README.md

regimes_of_SGD

Code to reproduce the paper "On the different regimes of Stochastic Gradient Descent"

What this code does:

1. Accepts many different parameters
2. Perform a single training of a neural network (depending on the parameters)
3. Compute and save observables during and at the end of the trianing (depending on the parameters)

The results are saved in a pickle format compatible with grid (grid allows to make sweeps in the paramters)

Paramters

A list of some of the paramters:

--arch architecture
--act activation function
--h width
--L depth for mlp architecture, i.e. number of hidden layers
--alpha initialization scale, is the inverse of the hinge loss margin
--dataset dataset
--ptr number of training points
--pte number of test points
--loss loss function
--dynamics training dynamics
--bs batch size for sgd dynamics
--dt learning rate
--temp temperature, defined as dt/(bs * h) (it is alternative to defining the learning rate)
--ckpt_grad_stats number of train (test) points to compute the Gram matrix of the neural tangent kernel
--max_wall maximum wall time (in seconds)
--seed_init initialization seed
--data_chi depletion exponent for the teacher-student perceptron

Tuto: execute a single training

python -m edm --dataset mnist_parity --ptr 1024 --pte 2048 --arch mlp --act gelu --h 64 --L 8 --dynamics sgd --alpha 1 --dt 0.1 --bs 64 --max_wall 120 --output test.pk

Many parameters are set by default!

Then the data can be loaded using pickle

import pickle

with open('test.pk', 'rb') as f:
    args = pickle.load(f)  # dict with the paramters
    data = pickle.load(f)  # all measurements
    
# data['sgd']['dynamics'] is a list of dict

print("Initial train loss is", data['sgd']['dynamics'][0]['train']['loss'])
print("Final test error is", data['sgd']['dynamics'][-1]['test']['err'])

Tuto: sweeping over many parameters

Install grid and the current repository (regimes_of_SGD). Execute the following line that makes a sweep along the parameter dt, note that grid accept python code to create the list of parameters to sweep along.

python -m grid tests "python -m edm --dataset mnist_parity --ptr 1024 --pte 2048 --arch mlp --act gelu --h 64 --L 8 --dynamics sgd --alpha 1 --bs 64 --max_wall 120" --dt "[2**i for i in range(-3, 1)]"

At the end of the execution, the runs are saved in the directory name tests (in this example) and can be loaded as follow

import grid
runs = grid.load('tests')

print("values of dt for the different runs", [r['args']['dt'] for r in runs])

See more info on how to sweep and load runs using grid in the readme.

Phase diagrams learning rate - batch size

Perceptron with Gaussian data

python -m grid perceptron_chi0 "python -m edm --arch linear --alpha 128 --dataset depleted_sign --pte 32768 --loss hinge --dynamics sgd --max_wall 10000 --data_chi 0.0 --d 128 --ptr 8192" --seed_init "[i for i in range(5)]" --bs "[2**i for i in range(0, 14)]" --dt "[2**i for i in range(-5, 14)]"

Perceptron with data with depletion exponent chi=1

python -m grid perceptron_chi1 "python -m edm --arch linear --alpha 128 --dataset depleted_sign --pte 32768 --loss hinge --dynamics sgd --max_wall 10000 --data_chi 1.0 --d 128 --ptr 8192" --seed_init "[i for i in range(5)]" --bs "[2**i for i in range(0, 14)]" --dt "[2**i for i in range(-10, 13)]"

Fully-connected on MNIST

python -m grid FC_small_margin "python -m edm --dataset mnist_parity --pte 32768 --arch mlp --act gelu --L 5 --h 128 --max_wall 40000 --loss hinge --dynamics sgd --alpha 32768 --ptr 32768 --ckpt_grad_stats 128" --seed_init "[i for i in range(5)]" --bs "[2**i for i in range(11)]" --dt "[2**i for i in range(-11, 12)]"

python -m grid FC_margin_one  "python -m edm --dataset mnist_parity --pte 32768 --arch mlp --act gelu --L 5 --h 128 --max_wall 40000 --loss hinge --dynamics sgd --ckpt_grad_stats 128 --alpha 1 --ptr 16384" --seed_init "[i for i in range(5)]" --bs "[2**i for i in range(0, 13)]" --dt "[2**i for i in range(-5,8)]"

CNN on CIFAR

python -m grid CNN_small_margin "python -m edm --dataset cifar_animal --pte 32768 --arch mnas --act relu --h 32 --max_wall 80000 --loss hinge --dynamics sgd --ckpt_grad_stats 128 --alpha 32768 --ptr 16384" --seed_init "[i for i in range(5)]" --bs "[2**i for i in range(11)]" --dt "[2**i for i in range(-6,11)]"

python -m grid CNN_margin_one "python -m edm --dataset cifar_animal --pte 32768 --arch mnas --act relu --h 32 --max_wall 160000 --loss hinge --dynamics sgd --ckpt_grad_stats 128 --alpha 1 --ptr 16384" --seed_init "[i for i in range(5)]" --bs "[2**i for i in range(12)]" --dt "[2**i for i in range(-7,10)]"