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ts_sne.cpp
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ts_sne.cpp
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/*
*
* Copyright (c) 2014, Laurens van der Maaten (Delft University of Technology)
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* This product includes software developed by the Delft University of Technology.
* 4. Neither the name of the Delft University of Technology nor the names of
* its contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY LAURENS VAN DER MAATEN ''AS IS'' AND ANY EXPRESS
* OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
* EVENT SHALL LAURENS VAN DER MAATEN BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
* BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
* IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
v * OF SUCH DAMAGE.
*
*/
#include <cfloat>
#include <cmath>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <ctime>
#include <chrono>
#include <boost/program_options.hpp>
#include <boost/filesystem.hpp>
#include "vptree.h"
#include "array_sptree.h"
#include "ts_sne.h"
// using namespace std;
// namespace po = boost::program_options;
// namespace fsys = boost::filesystem;
auto t_prev = chrono::high_resolution_clock::now();
void tic() {
t_prev = chrono::high_resolution_clock::now();
}
float toc() {
auto t_cur = chrono::high_resolution_clock::now();
return chrono::duration<float, std::milli>(t_cur - t_prev).count();
}
// arr[left] >= val > arr[right]
int binsearch(double *arr, double val, int left, int right) {
if (right <= left + 1) {
return left;
}
int mid = (left + right) / 2;
if (arr[mid] >= val) {
return binsearch(arr, val, mid, right);
} else {
return binsearch(arr, val, left, mid);
}
}
//
// Fisher-Yates shuffle
void randperm(ivec &selected, int N, int K) {
ivec tmp(N);
for (int i = 0; i < N; i++) {
tmp(i) = i;
}
for (int i = 0; i <= min(N - 2, K); i++) {
ivec r = randi(1, distr_param(i + 1, N - 1));
// Swap
int val = tmp(i);
tmp(i) = tmp(r(0));
tmp(r(0)) = val;
}
selected.set_size(K);
for (int i = 0; i < K; i++) {
selected(i) = tmp(i % N);
}
}
// Fisher-Yates shuffle for large matrix
void randperm(ivec &perm_indices, mat &base) {
int n = base.n_cols;
perm_indices.set_size(n);
for (int i = 0; i < n; i++) {
perm_indices(i) = i;
}
ivec r(1);
for (int i = 0; i <= n - 2; i++) {
r = randi(1, distr_param(i + 1, n - 1));
// Swap
base.swap_cols(i, r(0));
int val = perm_indices(i);
perm_indices(i) = perm_indices(r(0));
perm_indices(r(0)) = val;
}
}
void sort_P(int N, unsigned int *row_P, unsigned int *col_P, double *val_P) {
for (int i = 0; i < N; i++) {
int L = row_P[i+1] - row_P[i];
vec tmp_col(L);
vec tmp_val(L);
for (int j = 0; j < L; j++) {
tmp_col(j) = col_P[row_P[i]+j];
tmp_val(j) = val_P[row_P[i]+j];
}
uvec I = sort_index(tmp_val, "descend");
for (int j = 0; j < L; j++) {
col_P[row_P[i]+j] = tmp_col(I(j));
val_P[row_P[i]+j] = tmp_val(I(j));
}
}
}
void permute_P(ivec &perm_indices, unsigned int *row_P, unsigned int *col_P, double *val_P) {
int n = perm_indices.n_elem;
unsigned int *rP = (unsigned int *)malloc((n+1) * sizeof(unsigned int));
unsigned int *cP = (unsigned int *)malloc(row_P[n] * sizeof(unsigned int));
double *vP = (double *)malloc(row_P[n] * sizeof(double));
if (rP == NULL || cP == NULL || vP == NULL) {
printf("Memory allocaiton error in permute_P\n");
exit(1);
}
map<int,int> full2perm;
for (int i = 0; i < n; i++) {
full2perm[perm_indices(i)] = i;
}
rP[0] = 0;
for (int i = 0; i < n; i++) {
int ind = perm_indices(i);
unsigned int nelem = row_P[ind+1] - row_P[ind];
rP[i+1] = rP[i] + nelem;
for (unsigned int j = 0; j < nelem; j++) {
cP[rP[i]+j] = full2perm[(int)col_P[row_P[ind]+j]];
vP[rP[i]+j] = val_P[row_P[ind]+j];
}
}
memcpy(row_P, rP, (n+1) * sizeof(unsigned int));
memcpy(col_P, cP, row_P[n] * sizeof(unsigned int));
memcpy(val_P, vP, row_P[n] * sizeof(double));
free(rP);
free(cP);
free(vP);
}
void reorder_columns(mat &out, mat &in, ivec &ord) {
out.set_size(in.n_rows, in.n_cols);
for (int i = 0; i < out.n_cols; i++) {
out.col(ord[i]) = in.col(i);
}
}
bool TS_SNE::run(int N, unsigned int *row_P, unsigned int *col_P, double *val_P, mat &target_Y,
mat &X, mat &Y, int no_dims, double theta, int rand_seed,
int max_iter, boost::filesystem::path outdir, unsigned int time_steps,
int* assignments) {
bool use_sgd = SGD_FLAG;
bool use_target_Y = val_P == NULL;
bool no_target = NO_TARGET;
if (use_target_Y || !use_sgd) {
N_SAMPLE_LOCAL = 0;
MIN_SAMPLE_Z = 0;
}
// Comment
int stop_lying_iter = STOP_LYING;
int mom_switch_iter = MOM_SWITCH_ITER;
double momentum = MOM_INIT;
double final_momentum = MOM_FINAL;
double eta = LEARN_RATE;
int nunits = NUM_UNITS;
int nlayers = NUM_LAYERS;
int batch_norm = BATCH_NORM;
bool use_relu = ACT_FN == "relu";
int D = X.n_rows;
if (!TEST_RUN) {
printf("eta: %f, max_iter: %d, stop_lying: %d\n", LEARN_RATE, max_iter, stop_lying_iter);
if (use_sgd) {
printf("batch_frac: %f, n_sample_local: %d\n", BATCH_FRAC, N_SAMPLE_LOCAL);
}
if(rand_seed >= 0) {
printf("Using random seed: %d\n", rand_seed);
srand((unsigned int) rand_seed);
} else {
printf("Using current time as random seed...\n");
srand(time(NULL));
}
}
printf("Using no_dims = %d and theta = %f\n", no_dims, theta);
// Set learning parameters
float total_time = .0;
clock_t start, end;
auto t_start = chrono::high_resolution_clock::now();
auto t_end = chrono::high_resolution_clock::now();
boost::filesystem::path newfile;
/* TS_SNE */
double adam_b1 = 0.9;
double adam_b2 = 0.999;
double adam_eps = 1e-8;
double BN_eps = 1e-4;
/**********/
if (MODEL_PREFIX_FLAG) {
printf("Initializing with an existing model: %s\n", MODEL_PREFIX.c_str());
ifstream ifs(MODEL_PREFIX + "_param.txt");
if (!ifs.is_open()) {
cout << "Error: failed to open model parameter file " << MODEL_PREFIX + "_param.txt" << endl;
return false;
}
ifs >> nlayers >> nunits >> use_relu >> batch_norm;
ifs.close();
} else {
cout << "Creating a new model" << endl;
}
printf("nlayers: %d, nunits: %d, use_relu: %d, batch_norm: %d\n",
nlayers, nunits, use_relu, batch_norm);
// Allocate some memory
vector<mat> W(nlayers + 1); // Network weights
vector<mat> dW(nlayers + 1); // Gradients
// Batch normalization parameters/gradients
vector<vec> beta_BN(nlayers);
vector<vec> gamma_BN(nlayers);
vector<vec> dbeta_BN(nlayers);
vector<vec> dgamma_BN(nlayers);
vector<vec> mean_BN(nlayers); // for BN transformation in the testing phase
vector<vec> std_BN(nlayers); // for BN transformation in the testing phase
vector<mat> dW_m(nlayers + 1); // Adam first moments
vector<mat> dW_v(nlayers + 1); // Adam second moments
vector<vec> dbeta_BN_m(nlayers);
vector<vec> dbeta_BN_v(nlayers);
vector<vec> dgamma_BN_m(nlayers);
vector<vec> dgamma_BN_v(nlayers);
vector<mat> W_update(nlayers + 1); // Update history
vector<mat> W_gains(nlayers + 1); // Gains
vector<vec> beta_BN_update(nlayers);
vector<vec> beta_BN_gains(nlayers);
vector<vec> gamma_BN_update(nlayers);
vector<vec> gamma_BN_gains(nlayers);
vector<mat> A(nlayers); // activations. for BN, final y values
vector<mat> A_xhat(nlayers); // only for BN. normalized x_hat values
vector<vec> A_mu(nlayers);
vector<vec> A_sig2(nlayers);
vec X_mean;
vec X_std;
if (MODEL_PREFIX_FLAG) {
string filename = MODEL_PREFIX + "_X_mean.txt";
bool success = X_mean.load(filename, arma_ascii);
if (!success || X_mean.n_elem != D) {
printf("Error loading %s: file not found or dimension mismatch\n",
filename.c_str());
cout << "Got " << X_mean.n_elem << ", expected " << D << endl;
return false;
}
filename = MODEL_PREFIX + "_X_std.txt";
success = X_std.load(filename, arma_ascii);
if (!success || X_std.n_elem != D) {
printf("Error loading %s: file not found or dimension mismatch\n",
filename.c_str());
cout << "Got " << X_std.n_elem << ", expected " << D << endl;
return false;
}
for (int i = 0; i < nlayers + 1; i++) {
int indim = (i == 0) ? D : nunits;
int outdim = (i == nlayers) ? no_dims : nunits;
if (i < nlayers) indim++; // add intercept
filename = MODEL_PREFIX + "_L" + to_string(i) + "_W.txt";
success = W[i].load(filename, arma_ascii);
if (!success || W[i].n_rows != outdim || W[i].n_cols != indim) {
printf("Error loading %s: file not found or dimension mismatch\n",
filename.c_str());
cout << "Got " << W[i].n_rows << "x" << W[i].n_cols << ", expected "
<< outdim << "x" << indim << endl;
return false;
}
if (batch_norm && i < nlayers) {
filename = MODEL_PREFIX + "_L" + to_string(i) + "_BN_beta.txt";
success = beta_BN[i].load(filename, arma_ascii);
if (!success || beta_BN[i].n_elem != outdim) {
printf("Error loading %s: file not found or dimension mismatch\n",
filename.c_str());
cout << "Got " << beta_BN[i].n_elem << ", expected " << outdim << endl;
return false;
}
filename = MODEL_PREFIX + "_L" + to_string(i) + "_BN_gamma.txt";
success = gamma_BN[i].load(filename, arma_ascii);
if (!success || gamma_BN[i].n_elem != outdim) {
printf("Error loading %s: file not found or dimension mismatch\n",
filename.c_str());
cout << "Got " << gamma_BN[i].n_elem << ", expected " << outdim << endl;
return false;
}
if (TEST_RUN) {
filename = MODEL_PREFIX + "_L" + to_string(i) + "_BN_mean.txt";
success = mean_BN[i].load(filename, arma_ascii);
if (!success || mean_BN[i].n_elem != outdim) {
printf("Error loading %s: file not found or dimension mismatch\n",
filename.c_str());
cout << "Got " << mean_BN[i].n_elem << ", expected " << outdim << endl;
return false;
}
filename = MODEL_PREFIX + "_L" + to_string(i) + "_BN_std.txt";
success = std_BN[i].load(filename, arma_ascii);
if (!success || std_BN[i].n_elem != outdim) {
printf("Error loading %s: file not found or dimension mismatch\n",
filename.c_str());
cout << "Got " << std_BN[i].n_elem << ", expected " << outdim << endl;
return false;
}
}
}
}
} else {
X_mean = sum(X, 1) / N;
X_std = sqrt(sum(square(X.each_col() - X_mean), 1) / N + BN_eps);
for (int i = 0; i < nlayers + 1; i++) {
int indim = (i == 0) ? D : nunits;
int outdim = (i == nlayers) ? no_dims : nunits;
if (i < nlayers) indim++; // add intercept
W[i].randn(outdim, indim);
//W[i].randu(outdim, indim) - .5;
W[i] *= sqrt(2.0/(double)indim);// * sqrt(12.0);
if (batch_norm && i < nlayers) {
// For each output feature of the previous layer, create BN params
beta_BN[i].zeros(outdim);
gamma_BN[i].ones(outdim);
}
}
}
// Normalize input features
X.each_col() -= X_mean;
X.each_col() /= X_std;
// Initialize auxiliary variables for SGD
for (int i = 0; i < nlayers + 1; i++) {
int indim = (i == 0) ? D : nunits;
int outdim = (i == nlayers) ? no_dims : nunits;
if (i < nlayers) indim++; // add intercept
dW[i].zeros(outdim, indim);
if (i < nlayers) {
dbeta_BN[i].zeros(outdim);
dgamma_BN[i].zeros(outdim);
}
if (STEP_METHOD == "adam") {
dW_m[i].zeros(outdim, indim);
dW_v[i].zeros(outdim, indim);
if (i < nlayers) {
dbeta_BN_m[i].zeros(outdim);
dbeta_BN_v[i].zeros(outdim);
dgamma_BN_m[i].zeros(outdim);
dgamma_BN_v[i].zeros(outdim);
}
} else if (STEP_METHOD == "mom") {
W_update[i].zeros(outdim, indim);
W_gains[i].ones(outdim, indim);
if (i < nlayers) {
beta_BN_update[i].zeros(outdim);
beta_BN_gains[i].zeros(outdim);
gamma_BN_update[i].zeros(outdim);
gamma_BN_gains[i].zeros(outdim);
}
}
}
if (!no_target && !use_target_Y && use_sgd) {
printf("Sorting P ... ");
sort_P(N, row_P, col_P, val_P);
printf("done\n");
}
// Perform main training loop
printf("Learning embedding...\n");
t_start = chrono::high_resolution_clock::now();
ivec vec_1toN(N);
for (int i = 0; i < N; i++) {
vec_1toN(i) = i;
}
vec P_rowsum(N);
if (!no_target && !use_target_Y && use_sgd) {
for (int i = 0; i < N; i++) {
// Note P is sorted
// Add small values first for numerical stability
P_rowsum(i) = 0;
for (unsigned int j = 0; j < row_P[i+1]-row_P[i]; j++) {
P_rowsum(i) += val_P[row_P[i+1]-1-j];
if (MONTE_CARLO_POS) {
val_P[row_P[i+1]-1-j] = P_rowsum(i); // replace with running sum
// needed for weighted sampling
}
}
if (MONTE_CARLO_POS) {
for (unsigned int j = row_P[i]; j < row_P[i+1]; j++) {
if (j == row_P[i]) {
val_P[j] = 1;
} else {
val_P[j] /= P_rowsum(i); // normalize
}
}
}
}
printf("P_rowsum computed\n");
}
int subN, nbatch, min_sample;
if (!TEST_RUN && use_sgd) {
subN = ceil(N * BATCH_FRAC);
nbatch = ((N-1) / subN) + 1;
min_sample = ceil(N * MIN_SAMPLE_Z);
printf("subN: %d\n", subN);
printf("nbatch: %d\n", nbatch);
printf("min_sample: %d\n", min_sample);
} else {
subN = N;
nbatch = 1;
min_sample = N;
}
bool map_all_flag = min_sample == N;
Col<unsigned int> row_P_mini(subN + 1);
Col<unsigned int> col_P_mini(subN * N_SAMPLE_LOCAL);
Col<double> val_P_mini(subN * N_SAMPLE_LOCAL);
map<unsigned int,int> full2sub;
uvec sub2full;
ivec rand_indices(N_SAMPLE_LOCAL);
for (int i = 0; i <= subN; i++) {
row_P_mini(i) = i * N_SAMPLE_LOCAL;
}
if (!map_all_flag) {
sub2full.set_size(subN * (1 + N_SAMPLE_LOCAL) + min_sample);
}
newfile = outdir;
newfile /= "log.txt";
ofstream logfs(newfile.c_str());
logfs << "iter\tobjective\telapsed-time" << endl;
double C0 = DBL_MAX;
// Initial map
// Forward propagation - Full pass
if (COMPUTE_INIT || TEST_RUN) {
for (int i = 0; i < nlayers; i++) {
// Affine transformation
A[i] = W[i].head_cols(W[i].n_cols - 1) * ((i == 0) ? X : A[i-1]);
A[i].each_col() += W[i].tail_cols(1);
// Nonlinear activation
if (use_relu) {
A[i] = clamp(A[i], 0, datum::inf);
} else {
A[i] = 1 / (1 + exp(-A[i]));
}
// Batch normalization
if (batch_norm) { // NOTE this is only applied after each hidden layer
if (!TEST_RUN) {
mean_BN[i] = sum(A[i], 1) / A[i].n_cols;
std_BN[i] = sqrt(BN_eps + sum(square(A[i].each_col() - mean_BN[i]), 1) / A[i].n_cols);
}
A[i].each_col() -= mean_BN[i];
A[i].each_col() /= std_BN[i];
A[i].each_col() %= gamma_BN[i];
A[i].each_col() += beta_BN[i];
}
}
Y = W[nlayers] * A[nlayers - 1];
printf("Init Y computed\n");
if (!no_target) {
if (use_target_Y) {
C0 = sqrt(sum(sum(square(target_Y - Y))));
} else {
C0 = evaluateError(row_P, col_P, val_P, Y.memptr(), N, no_dims, theta, P_rowsum,
time_steps, assignments);
}
printf("Iteration 0: error is %f\n", C0);
iters.push_back(0);
objectives.push_back(C0);
elapsed_times.push_back(0);
logfs << iters[0] << "\t" << objectives[0] << "\t" << elapsed_times[0] << endl;
logfs.flush();
}
newfile = outdir;
if (TEST_RUN || max_iter <= 0) {
newfile /= "Y_final.txt";
} else {
newfile /= "Y_0.txt";
}
mat Y_tmp = Y.t();
Y_tmp.save(newfile.string(), arma_ascii);
}
if (TEST_RUN) {
return true; // We are done if this is a test run
}
ivec X_perm_indices, perm_indices;
// max_iter = 5000;
for (int iter = 0; iter < max_iter; iter++) {
tic();
if (use_sgd && (iter == 0 || (PERM_ITER > 0 && iter % PERM_ITER == 0))) {
/* Permute X and P for fast mini-batching */
printf("Permuting data points ... "); tic();
randperm(perm_indices, X); // in-place shuffle
if (use_target_Y) {
mat tmp(no_dims, N);
for (int i = 0; i < perm_indices.n_elem; i++) {
tmp.col(i) = target_Y.col(perm_indices(i));
}
target_Y = tmp;
} else {
permute_P(perm_indices, row_P, col_P, val_P);
}
if (iter > 0) {
for (int i = 0; i < perm_indices.n_elem; i++) {
perm_indices(i) = X_perm_indices(perm_indices(i));
}
}
X_perm_indices = perm_indices;
printf("done (%.2f secs)\n", toc() / 1000);
}
int batch_id = iter % nbatch;
int batch_start = batch_id * subN;
int batch_end = min(N, batch_start + subN);
int batch_N = batch_end - batch_start;
int extra_N = max(0, min_sample - batch_N);
full2sub.clear();
if (!map_all_flag) {
for (int i = 0; i < batch_N; i++) {
full2sub[batch_start + i] = i;
sub2full(i) = batch_start + i;
}
if (extra_N > 0) {
randperm(rand_indices, N - batch_N, extra_N);
for (int i = 0; i < extra_N; i++) {
unsigned int selected = (batch_end + rand_indices(i)) % N;
full2sub[selected] = batch_N + i;
sub2full(batch_N + i) = selected;
}
}
}
vec pos_correct;
int N_mini = batch_N + extra_N;
if (!use_target_Y && use_sgd) {
pos_correct.zeros(batch_N);
for (int i = 0; i < batch_N; i++) {
unsigned int full_ind;
if (map_all_flag) {
full_ind = batch_start + i;
} else {
full_ind = (unsigned int)sub2full(i);
}
int nnei = row_P[full_ind+1] - row_P[full_ind];
if (MONTE_CARLO_POS) {
vec u = randu(N_SAMPLE_LOCAL);
// binary search to find index for each random number
for (int s = 0; s < N_SAMPLE_LOCAL; s++) {
rand_indices(s) = binsearch(&val_P[row_P[full_ind]], u(s), 0, nnei);
}
} else {
randperm(rand_indices, nnei, N_SAMPLE_LOCAL);
}
for (int s = 0; s < N_SAMPLE_LOCAL; s++) {
unsigned int ind2 = rand_indices(s) + row_P[full_ind];
unsigned int full_ind2 = col_P[ind2];
if (!map_all_flag && full2sub.find(full_ind2) == full2sub.end()) {
sub2full(N_mini) = full_ind2;
full2sub[full_ind2] = N_mini;
N_mini++;
}
if (map_all_flag) {
col_P_mini(i*N_SAMPLE_LOCAL + s) = full_ind2;
} else {
col_P_mini(i*N_SAMPLE_LOCAL + s) = full2sub[full_ind2];
}
double val;
if (MONTE_CARLO_POS) {
val = 1;
} else {
val = val_P[ind2];
}
val_P_mini(i*N_SAMPLE_LOCAL + s) = val;
}
// Correction factor for positive force
if (MONTE_CARLO_POS) {
pos_correct(i) = P_rowsum(full_ind) / N_SAMPLE_LOCAL;
} else {
pos_correct(i) = nnei / N_SAMPLE_LOCAL;
}
}
}
// Forward propagation
for (int i = 0; i < nlayers; i++) {
// Affine transformation
if (i == 0) {
if (map_all_flag) {
A[i] = W[i].head_cols(W[i].n_cols - 1) * X;
} else {
A[i] = W[i].head_cols(W[i].n_cols - 1) * X.cols(sub2full.head(N_mini));
}
} else {
A[i] = W[i].head_cols(W[i].n_cols - 1) * A[i-1];
}
A[i].each_col() += W[i].tail_cols(1);
// Nonlinear activation
if (use_relu) {
A[i] = clamp(A[i], 0, datum::inf);
} else {
A[i] = 1 / (1 + exp(-A[i]));
}
// Batch normalization
if (batch_norm) { // NOTE this is only applied after each hidden layer
A_mu[i] = sum(A[i], 1) / A[i].n_cols;
A_sig2[i] = sum(square(A[i].each_col() - A_mu[i]), 1) / A[i].n_cols;
A[i].each_col() -= A_mu[i];
A[i].each_col() /= sqrt(A_sig2[i] + BN_eps);
A_xhat[i] = A[i]; // cache xhat values
A[i].each_col() %= gamma_BN[i];
A[i].each_col() += beta_BN[i];
}
}
// Output layer
mat Y_mini = W[nlayers] * A[nlayers - 1];
// Compute (approximate) gradient
mat dY(no_dims, batch_N);
if (use_target_Y) {
dY = 2 * (Y_mini - target_Y.cols(sub2full.head(N_mini)));
} else if (use_sgd) {
computeGradient(batch_N, extra_N, pos_correct, row_P_mini.memptr(),
col_P_mini.memptr(), val_P_mini.memptr(),
Y_mini.memptr(), N_mini, no_dims, dY.memptr(), theta,
iter < stop_lying_iter, map_all_flag ? batch_start : 0, time_steps,
assignments);
} else {
computeGradient(batch_N, extra_N, pos_correct, row_P,
col_P, val_P, Y_mini.memptr(), N_mini, no_dims, dY.memptr(), theta,
iter < stop_lying_iter, map_all_flag ? batch_start : 0, time_steps,
assignments);
// Look at the old compute gradient function
/*
old_computeGradient(batch_N, extra_N, pos_correct, row_P,
col_P, val_P, Y_mini.memptr(), N_mini, no_dims, dY.memptr(), theta,
iter < stop_lying_iter, map_all_flag ? batch_start : 0);
*/
}
/*
if (iter % 10 == 0) {
for (int y_i=0; y_i < 10; y_i++) {
cout << Y_mini(0, y_i) << ", " << Y_mini(1, y_i) << endl;
}
}
*/
/*
// DEBUG!!!
cout << "==== OUTPUT DY! ====" << endl;
for (int dy_i = 0; dy_i < batch_N; dy_i ++) {
cout << dY(0, dy_i) << ", " << dY(1, dy_i) << endl;
}
cout << " ==== DY DONE === " << endl;
*/
// Take the gradients/other related data for only the primary points in the mini-batch
// Note that the remaining points are used for approximating the gradients of the primary points
for (int i = 0; i < nlayers; i++) {
if (map_all_flag) {
A[i] = A[i].cols(batch_start, batch_end-1);
if (batch_norm) {
A_xhat[i] = A_xhat[i].cols(batch_start, batch_end-1);
}
} else {
A[i] = A[i].head_cols(batch_N);
if (batch_norm) {
A_xhat[i] = A_xhat[i].head_cols(batch_N);
}
}
}
// Backpropagation
dW[nlayers] = dY * A[nlayers - 1].t() * (N / (double)batch_N);
mat cur_dA = W[nlayers].t() * dY;
for (int i = nlayers - 1; i >= 0; i--) {
if (batch_norm) {
vec sigeps = sqrt(A_sig2[i] + BN_eps);
mat dxhat = cur_dA.each_col() % gamma_BN[i];
mat tmp = dxhat % A_xhat[i];
vec dsig2 = -0.5 * sum(tmp.each_col() / (A_sig2[i] + BN_eps), 1);
vec dmu = -sum(dxhat.each_col() / sigeps, 1) - 2 * dsig2 % sum(A_xhat[i].each_col() % sigeps, 1) / batch_N;
dgamma_BN[i] = sum(cur_dA % A_xhat[i], 1);
dbeta_BN[i] = sum(cur_dA, 1);
cur_dA = dxhat.each_col() / sigeps + 2 * (dsig2 % sigeps) % A_xhat[i].each_col() / batch_N;
cur_dA.each_col() += dmu / batch_N;
A[i] = A_xhat[i].each_col() % sigeps;
A[i].each_col() += A_mu[i];
}
mat dO;
if (use_relu) {
dO = cur_dA % (A[i] > 0);
} else {
dO = cur_dA % A[i] % (1 - A[i]);
}
if (i > 0) {
dW[i].head_cols(dW[i].n_cols - 1) = dO * A[i-1].t();
} else {
dW[i].head_cols(dW[i].n_cols - 1) = dO * X.cols(batch_start, batch_end-1).t();
}
dW[i].tail_cols(1) = sum(dO, 1);
if (i > 0) {
cur_dA = trans(W[i].head_cols(W[i].n_cols - 1)) * dO;
}
}
// L2 regularization on W
for (int i = 0; i <= nlayers; i++) {
dW[i] += 2 * L2_REG * W[i];
}
// Gradient update
if (STEP_METHOD == "adam") {
for (int i = 0; i < nlayers + 1; i++) {
dW_m[i] = adam_b1 * dW_m[i] + (1 - adam_b1) * dW[i];
dW_v[i] = adam_b2 * dW_v[i] + (1 - adam_b2) * (dW[i] % dW[i]);
W[i] -= eta * (dW_m[i] / (1.0 - adam_b1)) / (sqrt(dW_v[i] / (1.0 - adam_b2)) + adam_eps);
if (batch_norm && i < nlayers) {
dgamma_BN_m[i] = adam_b1 * dgamma_BN_m[i] + (1 - adam_b1) * dgamma_BN[i];
dgamma_BN_v[i] = adam_b2 * dgamma_BN_v[i] + (1 - adam_b2) * (dgamma_BN[i] % dgamma_BN[i]);
gamma_BN[i] -= eta * (dgamma_BN_m[i] / (1.0 - adam_b1)) / (sqrt(dgamma_BN_v[i] / (1.0 - adam_b2)) + adam_eps);
dbeta_BN_m[i] = adam_b1 * dbeta_BN_m[i] + (1 - adam_b1) * dbeta_BN[i];
dbeta_BN_v[i] = adam_b2 * dbeta_BN_v[i] + (1 - adam_b2) * (dbeta_BN[i] % dbeta_BN[i]);
beta_BN[i] -= eta * (dbeta_BN_m[i] / (1.0 - adam_b1)) / (sqrt(dbeta_BN_v[i] / (1.0 - adam_b2)) + adam_eps);
}
}
} else if (STEP_METHOD == "mom_gain") { // Momentum w/ gains
for (int i = 0; i < nlayers + 1; i++) {
// Update gains
umat selector = (dW[i] % W_update[i]) > 0;
W_gains[i] += 0.2 - selector % (W_gains[i] * 0.2 + 0.2);
W_gains[i] = clamp(W_gains[i], 0.01, datum::inf);
if (batch_norm && i < nlayers) {
uvec sel = (dgamma_BN[i] % gamma_BN_update[i]) > 0;
gamma_BN_gains[i] += 0.2 - sel % (gamma_BN_gains[i] * 0.2 + 0.2);
gamma_BN_gains[i] = clamp(gamma_BN_gains[i], 0.01, datum::inf);
sel = (dbeta_BN[i] % beta_BN_update[i]) > 0;
beta_BN_gains[i] += 0.2 - sel % (beta_BN_gains[i] * 0.2 + 0.2);
beta_BN_gains[i] = clamp(beta_BN_gains[i], 0.01, datum::inf);
}
double mom = (iter < mom_switch_iter) ? momentum : final_momentum;
// Perform gradient update (with momentum and gains)
W_update[i] *= mom;
W_update[i] -= eta * W_gains[i] % dW[i];
W[i] += W_update[i];
if (batch_norm && i < nlayers) {
gamma_BN_update[i] *= mom;
gamma_BN_update[i] -= eta * gamma_BN_gains[i] % dgamma_BN[i];
gamma_BN[i] += gamma_BN_update[i];
beta_BN_update[i] *= mom;
beta_BN_update[i] -= eta * beta_BN_gains[i] % dbeta_BN[i];
beta_BN[i] += beta_BN_update[i];
}
}
} else if (STEP_METHOD == "mom") { // Just momentum
for (int i = 0; i < nlayers + 1; i++) {
double mom = (iter < mom_switch_iter) ? momentum : final_momentum;
W_update[i] *= mom;
W_update[i] -= eta * dW[i];
W[i] += W_update[i];
if (batch_norm && i < nlayers) {
gamma_BN_update[i] *= mom;
gamma_BN_update[i] -= eta * dgamma_BN[i];
gamma_BN[i] += gamma_BN_update[i];
beta_BN_update[i] *= mom;
beta_BN_update[i] -= eta * dbeta_BN[i];
beta_BN[i] += beta_BN_update[i];
}
}
} else if (STEP_METHOD == "fixed") {
for (int i = 0; i < nlayers + 1; i++) {
W[i] -= eta * dW[i];
}
}
// Print out progress
if (((iter + 1) % 50 == 0 || iter == max_iter - 1)) {
t_end = chrono::high_resolution_clock::now();
// Forward propagation - Full pass
for (int i = 0; i < nlayers; i++) {
A[i] = W[i].head_cols(W[i].n_cols - 1) * ((i == 0) ? X : A[i-1]);
A[i].each_col() += W[i].tail_cols(1);
if (use_relu) {
A[i] = clamp(A[i], 0, datum::inf);
} else {
A[i] = 1 / (1 + exp(-A[i]));
}
if (batch_norm) {
mean_BN[i] = sum(A[i], 1) / A[i].n_cols;
std_BN[i] = sqrt(BN_eps + sum(square(A[i].each_col() - mean_BN[i]), 1) / A[i].n_cols);
A[i].each_col() -= mean_BN[i];
A[i].each_col() /= std_BN[i];
A[i].each_col() %= gamma_BN[i];
A[i].each_col() += beta_BN[i];
}
}
Y = W[nlayers] * A[nlayers - 1];
double C;
if (use_target_Y) {
C = sqrt(sum(sum(square(target_Y - Y))));
} else {
C = evaluateError(row_P, col_P, val_P, Y.memptr(), N, no_dims, theta, P_rowsum, time_steps,
assignments);
}
float elapsed = chrono::duration<float, std::milli>(t_end - t_start).count() / 1000.0;
printf("Iteration %d: error is %f (50 iterations in %4.2f seconds)\n", iter + 1, C, elapsed);
total_time += elapsed;
if ((iter + 1) % CACHE_ITER == 0 || iter == max_iter - 1) {
string it_str = to_string(iter + 1);
if (iter == max_iter - 1) {
it_str = "final";
}
// Revert the ordering of data points to the initial ordering
mat Y_tmp;
if (use_sgd) {
reorder_columns(Y_tmp, Y, X_perm_indices);
} else {
Y_tmp = Y;
}
newfile = outdir;
newfile /= "Y_" + it_str + ".txt";
Y_tmp = Y_tmp.t();
Y_tmp.save(newfile.string(), arma_ascii);
newfile = outdir;
newfile /= "model_" + it_str + "_param.txt";
ofstream ofs(newfile.string());
ofs << nlayers << " " << nunits << " " << use_relu << " " << batch_norm;
ofs.close();
newfile = outdir;
newfile /= "model_" + it_str + "_X_mean.txt";
X_mean.save(newfile.string(), arma_ascii);
newfile = outdir;
newfile /= "model_" + it_str + "_X_std.txt";
X_std.save(newfile.string(), arma_ascii);
for (int i = 0; i <= nlayers; i++) {
newfile = outdir;
newfile /= "model_" + it_str + "_L" + to_string(i) + "_W.txt";
W[i].save(newfile.string(), arma_ascii);
if (batch_norm && i < nlayers) {
newfile = outdir;
newfile /= "model_" + it_str + "_L" + to_string(i) + "_BN_beta.txt";
beta_BN[i].save(newfile.string(), arma_ascii);
newfile = outdir;
newfile /= "model_" + it_str + "_L" + to_string(i) + "_BN_gamma.txt";
gamma_BN[i].save(newfile.string(), arma_ascii);
newfile = outdir;
newfile /= "model_" + it_str + "_L" + to_string(i) + "_BN_mean.txt";
mean_BN[i].save(newfile.string(), arma_ascii);
newfile = outdir;
newfile /= "model_" + it_str + "_L" + to_string(i) + "_BN_std.txt";
std_BN[i].save(newfile.string(), arma_ascii);
}
}
}
iters.push_back(iter + 1);
objectives.push_back(C);
elapsed_times.push_back((double)total_time);
logfs << iters.back() << "\t" << objectives.back() << "\t" << elapsed_times.back() << endl;
logfs.flush();
t_start = chrono::high_resolution_clock::now();
}
}
logfs.close();