, fp);
+	for (i = 0; i < n_node; ++i) node[i]->tmp = i;
+	for (i = 0; i < n_node; ++i) kad_save1(fp, node[i]);
+	for (i = 0; i < n_node; ++i) node[i]->tmp = 0;
+	return 0;
+}
+
+kad_node_t **kad_load(FILE *fp, int *_n_node)
+{
+	int32_t i, n_node;
+	kad_node_t **node;
+	fread(&n_node, 4, 1, fp);
+	node = (kad_node_t**)malloc(n_node * sizeof(kad_node_t*));
+	for (i = 0; i < n_node; ++i) {
+		kad_node_t *p;
+		p = node[i] = kad_load1(fp, node);
+		if (p->n_child) {
+			kad_op_list[p->op](p, KAD_ALLOC);
+			kad_op_list[p->op](p, KAD_SYNC_DIM);
+		}
+	}
+	*_n_node = n_node;
+	kad_mark_back(n_node, node);
+	return node;
+}
+
+/***************
+ * Graph clone *
+ ***************/
+
+static inline kad_node_t *kad_dup1(const kad_node_t *p)
+{
+	kad_node_t *q;
+	q = (kad_node_t*)malloc(sizeof(kad_node_t));
+	memcpy(q, p, sizeof(kad_node_t));
+	q->pre = 0, q->tmp = 0, q->gtmp = 0;
+	if (p->ptr && p->ptr_size > 0) {
+		if (kad_use_rng(p) && !(p->flag & KAD_SHARE_RNG) && p->ptr_size == sizeof(kad_rng_t)) {
+			q->ptr = kad_rng(); /* each time step uses a different RNG */
+		} else {
+			q->ptr = malloc(p->ptr_size);
+			memcpy(q->ptr, p->ptr, p->ptr_size);
+		}
+	}
+	if (q->n_child) {
+		q->x = q->g = 0;
+		q->child = (kad_node_t**)calloc(q->n_child, sizeof(kad_node_t*));
+	}
+	return q;
+}
+
+kad_node_t **kad_clone(int n, kad_node_t **v, int batch_size)
+{
+	int i, j;
+	kad_node_t **u;
+	u = (kad_node_t**)calloc(n, sizeof(kad_node_t*));
+	for (i = 0; i < n; ++i) v[i]->tmp = i;
+	for (i = 0; i < n; ++i) {
+		kad_node_t *p = v[i], *q;
+		q = u[i] = kad_dup1(p);
+		if (p->pre) q->pre = u[p->pre->tmp];
+		if (p->n_child) {
+			for (j = 0; j < p->n_child; ++j)
+				q->child[j] = u[p->child[j]->tmp];
+		} else if (!kad_is_feed(p)) {
+			q->x = (float*)malloc(kad_len(p) * sizeof(float));
+			memcpy(q->x, p->x, kad_len(p) * sizeof(float));
+			q->g = 0;
+		}
+	}
+	for (i = 0; i < n; ++i) v[i]->tmp = 0;
+	kad_sync_dim(n, u, batch_size); /* this will allocate x[] and g[] at internal nodes */
+	return u;
+}
+
+/**************
+ * Unroll RNN *
+ **************/
+
+typedef struct {
+	int32_t n, m;
+	kad_node_t **v;
+} nodes_t;
+
+static inline void push_nodes(nodes_t *w, kad_node_t *p)
+{
+	if (w->n == w->m) {
+		w->m = w->m? w->m<<1 : 16;
+		w->v = (kad_node_t**)realloc(w->v, w->m * sizeof(kad_node_t*));
+	}
+	w->v[w->n++] = p;
+}
+
+static void kad_unroll_helper(int n_v, kad_node_t **v, int i_pivot, kad_node_t **t, int len, nodes_t *w)
+{
+	int i, j, l;
+	uint8_t *flag;
+	kad_node_t **aux;
+
+	assert(kad_is_pivot(v[i_pivot]) && t[i_pivot] == 0);
+	t[i_pivot] = kad_dup1(v[i_pivot]);
+	t[i_pivot]->n_child = len;
+	t[i_pivot]->child = (kad_node_t**)realloc(t[i_pivot]->child, len * sizeof(kad_node_t*));
+
+	flag = (uint8_t*)calloc(n_v, 1);
+	for (i = i_pivot, flag[i] = 16; i >= 0; --i) {
+		if (i < i_pivot && kad_is_pivot(v[i])) continue; /* don't trespass other pivots */
+		if (flag[i]&16) /* flag 16: nodes to unroll */
+			for (j = 0; j < v[i]->n_child; ++j)
+				flag[v[i]->child[j]->tmp] = 16;
+	}
+	for (i = 0; i < i_pivot; ++i) {
+		if (!(flag[i]&16)) continue;
+		if (kad_is_var(v[i]) || kad_is_const(v[i]) || kad_is_pivot(v[i])) flag[i] |= 1; /* external nodes that should not be duplicated */
+		if (v[i]->pre) flag[v[i]->pre->tmp] |= 2;
+	}
+	flag[v[i_pivot]->child[0]->tmp] |= 4;
+	aux = (kad_node_t**)calloc(n_v, sizeof(kad_node_t*));
+	for (l = 0; l < len; ++l) {
+		for (i = 0; i < i_pivot; ++i) {
+			if (!(flag[i]&16) || ((flag[i]&3) && t[i])) continue;
+			t[i] = kad_dup1(v[i]);
+			if (v[i]->n_child)
+				for (j = 0; j < v[i]->n_child; ++j)
+					t[i]->child[j] = t[v[i]->child[j]->tmp];
+			if (flag[i]&4) t[i_pivot]->child[l] = t[i];
+			if (l == 0 && (flag[i]&2)) aux[i] = t[i];
+			if (v[i]->pre) {
+				t[v[i]->pre->tmp] = t[i];
+				if (l == len - 1) t[i]->pre = aux[v[i]->pre->tmp]; /* this forms a cycle! */
+			}
+			push_nodes(w, t[i]);
+		}
+	}
+	push_nodes(w, t[i_pivot]);
+	free(aux); free(flag);
+}
+
+int kad_n_pivots(int n_v, kad_node_t **v)
+{
+	int i, n_pivots = 0;
+	for (i = 0; i < n_v; ++i)
+		if (kad_is_pivot(v[i])) ++n_pivots;
+	return n_pivots;
+}
+
+kad_node_t **kad_unroll(int n_v, kad_node_t **v, int *new_n, int *len)
+{
+	int i, j, n_pivots = 0;
+	kad_node_t **t;
+	nodes_t w = {0,0,0};
+
+	t = (kad_node_t**)calloc(n_v, sizeof(kad_node_t*));
+	n_pivots = kad_n_pivots(n_v, v);
+	for (i = 0; i < n_v; ++i) v[i]->tmp = i;
+	if (n_pivots) {
+		int k, *i_pivots;
+		i_pivots = (int*)calloc(n_pivots, sizeof(int));
+		for (i = k = 0; i < n_v; ++i) /* collect pivots */
+			if (kad_is_pivot(v[i])) i_pivots[k++] = i;
+		for (i = 0; i < n_pivots; ++i) /* unroll each pivot, from the lowest to the highest */
+			kad_unroll_helper(n_v, v, i_pivots[i], t, len[i], &w);
+		free(i_pivots);
+	}
+	for (i = 0; i < n_v; ++i) { /* copy over the rest of nodes */
+		if (t[i]) continue;
+		t[i] = kad_dup1(v[i]);
+		if (v[i]->n_child)
+			for (j = 0; j < v[i]->n_child; ++j)
+				t[i]->child[j] = t[v[i]->child[j]->tmp];
+		push_nodes(&w, t[i]);
+	}
+	free(t);
+	for (i = 0; i < n_v; ++i) v[i]->tmp = 0;
+	for (i = 0; i < w.n; ++i) /* stack may change the output dimension */
+		if (w.v[i]->n_child > 0)
+			kad_op_list[w.v[i]->op](w.v[i], KAD_SYNC_DIM);
+	kad_allocate_internal(w.n, w.v);
+	*new_n = w.n;
+	return w.v;
+}
+
+/********************************
+ * Vector and matrix operations *
+ ********************************/
+
+#ifdef __SSE__
+#include <xmmintrin.h>
+
+static inline float kad_sdot(int n, const float *x, const float *y) /* BLAS sdot using SSE */
+{
+	int i, n8 = n>>3<<3;
+	__m128 vs1, vs2;
+	float s, t[4];
+	vs1 = _mm_setzero_ps();
+	vs2 = _mm_setzero_ps();
+	for (i = 0; i < n8; i += 8) {
+		__m128 vx1, vx2, vy1, vy2;
+		vx1 = _mm_loadu_ps(&x[i]);
+		vx2 = _mm_loadu_ps(&x[i+4]);
+		vy1 = _mm_loadu_ps(&y[i]);
+		vy2 = _mm_loadu_ps(&y[i+4]);
+		vs1 = _mm_add_ps(vs1, _mm_mul_ps(vx1, vy1));
+		vs2 = _mm_add_ps(vs2, _mm_mul_ps(vx2, vy2));
+	}
+	for (s = 0.; i < n; ++i) s += x[i] * y[i];
+	_mm_storeu_ps(t, vs1);
+	s += t[0] + t[1] + t[2] + t[3];
+	_mm_storeu_ps(t, vs2);
+	s += t[0] + t[1] + t[2] + t[3];
+	return s;
+}
+static inline void kad_saxpy_inlined(int n, float a, const float *x, float *y) /* BLAS saxpy using SSE */
+{
+	int i, n8 = n>>3<<3;
+	__m128 va;
+	va = _mm_set1_ps(a);
+	for (i = 0; i < n8; i += 8) {
+		__m128 vx1, vx2, vy1, vy2, vt1, vt2;
+		vx1 = _mm_loadu_ps(&x[i]);
+		vx2 = _mm_loadu_ps(&x[i+4]);
+		vy1 = _mm_loadu_ps(&y[i]);
+		vy2 = _mm_loadu_ps(&y[i+4]);
+		vt1 = _mm_add_ps(_mm_mul_ps(va, vx1), vy1);
+		vt2 = _mm_add_ps(_mm_mul_ps(va, vx2), vy2);
+		_mm_storeu_ps(&y[i], vt1);
+		_mm_storeu_ps(&y[i+4], vt2);
+	}
+	for (; i < n; ++i) y[i] += a * x[i];
+}
+#else
+static inline float kad_sdot(int n, const float *x, const float *y) /* BLAS sdot */
+{
+	int i;
+	float s = 0.;
+	for (i = 0; i < n; ++i) s += x[i] * y[i];
+	return s;
+}
+static inline void kad_saxpy_inlined(int n, float a, const float *x, float *y) // BLAS saxpy
+{
+	int i;
+	for (i = 0; i < n; ++i) y[i] += a * x[i];
+}
+#endif
+
+void kad_vec_mul_sum(int n, float *a, const float *b, const float *c)
+{
+	int i;
+	for (i = 0; i < n; ++i) a[i] += b[i] * c[i];
+}
+
+void kad_saxpy(int n, float a, const float *x, float *y) { kad_saxpy_inlined(n, a, x, y); }
+
+#ifdef HAVE_CBLAS
+#include "cblas.h"
+void kad_sgemm_simple(int trans_A, int trans_B, int M, int N, int K, const float *A, const float *B, float *C)
+{
+	cblas_sgemm(CblasRowMajor, trans_A? CblasTrans : CblasNoTrans, trans_B? CblasTrans : CblasNoTrans, M, N, K, 1.0f, A, trans_A? M : K, B, trans_B? K : N, 1.0f, C, N);
+}
+#else
+void kad_sgemm_simple(int trans_A, int trans_B, int M, int N, int K, const float *A, const float *B, float *C) /* simplified BLAS sgemm */
+{
+	static const int x = 16;
+	int i, j, k;
+	if (!trans_A && trans_B) {
+		for (i = 0; i < M; i += x)
+			for (j = 0; j < N; j += x) {
+				int ii, ie = M < i + x? M : i + x;
+				int jj, je = N < j + x? N : j + x;
+				for (ii = i; ii < ie; ++ii) { /* loop tiling */
+					const float *aii = A + ii * K, *bjj;
+					float *cii = C + ii * N;
+					for (jj = j, bjj = B + j * K; jj < je; ++jj, bjj += K)
+						cii[jj] += kad_sdot(K, aii, bjj);
+				}
+			}
+	} else if (!trans_A && !trans_B) {
+		for (i = 0; i < M; ++i)
+			for (k = 0; k < K; ++k)
+				kad_saxpy_inlined(N, A[i*K+k], &B[k*N], &C[i*N]);
+	} else if (trans_A && !trans_B) {
+		for (k = 0; k < K; ++k)
+			for (i = 0; i < M; ++i)
+				kad_saxpy_inlined(N, A[k*M+i], &B[k*N], &C[i*N]);
+	} else abort(); /* not implemented for (trans_A && trans_B) */
+}
+#endif
+
+/***************************
+ * Random number generator *
+ ***************************/
+
+static kad_rng_t kad_rng_dat = { {0x50f5647d2380309dULL, 0x91ffa96fc4c62cceULL}, 0.0, 0, 0 };
+
+static inline uint64_t kad_splitmix64(uint64_t x)
+{
+	uint64_t z = (x += 0x9E3779B97F4A7C15ULL);
+	z = (z ^ (z >> 30)) * 0xBF58476D1CE4E5B9ULL;
+	z = (z ^ (z >> 27)) * 0x94D049BB133111EBULL;
+	return z ^ (z >> 31);
+}
+
+static inline uint64_t kad_xoroshiro128plus_next(kad_rng_t *r)
+{
+	const uint64_t s0 = r->s[0];
+	uint64_t s1 = r->s[1];
+	const uint64_t result = s0 + s1;
+	s1 ^= s0;
+	r->s[0] = (s0 << 55 | s0 >> 9) ^ s1 ^ (s1 << 14);
+	r->s[1] = s0 << 36 | s0 >> 28;
+	return result;
+}
+
+static inline void kad_xoroshiro128plus_jump(kad_rng_t *r)
+{
+	static const uint64_t JUMP[] = { 0xbeac0467eba5facbULL, 0xd86b048b86aa9922ULL };
+	uint64_t s0 = 0, s1 = 0;
+	int i, b;
+	for (i = 0; i < 2; ++i)
+		for (b = 0; b < 64; b++) {
+			if (JUMP[i] & 1ULL << b)
+				s0 ^= r->s[0], s1 ^= r->s[1];
+			kad_xoroshiro128plus_next(r);
+		}
+	r->s[0] = s0, r->s[1] = s1;
+}
+
+void kad_srand(void *d, uint64_t seed)
+{
+	kad_rng_t *r = d? (kad_rng_t*)d : &kad_rng_dat;
+	r->n_gset = 0.0, r->n_iset = 0;
+	r->s[0] = kad_splitmix64(seed);
+	r->s[1] = kad_splitmix64(r->s[0]);
+}
+
+void *kad_rng(void)
+{
+	kad_rng_t *r;
+	r = (kad_rng_t*)calloc(1, sizeof(kad_rng_t));
+	kad_xoroshiro128plus_jump(&kad_rng_dat);
+	r->s[0] = kad_rng_dat.s[0], r->s[1] = kad_rng_dat.s[1];
+	return r;
+}
+
+uint64_t kad_rand(void *d) { return kad_xoroshiro128plus_next(d? (kad_rng_t*)d : &kad_rng_dat); }
+
+double kad_drand(void *d)
+{
+	union { uint64_t i; double d; } u;
+	u.i = 0x3FFULL << 52 | kad_xoroshiro128plus_next(d? (kad_rng_t*)d : &kad_rng_dat) >> 12;
+	return u.d - 1.0;
+}
+
+double kad_drand_normal(void *d)
+{
+	kad_rng_t *r = d? (kad_rng_t*)d : &kad_rng_dat;
+	if (r->n_iset == 0) {
+		double fac, rsq, v1, v2;
+		do {
+			v1 = 2.0 * kad_drand(d) - 1.0;
+			v2 = 2.0 * kad_drand(d) - 1.0;
+			rsq = v1 * v1 + v2 * v2;
+		} while (rsq >= 1.0 || rsq == 0.0);
+		fac = sqrt(-2.0 * log(rsq) / rsq);
+		r->n_gset = v1 * fac;
+		r->n_iset = 1;
+		return v2 * fac;
+	} else {
+		r->n_iset = 0;
+		return r->n_gset;
+	}
+}
+
+/*************
+ * Operators *
+ *************/
+
+static inline void kad_copy_dim1(kad_node_t *dst, const kad_node_t *src) /* set the dimension/shape of dst to src */
+{
+	dst->n_d = src->n_d;
+	if (src->n_d) memcpy(dst->d, src->d, src->n_d * sizeof(int));
+}
+
+/********** Arithmetic operations **********/
+
+int kad_op_add(kad_node_t *p, int action)
+{
+	int i, n0, n1;
+	kad_node_t *q[2];
+
+	q[0] = p->child[0], n0 = kad_len(q[0]);
+	q[1] = p->child[1], n1 = kad_len(q[1]);
+	if (action == KAD_SYNC_DIM) {
+		if (n0 % n1 != 0) return -1;
+		kad_copy_dim1(p, q[0]);
+	} else if (action == KAD_FORWARD) {
+		assert(n0 >= n1);
+		memcpy(p->x, q[0]->x, n0 * sizeof(float));
+		for (i = 0; i < n0; i += n1)
+			kad_saxpy(n1, 1.0f, q[1]->x, p->x + i);
+	} else if (action == KAD_BACKWARD) {
+		if (kad_is_back(q[0])) kad_saxpy(n0, 1.0f, p->g, q[0]->g);
+		if (kad_is_back(q[1]))
+			for (i = 0; i < n0; i += n1)
+				kad_saxpy(n1, 1.0f, p->g + i, q[1]->g);
+	}
+	return 0;
+}
+
+int kad_op_sub(kad_node_t *p, int action)
+{
+	int i, n0, n1;
+	kad_node_t *q[2];
+
+	q[0] = p->child[0], n0 = kad_len(q[0]);
+	q[1] = p->child[1], n1 = kad_len(q[1]);
+	if (action == KAD_SYNC_DIM) {
+		if (n0 % n1 != 0) return -1;
+		kad_copy_dim1(p, q[0]);
+	} else if (action == KAD_FORWARD) {
+		assert(n0 >= n1);
+		memcpy(p->x, q[0]->x, n0 * sizeof(float));
+		for (i = 0; i < n0; i += n1)
+			kad_saxpy(n1, -1.0f, q[1]->x, p->x + i);
+	} else if (action == KAD_BACKWARD) {
+		if (kad_is_back(q[0])) kad_saxpy(n0, 1.0f, p->g, q[0]->g);
+		if (kad_is_back(q[1]))
+			for (i = 0; i < n0; i += n1)
+				kad_saxpy(n1, -1.0f, p->g + i, q[1]->g);
+	}
+	return 0;
+}
+
+int kad_op_mul(kad_node_t *p, int action)
+{
+	int i, n0, n1;
+	kad_node_t *q[2];
+
+	q[0] = p->child[0], n0 = kad_len(q[0]);
+	q[1] = p->child[1], n1 = kad_len(q[1]);
+	if (action == KAD_SYNC_DIM) {
+		if (n0 % n1 != 0) return -1;
+		kad_copy_dim1(p, q[0]);
+	} else if (action == KAD_FORWARD) {
+		assert(n0 >= n1);
+		memset(p->x, 0, n0 * sizeof(float));
+		if (q[0]->x != 0 && q[1]->x != 0)
+			for (i = 0; i < n0; i += n1) /* TODO: optimize when n1==1 */
+				kad_vec_mul_sum(n1, p->x + i, q[0]->x + i, q[1]->x);
+	} else if (action == KAD_BACKWARD) {
+		if (kad_is_back(q[0]) && q[1]->x)
+			for (i = 0; i < n0; i += n1)
+				kad_vec_mul_sum(n1, q[0]->g + i, p->g + i, q[1]->x);
+		if (kad_is_back(q[1]) && q[0]->x)
+			for (i = 0; i < n0; i += n1)
+				kad_vec_mul_sum(n1, q[1]->g, p->g + i, q[0]->x + i);
+	}
+	return 0;
+}
+
+int kad_op_cmul(kad_node_t *p, int action)
+{
+	int i, n_a_row, n_b_row, n_col, n_a_col = 1, n_b_col = 1;
+	kad_node_t *q[2];
+
+	q[0] = p->child[0], q[1] = p->child[1];
+	n_col = q[0]->d[q[0]->n_d - 1] > q[1]->d[q[1]->n_d - 1]? q[0]->d[q[0]->n_d - 1] : q[1]->d[q[1]->n_d - 1];
+	for (i = q[0]->n_d - 1; i >= 0; --i) if (n_a_col < n_col) n_a_col *= q[0]->d[i];
+	for (i = q[1]->n_d - 1; i >= 0; --i) if (n_b_col < n_col) n_b_col *= q[1]->d[i];
+	n_a_row = kad_len(q[0]) / n_a_col, n_b_row = kad_len(q[1]) / n_b_col;
+	if (action == KAD_SYNC_DIM) {
+		if (n_a_col != n_b_col) return -1;
+		p->n_d = 2, p->d[0] = n_a_row, p->d[1] = n_b_row;
+	} else if (action == KAD_FORWARD) {
+		memset(p->x, 0, n_a_row * n_b_row * sizeof(float));
+		if (q[0]->x && q[1]->x)
+			kad_sgemm_simple(0, 1, n_a_row, n_b_row, n_col, q[0]->x, q[1]->x, p->x); /* Y = X * trans(W) */
+	} else if (action == KAD_BACKWARD) {
+		if (kad_is_back(q[0]) && q[1]->x)
+			kad_sgemm_simple(0, 0, n_a_row, n_col, n_b_row, p->g, q[1]->x, q[0]->g); /* G_x <- G_y * W */
+		if (kad_is_back(q[1]) && q[0]->x)
+			kad_sgemm_simple(1, 0, n_b_row, n_col, n_a_row, p->g, q[0]->x, q[1]->g); /* G_w <- trans(G_y) * X */
+	}
+	return 0;
+}
+
+int kad_op_matmul(kad_node_t *p, int action) /* TODO: matmul and cmul have different broadcasting rules */
+{
+	int n_a_row, n_b_row, n_a_col, n_b_col;
+	kad_node_t *q[2];
+
+	q[0] = p->child[0];
+	q[1] = p->child[1];
+	n_a_row = q[0]->n_d == 1? 1 : q[0]->d[0];
+	n_b_row = q[1]->n_d == 1? 1 : q[1]->d[0];
+	n_a_col = kad_len(q[0]) / n_a_row;
+	n_b_col = kad_len(q[1]) / n_b_row;
+	if (action == KAD_SYNC_DIM) {
+		if (n_a_col != n_b_row) return -1;
+		p->n_d = 2, p->d[0] = n_a_row, p->d[1] = n_b_col;
+	} else if (action == KAD_FORWARD) {
+		memset(p->x, 0, n_a_row * n_b_col * sizeof(float));
+		if (q[0]->x && q[1]->x)
+			kad_sgemm_simple(0, 0, n_a_row, n_b_col, n_a_col, q[0]->x, q[1]->x, p->x); /* Y = X * W */
+	} else if (action == KAD_BACKWARD) {
+		if (kad_is_back(q[0]) && q[1]->x)
+			kad_sgemm_simple(0, 1, n_a_row, n_a_col, n_b_col, p->g, q[1]->x, q[0]->g); /* G_x <- G_y * trans(W) */
+		if (kad_is_back(q[1]) && q[0]->x)
+			kad_sgemm_simple(1, 0, n_b_row, n_b_col, n_a_row, q[0]->x, p->g, q[1]->g); /* G_y <- trans(A) * G_y */
+	}
+	return 0;
+}
+
+int kad_op_square(kad_node_t *p, int action)
+{
+	int i, n;
+	kad_node_t *q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		for (i = 0; i < n; ++i)
+			p->x[i] = q->x[i] * q->x[i];
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		for (i = 0; i < n; ++i)
+			q->g[i] += p->g[i] * (q->x[i] + q->x[i]);
+	}
+	return 0;
+}
+
+int kad_op_1minus(kad_node_t *p, int action)
+{
+	int i, n;
+	kad_node_t *q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		for (i = 0; i < n; ++i) p->x[i] = 1.0f - q->x[i];
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		kad_saxpy(n, -1.0f, p->g, q->g);
+	}
+	return 0;
+}
+
+int kad_op_exp(kad_node_t *p, int action)
+{
+	int i, n;
+	kad_node_t *q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		for (i = 0; i < n; ++i) p->x[i] = expf(q->x[i]);
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		for (i = 0; i < n; ++i)
+			q->g[i] += p->g[i] * p->x[i];
+	}
+	return 0;
+}
+
+int kad_op_log(kad_node_t *p, int action)
+{
+	int i, n;
+	kad_node_t *q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		for (i = 0; i < n; ++i) p->x[i] = logf(q->x[i]);
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		for (i = 0; i < n; ++i)
+			q->g[i] += p->g[i] / q->x[i];
+	}
+	return 0;
+}
+
+int kad_op_reduce_sum(kad_node_t *p, int action)
+{
+	kad_node_t *q = p->child[0];
+	int i, j, k, axis, d0, d1;
+
+	assert(p->ptr);
+	axis = *(int32_t*)p->ptr;
+	if (axis < 0 || axis >= q->n_d) return -1;
+	for (i = 0, d0 = 1; i < axis; ++i) d0 *= q->d[i];
+	for (i = axis + 1, d1 = 1; i < q->n_d; ++i) d1 *= q->d[i];
+	if (action == KAD_SYNC_DIM) {
+		p->n_d = q->n_d - 1;
+		for (i = j = 0; i < q->n_d; ++i)
+			if (i != axis) p->d[j++] = q->d[i];
+	} else if (action == KAD_FORWARD) {
+		memset(p->x, 0, kad_len(p) * sizeof(float));
+		for (i = 0; i < d0; ++i)
+			for (j = 0; j < q->d[axis]; ++j)
+				for (k = 0; k < d1; ++k)
+					p->x[i * d1 + k] += q->x[(i * q->d[axis] + j) * d1 + k];
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		for (i = 0; i < d0; ++i)
+			for (j = 0; j < q->d[axis]; ++j)
+				for (k = 0; k < d1; ++k)
+					q->g[(i * q->d[axis] + j) * d1 + k] += p->g[i * d1 + k];
+	}
+	return 0;
+}
+
+int kad_op_reduce_mean(kad_node_t *p, int action)
+{
+	kad_node_t *q = p->child[0];
+	int i, j, k, axis, d0, d1;
+
+	assert(p->ptr);
+	axis = *(int32_t*)p->ptr;
+	if (axis < 0 || axis >= q->n_d) return -1;
+	for (i = 0, d0 = 1; i < axis; ++i) d0 *= q->d[i];
+	for (i = axis + 1, d1 = 1; i < q->n_d; ++i) d1 *= q->d[i];
+	if (action == KAD_SYNC_DIM) {
+		p->n_d = q->n_d - 1;
+		for (i = j = 0; i < q->n_d; ++i)
+			if (i != axis) p->d[j++] = q->d[i];
+	} else if (action == KAD_FORWARD) {
+		float t = 1.0f / q->d[axis];
+		memset(p->x, 0, kad_len(p) * sizeof(float));
+		for (i = 0; i < d0; ++i)
+			for (j = 0; j < q->d[axis]; ++j)
+				for (k = 0; k < d1; ++k)
+					p->x[i * d1 + k] += t * q->x[(i * q->d[axis] + j) * d1 + k];
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		float t = 1.0f / q->d[axis];
+		for (i = 0; i < d0; ++i)
+			for (j = 0; j < q->d[axis]; ++j)
+				for (k = 0; k < d1; ++k)
+					q->g[(i * q->d[axis] + j) * d1 + k] += t * p->g[i * d1 + k];
+	}
+	return 0;
+}
+
+/********** Miscellaneous **********/
+
+int kad_op_dropout(kad_node_t *p, int action)
+{
+	int i, n;
+	kad_node_t *q = p->child[0];
+	assert(p->child[1]->n_d == 0);
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_ALLOC) {
+		if (kad_is_back(p->child[0]))
+			p->gtmp = realloc(p->gtmp, n);
+	} else if (action == KAD_FORWARD) {
+		float r = kad_is_const(q) || kad_is_var(q)? 0.0f : *p->child[1]->x, z = 1.0f / (1.0f - r);
+		uint8_t *flag = (uint8_t*)p->gtmp;
+		for (i = 0; i < n; ++i) {
+			int kept = (kad_drand(p->ptr) >= r);
+			p->x[i] = kept? q->x[i] * z : 0.0f;
+			if (flag) flag[i] = kept;
+		}
+	} else if (action == KAD_BACKWARD && kad_is_back(p->child[0])) {
+		float r = kad_is_const(q) || kad_is_var(q)? 0.0f : *p->child[1]->x, z = 1.0f / (1.0f - r);
+		uint8_t *flag = (uint8_t*)p->gtmp;
+		for (i = 0; i < n; ++i)
+			if (flag[i]) q->g[i] += z * p->g[i];
+	}
+	return 0;
+}
+
+int kad_op_sample_normal(kad_node_t *p, int action) /* not tested */
+{
+	int i, n;
+	kad_node_t *q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_ALLOC) {
+		if (kad_is_back(p->child[0]))
+			p->gtmp = realloc(p->gtmp, n * sizeof(float));
+	} else if (action == KAD_FORWARD) {
+		float *r = (float*)p->gtmp;
+		for (i = 0; i < n; ++i) {
+			float z;
+			z = (float)kad_drand_normal(p->ptr);
+			p->x[i] = q->x[i] * z;
+			if (r) r[i] = z;
+		}
+	} else if (action == KAD_BACKWARD && kad_is_back(p->child[0])) {
+		float *r = (float*)p->gtmp;
+		for (i = 0; i < n; ++i)
+			q->g[i] += p->g[i] * r[i];
+	}
+	return 0;
+}
+
+int kad_op_slice(kad_node_t *p, int action)
+{
+	kad_node_t *q = p->child[0];
+	int32_t *aux, *range;
+	int i, axis, d0, d1;
+
+	assert(p->ptr);
+	aux = (int32_t*)p->ptr, axis = aux[0], range = aux + 1;
+	if (axis < 0 || axis >= q->n_d) return -1;
+	for (i = 0, d0 = 1; i < axis; ++i) d0 *= q->d[i];
+	for (i = axis + 1, d1 = 1; i < q->n_d; ++i) d1 *= q->d[i];
+	if (action == KAD_SYNC_DIM) {
+		if (range[0] >= range[1] || range[0] < 0 || range[1] > q->d[axis]) return -1;
+		kad_copy_dim1(p, q);
+		p->d[axis] = range[1] - range[0];
+	} else if (action == KAD_FORWARD) {
+		for (i = 0; i < d0; ++i)
+			memcpy(&p->x[i * p->d[axis] * d1], &q->x[(i * q->d[axis] + range[0]) * d1], (range[1] - range[0]) * d1 * sizeof(float));
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		for (i = 0; i < d0; ++i)
+			kad_saxpy((range[1] - range[0]) * d1, 1.0f, &p->g[i * p->d[axis] * d1], &q->g[(i * q->d[axis] + range[0]) * d1]);
+	}
+	return 0;
+}
+
+int kad_op_concat(kad_node_t *p, int action)
+{
+	kad_node_t *q = p->child[0];
+	int32_t *aux;
+	int i, j, k, axis, d0, d1;
+
+	assert(p->ptr);
+	aux = (int32_t*)p->ptr, axis = aux[0];
+	for (i = 0, d0 = 1; i < axis; ++i) d0 *= q->d[i];
+	for (i = axis + 1, d1 = 1; i < q->n_d; ++i) d1 *= q->d[i];
+	if (action == KAD_SYNC_DIM) {
+		for (i = 1; i < p->n_child; ++i) {
+			if (p->child[i]->n_d != q->n_d) return -1;
+			for (j = 0; j < q->n_d; ++j)
+				if (j != axis && q->d[j] != p->child[i]->d[j]) return -1;
+		}
+		kad_copy_dim1(p, q);
+		for (i = 1; i < p->n_child; ++i)
+			p->d[axis] += p->child[i]->d[axis];
+	} else if (action == KAD_FORWARD) {
+		for (i = 0; i < d0; ++i)
+			for (j = k = 0; j < p->n_child; ++j) {
+				q = p->child[j];
+				memcpy(&p->x[(i * p->d[axis] + k) * d1], &q->x[i * q->d[axis] * d1], q->d[axis] * d1 * sizeof(float));
+				k += q->d[axis];
+			}
+	} else if (action == KAD_BACKWARD) {
+		for (i = 0; i < d0; ++i)
+			for (j = k = 0; j < p->n_child; ++j) {
+				q = p->child[j];
+				if (!kad_is_back(q)) continue;
+				kad_saxpy(q->d[axis] * d1, 1.0f, &p->g[(i * p->d[axis] + k) * d1], &q->g[i * q->d[axis] * d1]);
+				k += q->d[axis];
+			}
+	}
+	return 0;
+}
+
+int kad_op_reshape(kad_node_t *p, int action)
+{
+	kad_node_t *q = p->child[0];
+
+	if (action == KAD_SYNC_DIM) {
+		if (p->ptr) {
+			int32_t *aux = (int32_t*)p->ptr;
+			int i, len = 1, n_missing = 0;
+			p->n_d = p->ptr_size / 4;
+			for (i = 0; i < p->n_d; ++i) p->d[i] = aux[i];
+			for (i = 0; i < p->n_d; ++i)
+				if (p->d[i] <= 0) ++n_missing;
+				else len *= p->d[i];
+			if (n_missing == 0 && len != kad_len(q)) return -1;
+			if (n_missing > 1) { /* attempt to infer missing dimensions except the last one */
+				for (i = 0; i < p->n_d; ++i)
+					if (p->d[i] <= 0 && i < q->n_d) {
+						p->d[i] = q->d[i], len *= p->d[i];
+						if (--n_missing == 1) break;
+					}
+				if (n_missing > 1) return -1;
+			}
+			if (n_missing == 1) { /* infer the last missing dimension */
+				if (kad_len(q) % len != 0) return -1;
+				for (i = 0; i < p->n_d; ++i)
+					if (p->d[i] <= 0) p->d[i] = kad_len(q) / len;
+			}
+		} else kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		memcpy(p->x, q->x, kad_len(p) * sizeof(float));
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		kad_saxpy(kad_len(p), 1.0f, p->g, q->g);
+	}
+	return 0;
+}
+
+int kad_op_reverse(kad_node_t *p, int action)
+{
+	kad_node_t *q = p->child[0];
+	int axis, i, j, n, d0, d1;
+
+	axis = p->ptr? *(int32_t*)p->ptr : 0;
+	if (axis < 0) axis += q->n_d;
+	assert(axis >= 0 && axis < q->n_d);
+	for (i = 0, d0 = 1; i < axis; ++i) d0 *= q->d[i];
+	n = q->d[axis];
+	for (i = axis + 1, d1 = 1; i < q->n_d; ++i) d1 *= q->d[i];
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		for (i = 0; i < d0; ++i)
+			for (j = 0; j < n; ++j)
+				memcpy(&p->x[(i * n + n - 1 - j) * d1], &q->x[(i * n + j) * d1], d1 * sizeof(float));
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		for (i = 0; i < d0; ++i)
+			for (j = 0; j < n; ++j)
+				kad_saxpy(d1, 1.0f, &p->g[(i * n + n - 1 - j) * d1], &q->g[(i * n + j) * d1]);
+	}
+	return 0;
+}
+
+/********** Cost functions **********/
+
+int kad_op_mse(kad_node_t *p, int action)
+{
+	kad_node_t *y1 = p->child[0]; /* test */
+	kad_node_t *y0 = p->child[1]; /* truth */
+	int i, n;
+
+	n = kad_len(y0);
+	if (action == KAD_SYNC_DIM) {
+		if (n != kad_len(y1)) return -1;
+		p->n_d = 0;
+	} else if (action == KAD_FORWARD) {
+		double cost = 0.0;
+		for (i = 0; i < n; ++i)
+			cost += (y1->x[i] - y0->x[i]) * (y1->x[i] - y0->x[i]);
+		p->x[0] = (float)(cost / n);
+	} else if (action == KAD_BACKWARD && kad_is_back(y1)) {
+		float t = 2.0f * p->g[0] / n;
+		for (i = 0; i < n; ++i)
+			y1->g[i] += t * (y1->x[i] - y0->x[i]);
+	}
+	return 0;
+}
+
+int kad_op_ce_bin(kad_node_t *p, int action)
+{
+	static const float tiny = 1e-9f;
+	kad_node_t *y1 = p->child[0]; /* test */
+	kad_node_t *y0 = p->child[1]; /* truth */
+	int i, n;
+
+	n = kad_len(y0);
+	if (action == KAD_SYNC_DIM) {
+		if (n != kad_len(y1)) return -1;
+		p->n_d = 0;
+	} else if (action == KAD_FORWARD) {
+		double cost = 0.0;
+		for (i = 0; i < n; ++i) {
+			if (y0->x[i] > 0.0f)
+				cost += y0->x[i] * log(y0->x[i] / (y1->x[i] > tiny? y1->x[i] : tiny));
+			if (1.0f - y0->x[i] > 0.0f)
+				cost += (1.0f - y0->x[i]) * log((1.0f - y0->x[i]) / (1.0f - y1->x[i] > tiny? 1.0f - y1->x[i] : tiny));
+		}
+		p->x[0] = (float)(cost / n);
+	} else if (action == KAD_BACKWARD && kad_is_back(y1)) {
+		float t = p->g[0] / n;
+		for (i = 0; i < n; ++i) {
+			if (y0->x[i] > 0.0f)
+				y1->g[i] -= t * y0->x[i] / (y1->x[i] > tiny? y1->x[i] : tiny);
+			if (1.0f - y0->x[i] > 0.0f)
+				y1->g[i] += t * (1.0f - y0->x[i]) / (1.0f - y1->x[i] > tiny? 1.0f - y1->x[i] : tiny);
+		}
+	}
+	return 0;
+}
+
+int kad_op_ce_bin_neg(kad_node_t *p, int action)
+{
+	static const float tiny = 1e-9f;
+	kad_node_t *y1 = p->child[0]; /* test */
+	kad_node_t *y0 = p->child[1]; /* truth */
+	int i, n;
+
+	n = kad_len(y0);
+	if (action == KAD_SYNC_DIM) {
+		if (n != kad_len(y1)) return -1;
+		p->n_d = 0;
+	} else if (action == KAD_FORWARD) {
+		double cost = 0.0;
+		for (i = 0; i < n; ++i) {
+			if (1.0f + y0->x[i] > 0.0f)
+				cost += .5f * (1.0f + y0->x[i]) * log((1.0f + y0->x[i]) / (1.0f + y1->x[i] > tiny? 1.0f + y1->x[i] : tiny));
+			if (1.0f - y0->x[i] > 0.0f)
+				cost += .5f * (1.0f - y0->x[i]) * log((1.0f - y0->x[i]) / (1.0f - y1->x[i] > tiny? 1.0f - y1->x[i] : tiny));
+		}
+		p->x[0] = (float)(cost / n);
+	} else if (action == KAD_BACKWARD && kad_is_back(y1)) {
+		float t = p->g[0] / n;
+		for (i = 0; i < n; ++i) {
+			if (1.0f + y0->x[i] > 0.0f)
+				y1->g[i] -= .5f * t * (1.0f + y0->x[i]) / (1.0f + y1->x[i] > tiny? 1.0f + y1->x[i] : tiny);
+			if (1.0f - y0->x[i] > 0.0f)
+				y1->g[i] += .5f * t * (1.0f - y0->x[i]) / (1.0f - y1->x[i] > tiny? 1.0f - y1->x[i] : tiny);
+		}
+	}
+	return 0;
+}
+
+int kad_op_ce_multi(kad_node_t *p, int action)
+{
+	static const float tiny = 1e-9f;
+	kad_node_t *y1 = p->child[0]; /* test */
+	kad_node_t *y0 = p->child[1]; /* truth */
+	kad_node_t *c = 0;
+	int i, j, n1, d0;
+
+	n1 = y0->d[y0->n_d - 1];
+	d0 = kad_len(y0) / n1;
+	if (p->n_child == 3) {
+		c = p->child[2];
+		assert(c->n_d == 1 && c->d[0] == n1);
+	}
+	if (action == KAD_SYNC_DIM) {
+		if (kad_len(y0) != kad_len(y1) || y0->d[y0->n_d - 1] != y1->d[y1->n_d - 1]) return -1;
+		p->n_d = 0;
+	} else if (action == KAD_FORWARD) {
+		double cost = 0.0;
+		if (c == 0) {
+			for (j = 0; j < d0; ++j) {
+				float *x1 = &y1->x[j * n1], *x0 = &y0->x[j * n1];
+				for (i = 0; i < n1; ++i)
+					if (x0[i] > 0.0f)
+						cost += x0[i] * log(x0[i] / (x1[i] > tiny? x1[i] : tiny));
+			}
+		} else {
+			for (j = 0; j < d0; ++j) {
+				float *x1 = &y1->x[j * n1], *x0 = &y0->x[j * n1];
+				for (i = 0; i < n1; ++i)
+					if (x0[i] > 0.0f)
+						cost += c->x[i] * x0[i] * log(x0[i] / (x1[i] > tiny? x1[i] : tiny));
+			}
+		}
+		p->x[0] = (float)(cost / d0);
+	} else if (action == KAD_BACKWARD && kad_is_back(y1)) {
+		float t = p->g[0] / d0;
+		if (c == 0) {
+			for (j = 0; j < d0; ++j) {
+				float *g = &y1->g[j * n1], *x1 = &y1->x[j * n1], *x0 = &y0->x[j * n1];
+				for (i = 0; i < n1; ++i)
+					g[i] -= t * x0[i] / (x1[i] > tiny? x1[i] : tiny);
+			}
+		} else {
+			for (j = 0; j < d0; ++j) {
+				float *g = &y1->g[j * n1], *x1 = &y1->x[j * n1], *x0 = &y0->x[j * n1];
+				for (i = 0; i < n1; ++i)
+					g[i] -= t * c->x[i] * x0[i] / (x1[i] > tiny? x1[i] : tiny);
+			}
+		}
+	}
+	return 0;
+}
+
+/********** Normalization **********/
+
+int kad_op_stdnorm(kad_node_t *p, int action)
+{
+	int i, j, n, m;
+	kad_node_t *q = p->child[0];
+	assert(q->n_d > 0);
+	n = q->d[q->n_d - 1];
+	m = kad_len(q) / n;
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_ALLOC) {
+		p->gtmp = realloc(p->gtmp, m * sizeof(float));
+	} else if (action == KAD_FORWARD) {
+		float *si = (float*)p->gtmp;
+		for (j = 0; j < m; ++j) {
+			float *px = &p->x[j * n], *qx = &q->x[j * n];
+			float avg, std_inv;
+			double s;
+			for (i = 0, s = 0.0; i < n; ++i) s += qx[i];
+			avg = (float)(s / n);
+			for (i = 0; i < n; ++i) px[i] = qx[i] - avg;
+			for (i = 0, s = 0.0; i < n; ++i) s += px[i] * px[i];
+			std_inv = s == 0.0? 1.0f : (float)(1.0 / sqrt(s / n));
+			for (i = 0; i < n; ++i) px[i] *= std_inv;
+			si[j] = std_inv;
+		}
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		float *si = (float*)p->gtmp;
+		for (j = 0; j < m; ++j) {
+			float *pg = &p->g[j * n], *qg = &q->g[j * n], *px = &p->x[j * n], std_inv = si[j];
+			double s, t;
+			for (i = 0, s = t = 0.0; i < n; ++i)
+				s += pg[i], t += px[i] * pg[i];
+			s /= n, t /= n;
+			for (i = 0; i < n; ++i)
+				qg[i] += std_inv * (pg[i] - s - px[i] * t);
+		}
+	}
+	return 0;
+}
+
+/********** Activation functions **********/
+
+int kad_op_sigm(kad_node_t *p, int action)
+{
+	int i, n;
+	kad_node_t *q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		for (i = 0; i < n; ++i)
+			p->x[i] = 1.0f / (1.0f + expf(-q->x[i]));
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		for (i = 0; i < n; ++i)
+			q->g[i] += p->g[i] * (p->x[i] * (1.0f - p->x[i]));
+	}
+	return 0;
+}
+
+int kad_op_tanh(kad_node_t *p, int action)
+{
+	int i, n;
+	kad_node_t *q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		for (i = 0; i < n; ++i) {
+			if (q->x[i] < -20.0f) p->x[i] = -1.0f;
+			else {
+				float y;
+				y = expf(-2.0f * q->x[i]);
+				p->x[i] = (1.0f - y) / (1.0f + y);
+			}
+		}
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		for (i = 0; i < n; ++i)
+			q->g[i] += p->g[i] * (1.0f - p->x[i] * p->x[i]);
+	}
+	return 0;
+}
+
+int kad_op_relu(kad_node_t *p, int action)
+{
+	int i, n;
+	kad_node_t *q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		for (i = 0; i < n; ++i)
+			p->x[i] = q->x[i] > 0.0f? q->x[i] : 0.0f;
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		for (i = 0; i < n; ++i)
+			if (q->x[i] > 0.0f)
+				q->g[i] += p->g[i];
+	}
+	return 0;
+}
+
+int kad_op_sin(kad_node_t *p, int action)
+{
+	int i, n;
+	kad_node_t *q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		for (i = 0; i < n; ++i) p->x[i] = sinf(q->x[i]);
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		for (i = 0; i < n; ++i)
+			q->g[i] += p->g[i] * cosf(q->x[i]);
+	}
+	return 0;
+}
+
+int kad_op_softmax(kad_node_t *p, int action)
+{
+	int i, j, n1, d0;
+	kad_node_t *q = p->child[0];
+
+	n1 = q->d[q->n_d - 1];
+	d0 = kad_len(q) / n1;
+	if (action == KAD_SYNC_DIM) {
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		for (j = 0; j < d0; ++j) {
+			float s, max, *x = &q->x[j * n1], *y = &p->x[j * n1];
+			for (i = 0, max = -FLT_MAX; i < n1; ++i)
+				max = max > x[i]? max : x[i];
+			for (i = 0, s = 0.0f; i < n1; ++i) {
+				y[i] = expf(x[i] - max);
+				s += y[i];
+			}
+			for (i = 0, s = 1.0f / s; i < n1; ++i) y[i] *= s;
+		}
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		for (j = 0; j < d0; ++j) {
+			float s, *g = &p->g[j * n1], *y = &p->x[j * n1], *h = &q->g[j * n1];
+			for (i = 0, s = 0.0f; i < n1; ++i)
+				s += g[i] * y[i];
+			for (i = 0; i < n1; ++i)
+				h[i] += y[i] * (g[i] - s);
+		}
+	}
+	return 0;
+}
+
+/********** Multi-node pooling **********/
+
+int kad_op_avg(kad_node_t *p, int action)
+{
+	int i, n;
+	float tmp;
+	kad_node_t *q;
+
+	assert(p->n_child > 0);
+	tmp = 1.0f / p->n_child;
+	q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		for (i = 1; i < p->n_child; ++i)
+			if (kad_len(p->child[i]) != n) return -1;
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		memcpy(p->x, q->x, n * sizeof(float));
+		for (i = 1; i < p->n_child; ++i)
+			kad_saxpy(n, 1.0f, p->child[i]->x, p->x);
+		for (i = 0; i < n; ++i) p->x[i] *= tmp;
+	} else if (action == KAD_BACKWARD) {
+		for (i = 0; i < p->n_child; ++i)
+			if (kad_is_back(p->child[i]))
+				kad_saxpy(n, tmp, p->g, p->child[i]->g);
+	}
+	return 0;
+}
+
+int kad_op_max(kad_node_t *p, int action)
+{
+	int i, n;
+	kad_node_t *q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		int *max_j;
+		for (i = 1; i < p->n_child; ++i)
+			if (kad_len(p->child[i]) != n) return -1;
+		kad_copy_dim1(p, q);
+		max_j = (int*)calloc(n, sizeof(int));
+		p->gtmp = max_j;
+	} else if (action == KAD_FORWARD) {
+		int j, *max_j = (int*)p->gtmp;
+		memset(max_j, 0, n * sizeof(int));
+		memcpy(p->x, q->x, n * sizeof(float));
+		for (j = 1; j < p->n_child; ++j)
+			for (i = 0, q = p->child[j]; i < n; ++i)
+				if (q->x[i] > p->x[i]) p->x[i] = q->x[i], max_j[i] = j;
+	} else if (action == KAD_BACKWARD) {
+		int *max_j = (int*)p->gtmp;
+		for (i = 0; i < n; ++i)
+			p->child[max_j[i]]->g[i] += p->g[i];
+	}
+	return 0;
+}
+
+int kad_op_stack(kad_node_t *p, int action) /* TODO: allow axis, as in TensorFlow */
+{
+	int i, n, axis = 0;
+	kad_node_t *q;
+
+	assert(p->n_child > 0);
+	q = p->child[0];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		for (i = 1; i < p->n_child; ++i)
+			if (kad_len(p->child[i]) != n) return -1;
+		p->n_d = q->n_d + 1;
+		for (i = 0; i < axis; ++i) p->d[i] = q->d[i];
+		p->d[axis] = p->n_child;
+		for (; i < q->n_d; ++i) p->d[i+1] = q->d[i];
+	} else if (action == KAD_FORWARD) { /* TODO: doesn't work when axis != 0 */
+		for (i = 0; i < p->n_child; ++i)
+			memcpy(&p->x[i * n], p->child[i]->x, n * sizeof(float));
+	} else if (action == KAD_BACKWARD) {
+		for (i = 0; i < p->n_child; ++i)
+			if (kad_is_back(p->child[i]))
+				kad_saxpy(n, 1.0f, &p->g[i * n], p->child[i]->g);
+	}
+	return 0;
+}
+
+int kad_op_select(kad_node_t *p, int action)
+{
+	kad_node_t *q;
+	int i, n, which;
+
+	which = *(int32_t*)p->ptr;
+	if (which < 0) which += p->n_child;
+	assert(which >= 0 && which < p->n_child);
+	q = p->child[which];
+	n = kad_len(q);
+	if (action == KAD_SYNC_DIM) {
+		for (i = 0; i < p->n_child; ++i)
+			if (p->child[i]->n_d != q->n_d || kad_len(p->child[i]) != n)
+				break;
+		if (i < p->n_child) return -1;
+		kad_copy_dim1(p, q);
+	} else if (action == KAD_FORWARD) {
+		memcpy(p->x, q->x, n * sizeof(float));
+	} else if (action == KAD_BACKWARD && kad_is_back(q)) {
+		kad_saxpy(n, 1.0f, p->g, q->g);
+	}
+	return 0;
+}
+
+/********** 2D convolution **********/
+
+static void conv_rot180(int d0, int d1, float *x) /* rotate/reverse a weight martix */
+{
+	int i, j;
+	for (i = 0; i < d0; ++i) {
+		float tmp, *xi = &x[i * d1];
+		for (j = 0; j < d1>>1; ++j)
+			tmp = xi[j], xi[j] = xi[d1-1-j], xi[d1-1-j] = tmp;
+	}
+}
+
+static void conv2d_move_1to3(int d[4], const float *x, float *y) /* convert the NCHW shape to the NHWC shape */
+{
+	int i, j, k, l;
+	for (i = 0; i < d[0]; ++i)
+		for (j = 0; j < d[1]; ++j)
+			for (k = 0; k < d[2]; ++k) {
+				int ik = (i * d[2] + k) * d[3], ijk = ((i * d[1] + j) * d[2] + k) * d[3];
+				for (l = 0; l < d[3]; ++l)
+					y[(ik + l) * d[1] + j] = x[ijk + l];
+			}
+}
+
+static void conv2d_add_3to1(int d[4], const float *y, float *x) /* convert the NHWC shape back to NCHW and add to another NCHW-shaped array */
+{
+	int i, j, k, l;
+	for (i = 0; i < d[0]; ++i)
+		for (j = 0; j < d[1]; ++j)
+			for (k = 0; k < d[2]; ++k) {
+				int ik = (i * d[2] + k) * d[3], ijk = ((i * d[1] + j) * d[2] + k) * d[3];
+				for (l = 0; l < d[3]; ++l)
+					x[ijk + l] += y[(ik + l) * d[1] + j];
+			}
+}
+
+#define conv_out_size(in_size, aux) (((in_size) - (aux)->kernel_size + (aux)->pad[0] + (aux)->pad[1]) / (aux)->stride + 1)
+
+#define process_row_for(_xx, _ww, _yy, _wn, _pn, _stride, _pad, _t) do { \
+	int j, l; \
+	if (_stride > 1) { \
+		for (l = 0; l < _wn; ++l) { \
+			const float *xl = &_xx[l - _pad]; \
+			for (j = 0; j < _pn; ++j, xl += _stride) _t[j] = *xl; \
+			kad_saxpy(_pn, _ww[l], _t, _yy); \
+		} \
+	} else for (l = 0; l < _wn; ++l) kad_saxpy(_pn, _ww[l], &_xx[l - _pad], _yy); \
+} while (0)
+
+#define process_row_back_x(_xx, _ww, _yy, _wn, _pn, _stride, _pad, _t) do { \
+	int j, l; \
+	if (_stride > 1) { \
+		for (l = 0; l < _wn; ++l) { \
+			float *xl = &_xx[l - _pad]; \
+			memset(_t, 0, _pn * sizeof(float)); \
+			kad_saxpy(_pn, _ww[l], _yy, _t); \
+			for (j = 0; j < _pn; ++j, xl += _stride) *xl += _t[j]; \
+		} \
+	} else for (l = 0; l < _wn; ++l) kad_saxpy(_pn, _ww[l], _yy, &_xx[l - _pad]); \
+} while (0)
+
+#define process_row_back_w(_xx, _ww, _yy, _wn, _pn, _stride, _pad, _t) do { \
+	int j, l; \
+	if (_stride > 1) { \
+		for (l = 0; l < _wn; ++l) { \
+			const float *xl = &_xx[l - _pad]; \
+			for (j = 0; j < _pn; ++j, xl += _stride) _t[j] = *xl; \
+			_ww[l] += kad_sdot(_pn, _yy, _t); \
+		} \
+	} else for (l = 0; l < _wn; ++l) _ww[l] += kad_sdot(_pn, _yy, &_xx[l - _pad]); \
+} while (0)
+
+/* Forward and backward passes are implemented with two different algorithms.
+ * The first is faster for small kernels with few input channels; otherwise the
+ * second algorithm is faster. Both algorithms should produce identical
+ * results, up to the precision of "float".
+ */
+int kad_op_conv2d(kad_node_t *p, int action) /* in the number-channel-height-width (NCHW) shape */
+{
+#define conv2d_loop1(_x, _w, _y, _tmp, _row_func) do { /* for the NCHW shape */ \
+		int n, c1, c0, i, k, ii; \
+		for (n = 0; n < q->d[0]; ++n) /* mini-batch */ \
+			for (c1 = 0; c1 < w->d[0]; ++c1) /* output channel */ \
+				for (c0 = 0; c0 < w->d[1]; ++c0) /* input channel */ \
+					for (k = 0; k < w->d[2]; ++k) { /* kernel row */ \
+						float *_ww = &(_w)[((c1 * w->d[1] + c0) * w->d[2] + k) * w->d[3]]; \
+						for (i = 0, ii = k - aux[0].pad[0]; i < p->d[2] && ii >= 0 && ii < q->d[2]; ++i, ii += aux[0].stride) { /* output row */ \
+							float *_xx = &(_x)[((n * q->d[1] + c0) * q->d[2] + ii) * q->d[3]]; \
+							float *_yy = &(_y)[((n * p->d[1] + c1) * p->d[2] + i)  * p->d[3]]; \
+							if (x_padded) { \
+								memcpy(x_padded + aux[1].pad[0], _xx, q->d[3] * sizeof(float)); \
+								_xx = x_padded + aux[1].pad[0]; \
+							} \
+							_row_func(_xx, _ww, _yy, w->d[3], p->d[3], aux[1].stride, aux[1].pad[0], (_tmp)); \
+						} /* ~i */ \
+					} /* ~k, c0, c1, n */ \
+	} while (0)
+
+#define conv2d_loop2(_x, _w, _y, _code) do { /* for the NHWC shape */ \
+		int n, c1, i, j, k, ii, j_skip = aux[1].stride * q->d[1], m = w->d[3] * w->d[1]; \
+		for (n = 0; n < q->d[0]; ++n) /* mini-batch */ \
+			for (c1 = 0; c1 < w->d[0]; ++c1) /* output channel */ \
+				for (k = 0; k < w->d[2]; ++k) { /* kernel row */ \
+					float *_ww = &(_w)[(c1 * w->d[2] + k) * m]; \
+					for (i = 0, ii = k - aux[0].pad[0]; i < p->d[2] && ii >= 0 && ii < q->d[2]; ++i, ii += aux[0].stride) { /* output and input row */ \
+						float *_xx = &(_x)[(n * q->d[2] + ii) * q->d[3] * q->d[1]]; \
+						float *_yy = &(_y)[((n * p->d[1] + c1) * p->d[2] + i) * p->d[3]]; \
+						if (x_padded) { \
+							memcpy(x_padded + aux[1].pad[0] * q->d[1], _xx, q->d[3] * q->d[1] * sizeof(float)); \
+							_xx = x_padded; \
+						} \
+						for (j = 0; j < p->d[3]; ++j, _xx += j_skip, ++_yy) _code; /* output and input column */ \
+					} /* ~i */ \
+				} /* ~k, c1, n */ \
+	} while (0)
+
+	conv_conf_t *aux = (conv_conf_t*)p->ptr;
+	kad_node_t *q = p->child[0], *w = p->child[1];
+	float *t = 0, *q1 = 0, *w1 = 0, *x_padded = 0;
+	int algo_switch = 0;
+
+	if (action == KAD_FORWARD || action == KAD_BACKWARD) { /* allocate working space */
+		if (w->d[3] * w->d[1] < 16) {
+			t = (float*)malloc(p->d[3] * sizeof(float));
+			x_padded = aux[1].pad[0] + aux[1].pad[1] > 0? (float*)calloc(q->d[3] + aux[1].pad[0] + aux[1].pad[1], sizeof(float)) : 0;
+		} else {
+			q1 = (float*)malloc(kad_len(q) * sizeof(float));
+			w1 = (float*)malloc(kad_len(w) * sizeof(float));
+			x_padded = aux[1].pad[0] + aux[1].pad[1] > 0? (float*)calloc((q->d[3] + aux[1].pad[0] + aux[1].pad[1]) * q->d[1], sizeof(float)) : 0;
+			algo_switch = 1;
+		}
+	}
+	if (action == KAD_SYNC_DIM) {
+		if (q->n_d != 4 || w->n_d != 4) return -1;
+		if (q->d[1] != w->d[1]) return -1; /* unmatched input channels */
+		p->n_d = 4;
+		p->d[0] = q->d[0], p->d[1] = w->d[0], p->d[2] = conv_out_size(q->d[2], &aux[0]), p->d[3] = conv_out_size(q->d[3], &aux[1]);
+	} else if (action == KAD_FORWARD) {
+		conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->x);
+		memset(p->x, 0, kad_len(p) * sizeof(float));
+		if (!algo_switch) { /* this is the first algorithm */
+			conv2d_loop1(q->x, w->x, p->x, t, process_row_for);
+		} else { /* this is the second algorithm */
+			conv2d_move_1to3(q->d, q->x, q1);
+			conv2d_move_1to3(w->d, w->x, w1);
+			conv2d_loop2(q1, w1, p->x, (*_yy += kad_sdot(m, _ww, _xx)));
+		}
+		conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->x);
+	} else if (action == KAD_BACKWARD) {
+		if (kad_is_back(p->child[0])) { /* backprop to the input array */
+			conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->x);
+			if (!algo_switch) {
+				conv2d_loop1(q->g, w->x, p->g, t, process_row_back_x);
+			} else {
+				memset(q1, 0, kad_len(q) * sizeof(float));
+				conv2d_move_1to3(w->d, w->x, w1);
+				conv2d_loop2(q1, w1, p->g, kad_saxpy(m, *_yy, _ww, _xx));
+				conv2d_add_3to1(q->d, q1, q->g);
+			}
+			conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->x);
+		}
+		if (kad_is_back(p->child[1])) { /* backprop to the weight matrix */
+			conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->g);
+			if (!algo_switch) {
+				conv2d_loop1(q->x, w->g, p->g, t, process_row_back_w);
+			} else {
+				conv2d_move_1to3(q->d, q->x, q1);
+				memset(w1, 0, kad_len(w) * sizeof(float));
+				conv2d_loop2(q1, w1, p->g, kad_saxpy(m, *_yy, _xx, _ww));
+				conv2d_add_3to1(w->d, w1, w->g);
+			}
+			conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->g);
+		}
+	}
+	free(t); free(q1); free(w1); free(x_padded);
+	return 0;
+}
+
+int kad_op_max2d(kad_node_t *p, int action)
+{
+	conv_conf_t *aux = (conv_conf_t*)p->ptr;
+	kad_node_t *q = p->child[0];
+	if (action == KAD_SYNC_DIM) {
+		if (q->n_d != 4) return -1;
+		p->n_d = 4;
+		p->d[0] = q->d[0], p->d[1] = q->d[1], p->d[2] = conv_out_size(q->d[2], &aux[0]), p->d[3] = conv_out_size(q->d[3], &aux[1]);
+	} else if (action == KAD_ALLOC) {
+		p->gtmp = realloc(p->gtmp, kad_len(p) * sizeof(int));
+	} else if (action == KAD_FORWARD) {
+		int rest = 1, len, t, i;
+		int *f = (int*)p->gtmp;
+		len = kad_len(p);
+		for (i = 0; i < len; ++i) p->x[i] = -FLT_MAX;
+		for (i = 0; i < p->n_d - 2; ++i) rest *= p->d[i];
+		for (t = 0; t < rest; ++t) {
+			int i, j, k, l, p_row = p->d[p->n_d - 2], p_col = p->d[p->n_d - 1];
+			for (i = 0; i < p_row; ++i) {
+				int u = (t * p_row + i) * p_col;
+				for (k = 0; k < aux[0].kernel_size; ++k) {
+					int v, v0, v_end, ii = i * aux[0].stride + k - aux[0].pad[0];
+					if (ii < 0 || ii >= q->d[p->n_d - 2]) continue;
+					v0 = (t * q->d[p->n_d - 2] + ii) * q->d[p->n_d - 1];
+					v_end = v0 + q->d[p->n_d - 1];
+					for (l = 0; l < aux[1].kernel_size; ++l)
+						for (j = 0, v = v0 + (l > aux[1].pad[0]? l - aux[1].pad[0] : 0); j < p_col && v < v_end; ++j, v += aux[1].stride)
+							if (p->x[u + j] < q->x[v])
+								p->x[u + j] = q->x[v], f[u + j] = v;
+				} /* ~k */
+			} /* ~i */
+		}
+	} else if (action == KAD_BACKWARD) {
+		int i, len, *f = (int*)p->gtmp;
+		len = kad_len(p);
+		for (i = 0; i < len; ++i) q->g[f[i]] += p->g[i];
+	}
+	return 0;
+}
+
+/********** 1D convolution **********/
+
+static void conv1d_move_1to2(int d[3], const float *x, float *y)
+{
+	int i, j, k;
+	for (k = 0; k < d[0]; ++k)
+		for (j = 0; j < d[1]; ++j)
+			for (i = 0; i < d[2]; ++i)
+				y[(k * d[2] + i) * d[1] + j] = x[(k * d[1] + j) * d[2] + i];
+}
+
+static void conv1d_add_2to1(int d[3], const float *y, float *x)
+{
+	int i, j, k;
+	for (k = 0; k < d[0]; ++k)
+		for (j = 0; j < d[1]; ++j)
+			for (i = 0; i < d[2]; ++i)
+				x[(k * d[1] + j) * d[2] + i] += y[(k * d[2] + i) * d[1] + j];
+}
+
+int kad_op_conv1d(kad_node_t *p, int action) /* in the number-channel-width (NCW) shape */
+{
+#define conv1d_loop1(_x, _w, _y, _tmp, _row_func) do { /* for the NCW shape */ \
+		int n, c1, c0; \
+		for (n = 0; n < q->d[0]; ++n) /* mini-batch */ \
+			for (c1 = 0; c1 < w->d[0]; ++c1) /* output channel */ \
+				for (c0 = 0; c0 < w->d[1]; ++c0) { /* input channel */ \
+					float *_ww = &(_w)[(c1 * w->d[1] + c0) * w->d[2]]; \
+					float *_xx = &(_x)[(n  * q->d[1] + c0) * q->d[2]]; \
+					float *_yy = &(_y)[(n  * p->d[1] + c1) * p->d[2]]; \
+					if (x_padded) { \
+						memcpy(x_padded + aux->pad[0], _xx, q->d[2] * sizeof(float)); \
+						_xx = x_padded + aux->pad[0]; \
+					} \
+					_row_func(_xx, _ww, _yy, w->d[2], p->d[2], aux->stride, aux->pad[0], (_tmp)); \
+				} /* ~c0, c1, n */ \
+	} while (0)
+
+#define conv1d_loop2(_x, _w, _y, _code) do { /* for the NWC shape */ \
+		int n, c1, j, j_skip = aux->stride * q->d[1], m = w->d[2] * w->d[1]; \
+		for (n = 0; n < q->d[0]; ++n) /* mini-batch */ \
+			for (c1 = 0; c1 < w->d[0]; ++c1) { /* output channel */ \
+				float *_ww = &(_w)[c1 * m]; \
+				float *_xx = &(_x)[n * q->d[1] * q->d[2]]; \
+				float *_yy = &(_y)[(n * p->d[1] + c1) * p->d[2]]; \
+				if (x_padded) { \
+					memcpy(x_padded + aux->pad[0] * q->d[1], _xx, q->d[2] * q->d[1] * sizeof(float)); \
+					_xx = x_padded; \
+				} \
+				for (j = 0; j < p->d[2]; ++j, _xx += j_skip, ++_yy) _code; \
+			} /* ~c1, n */ \
+	} while (0)
+
+	conv_conf_t *aux = (conv_conf_t*)p->ptr;
+	kad_node_t *q = p->child[0], *w = p->child[1];
+	float *t = 0, *q1 = 0, *w1 = 0, *x_padded = 0;
+	int algo_switch = 0;
+
+	if (action == KAD_FORWARD || action == KAD_BACKWARD) { /* allocate working space */
+		if (w->d[2] * w->d[1] < 32) {
+			t = (float*)malloc(p->d[2] * sizeof(float));
+			x_padded = aux->pad[0] + aux->pad[1] > 0? (float*)calloc(q->d[2] + aux->pad[0] + aux->pad[1], sizeof(float)) : 0;
+		} else {
+			q1 = (float*)malloc(kad_len(q) * sizeof(float));
+			w1 = (float*)malloc(kad_len(w) * sizeof(float));
+			x_padded = aux->pad[0] + aux->pad[1] > 0? (float*)calloc((q->d[2] + aux->pad[0] + aux->pad[1]) * q->d[1], sizeof(float)) : 0;
+			algo_switch = 1;
+		}
+	}
+	if (action == KAD_SYNC_DIM) {
+		if (q->n_d != 3 || w->n_d != 3) return -1;
+		if (q->d[1] != w->d[1]) return -1; /* unmatched input channels */
+		p->n_d = 3;
+		p->d[0] = q->d[0], p->d[1] = w->d[0], p->d[2] = conv_out_size(q->d[2], aux);
+	} else if (action == KAD_FORWARD) {
+		conv_rot180(w->d[0] * w->d[1], w->d[2], w->x);
+		memset(p->x, 0, kad_len(p) * sizeof(float));
+		if (!algo_switch) { /* this is the first algorithm */
+			conv1d_loop1(q->x, w->x, p->x, t, process_row_for);
+		} else { /* this is the second algorithm */
+			conv1d_move_1to2(q->d, q->x, q1);
+			conv1d_move_1to2(w->d, w->x, w1);
+			conv1d_loop2(q1, w1, p->x, (*_yy += kad_sdot(m, _ww, _xx)));
+		}
+		conv_rot180(w->d[0] * w->d[1], w->d[2], w->x);
+	} else if (action == KAD_BACKWARD) {
+		if (kad_is_back(p->child[0])) { /* backprop to the input array */
+			conv_rot180(w->d[0] * w->d[1], w->d[2], w->x);
+			if (!algo_switch) {
+				conv1d_loop1(q->g, w->x, p->g, t, process_row_back_x);
+			} else {
+				memset(q1, 0, kad_len(q) * sizeof(float));
+				conv1d_move_1to2(w->d, w->x, w1);
+				conv1d_loop2(q1, w1, p->g, kad_saxpy(m, *_yy, _ww, _xx));
+				conv1d_add_2to1(q->d, q1, q->g);
+			}
+			conv_rot180(w->d[0] * w->d[1], w->d[2], w->x);
+		}
+		if (kad_is_back(p->child[1])) { /* backprop to the weight matrix */
+			conv_rot180(w->d[0] * w->d[1], w->d[2], w->g);
+			if (!algo_switch) {
+				conv1d_loop1(q->x, w->g, p->g, t, process_row_back_w);
+			} else {
+				conv1d_move_1to2(q->d, q->x, q1);
+				memset(w1, 0, kad_len(w) * sizeof(float));
+				conv1d_loop2(q1, w1, p->g, kad_saxpy(m, *_yy, _xx, _ww));
+				conv1d_add_2to1(w->d, w1, w->g);
+			}
+			conv_rot180(w->d[0] * w->d[1], w->d[2], w->g);
+		}
+	}
+	free(t); free(q1); free(w1); free(x_padded);
+	return 0;
+}
+
+int kad_op_max1d(kad_node_t *p, int action)
+{
+	conv_conf_t *aux = (conv_conf_t*)p->ptr;
+	kad_node_t *q = p->child[0];
+	if (action == KAD_SYNC_DIM) {
+		if (q->n_d != 3) return -1;
+		p->n_d = 3;
+		p->d[0] = q->d[0], p->d[1] = q->d[1], p->d[2] = conv_out_size(q->d[2], aux);
+	} else if (action == KAD_ALLOC) {
+		p->gtmp = realloc(p->gtmp, kad_len(p) * sizeof(int));
+	} else if (action == KAD_FORWARD) {
+		int rest = 1, len, t, i;
+		int *f = (int*)p->gtmp;
+		len = kad_len(p);
+		for (i = 0; i < len; ++i) p->x[i] = -FLT_MAX;
+		for (i = 0; i < p->n_d - 1; ++i) rest *= p->d[i];
+		for (t = 0; t < rest; ++t) {
+			int j, l, p_width = p->d[p->n_d - 1];
+			int u = t * p_width, v, v0 = t * q->d[p->n_d - 1], v_end = v0 + q->d[p->n_d - 1];
+			for (l = 0; l < aux->kernel_size; ++l)
+				for (j = 0, v = v0 + (l > aux->pad[0]? l - aux->pad[0] : 0); j < p_width && v < v_end; ++j, v += aux->stride)
+					if (p->x[u + j] < q->x[v])
+						p->x[u + j] = q->x[v], f[u + j] = v;
+		}
+	} else if (action == KAD_BACKWARD) {
+		int i, len, *f = (int*)p->gtmp;
+		len = kad_len(p);
+		for (i = 0; i < len; ++i) q->g[f[i]] += p->g[i];
+	}
+	return 0;
+}
+
+int kad_op_avg1d(kad_node_t *p, int action)
+{
+	conv_conf_t *aux = (conv_conf_t*)p->ptr;
+	kad_node_t *q = p->child[0];
+	if (action == KAD_SYNC_DIM) {
+		if (q->n_d != 3) return -1;
+		p->n_d = 3;
+		p->d[0] = q->d[0], p->d[1] = q->d[1], p->d[2] = conv_out_size(q->d[2], aux);
+	} else if (action == KAD_ALLOC) {
+		p->gtmp = realloc(p->gtmp, kad_len(p) * sizeof(int));
+	} else if (action == KAD_FORWARD) {
+		int rest = 1, len, t, i;
+		int *f = (int*)p->gtmp;
+		len = kad_len(p);
+		for (i = 0; i < len; ++i) p->x[i] = 0.0f, f[i] = 0;
+		for (i = 0; i < p->n_d - 1; ++i) rest *= p->d[i];
+		for (t = 0; t < rest; ++t) {
+			int j, l, p_width = p->d[p->n_d - 1];
+			int u = t * p_width, v, v0 = t * q->d[p->n_d - 1], v_end = v0 + q->d[p->n_d - 1];
+			for (l = 0; l < aux->kernel_size; ++l)
+				for (j = 0, v = v0 + (l > aux->pad[0]? l - aux->pad[0] : 0); j < p_width && v < v_end; ++j, v += aux->stride)
+					p->x[u + j] += q->x[v], ++f[u + j];
+		}
+		for (i = 0; i < len; ++i) p->x[i] /= f[i];
+	} else if (action == KAD_BACKWARD) {
+		int rest = 1, t, i;
+		int *f = (int*)p->gtmp;
+		for (i = 0; i < p->n_d - 1; ++i) rest *= p->d[i];
+		for (t = 0; t < rest; ++t) {
+			int j, l, p_width = p->d[p->n_d - 1];
+			int u = t * p_width, v, v0 = t * q->d[p->n_d - 1], v_end = v0 + q->d[p->n_d - 1];
+			for (l = 0; l < aux->kernel_size; ++l)
+				for (j = 0, v = v0 + (l > aux->pad[0]? l - aux->pad[0] : 0); j < p_width && v < v_end; ++j, v += aux->stride)
+					q->g[v] += p->g[u + j] / f[u + j];
+		}
+	}
+	return 0;
+}
+
+/********** List of operators **********/
+
+kad_op_f kad_op_list[KAD_MAX_OP] = {
+	0,
+	kad_op_add,        /* 1:  element-wise addition */
+	kad_op_mul,        /* 2:  element-wise multiplication */
+	kad_op_cmul,       /* 3:  column multiplication */
+	kad_op_ce_bin_neg, /* 4:  binary cross-entropy for (-1,1) */
+	kad_op_square,     /* 5:  square */
+	kad_op_sigm,       /* 6:  sigmoid */
+	kad_op_tanh,       /* 7:  tanh */
+	kad_op_relu,       /* 8:  ReLU */
+	kad_op_matmul,     /* 9:  matrix multiplication */
+	kad_op_avg,        /* 10: general average pooling (not for ConvNet) */
+	kad_op_1minus,     /* 11: 1-x */
+	kad_op_select,     /* 12: choose between one of the children */
+	kad_op_ce_multi,   /* 13: multi-class cross-entropy */
+	kad_op_softmax,    /* 14: softmax */
+	kad_op_dropout,    /* 15: dropout */
+	kad_op_conv2d,     /* 16: 2D convolution */
+	kad_op_max2d,      /* 17: 2D max pooling (for 2D ConvNet) */
+	kad_op_conv1d,     /* 18: 1D convolution */
+	kad_op_max1d,      /* 19: 1D max pooling (for 1D ConvNet) */
+	kad_op_slice,      /* 20: slice data at a dimension */
+	kad_op_max,        /* 21: general max pooling */
+	kad_op_ce_bin,     /* 22: binary cross-entropy for (0,1) */
+	kad_op_sub,        /* 23: element-wise subtraction */
+	kad_op_sample_normal,  /* 24: sample from a normal distribution */
+	kad_op_reduce_sum,     /* 25 */
+	kad_op_reduce_mean,    /* 26 */
+	kad_op_log,        /* 27: log() */
+	kad_op_avg1d,      /* 28: 1D average pooling (for 1D ConvNet) */
+	kad_op_mse,        /* 29: mean square error */
+	kad_op_reshape,    /* 30 */
+	kad_op_concat,     /* 31 */
+	kad_op_stdnorm,    /* 32: layer normalization */
+	kad_op_exp,        /* 33: exp() */
+	kad_op_sin,        /* 34: sin() */
+	kad_op_stack,      /* 35: tf.stack, but on the first axis only */
+	kad_op_reverse     /* 36: tf.reverse, but on one axis only */
+};
+
+char *kad_op_name[KAD_MAX_OP] = {
+	0, "add", "mul", "cmul", "ce_bin_neg", "square", "sigm", "tanh", "relu", "matmul", "avg", "1minus", "select", "ce_multi", "softmax",
+	"dropout", "conv2d", "max2d", "conv1d", "max1d", "slice", "max", "ce_bin", "sub", "sample_normal", "reduce_sum", "reduce_mean", "log",
+	"avg1d", "mse", "reshape", "concat", "stdnorm", "exp", "sin", "stack", "reverse"
+};
+
+/**************************
+ *** Debugging routines ***
+ **************************/
+
+void kad_trap_fe(void)
+{
+#ifdef __SSE__
+	_MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() & ~(_MM_MASK_INVALID | _MM_MASK_DIV_ZERO));
+#endif
+}
+
+void kad_print_graph(FILE *fp, int n, kad_node_t **v)
+{
+	int i, j;
+	for (i = 0; i < n; ++i) v[i]->tmp = i;
+	for (i = 0; i < n; ++i) {
+		kad_node_t *p = v[i];
+		fprintf(fp, "%d\t%x:%x\t%d\t", i, p->flag, p->ext_flag, p->ext_label);
+		if (p->pre) fprintf(fp, "%d\t", p->pre->tmp);
+		else fprintf(fp, ".\t");
+		fputs("[", fp);
+		for (j = 0; j < p->n_d; ++j) {
+			if (j) fputc(',', fp);
+			fprintf(fp, "%d", p->d[j]);
+		}
+		fprintf(fp, "]\t");
+		if (p->n_child) {
+			fprintf(fp, "%s(", kad_op_name[p->op]);
+			for (j = 0; j < p->n_child; ++j) {
+				if (j) fputc(',', fp);
+				fprintf(fp, "$%d", p->child[j]->tmp);
+			}
+			fprintf(fp, ")");
+		} else fprintf(fp, "%s", kad_is_feed(p)? "feed" : kad_is_var(p)? "var" : kad_is_const(p)? "const" : "N/A");
+		fputc('\n', fp);
+	}
+	for (i = 0; i < n; ++i) v[i]->tmp = 0;
+}
+
+static void kad_add_delta(int n, kad_node_t **a, float c, float *delta)
+{
+	int i, k;
+	for (i = k = 0; i < n; ++i)
+		if (kad_is_var(a[i])) {
+			kad_saxpy(kad_len(a[i]), c, &delta[k], a[i]->x);
+			k += kad_len(a[i]);
+		}
+}
+
+void kad_check_grad(int n, kad_node_t **a, int from)
+{
+	const float eps = 1e-5f, rel = 1e-7f / eps;
+	int i, k, n_var;
+	float *g0, *delta, f0, f_minus, f_plus, s0, s1, rel_err, p_m_err;
+	n_var = kad_size_var(n, a);
+	g0 = (float*)calloc(n_var, sizeof(float));
+	f0 = *kad_eval_at(n, a, from);
+	kad_grad(n, a, from);
+	for (i = k = 0; i < n; ++i)
+		if (kad_is_var(a[i])) {
+			memcpy(&g0[k], a[i]->g, kad_len(a[i]) * sizeof(float));
+			k += kad_len(a[i]);
+		}
+	delta = (float*)calloc(n_var, sizeof(float));
+	for (k = 0; k < n_var; ++k) delta[k] = (float)kad_drand(0) * eps;
+	kad_add_delta(n, a, 1.0f, delta);
+	f_plus = *kad_eval_at(n, a, from);
+	kad_add_delta(n, a, -2.0f, delta);
+	f_minus = *kad_eval_at(n, a, from);
+	kad_add_delta(n, a, 1.0f, delta);
+	s0 = kad_sdot(n_var, g0, delta);
+	s1 = .5f * (f_plus - f_minus);
+	fprintf(stderr, "Gradient check -- %g <=> %g @ %g -- ", s0/eps, s1/eps, f0);
+	if (fabs(s1) >= rel * eps) {
+		rel_err = fabsf(fabsf(s0) - fabsf(s1)) / (fabsf(s0) + fabsf(s1));
+		p_m_err = fabsf(f_plus + f_minus - 2.0f * f0) / fabsf(f_plus - f_minus);
+		fprintf(stderr, "rel_err:%g p_m_err:%g -- ", rel_err, p_m_err);
+		if (rel_err >= rel && rel_err > p_m_err) fprintf(stderr, "failed\n");
+		else fprintf(stderr, "passed\n");
+	} else fprintf(stderr, "skipped\n");
+	free(delta); free(g0);
+}
diff --git a/contrib/kann/kautodiff.h b/contrib/kann/kautodiff.h
new file mode 100644
index 000000000..a2c648835
--- /dev/null
+++ b/contrib/kann/kautodiff.h
@@ -0,0 +1,246 @@
+/*
+  The MIT License
+
+  Copyright (c) 2018-2019 Dana-Farber Cancer Institute
+                2016-2018 Broad Institute
+
+  Permission is hereby granted, free of charge, to any person obtaining
+  a copy of this software and associated documentation files (the
+  "Software"), to deal in the Software without restriction, including
+  without limitation the rights to use, copy, modify, merge, publish,
+  distribute, sublicense, and/or sell copies of the Software, and to
+  permit persons to whom the Software is furnished to do so, subject to
+  the following conditions:
+
+  The above copyright notice and this permission notice shall be
+  included in all copies or substantial portions of the Software.
+
+  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+  NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+  BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+  ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+  CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+  SOFTWARE.
+*/
+
+#ifndef KANN_AUTODIFF_H
+#define KANN_AUTODIFF_H
+
+#define KAD_VERSION "r544"
+
+#include <stdio.h>
+#include <stdint.h>
+
+#ifdef __STRICT_ANSI__
+#define inline
+#endif
+
+#define KAD_MAX_DIM 4     /* max dimension */
+#define KAD_MAX_OP  64    /* max number of operators */
+
+/* A computational graph is a directed acyclic graph. In the graph, an external
+ * node represents a variable, a constant or a feed; an internal node
+ * represents an operator; an edge from node v to w indicates v is an operand
+ * of w.
+ */
+
+#define KAD_VAR        0x1
+#define KAD_CONST      0x2
+#define KAD_POOL       0x4
+#define KAD_SHARE_RNG  0x10 /* with this flag on, different time step shares the same RNG status after unroll */
+
+#define kad_is_back(p)  ((p)->flag & KAD_VAR)
+#define kad_is_ext(p)   ((p)->n_child == 0)
+#define kad_is_var(p)   (kad_is_ext(p) && kad_is_back(p))
+#define kad_is_const(p) (kad_is_ext(p) && ((p)->flag & KAD_CONST))
+#define kad_is_feed(p)  (kad_is_ext(p) && !kad_is_back(p) && !((p)->flag & KAD_CONST))
+#define kad_is_pivot(p) ((p)->n_child == 1 && ((p)->flag & KAD_POOL))
+#define kad_is_switch(p) ((p)->op == 12 && !((p)->flag & KAD_POOL))
+#define kad_use_rng(p)  ((p)->op == 15 || (p)->op == 24)
+
+#define kad_eval_enable(p) ((p)->tmp = 1)
+#define kad_eval_disable(p) ((p)->tmp = -1)
+
+/* a node in the computational graph */
+typedef struct kad_node_t {
+	uint8_t     n_d;            /* number of dimensions; no larger than KAD_MAX_DIM */
+	uint8_t     flag;           /* type of the node; see KAD_F_* for valid flags */
+	uint16_t    op;             /* operator; kad_op_list[op] is the actual function */
+	int32_t     n_child;        /* number of operands/child nodes */
+	int32_t     tmp;            /* temporary field; MUST BE zero before calling kad_compile() */
+	int32_t     ptr_size;       /* size of ptr below */
+	int32_t     d[KAD_MAX_DIM]; /* dimensions */
+	int32_t     ext_label;      /* labels for external uses (not modified by the kad_* APIs) */
+	uint32_t    ext_flag;       /* flags for external uses (not modified by the kad_* APIs) */
+	float      *x;              /* value; allocated for internal nodes */
+	float      *g;              /* gradient; allocated for internal nodes */
+	void       *ptr;            /* for special operators that need additional parameters (e.g. conv2d) */
+	void       *gtmp;           /* temporary data generated at the forward pass but used at the backward pass */
+	struct kad_node_t **child;  /* operands/child nodes */
+	struct kad_node_t  *pre;    /* usually NULL; only used for RNN */
+} kad_node_t, *kad_node_p;
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/**
+ * Compile/linearize a computational graph
+ *
+ * @param n_node   number of nodes (out)
+ * @param n_roots  number of nodes without predecessors
+ * @param roots    list of nodes without predecessors
+ *
+ * @return list of nodes, of size *n_node
+ */
+kad_node_t **kad_compile_array(int *n_node, int n_roots, kad_node_t **roots);
+
+kad_node_t **kad_compile(int *n_node, int n_roots, ...); /* an alternative API to above */
+void kad_delete(int n, kad_node_t **a); /* deallocate a compiled/linearized graph */
+
+/**
+ * Compute the value at a node
+ * 
+ * @param n       number of nodes
+ * @param a       list of nodes
+ * @param from    compute the value at this node, 0<=from<n
+ *
+ * @return a pointer to the value (pointing to kad_node_t::x, so don't call
+ *         free() on it!)
+ */
+const float *kad_eval_at(int n, kad_node_t **a, int from);
+
+void kad_eval_marked(int n, kad_node_t **a);
+int kad_sync_dim(int n, kad_node_t **v, int batch_size);
+
+/**
+ * Compute gradient
+ *
+ * @param n       number of nodes
+ * @param a       list of nodes
+ * @param from    the function node; must be a scalar (compute \nabla a[from])
+ */
+void kad_grad(int n, kad_node_t **a, int from);
+
+/**
+ * Unroll a recurrent computation graph
+ *
+ * @param n_v     number of nodes
+ * @param v       list of nodes
+ * @param new_n   number of nodes in the unrolled graph (out)
+ * @param len     how many times to unroll, one for each pivot
+ *
+ * @return list of nodes in the unrolled graph
+ */
+kad_node_t **kad_unroll(int n_v, kad_node_t **v, int *new_n, int *len);
+int kad_n_pivots(int n_v, kad_node_t **v);
+
+kad_node_t **kad_clone(int n, kad_node_t **v, int batch_size);
+
+/* define a variable, a constant or a feed (placeholder in TensorFlow) */
+kad_node_t *kad_var(float *x, float *g, int n_d, ...); /* a variable; gradients to be computed; not unrolled */
+kad_node_t *kad_const(float *x, int n_d, ...);         /* a constant; no gradients computed; not unrolled */
+kad_node_t *kad_feed(int n_d, ...);                    /* an input/output; no gradients computed; unrolled */
+
+/* operators taking two operands */
+kad_node_t *kad_add(kad_node_t *x, kad_node_t *y); /* f(x,y) = x + y (generalized element-wise addition; f[i*n+j]=x[i*n+j]+y[j], n=kad_len(y), 0<j<n, 0<i<kad_len(x)/n) */
+kad_node_t *kad_sub(kad_node_t *x, kad_node_t *y); /* f(x,y) = x - y (generalized element-wise subtraction) */
+kad_node_t *kad_mul(kad_node_t *x, kad_node_t *y); /* f(x,y) = x * y (generalized element-wise product) */
+
+kad_node_t *kad_matmul(kad_node_t *x, kad_node_t *y);     /* f(x,y) = x * y   (general matrix product) */
+kad_node_t *kad_cmul(kad_node_t *x, kad_node_t *y);       /* f(x,y) = x * y^T (column-wise matrix product; i.e. y is transposed) */
+
+/* loss functions; output scalar */
+kad_node_t *kad_mse(kad_node_t *x, kad_node_t *y);        /* mean square error */
+kad_node_t *kad_ce_multi(kad_node_t *x, kad_node_t *y);   /* multi-class cross-entropy; x is the preidction and y is the truth */
+kad_node_t *kad_ce_bin(kad_node_t *x, kad_node_t *y);     /* binary cross-entropy for (0,1) */
+kad_node_t *kad_ce_bin_neg(kad_node_t *x, kad_node_t *y); /* binary cross-entropy for (-1,1) */
+kad_node_t *kad_ce_multi_weighted(kad_node_t *pred, kad_node_t *truth, kad_node_t *weight);
+
+#define KAD_PAD_NONE  0      /* use the smallest zero-padding */
+#define KAD_PAD_SAME  (-2)   /* output to have the same dimension as input */
+
+kad_node_t *kad_conv2d(kad_node_t *x, kad_node_t *w, int r_stride, int c_stride, int r_pad, int c_pad);             /* 2D convolution with weight matrix flipped */
+kad_node_t *kad_max2d(kad_node_t *x, int kernel_h, int kernel_w, int r_stride, int c_stride, int r_pad, int c_pad); /* 2D max pooling */
+kad_node_t *kad_conv1d(kad_node_t *x, kad_node_t *w, int stride, int pad);  /* 1D convolution with weight flipped */
+kad_node_t *kad_max1d(kad_node_t *x, int kernel_size, int stride, int pad); /* 1D max pooling */
+kad_node_t *kad_avg1d(kad_node_t *x, int kernel_size, int stride, int pad); /* 1D average pooling */
+
+kad_node_t *kad_dropout(kad_node_t *x, kad_node_t *r);                      /* dropout at rate r */
+kad_node_t *kad_sample_normal(kad_node_t *x);                               /* f(x) = x * r, where r is drawn from a standard normal distribution */
+
+/* operators taking one operand */
+kad_node_t *kad_square(kad_node_t *x); /* f(x) = x^2                         (element-wise square) */
+kad_node_t *kad_sigm(kad_node_t *x);   /* f(x) = 1/(1+exp(-x))               (element-wise sigmoid) */
+kad_node_t *kad_tanh(kad_node_t *x);   /* f(x) = (1-exp(-2x)) / (1+exp(-2x)) (element-wise tanh) */
+kad_node_t *kad_relu(kad_node_t *x);   /* f(x) = max{0,x}                    (element-wise rectifier, aka ReLU) */
+kad_node_t *kad_softmax(kad_node_t *x);/* f_i(x_1,...,x_n) = exp(x_i) / \sum_j exp(x_j) (softmax: tf.nn.softmax(x,dim=-1)) */
+kad_node_t *kad_1minus(kad_node_t *x); /* f(x) = 1 - x */
+kad_node_t *kad_exp(kad_node_t *x);    /* f(x) = exp(x) */
+kad_node_t *kad_log(kad_node_t *x);    /* f(x) = log(x) */
+kad_node_t *kad_sin(kad_node_t *x);    /* f(x) = sin(x) */
+
+kad_node_t *kad_stdnorm(kad_node_t *x); /* layer normalization; applied to the last dimension */
+
+/* operators taking an indefinite number of operands (e.g. pooling) */
+kad_node_t *kad_avg(int n, kad_node_t **x);   /* f(x_1,...,x_n) = \sum_i x_i/n      (mean pooling) */
+kad_node_t *kad_max(int n, kad_node_t **x);   /* f(x_1,...,x_n) = max{x_1,...,x_n}  (max pooling) */
+kad_node_t *kad_stack(int n, kad_node_t **x); /* f(x_1,...,x_n) = [x_1,...,x_n]     (stack pooling) */
+kad_node_t *kad_select(int n, kad_node_t **x, int which); /* f(x_1,...,x_n;i) = x_i (select pooling; -1 for the last) */
+
+/* dimension reduction */
+kad_node_t *kad_reduce_sum(kad_node_t *x, int axis);  /* tf.reduce_sum(x, axis) */
+kad_node_t *kad_reduce_mean(kad_node_t *x, int axis); /* tf.reduce_mean(x, axis) */
+
+/* special operators */
+kad_node_t *kad_slice(kad_node_t *x, int axis, int start, int end); /* take a slice on the axis-th dimension */
+kad_node_t *kad_concat(int axis, int n, ...);                       /* concatenate on the axis-th dimension */
+kad_node_t *kad_concat_array(int axis, int n, kad_node_t **p);      /* the array version of concat */
+kad_node_t *kad_reshape(kad_node_t *x, int n_d, int *d);            /* reshape; similar behavior to TensorFlow's reshape() */
+kad_node_t *kad_reverse(kad_node_t *x, int axis);
+kad_node_t *kad_switch(int n, kad_node_t **p);                      /* manually (as a hyperparameter) choose one input, default to 0 */
+
+/* miscellaneous operations on a compiled graph */
+int kad_size_var(int n, kad_node_t *const* v);   /* total size of all variables */
+int kad_size_const(int n, kad_node_t *const* v); /* total size of all constants */
+
+/* graph I/O */
+int kad_save(FILE *fp, int n_node, kad_node_t **node);
+kad_node_t **kad_load(FILE *fp, int *_n_node);
+
+/* random number generator */
+void *kad_rng(void);
+void kad_srand(void *d, uint64_t seed);
+uint64_t kad_rand(void *d);
+double kad_drand(void *d);
+double kad_drand_normal(void *d);
+void kad_saxpy(int n, float a, const float *x, float *y);
+
+/* debugging routines */
+void kad_trap_fe(void); /* abort on divide-by-zero and NaN */
+void kad_print_graph(FILE *fp, int n, kad_node_t **v);
+void kad_check_grad(int n, kad_node_t **a, int from);
+
+#ifdef __cplusplus
+}
+#endif
+
+#define KAD_ALLOC      1
+#define KAD_FORWARD    2
+#define KAD_BACKWARD   3
+#define KAD_SYNC_DIM   4
+
+typedef int (*kad_op_f)(kad_node_t*, int);
+extern kad_op_f kad_op_list[KAD_MAX_OP];
+extern char *kad_op_name[KAD_MAX_OP];
+
+static inline int kad_len(const kad_node_t *p) /* calculate the size of p->x */
+{
+	int n = 1, i;
+	for (i = 0; i < p->n_d; ++i) n *= p->d[i];
+	return n;
+}
+
+#endif