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higher is a library providing support for higher-order optimization, e.g. through unrolled first-order optimization loops, of "meta" aspects of these loops. It provides tools for turning existingtorch.nn.Module instances "stateless", meaning that changes to the parameters thereof can be tracked, and gradient with regard to intermediate parameters can be taken. It also provides a suite of differentiable optimizers, to facilitate the implementation of various meta-learning approaches.

Full documentation is available athttps://higher.readthedocs.io/en/latest/.

• Python version >= 3.5
• PyTorch version >= 1.3

To installhigher fromPyPi:

pip install higher

To installhigher from source:

git clone git@github.com:facebookresearch/higher.gitcd higherpip install.

Alternativelypython setup.py install will do the same thing.

If you usehigher in your research and found it helpful, please consider citing the following paper:

@article{grefenstette2019generalized,title={Generalized Inner Loop Meta-Learning},author={Grefenstette, Edward and Amos, Brandon and Yarats, Denis and Htut, Phu Mon and Molchanov, Artem and Meier, Franziska and Kiela, Douwe and Cho, Kyunghyun and Chintala, Soumith},journal={arXiv preprint arXiv:1910.01727},year={2019}}

You have amodel with parametersP, whereP[t] denotes the parameters at update timestept.You want to update the model throughk steps of optimization, and compute gradients through the optimization process,i.e. computetorch.autograd.grad(P[k], P[0]) or obtain gradients that depend on this gradient pathway existing.

You are using some existing code for yourmodel, so the parameters are stateful, preventing you from forming a graph withP[t] as nodes.Even if you roll your own solution, you want to use optimization techniques beyond normal SGD, andtorch.optim optimizers don't let you optimize "through" them.

Good news:higher has got you covered! Using our growing set of tools and utility functions, you can backpropagate through an unbounded number of model update steps for all your meta-learning needs.This library includes:

• Helper functions for monkey-patchingtorch.nn modules to make them functional (non-stateful), i.e. feed their parameters as an extra argument during the forward pass.
• Classes implementing differentiable versions oftorch.optim.Adam (and SGD), designed to track or branch out from the state of a "normal"Adam instance.

Say your training code looks like this:

model=MyModel()opt=torch.optim.Adam(model.parameters())forxs,ysindata:opt.zero_grad()logits=model(xs)loss=loss_function(logits,ys)loss.backward()opt.step()

To turn this into a differentiable version, the following changes should be introduced:

model=MyModel()opt=torch.optim.Adam(model.parameters())# When you want to branch from the current state of your model and unroll# optimization, follow this example. This context manager gets a snapshot of the# current version of the model and optimizer at the point where you want to# start unrolling and create a functional version `fmodel` which executes the# forward pass of `model` with implicit fast weights which can be read by doing# `fmodel.parameters()`, and a differentiable optimizer `diffopt` which ensures# that at each step, gradient of `fmodel.parameters()` with regard to initial# fast weights `fmodel.parameters(time=0)` (or any other part of the unrolled# model history) is defined.withhigher.innerloop_ctx(model,opt)as (fmodel,diffopt):forxs,ysindata:logits=fmodel(xs)# modified `params` can also be passed as a kwargloss=loss_function(logits,ys)# no need to call loss.backwards()diffopt.step(loss)# note that `step` must take `loss` as an argument!# The line above gets P[t+1] from P[t] and loss[t]. `step` also returns# these new parameters, as an alternative to getting them from# `fmodel.fast_params` or `fmodel.parameters()` after calling# `diffopt.step`.# At this point, or at any point in the iteration, you can take the# gradient of `fmodel.parameters()` (or equivalently# `fmodel.fast_params`) w.r.t. `fmodel.parameters(time=0)` (equivalently# `fmodel.init_fast_params`). i.e. `fast_params` will always have# `grad_fn` as an attribute, and be part of the gradient tape.# At the end of your inner loop you can obtain these e.g. ...grad_of_grads=torch.autograd.grad(meta_loss_fn(fmodel.parameters()),fmodel.parameters(time=0))

Beware that when unrolling your optimisation like this fork, all gradients and all activations of your model at each step is kept in memory,meaning the memory footprint of your model isk times greater.

For more complete examples, please look atexamples.

It is possible to use optimizers other that those found intorch.optim. A differentiable version must be implemented first. This can be done by subclassinghigher.optim.DifferentiableOptimizer and overriding the_update method, following the arguments of the original. Assuming the logic of the optimizer being added follows the logic of those found intorch.optim, the steps to follow are more or less:

1. Remove the following code (no support for closures).

   loss = Noneif closure is not None:    loss = closure()

2. Replace

   for group in self.param_groups:    for p in group['params']:        if p.grad is None:            continue        grad = p.grad.data

   with

   zipped = zip(self.param_groups, grouped_grads)for group_idx, (group, grads) in enumerate(zipped):    for p_idx, (p, g) in enumerate(zip(group['params'], grads)):      if g is None:          continue

3. Replacestate = self.state[p] withstate = self.state[group_idx][p_idx].
4. Replace any in-place op with a non in-place op, e.g.t.add_(a, x).mul_(y) should becomet = t.add(a, x).mul(y) (note the assignment). Be careful to also track where dictionaries are being implicitly updated by such ops, e.g. if there is code of the form:

   p = state['k']...p.add_(a, x)

   in the original optimizer, this code should be converted to

   p = state['k']...state['k'] = p = p.add(a, x)

   to ensure the corresponding dictionary is.
5. Except where used for shape inference, replace instances oft.data witht for allt.
6. Be sure to updategroup['params'][p_idx] for eachp_idx in need of update (those ignored will yield the original parameters in the fast weight collection). The latest fast weights will be returned by the inheritedstep function.
7. Importantly, you need to register your new differentiable optimizer withhigher usinghigher.register_optim to ensure that it is recognized as an option by the library's methods. You can do this at any point after the definition of an optimizer, and before anyhigher code involving that optimizer is called. For example, if you have implementedMyDiffOpt as a differentiable version of some optimizerMyOpt, register it by adding the linehigher.register_optim(MyOpt, MyDiffOpt) after the classes are defined.

You can find examples of how to test for gradient correctness using finite difference methods intests/test_optim.py. Please note that some stability tricks may be needed to avoidnans in the gradients. See thehigher.optim.DifferentiableAdam implementation for examples of mitigation strategies, e.g. identify operations that yield exploding gradients, e.g. typically those taking the square roots of moving averages (which are intially zero), and register a backward hook usingx.register_hook on the inputsx to those functions, using the helper function_get_mask_closure fromhigher.optim.

The following papers and codebases reference or directly usehigher:

• Bechtle, Sarah, et al. "Meta-learning via learned loss." (2019).
• Wang, Haoxiang, Ruoyu Sun, and Bo Li. "Global convergence and induced kernels of gradient-based meta-learning with neural nets." (2020)
• Morse, Kristen, et al. "Learning State-Dependent Losses for Inverse Dynamics Learning." (2020)
• Holla, Nithin, et al. "Learning to Learn to Disambiguate: Meta-Learning for Few-Shot Word Sense Disambiguation." (2020)
• De Angeli, Nicola. "State of the Art on: Meta-learning for Few-Shot Classification." (2020)
• Zhou, Allan, Tom Knowles, and Chelsea Finn. "Meta-Learning Symmetries by Reparameterization." (2020)

Is yours missing? Raise anissue or add it via apull request!

See thechangelog for release notes.

• See theissues tracker for an up-to-date list.
• No support (or planned support) fortorch.nn.DataParallel at this time. This would require a rewrite ofDataParallel. Please raise an issue on the pytorch issue tracker if this matters to you.
• Some of the adaptative gradient-style differentiable optimizers may be unstable and yield NaNs when taking higher order gradients. Some tricks have been used to mitigate this risk. Please raise an issue if these are not sufficient in practice.
• Second-order gradients may not work with some CUDNN modules (mostly RNNs). From PyTorch v1.3 onwards, wrapping the code where models are used withhigher using the following context manager should solve the issue:

withtorch.backends.cudnn.flags(enabled=False):# Your meta-learning code here...

higher is released under Apache License Version 2.0.

Thanks toAdam Paszkewhosegistwas the source of inspiration (and starting point) for our method for monkeypatching arbitrarytorch.nn modules.

Thanks for the many interns, researchers, and engineers who helped road-test early versions of this library.