├── figures ├── test.png └── computational_graph.png ├── models └── params.eqx ├── pyproject.toml ├── tasks.py ├── model.py ├── README.md ├── eval.py ├── .gitignore ├── train.py └── uv.lock /figures/test.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/teddykoker/learning-to-learn-jax/HEAD/figures/test.png -------------------------------------------------------------------------------- /models/params.eqx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/teddykoker/learning-to-learn-jax/HEAD/models/params.eqx -------------------------------------------------------------------------------- /figures/computational_graph.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/teddykoker/learning-to-learn-jax/HEAD/figures/computational_graph.png -------------------------------------------------------------------------------- /pyproject.toml: -------------------------------------------------------------------------------- 1 | [project] 2 | name = "learning-to-learn-jax" 3 | version = "0.1.0" 4 | description = "Learning to learn with JAX" 5 | readme = "README.md" 6 | requires-python = ">=3.10" 7 | dependencies = [ 8 | "jax[cuda12]>=0.4.31; sys_platform == 'linux'", 9 | "jax>=0.4.31; sys_platform == 'darwin'", 10 | "equinox>=0.11.7", 11 | "matplotlib>=3.9.2", 12 | "optax>=0.2.3", 13 | "wandb>=0.18.3", 14 | "tqdm>=4.67.1", 15 | ] 16 | -------------------------------------------------------------------------------- /tasks.py: -------------------------------------------------------------------------------- 1 | import jax 2 | from jax import vmap, lax 3 | import jax.numpy as jnp 4 | 5 | 6 | def quadratic_data(rng, batch_size=128, dim=10): 7 | keys = jax.random.split(rng, 3) 8 | w = jax.random.normal(keys[0], (batch_size, dim, dim)) 9 | y = jax.random.normal(keys[1], (batch_size, dim)) 10 | theta = jax.random.normal(keys[2], (batch_size, dim)) 11 | return w, y, theta 12 | 13 | 14 | def quadratic_task(w, y, theta, opt_fn, opt_state, steps=100): 15 | @jax.jit 16 | def f(theta): 17 | product = vmap(jnp.matmul)(w, theta) 18 | return jnp.mean(jnp.sum((product - y) ** 2, axis=1)) 19 | 20 | def step_fn(carry, _): 21 | theta, opt_state = carry 22 | loss, grads = jax.value_and_grad(f)(theta) 23 | updates, opt_state = opt_fn(grads, opt_state) 24 | theta += updates 25 | return (theta, opt_state), loss 26 | 27 | (theta, opt_state), losses = lax.scan(step_fn, (theta, opt_state), None, length=steps) 28 | 29 | return losses, theta, opt_state 30 | -------------------------------------------------------------------------------- /model.py: -------------------------------------------------------------------------------- 1 | from functools import partial 2 | 3 | import equinox as eqx 4 | import jax 5 | import jax.numpy as jnp 6 | 7 | 8 | class LSTMOptimizer(eqx.Module): 9 | lstm1: eqx.nn.LSTMCell 10 | lstm2: eqx.nn.LSTMCell 11 | fc: eqx.nn.Linear 12 | hidden_units: int = 32 13 | 14 | def __init__(self, key): 15 | keys = jax.random.split(key, 3) 16 | self.lstm1 = eqx.nn.LSTMCell(1, self.hidden_units, key=keys[0]) 17 | self.lstm2 = eqx.nn.LSTMCell(self.hidden_units, self.hidden_units, key=keys[1]) 18 | self.fc = eqx.nn.Linear(self.hidden_units, 1, key=keys[2]) 19 | 20 | @partial(jax.vmap, in_axes=(None, 0, 0)) 21 | @partial(jax.vmap, in_axes=(None, 0, 0)) 22 | def __call__(self, gradient, state): 23 | # gradients of optimizee do not depend on optimizer 24 | gradient = jax.lax.stop_gradient(gradient) 25 | 26 | # expand parameter dimension to extra batch dimension so that network 27 | # is "coodinatewise" 28 | gradient = gradient[..., None] 29 | 30 | carry1, carry2 = state 31 | carry1 = self.lstm1(gradient, carry1) 32 | carry2 = self.lstm2(carry1[0], carry2) 33 | update = self.fc(carry2[0]) 34 | update = update[..., 0] # remove last dimension 35 | return update, (carry1, carry2) 36 | 37 | def initialize_carry(self, input_shape): 38 | shape = input_shape + (self.hidden_units,) 39 | return ( 40 | (jnp.zeros(shape), jnp.zeros(shape)), 41 | (jnp.zeros(shape), jnp.zeros(shape)), 42 | ) 43 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 2 | ![](figures/computational_graph.png) 3 | 4 | ## Learning to learn by gradient descent by gradient descent - Jax 5 | 6 | Implementation of [Learning to learn by gradient descent by gradient 7 | descent](https://arxiv.org/abs/1606.04474). It demonstrates how a learned 8 | optimizer, implemented as an LSTM, can outperform commonly used hand-crafted 9 | optimizers. 10 | 11 | Read more about this on my blog post [Learning JAX By Learning to 12 | Learn](https://teddykoker.com/2022/04/learning-to-learn-jax/). 13 | 14 | *2024 Update: updated code to work with latest version of JAX. Also using 15 | [`equinox`](https://github.com/patrick-kidger/equinox) instead of `flax`*. 16 | 17 | ## Usage 18 | 19 | ### Dependencies 20 | 21 | Environment can be created very quickly with [uv](https://github.com/astral-sh/uv): 22 | 23 | ```bash 24 | pip install uv 25 | uv sync 26 | source .venv/bin/activate 27 | ``` 28 | 29 | ### Train LSTM Optimizer 30 | 31 | Train the LSTM optimizer on random quadratic tasks. [wandb](https://wandb.ai/) 32 | is used for experiment tracking. 33 | 34 | ```bash 35 | python train.py \ 36 | --unroll_steps 20 \ 37 | --unrolls 5 \ 38 | --learning_rate 1e-2 \ 39 | --steps 1000 40 | ``` 41 | 42 | ### Evaluate Optimizers 43 | 44 | A search in log-space (e.g. [0.01, 0.03, 0.1, ...]) is performed for each of the 45 | non-learned optimizers to achieve the best final loss on the test task. 46 | 47 | ```bash 48 | python eval.py --optimizers sgd adam rmsprop nag lstm 49 | ``` 50 | 51 | ![optimizer loss plots](./figures/test.png) 52 | 53 | ## Citations 54 | 55 | ```bibtex 56 | @article{andrychowicz2016learning, 57 | title={Learning to learn by gradient descent by gradient descent}, 58 | author={Andrychowicz, Marcin and Denil, Misha and Gomez, Sergio and Hoffman, Matthew W and Pfau, David and Schaul, Tom and Shillingford, Brendan and De Freitas, Nando}, 59 | journal={Advances in neural information processing systems}, 60 | volume={29}, 61 | year={2016} 62 | } 63 | ``` 64 | 65 | 66 | 67 | -------------------------------------------------------------------------------- /eval.py: -------------------------------------------------------------------------------- 1 | from argparse import ArgumentParser 2 | from functools import partial 3 | 4 | import jax 5 | import equinox as eqx 6 | import jax.numpy as jnp 7 | import matplotlib.pyplot as plt 8 | import optax 9 | 10 | from model import LSTMOptimizer 11 | from tasks import quadratic_data, quadratic_task 12 | 13 | HAND_OPTIMIZERS = { 14 | "sgd": optax.sgd, 15 | "adam": optax.adam, 16 | "rmsprop": partial(optax.rmsprop), 17 | "nag": partial(optax.sgd, momentum=0.9, nesterov=True), 18 | } 19 | 20 | 21 | def eval(args): 22 | rng = jax.random.PRNGKey(args.seed) 23 | w, y, theta = quadratic_data(rng, args.batch_size, args.dim) 24 | 25 | plt.figure(dpi=300, figsize=(5, 3)) 26 | 27 | for name, optimizer in HAND_OPTIMIZERS.items(): 28 | if name not in args.optimizers: 29 | continue 30 | 31 | best_losses = None 32 | for learning_rate in jnp.logspace(-2, 1, num=7): 33 | opt = optimizer(learning_rate=learning_rate) 34 | opt_state = opt.init(theta) 35 | losses, *_ = eqx.filter_jit(quadratic_task)(w, y, theta, opt_state=opt_state, opt_fn=opt.update) 36 | 37 | if best_losses is None or losses[-1] < best_losses[-1]: 38 | best_losses = losses 39 | print(f"{name}, best lr: {learning_rate:.0e}") 40 | 41 | plt.plot(best_losses, label=name, linestyle="--") 42 | 43 | if "lstm" in args.optimizers: 44 | lstm_opt = LSTMOptimizer(rng) 45 | lstm_opt = eqx.tree_deserialise_leaves(args.model_path, lstm_opt) 46 | lstm_state = lstm_opt.initialize_carry(theta.shape) 47 | losses, *_ = quadratic_task(w, y, theta, opt_state=lstm_state, opt_fn=lstm_opt) 48 | plt.plot(losses, label="lstm") 49 | 50 | plt.legend() 51 | plt.title("losses") 52 | plt.xlabel("steps ($t$)") 53 | plt.ylabel("$f(\\theta)$") 54 | plt.yscale("log") 55 | plt.savefig(args.save_path, bbox_inches="tight") 56 | 57 | 58 | if __name__ == "__main__": 59 | parser = ArgumentParser() 60 | parser.add_argument("--seed", type=int, default=0) 61 | parser.add_argument("--optimizers", nargs="+", default=["sgd"]) 62 | parser.add_argument("--batch_size", type=int, default=128) 63 | parser.add_argument("--dim", type=int, default=10) 64 | parser.add_argument("--model_path", default="models/params.eqx") 65 | parser.add_argument("--save_path", default="figures/test.png") 66 | args = parser.parse_args() 67 | eval(args) 68 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | wandb 2 | logs 3 | 4 | # Byte-compiled / optimized / DLL files 5 | __pycache__/ 6 | *.py[cod] 7 | *$py.class 8 | 9 | # C extensions 10 | *.so 11 | 12 | # Distribution / packaging 13 | .Python 14 | build/ 15 | develop-eggs/ 16 | dist/ 17 | downloads/ 18 | eggs/ 19 | .eggs/ 20 | lib/ 21 | lib64/ 22 | parts/ 23 | sdist/ 24 | var/ 25 | wheels/ 26 | pip-wheel-metadata/ 27 | share/python-wheels/ 28 | *.egg-info/ 29 | .installed.cfg 30 | *.egg 31 | MANIFEST 32 | 33 | # PyInstaller 34 | # Usually these files are written by a python script from a template 35 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 36 | *.manifest 37 | *.spec 38 | 39 | # Installer logs 40 | pip-log.txt 41 | pip-delete-this-directory.txt 42 | 43 | # Unit test / coverage reports 44 | htmlcov/ 45 | .tox/ 46 | .nox/ 47 | .coverage 48 | .coverage.* 49 | .cache 50 | nosetests.xml 51 | coverage.xml 52 | *.cover 53 | *.py,cover 54 | .hypothesis/ 55 | .pytest_cache/ 56 | 57 | # Translations 58 | *.mo 59 | *.pot 60 | 61 | # Django stuff: 62 | *.log 63 | local_settings.py 64 | db.sqlite3 65 | db.sqlite3-journal 66 | 67 | # Flask stuff: 68 | instance/ 69 | .webassets-cache 70 | 71 | # Scrapy stuff: 72 | .scrapy 73 | 74 | # Sphinx documentation 75 | docs/_build/ 76 | 77 | # PyBuilder 78 | target/ 79 | 80 | # Jupyter Notebook 81 | .ipynb_checkpoints 82 | 83 | # IPython 84 | profile_default/ 85 | ipython_config.py 86 | 87 | # pyenv 88 | .python-version 89 | 90 | # pipenv 91 | # According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. 92 | # However, in case of collaboration, if having platform-specific dependencies or dependencies 93 | # having no cross-platform support, pipenv may install dependencies that don't work, or not 94 | # install all needed dependencies. 95 | #Pipfile.lock 96 | 97 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow 98 | __pypackages__/ 99 | 100 | # Celery stuff 101 | celerybeat-schedule 102 | celerybeat.pid 103 | 104 | # SageMath parsed files 105 | *.sage.py 106 | 107 | # Environments 108 | .env 109 | .venv 110 | env/ 111 | venv/ 112 | ENV/ 113 | env.bak/ 114 | venv.bak/ 115 | 116 | # Spyder project settings 117 | .spyderproject 118 | .spyproject 119 | 120 | # Rope project settings 121 | .ropeproject 122 | 123 | # mkdocs documentation 124 | /site 125 | 126 | # mypy 127 | .mypy_cache/ 128 | .dmypy.json 129 | dmypy.json 130 | 131 | # Pyre type checker 132 | .pyre/ 133 | -------------------------------------------------------------------------------- /train.py: -------------------------------------------------------------------------------- 1 | from argparse import ArgumentParser 2 | 3 | import equinox as eqx 4 | import jax 5 | import jax.numpy as jnp 6 | import optax 7 | import wandb 8 | from tqdm import tqdm 9 | 10 | from model import LSTMOptimizer 11 | from tasks import quadratic_data, quadratic_task 12 | 13 | 14 | def train(args): 15 | 16 | rng = jax.random.PRNGKey(seed=args.seed) 17 | 18 | lstm_opt = LSTMOptimizer(rng) 19 | lstm_state = lstm_opt.initialize_carry((args.batch_size, args.dim)) 20 | 21 | meta_opt = optax.adam(learning_rate=args.learning_rate) 22 | meta_opt_state = meta_opt.init(lstm_opt) 23 | 24 | @eqx.filter_jit 25 | def train_step(opt, w, y, theta, state, meta_opt_state): 26 | def loss_fn(opt): 27 | losses, _theta, _state = quadratic_task( 28 | w, y, theta, opt, state, args.unroll_steps 29 | ) 30 | return losses.sum(), (_theta, _state) 31 | 32 | (loss, (_theta, _state)), grads = eqx.filter_value_and_grad(loss_fn, has_aux=True)(opt) 33 | updates, meta_opt_state = meta_opt.update(grads, meta_opt_state) 34 | opt = optax.apply_updates(opt, updates) 35 | return opt, loss, _theta, _state, meta_opt_state 36 | 37 | best_loss = jnp.inf 38 | 39 | pbar = tqdm(range(args.steps)) 40 | for _ in pbar: 41 | rng, subkey = jax.random.split(rng) 42 | w, y, theta = quadratic_data(subkey, args.batch_size, args.dim) 43 | lstm_state = lstm_opt.initialize_carry((args.batch_size, args.dim)) 44 | meta_loss = 0.0 45 | 46 | for _ in range(args.unrolls): 47 | lstm_opt, loss, theta, lstm_state, meta_opt_state = train_step(lstm_opt, w, y, theta, lstm_state, meta_opt_state) 48 | meta_loss += loss 49 | 50 | if meta_loss < best_loss: 51 | best_loss = meta_loss 52 | eqx.tree_serialise_leaves(args.model_path, lstm_opt) 53 | 54 | wandb.log({"loss": meta_loss}) 55 | pbar.set_postfix({"loss": f"{meta_loss:.2f}"}) 56 | 57 | wandb.log({"best_loss": best_loss}) 58 | 59 | 60 | if __name__ == "__main__": 61 | parser = ArgumentParser() 62 | parser.add_argument("--seed", type=int, default=0) 63 | parser.add_argument("--batch_size", type=int, default=128) 64 | parser.add_argument("--dim", type=int, default=10) 65 | parser.add_argument("--unroll_steps", type=int, default=20) 66 | parser.add_argument("--unrolls", type=int, default=5) 67 | parser.add_argument("--learning_rate", type=float, default=1e-2) 68 | parser.add_argument("--steps", type=int, default=1000) 69 | parser.add_argument("--model_path", default="models/params.eqx") 70 | args = parser.parse_args() 71 | wandb.init(config=args, project="learning-to-learn-jax") 72 | train(args) 73 | -------------------------------------------------------------------------------- /uv.lock: -------------------------------------------------------------------------------- 1 | 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