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//
// Copyright (c) 2020 Idiap Research Institute, http://www.idiap.ch/
// Written by Angelos Katharopoulos <[email protected]>,
// Apoorv Vyas <[email protected]>
//
#include <torch/extension.h>
/**
* Compute a*b^T and save it into out.
*
* a \in R^A
* b \in R^B
*/
inline void vvt_dot(float *a, float *b, float *out, int A, int B) {
for (int i=0; i<A; i++) {
float * bi = b;
for (int j=0; j<B; j++) {
*out += (*a) * (*bi);
out++;
bi++;
}
a++;
}
}
/**
* Implement a vector matrix product v*m and save it into out.
*
* v \in R^A
* m \in R^{AxB}
*/
inline void vm_dot(float *v, float *m, float *out, int A, int B) {
// TODO: Consider removing the zeroing part and assuming out already
// contains 0s
for (int i=0; i<B; i++) {
out[i] = 0;
}
for (int i=0; i<A; i++) {
float *oi = out;
for (int j=0; j<B; j++) {
*oi += (*v) * (*m);
oi++;
m++;
}
v++;
}
}
/**
* Implement a vector transposed-matrix product and save it into out.
*
* v \in R^B
* m \in R^{AxB}
*/
inline void vmt_dot(float *v, float *m, float *out, int A, int B) {
for (int i=0; i<A; i++) {
float *vi = v;
float s = 0;
for (int j=0; j<B; j++) {
s += (*vi) * (*m);
vi++;
m++;
}
// TODO: Should we be aggregating? See the comment on vm_dot.
*out = s;
out++;
}
}
/**
* Compute the causally masked dot products of queries, keys and values.
*
* Basically compute V_j' = (Q_{0:j} * K_{0:j}^T) * V_{0:j} for all j. The
* computation is done efficiently by changing the order of the dot products.
*/
void causal_dot_product(
const torch::Tensor queries,
const torch::Tensor keys,
const torch::Tensor values,
torch::Tensor product
) {
// Extract some shapes
int N = queries.size(0);
int H = queries.size(1);
int L = queries.size(2);
int E = queries.size(3);
int M = values.size(3);
// Create accessors for all the arguments
auto qa = queries.accessor<float, 4>();
auto ka = keys.accessor<float, 4>();
auto va = values.accessor<float, 4>();
auto pa = product.accessor<float, 4>();
#pragma omp parallel for collapse(2)
for (int n=0; n<N; n++) {
for (int h=0; h<H; h++) {
auto kv = torch::zeros({E, M}, queries.options());
float *kvp = kv.data_ptr<float>();
for (int l=0; l<L; l++) {
vvt_dot(
&ka[n][h][l][0],
&va[n][h][l][0],
kvp,
E,
M
);
vm_dot(
&qa[n][h][l][0],
kvp,
&pa[n][h][l][0],
E,
M
);
}
}
}
}
/**
* Compute the gradients of queries, keys and values given the gradient of the
* causal_dot_product output.
*
* Make sure that everything is computed in O(N D^2) complexity.
*/
void causal_dot_backward(
const torch::Tensor queries,
const torch::Tensor keys,
const torch::Tensor values,
const torch::Tensor grad_out,
torch::Tensor grad_queries,
torch::Tensor grad_keys,
torch::Tensor grad_values
) {
// Extract some shapes
int N = queries.size(0);
int H = queries.size(1);
int L = queries.size(2);
int E = queries.size(3);
int M = values.size(3);
// Create accessors for all the arguments
auto qa = queries.accessor<float, 4>();
auto ka = keys.accessor<float, 4>();
auto va = values.accessor<float, 4>();
auto ga = grad_out.accessor<float, 4>();
auto gqa = grad_queries.accessor<float, 4>();
auto gka = grad_keys.accessor<float, 4>();
auto gva = grad_values.accessor<float, 4>();
#pragma omp parallel for collapse(2)
for (int n=0; n<N; n++) {
for (int h=0; h<H; h++) {
auto kv = torch::zeros({E, M}, queries.options());
float *kvp = kv.data_ptr<float>();
// Compute the gradient wrt the queries
for (int l=0; l<L; l++) {
vvt_dot(
&ka[n][h][l][0],
&va[n][h][l][0],
kvp,
E,
M
);
vmt_dot(
&ga[n][h][l][0],
kvp,
&gqa[n][h][l][0],
E,
M
);
}
// Compute the gradient wrt the keys and values
kv.zero_();
for (int l=L-1; l>=0; l--) {
vvt_dot(
&qa[n][h][l][0],
&ga[n][h][l][0],
kvp,
E,
M
);
vmt_dot(
&va[n][h][l][0],
kvp,
&gka[n][h][l][0],
E,
M
);
vm_dot(
&ka[n][h][l][0],
kvp,
&gva[n][h][l][0],
E,
M
);
}
}
}
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
m.def(
"causal_dot_product",
&causal_dot_product,
"Compute the weighted sum of values but attending only to previous "
"values."
);
m.def(
"causal_dot_backward",
&causal_dot_backward,
"Compute the gradient of queries, keys and values given the gradient "
"of causal_dot_product."
);
} |