Package laplace

Laplace ![pytest](https://github.com/aleximmer/laplace/actions/workflows/pytest.yml/badge.svg) ![lint](https://github.com/aleximmer/laplace/actions/workflows/lint-ruff.yml/badge.svg) ![format](https://github.com/aleximmer/laplace/actions/workflows/format-ruff.yml/badge.svg)

The laplace package facilitates the application of Laplace approximations for entire neural networks, subnetworks of neural networks, or just their last layer. The package enables posterior approximations, marginal-likelihood estimation, and various posterior predictive computations. The library documentation is available at https://aleximmer.github.io/Laplace.

There is also a corresponding paper, Laplace Redux — Effortless Bayesian Deep Learning, which introduces the library, provides an introduction to the Laplace approximation, reviews its use in deep learning, and empirically demonstrates its versatility and competitiveness. Please consider referring to the paper when using our library:

@inproceedings{laplace2021,
  title={Laplace Redux--Effortless {B}ayesian Deep Learning},
  author={Erik Daxberger and Agustinus Kristiadi and Alexander Immer
          and Runa Eschenhagen and Matthias Bauer and Philipp Hennig},
  booktitle={{N}eur{IPS}},
  year={2021}
}

The code to reproduce the experiments in the paper is also publicly available; it provides examples of how to use our library for predictive uncertainty quantification, model selection, and continual learning.

[!IMPORTANT] As a user, one should not expect Laplace to work automatically. That is, one should experiment with different Laplace's options (hessian_factorization, prior precision tuning method, predictive method, backend, etc!). Try looking at various papers that use Laplace for references on how to set all those options depending on the applications/problems at hand.

Table of contents

  1. Setup
  2. Example usage
  3. Simple usage
  4. Marginal likelihood
  5. Laplace on LLM
  6. Subnetwork Laplace
  7. Serialization
  8. Structure
  9. Extendability
  10. When to use which backend?
  11. Contributing
  12. References

Setup

For full compatibility, install this package in a fresh virtual env. We assume Python >= 3.9 since lower versions are (soon to be) deprecated. PyTorch version 2.0 and up is also required for full compatibility. To install laplace with pip, run the following:

pip install laplace-torch

For development purposes, clone the repository and then install:

# first install the build system:
pip install --upgrade pip wheel packaging

# then install the develop 
pip install -e ".[all]"

Example usage

Simple usage

In the following example, a pre-trained model is loaded, then the Laplace approximation is fit to the training data (using a diagonal Hessian approximation over all parameters), and the prior precision is optimized with cross-validation "gridsearch". After that, the resulting LA is used for prediction with the "probit" predictive for classification.

[!IMPORTANT] Laplace expects all data loaders, e.g. train_loader and val_loader below, to be instances of PyTorch DataLoader. Each batch, next(iter(data_loader)) must either be the standard (X, y) tensors or a dict-like object containing at least the keys specified in dict_key_x and dict_key_y in Laplace's constructor.

[!IMPORTANT] The total number of data points in all data loaders must be accessible via len(train_loader.dataset).

[!IMPORTANT] In optimize_prior_precision, make sure to match the arguments with the ones you want to pass in la(x, …) during prediction.

from laplace import Laplace

# Pre-trained model
model = load_map_model()

# User-specified LA flavor
la = Laplace(model, "classification",
             subset_of_weights="all",
             hessian_structure="diag")
la.fit(train_loader)
la.optimize_prior_precision(
    method="gridsearch", 
    pred_type="glm", 
    link_approx="probit", 
    val_loader=val_loader
)

# User-specified predictive approx.
pred = la(x, pred_type="glm", link_approx="probit")

Marginal likelihood

The marginal likelihood can be used for model selection [10] and is differentiable for continuous hyperparameters like the prior precision or observation noise. Here, we fit the library default, KFAC last-layer LA and differentiate the log marginal likelihood.

from laplace import Laplace

# Un- or pre-trained model
model = load_model()

# Default to recommended last-layer KFAC LA:
la = Laplace(model, likelihood="regression")
la.fit(train_loader)

# ML w.r.t. prior precision and observation noise
ml = la.log_marginal_likelihood(prior_prec, obs_noise)
ml.backward()

Laplace on LLM

[!TIP] This library also supports Huggingface models and parameter-efficient fine-tuning. See examples/huggingface_examples.py and examples/huggingface_examples.md for the full exposition.

First, we need to wrap the pretrained model so that the forward method takes a dict-like input. Note that when you iterate over a Huggingface dataloader, this is what you get by default. Having a dict-like input is nice since different models have different number of inputs (e.g. GPT-like LLMs only take input_ids, while BERT-like ones take both input_ids and attention_mask, etc.). Inside this forward method you can do your usual preprocessing like moving the tensor inputs into the correct device.

class MyGPT2(nn.Module):
    def __init__(self, tokenizer: PreTrainedTokenizer) -> None:
        super().__init__()
        config = GPT2Config.from_pretrained("gpt2")
        config.pad_token_id = tokenizer.pad_token_id
        config.num_labels = 2
        self.hf_model = GPT2ForSequenceClassification.from_pretrained(
            "gpt2", config=config
        )

    def forward(self, data: MutableMapping) -> torch.Tensor:
        device = next(self.parameters()).device
        input_ids = data["input_ids"].to(device)
        attn_mask = data["attention_mask"].to(device)
        output_dict = self.hf_model(input_ids=input_ids, attention_mask=attn_mask)
        return output_dict.logits

Then you can "select" which parameters of the LLM you want to apply the Laplace approximation on, by switching off the gradients of the "unneeded" parameters. For example, we can replicate a last-layer Laplace: (in actual practice, use Laplace(..., subset_of_weights='last_layer', ...) instead, though!)

model = MyGPT2(tokenizer)
model.eval()

# Enable grad only for the last layer
for p in model.hf_model.parameters():
    p.requires_grad = False
for p in model.hf_model.score.parameters():
    p.requires_grad = True

la = Laplace(
    model,
    likelihood="classification",
    # Will only hit the last-layer since it's the only one that is grad-enabled
    subset_of_weights="all",
    hessian_structure="diag",
)
la.fit(dataloader)
la.optimize_prior_precision()

test_data = next(iter(dataloader))
pred = la(test_data)

This is useful because we can apply the LA only on the parameter-efficient finetuning weights. E.g., we can fix the LLM itself, and apply the Laplace approximation only on the LoRA weights. Huggingface will automatically switch off the non-LoRA weights' gradients.

def get_lora_model():
    model = MyGPT2(tokenizer)  # Note we don't disable grad
    config = LoraConfig(
        r=4,
        lora_alpha=16,
        target_modules=["c_attn"],  # LoRA on the attention weights
        lora_dropout=0.1,
        bias="none",
    )
    lora_model = get_peft_model(model, config)
    return lora_model

lora_model = get_lora_model()

# Train it as usual here...

lora_model.eval()

lora_la = Laplace(
    lora_model,
    likelihood="classification",
    subset_of_weights="all",
    hessian_structure="diag",
    backend=AsdlGGN,
)

test_data = next(iter(dataloader))
lora_pred = lora_la(test_data)

Subnetwork Laplace

This example shows how to fit the Laplace approximation over only a subnetwork within a neural network (while keeping all other parameters fixed at their MAP estimates), as proposed in [11]. It also exemplifies different ways to specify the subnetwork to perform inference over.

from laplace import Laplace

# Pre-trained model
model = load_model()

# Examples of different ways to specify the subnetwork
# via indices of the vectorized model parameters
#
# Example 1: select the 128 parameters with the largest magnitude
from laplace.utils import LargestMagnitudeSubnetMask
subnetwork_mask = LargestMagnitudeSubnetMask(model, n_params_subnet=128)
subnetwork_indices = subnetwork_mask.select()

# Example 2: specify the layers that define the subnetwork
from laplace.utils import ModuleNameSubnetMask
subnetwork_mask = ModuleNameSubnetMask(model, module_names=["layer.1", "layer.3"])
subnetwork_mask.select()
subnetwork_indices = subnetwork_mask.indices

# Example 3: manually define the subnetwork via custom subnetwork indices
import torch
subnetwork_indices = torch.tensor([0, 4, 11, 42, 123, 2021])

# Define and fit subnetwork LA using the specified subnetwork indices
la = Laplace(model, "classification",
             subset_of_weights="subnetwork",
             hessian_structure="full",
             subnetwork_indices=subnetwork_indices)
la.fit(train_loader)

Serialization

As with plain torch, we support to ways to serialize data.

One is the familiar state_dict approach. Here you need to save and re-create both model and Laplace(). Use this for long-term storage of models and sharing of a fitted Laplace() instance.

# Save model and Laplace instance
torch.save(model.state_dict(), "model_state_dict.bin")
torch.save(la.state_dict(), "la_state_dict.bin")

# Load serialized data
model2 = MyModel(...)
model2.load_state_dict(torch.load("model_state_dict.bin"))
la2 = Laplace(model2, "classification",
              subset_of_weights="all",
              hessian_structure="diag")
la2.load_state_dict(torch.load("la_state_dict.bin"))

The second approach is to save the whole Laplace() object, including self.model. This is less verbose and more convenient since you have the trained model and the fitted Laplace() data stored in one place, but also comes with some drawbacks. Use this for quick save-load cycles during experiments, say.

# Save Laplace, including la.model
torch.save(la, "la.pt")

# Load both
torch.load("la.pt")

Some Laplace variants such as LLLaplace might have trouble being serialized using the default pickle module, which torch.save() and torch.load() use (AttributeError: Can't pickle local object ...). In this case, the dill package will come in handy.

import dill

torch.save(la, "la.pt", pickle_module=dill)

With both methods, you are free to switch devices, for instance when you trained on a GPU but want to run predictions on CPU. In this case, use

torch.load(..., map_location="cpu")

[!WARNING] Currently, this library always assumes that the model has an output tensor of shape (batch_size, …, n_classes), so in the case of image outputs, you need to rearrange from NCHW to NHWC.

Structure

The laplace package consists of two main components:

  1. The subclasses of laplace.BaseLaplace that implement different sparsity structures: different subsets of weights ("all", "subnetwork" and "last_layer") and different structures of the Hessian approximation ("full", "kron", "lowrank" and "diag"). This results in nine currently available options: FullLaplace, KronLaplace, DiagLaplace, the corresponding last-layer variations FullLLLaplace, KronLLLaplace, and DiagLLLaplace (which are all subclasses of laplace.LLLaplace), laplace.SubnetLaplace (which only supports "full" and "diag" Hessian approximations) and LowRankLaplace (which only supports inference over "all" weights). All of these can be conveniently accessed via the laplace.Laplace function.
  2. The backends in laplace.curvature which provide access to Hessian approximations of the corresponding sparsity structures, for example, the diagonal GGN.

Additionally, the package provides utilities for decomposing a neural network into feature extractor and last layer for LLLaplace subclasses (laplace.utils.feature_extractor) and effectively dealing with Kronecker factors (laplace.utils.matrix).

Finally, the package implements several options to select/specify a subnetwork for SubnetLaplace (as subclasses of laplace.utils.subnetmask.SubnetMask). Automatic subnetwork selection strategies include: uniformly at random (RandomSubnetMask), by largest parameter magnitudes (LargestMagnitudeSubnetMask), and by largest marginal parameter variances (LargestVarianceDiagLaplaceSubnetMask and LargestVarianceSWAGSubnetMask). In addition to that, subnetworks can also be specified manually, by listing the names of either the model parameters (ParamNameSubnetMask) or modules (ModuleNameSubnetMask) to perform Laplace inference over.

Extendability

To extend the laplace package, new BaseLaplace subclasses can be designed, for example, Laplace with a block-diagonal Hessian structure. One can also implement custom subnetwork selection strategies as new subclasses of SubnetMask.

Alternatively, extending or integrating backends (subclasses of curvature.curvature) allows to provide different Hessian approximations to the Laplace approximations. For example, currently the curvature.CurvlinopsInterface based on Curvlinops and the native torch.func (previously known as functorch), curvature.BackPackInterface based on BackPACK and curvature.AsdlInterface based on ASDL are available.

When to use which backend

[!TIP] Each backend as its own caveat/behavior. The use the following to guide you picking the suitable backend, depending on you model & application.

  • Small, simple MLP, or last-layer Laplace: Any backend should work well. CurvlinopsGGN or CurvlinopsEF is recommended if hessian_factorization = 'kron', but it's inefficient for other factorizations.
  • LLMs with PEFT (e.g. LoRA): AsdlGGN and AsdlEF are recommended.
  • Continuous Bayesian optimization: CurvlinopsGGN/EF and BackpackGGN/EF are recommended since they are the only ones supporting backprop over Jacobians.

[!CAUTION] The curvlinops backends are inefficient for full and diagonal factorizations. Moreover, they're also inefficient for computing the Jacobians of large models since they rely on torch.func.jacrev along torch.func.vmap! Finally, curvlinops only computes K-FAC (hessian_factorization = 'kron') for nn.Linear and nn.Conv2d modules (including those inside larger modules like Attention).

[!CAUTION] The BackPack backends are limited to models expressed as nn.Sequential. Also, they're not compatible with normalization layers.

Documentation

The documentation is available here or can be generated and/or viewed locally:

# assuming the repository was cloned
pip install -e ".[docs]"
# create docs and write to html
bash update_docs.sh
# .. or serve the docs directly
pdoc --http 0.0.0.0:8080 laplace --template-dir template

Contributing

Pull requests are very welcome. Please follow these guidelines:

  1. Install Laplace via pip install -e ".[dev]" which will install ruff and all requirements necessary to run the tests and build the docs.
  2. Use ruff as autoformatter. Please refer to the following makefile and run it via make ruff. Please note that the order of ruff check --fix and ruff format is important!
  3. Also use ruff as linter. Please manually fix all linting errors/warnings before opening a pull request.
  4. Fully document your changes in the form of Python docstrings, typehinting, and (if applicable) code/markdown examples in the ./examples subdirectory.
  5. Provide as many test cases as possible. Make sure all test cases pass.

Issues, bug reports, and ideas are also very welcome!

References

This package relies on various improvements to the Laplace approximation for neural networks, which was originally due to MacKay [1]. Please consider citing the respective papers if you use any of their proposed methods via our laplace library.

Full example: Optimization of the marginal likelihood and prediction

Sinusoidal toy data

We show how the marginal likelihood can be used after training a MAP network on a simple sinusoidal regression task. Subsequently, we use the optimized LA to predict which provides uncertainty on top of the MAP prediction. We also show how the marglik_training() utility method can be used to jointly train the MAP and hyperparameters. First, we set up the training data for the problem with observation noise \(\sigma=0.3\):

from laplace.baselaplace import FullLaplace
from laplace.curvature.backpack import BackPackGGN
import numpy as np
import torch

from laplace import Laplace, marglik_training

from helper.dataloaders import get_sinusoid_example
from helper.util import plot_regression

n_epochs = 1000
torch.manual_seed(711)
# sample toy data example
X_train, y_train, train_loader, X_test = get_sinusoid_example(sigma_noise=0.3)

Training a MAP

We now use pytorch to train a neural network with single hidden layer and Tanh activation. The trained neural network will be our MAP estimate. This is standard so nothing new here, yet:

# create and train MAP model
def get_model():
    torch.manual_seed(711)
    return torch.nn.Sequential(
        torch.nn.Linear(1, 50), torch.nn.Tanh(), torch.nn.Linear(50, 1)
    )
model = get_model()

criterion = torch.nn.MSELoss()
optimizer = torch.optim.Adam(model.parameters(), lr=1e-2)
for i in range(n_epochs):
    for X, y in train_loader:
        optimizer.zero_grad()
        loss = criterion(model(X), y)
        loss.backward()
        optimizer.step()

Fitting and optimizing the Laplace approximation using empirical Bayes

With the MAP-trained model at hand, we can estimate the prior precision and observation noise using empirical Bayes after training. The Laplace() method is called to construct a LA for "regression" with "all" weights. As default Laplace() returns a Kronecker factored LA, we use "full" instead on this small example. We fit the LA to the training data and initialize log_prior and log_sigma. Using Adam, we minimize the negative log marginal likelihood for n_epochs.

la = Laplace(model, "regression", subset_of_weights="all", hessian_structure="full")
la.fit(train_loader)
log_prior, log_sigma = torch.ones(1, requires_grad=True), torch.ones(1, requires_grad=True)
hyper_optimizer = torch.optim.Adam([log_prior, log_sigma], lr=1e-1)
for i in range(n_epochs):
    hyper_optimizer.zero_grad()
    neg_marglik = - la.log_marginal_likelihood(log_prior.exp(), log_sigma.exp())
    neg_marglik.backward()
    hyper_optimizer.step()

The obtained observation noise is close to the ground truth with a value of \(\sigma \approx 0.28\) without the need for any validation data. The resulting prior precision is \(\delta \approx 0.10\).

Bayesian predictive

Here, we compare the MAP prediction to the obtained LA prediction. For LA, we have a closed-form predictive distribution on the output \(f\) which is a Gaussian \(\mathcal{N}(f(x;\theta_{MAP}), \mathbb{V}[f] + \sigma^2)\):

x = X_test.flatten().cpu().numpy()
f_mu, f_var = la(X_test)
f_mu = f_mu.squeeze().detach().cpu().numpy()
f_sigma = f_var.squeeze().sqrt().cpu().numpy()
pred_std = np.sqrt(f_sigma**2 + la.sigma_noise.item()**2)

plot_regression(X_train, y_train, x, f_mu, pred_std)

:align: center

In comparison to the MAP, the predictive shows useful uncertainties. When our MAP is over or underfit, the Laplace approximation cannot fix this anymore. In this case, joint optimization of MAP and marginal likelihood can be useful.

Jointly optimize MAP and hyperparameters using online empirical Bayes

We provide a utility method marglik_training() that implements the algorithm proposed in [1]. The method optimizes the neural network and the hyperparameters in an interleaved way and returns an optimally regularized LA. Below, we use this method and plot the corresponding predictive uncertainties again:

model = get_model()
la, model, margliks, losses = marglik_training(
    model=model, train_loader=train_loader, likelihood="regression",
    hessian_structure="full", backend=BackPackGGN, n_epochs=n_epochs,
    optimizer_kwargs={"lr": 1e-2}, prior_structure="scalar"
)

f_mu, f_var = la(X_test)
f_mu = f_mu.squeeze().detach().cpu().numpy()
f_sigma = f_var.squeeze().sqrt().cpu().numpy()
pred_std = np.sqrt(f_sigma**2 + la.sigma_noise.item()**2)

plot_regression(X_train, y_train, x, f_mu, pred_std)

:align: center

Full example: post-hoc Laplace on a large image classifier

An advantage of the Laplace approximation over variational Bayes and Markov Chain Monte Carlo methods is its post-hoc nature. That means we can apply LA on (almost) any pre-trained neural network. In this example, we will see how we can apply the last-layer LA on a deep WideResNet model, trained on CIFAR-10.

Data loading

First, let us load the CIFAR-10 dataset. The helper scripts for CIFAR-10 and WideResNet are available in the examples/helper directory in the main repository.

import torch
import torch.distributions as dists
import numpy as np
import helper.wideresnet as wrn
import helper.dataloaders as dl
from helper import util
from netcal.metrics import ECE

from laplace import Laplace


np.random.seed(7777)
torch.manual_seed(7777)
torch.backends.cudnn.deterministic = True
torch.backends.cudnn.benchmark = True

train_loader = dl.CIFAR10(train=True)
test_loader = dl.CIFAR10(train=False)
targets = torch.cat([y for x, y in test_loader], dim=0).numpy()

Load a pre-trained model

Next, we will load a pre-trained WideResNet-16-4 model. Note that a GPU with CUDA support is needed for this example.

# The model is a standard WideResNet 16-4
# Taken as is from https://github.com/hendrycks/outlier-exposure
model = wrn.WideResNet(16, 4, num_classes=10).cuda().eval()

util.download_pretrained_model()
model.load_state_dict(torch.load("./temp/CIFAR10_plain.pt"))

To simplify the downstream tasks, we will use the following helper function to make predictions. It simply iterates through all minibatches and obtains the predictive probabilities of the CIFAR-10 classes.

@torch.no_grad()
def predict(dataloader, model, laplace=False):
    py = []

    for x, _ in dataloader:
        if laplace:
            py.append(model(x.cuda()))
        else:
            py.append(torch.softmax(model(x.cuda()), dim=-1))

    return torch.cat(py).cpu().numpy()

The calibration of MAP

We are now ready to see how calibrated is the model. The metrics we use are the expected calibration error (ECE, Naeni et al., AAAI 2015) and the negative (Categorical) log-likelihood. Note that lower values are better for both these metrics.

First, let us inspect the MAP model. We shall use the netcal library to easily compute the ECE.

probs_map = predict(test_loader, model, laplace=False)
acc_map = (probs_map.argmax(-1) == targets).float().mean()
ece_map = ECE(bins=15).measure(probs_map.numpy(), targets.numpy())
nll_map = -dists.Categorical(probs_map).log_prob(targets).mean()

print(f"[MAP] Acc.: {acc_map:.1%}; ECE: {ece_map:.1%}; NLL: {nll_map:.3}")

Running this snippet, we would get:

[MAP] Acc.: 94.8%; ECE: 2.0%; NLL: 0.172

The calibration of Laplace

Now we inspect the benefit of the LA. Let us apply the simple last-layer LA model, and optimize the prior precision hyperparameter using a post-hoc marginal likelihood maximization.

# Laplace
la = Laplace(model, "classification",
             subset_of_weights="last_layer",
             hessian_structure="kron")
la.fit(train_loader)
la.optimize_prior_precision(method="marglik")

Then, we are ready to see how well does LA improves the calibration of the MAP model:

probs_laplace = predict(test_loader, la, laplace=True)
acc_laplace = (probs_laplace.argmax(-1) == targets).float().mean()
ece_laplace = ECE(bins=15).measure(probs_laplace.numpy(), targets.numpy())
nll_laplace = -dists.Categorical(probs_laplace).log_prob(targets).mean()

print(f"[Laplace] Acc.: {acc_laplace:.1%}; ECE: {ece_laplace:.1%}; NLL: {nll_laplace:.3}")

Running this snippet, we obtain:

[Laplace] Acc.: 94.8%; ECE: 0.8%; NLL: 0.157

Notice that the last-layer LA does not do any harm to the accuracy, yet it improves the calibration of the MAP model substantially.

Full Example: Applying Laplace on a Huggingface LLM model

In this example, we will see how to apply Laplace on a GPT2 Huggingface (HF) model. Laplace only has lightweight requirements for this; namely that the model's forward method must only take a single dict-like object (dict, UserDict, or in general, collections.abc.MutableMapping). This is entirely compatible with HF since HF's data loaders are assumed to emit an object derived from UserDict. However, you need to ensure this yourself — you need to wrap the standard HF model to conform to that requirement. Also, you need to e.g. do torch.to(device) inside the said forward method.

Let's start with as usual with importing stuff.

from collections.abc import MutableMapping
from collections import UserDict
import numpy
import torch
from torch import nn
import torch.utils.data as data_utils

from laplace import Laplace

import logging
import warnings

logging.basicConfig(level="ERROR")
warnings.filterwarnings("ignore")

from transformers import ( # noqa: E402
    GPT2Config,
    GPT2ForSequenceClassification,
    GPT2Tokenizer,
    DataCollatorWithPadding,
    PreTrainedTokenizer,
)
from peft import LoraConfig, get_peft_model # noqa: E402
from datasets import Dataset # noqa: E402

# make deterministic

torch.manual_seed(0)
numpy.random.seed(0)

Next, we create a toy dataset. You can use any HF datasets or your own, of course.

tokenizer = GPT2Tokenizer.from_pretrained("gpt2")
tokenizer.pad_token_id = tokenizer.eos_token_id

data = [
    {"text": "Today is hot, but I will manage!!!!", "label": 1},
    {"text": "Tomorrow is cold", "label": 0},
    {"text": "Carpe diem", "label": 1},
    {"text": "Tempus fugit", "label": 1},
]
dataset = Dataset.from_list(data)

def tokenize(row):
    return tokenizer(row["text"])

dataset = dataset.map(tokenize, remove_columns=["text"])
dataset.set_format(type="torch", columns=["input_ids", "attention_mask", "label"])
dataloader = data_utils.DataLoader(
    dataset, batch_size=100, collate_fn=DataCollatorWithPadding(tokenizer)
)

data = next(iter(dataloader))
print(
    f"Huggingface data defaults to UserDict, which is a MutableMapping? {isinstance(data, UserDict)}"
)
for k, v in data.items():
    print(k, v.shape)

This is the output:

Huggingface data defaults to UserDict, which is a MutableMapping? True
input_ids torch.Size([4, 9])
attention_mask torch.Size([4, 9])
labels torch.Size([4])

Laplace on a subset of an LLM's weights

Now, let's do the main "meat" of this example: Wrapping the HF model into a model that is compatible with Laplace. Notice that this wrapper just wraps the HF model and nothing else. Notice also we do inputs.to(device) inside self.forward().

class MyGPT2(nn.Module):
    """
    Huggingface LLM wrapper.

    Args:
        tokenizer: The tokenizer used for preprocessing the text data. Needed
            since the model needs to know the padding token id.
    """

    def __init__(self, tokenizer: PreTrainedTokenizer) -> None:
        super().__init__()
        config = GPT2Config.from_pretrained("gpt2")
        config.pad_token_id = tokenizer.pad_token_id
        config.num_labels = 2
        self.hf_model = GPT2ForSequenceClassification.from_pretrained(
            "gpt2", config=config
        )

    def forward(self, data: MutableMapping) -> torch.Tensor:
        """
        Custom forward function. Handles things like moving the
        input tensor to the correct device inside.

        Args:
            data: A dict-like data structure with `input_ids` inside.
                This is the default data structure assumed by Huggingface
                dataloaders.

        Returns:
            logits: An `(batch_size, n_classes)`-sized tensor of logits.
        """
        device = next(self.parameters()).device
        input_ids = data["input_ids"].to(device)
        attn_mask = data["attention_mask"].to(device)
        output_dict = self.hf_model(input_ids=input_ids, attention_mask=attn_mask)
        return output_dict.logits

model = MyGPT2(tokenizer)

Now, let's apply Laplace. Let's do a last-layer Laplace first. Notice that we add an argument feature_reduction there. This is because Huggingface models reduce the logits and not the features.

model = MyGPT2(tokenizer)
model.eval()

la = Laplace(
    model,
    likelihood="classification",
    subset_of_weights="last_layer",
    hessian_structure="full",
    # This must reflect faithfully the reduction technique used in the model
    # Otherwise, correctness is not guaranteed
    feature_reduction="pick_last",
)
la.fit(dataloader)
la.optimize_prior_precision()

X_test = next(iter(dataloader))
print(f"[Last-layer Laplace] The predictive tensor is of shape: {la(X_test).shape}.")

Here's the output:

[Last-layer Laplace] The predictive tensor is of shape: torch.Size([4, 2]).

Subnetwork Laplace

Also, we can do the same thing by switching off the gradients of all layers except the top layer. Laplace will automatically only compute the Hessian (and Jacobians) of the parameters in which requires_grad is True.

Notice that you can "mix-and-match" this gradient switching. You can do a subnetwork Laplace easily by doing so!

model.eval()

# Enable grad only for the last layer

for p in model.hf_model.parameters():
    p.requires_grad = False

for p in model.hf_model.score.parameters():
    p.requires_grad = True

la = Laplace(
    model,
    # Will only hit the last-layer since it's the only one that is grad-enabled
    likelihood="classification",
    subset_of_weights="all",
    hessian_structure="diag",
)
la.fit(dataloader)
la.optimize_prior_precision()

X_test = next(iter(dataloader))
print(f"[Subnetwork Laplace] The predictive tensor is of shape: {la(X_test).shape}.")

Here are the outputs to validate that Laplace works:

[Subnetwork Laplace] The predictive tensor is of shape: torch.Size([4, 2]).

Full Laplace on LoRA parameters only

Of course, you can also apply Laplace on the parameter-efficient fine tuning weights (like LoRA). To do this, simply extend your LLM with LoRA, using HF's peft library, and apply Laplace as usual. Note that peft automatically switches off the non-LoRA weights.

def get_lora_model():
    model = MyGPT2(tokenizer) # Note we don't disable grad
    config = LoraConfig(
        r=4,
        lora_alpha=16,
        target_modules=["c_attn"], # LoRA on the attention weights
        lora_dropout=0.1,
        bias="none",
    )
    lora_model = get_peft_model(model, config)
    return lora_model

lora_model = get_lora_model()

# Train it as usual

lora_model.eval()

lora_la = Laplace(
    lora_model,
    likelihood="classification",
    subset_of_weights="all",
    hessian_structure="kron",
)
lora_la.fit(dataloader)

X_test = next(iter(dataloader))
print(f"[LoRA-LLM] The predictive tensor is of shape: {lora_la(X_test).shape}.")

Here is the output, as expected:

[LoRA-LLM] The predictive tensor is of shape: torch.Size([4, 2]).

As a final note, the dict-like input requirement of Laplace is very flexible. It can essentially be applicable to any tasks and any models. You just need to wrap the said model and make sure that your data loaders emit dict-like objects, where the input tensors are the dicts' values.

Caveats

Currently, diagonal EF with the Curvlinops backend is unsupported for dict-based inputs. This is because we use torch.func's vmap to compute the diag-EF, and it only accepts tensor input in the model's forward. See this issue. So, if you can write down your Huggingface model's forward to accept only a single tensor, this is much preferable.

For instance, in the case of causal LLM like GPTs, only input_ids tensor is necessary. Then, any backend and any hessian factorization can be used in this case.

Otherwise, if you must use dict-based inputs, choose the following backends:

  • CurvlinopsGGN for hessian_factorization = {"kron", "diag"}
  • CurvlinopsEF for hessian_factorization = {"kron"}
  • AsdlGGN for hessian_factorization = {"kron", "diag"}
  • AsdlEF for hessian_factorization = {"kron", "diag"}

Full Example: Bayesian Bradley-Terry Reward Modeling

The laplace-torch library can also be used to "Bayesianize" a pretrained Bradley-Terry reward model, popular in large language models. See http://arxiv.org/abs/2009.01325 for a primer in reward modeling.

First order of business, let's define our comparison dataset. We will use the datasets library from Huggingface to handle the data.

import numpy as np
import torch
from torch import nn, optim
from torch.nn import functional as F
import torch.utils.data as data_utils

from datasets import Dataset

from laplace import Laplace

import logging
import warnings

logging.basicConfig(level="ERROR")
warnings.filterwarnings("ignore")

# make deterministic
torch.manual_seed(0)
np.random.seed(0)


# Pairwise comparison dataset. The label indicates which `x0` or `x1` is preferred.
data_dict = [
    {
        "x0": torch.randn(3),
        "x1": torch.randn(3),
        "label": torch.randint(2, size=(1,)).item(),
    }
    for _ in range(10)
]
dataset = Dataset.from_list(data_dict)

Now, let's define the reward model. During training, it assumes that x is a tensor of shape (batch_size, 2, dim), which is a concatenation of x0 and x1 above. The second dimension of size 2 is preserved through the forward pass, resulting in a logit tensor of shape (batch_size, 2) (the network itself is single-output). Then, the standard cross-entropy loss is applied.

Note that this requirement is quite weak and can covers general cases. However, if you prefer to use the dict-like inputs as in Huggingface LLM models, this can also be done. Simply combine what you have learned from this example with the Huggingface LLM example provided in this library.

During testing, this model behaves like a standard single-output regression model.

class SimpleRewardModel(nn.Module):
    """A simple reward model, compatible with the Bradley-Terry likelihood.
    """

    def __init__(self):
        super().__init__()
        self.net = nn.Sequential(nn.Linear(3, 100), nn.ReLU(), nn.Linear(100, 1))

    def forward(self, x):
        """Args:
            x: torch.Tensor
                If training == True then shape (batch_size, 2, dim)
                Else shape (batch_size, dim)

        Returns:
            logits: torch.Tensor
                If training then shape (batch_size, 2)
                Else shape (batch_size, 1)
        """
        if len(x.shape) == 3:
            batch_size, _, dim = x.shape

            # Flatten to (batch_size*2, dim)
            flat_x = x.reshape(-1, dim)

            # Forward
            flat_logits = self.net(flat_x)  # (batch_size*2, 1)

            # Reshape back to (batch_size, 2)
            return flat_logits.reshape(batch_size, 2)
        else:
            logits = self.net(x)  # (batch_size, 1)
            return logits

To fulfill the 3D tensor requirement, we need to preprocess the dict-based dataset.

# Preprocess to coalesce x0 and x1 into a single array/tensor
def append_x0_x1(row):
    # The tensor values above are automatically casted as lists by `Dataset`
    row["x"] = np.stack([row["x0"], row["x1"]])  # (2, dim)
    return row


tensor_dataset = dataset.map(append_x0_x1, remove_columns=["x0", "x1"])
tensor_dataset.set_format(type="torch", columns=["x", "label"])
tensor_dataloader = data_utils.DataLoader(
    data_utils.TensorDataset(tensor_dataset["x"], tensor_dataset["label"]), batch_size=3
)

Then, we can train as usual using the cross entropy loss.

reward_model = SimpleRewardModel()
opt = optim.AdamW(reward_model.parameters(), weight_decay=1e-3)

# Train as usual
for epoch in range(10):
    for x, y in tensor_dataloader:
        opt.zero_grad()
        out = reward_model(x)
        loss = F.cross_entropy(out, y)
        loss.backward()
        opt.step()

Applying Laplace to this model is a breeze. Simply state that the likelihood is reward_modeling.

# Laplace !!! Notice the likelihood !!!
reward_model.eval()
la = Laplace(reward_model, likelihood="reward_modeling", subset_of_weights="all")
la.fit(tensor_dataloader)
la.optimize_prior_precision()

As we can see, during prediction, even though we train & fit Laplace using the cross entropy loss (i.e. classification), in test time, the model behaves like a regression model. So, you don't get probability vectors as outputs. Instead, you get two tensors containing the predictive means and predictive variance.

x_test = torch.randn(5, 3)
pred_mean, pred_var = la(x_test)
print(
    f"Input shape {tuple(x_test.shape)}, predictive mean of shape "
    + f"{tuple(pred_mean.shape)}, predictive covariance of shape "
    + f"{tuple(pred_var.shape)}"
)

Here's the output:

Input shape (5, 3), predictive mean of shape (5, 1), predictive covariance of shape (5, 1, 1)

Sub-modules

laplace.baselaplace
laplace.curvature
laplace.laplace
laplace.lllaplace
laplace.subnetlaplace
laplace.utils

Functions

def Laplace(model: torch.nn.Module, likelihood: Likelihood | str, subset_of_weights: SubsetOfWeights | str = SubsetOfWeights.LAST_LAYER, hessian_structure: HessianStructure | str = HessianStructure.KRON, *args, **kwargs) ‑> ParametricLaplace

Simplified Laplace access using strings instead of different classes.

Parameters

model : torch.nn.Module
 
likelihood : Likelihood or str in {'classification', 'regression'}
 
subset_of_weights : SubsetofWeights or {'last_layer', 'subnetwork', 'all'}, default=SubsetOfWeights.LAST_LAYER
subset of weights to consider for inference
hessian_structure : HessianStructure or str in {'diag', 'kron', 'full', 'lowrank'}, default=HessianStructure.KRON
structure of the Hessian approximation

Returns

laplace : ParametricLaplace
chosen subclass of ParametricLaplace instantiated with additional arguments
def marglik_training(model: torch.nn.Module, train_loader: DataLoader, likelihood: Likelihood | str = Likelihood.CLASSIFICATION, hessian_structure: HessianStructure | str = HessianStructure.KRON, backend: Type[CurvatureInterface] = laplace.curvature.asdl.AsdlGGN, optimizer_cls: Type[Optimizer] = torch.optim.adam.Adam, optimizer_kwargs: dict | None = None, scheduler_cls: Type[LRScheduler] | None = None, scheduler_kwargs: dict | None = None, n_epochs: int = 300, lr_hyp: float = 0.1, prior_structure: PriorStructure | str = PriorStructure.LAYERWISE, n_epochs_burnin: int = 0, n_hypersteps: int = 10, marglik_frequency: int = 1, prior_prec_init: float = 1.0, sigma_noise_init: float = 1.0, temperature: float = 1.0, fix_sigma_noise: bool = False, progress_bar: bool = False, enable_backprop: bool = False, dict_key_x: str = 'input_ids', dict_key_y: str = 'labels') ‑> tuple[BaseLaplace, nn.Module, list[Number], list[Number]]

Marginal-likelihood based training (Algorithm 1 in [1]). Optimize model parameters and hyperparameters jointly. Model parameters are optimized to minimize negative log joint (train loss) while hyperparameters minimize negative log marginal likelihood.

This method replaces standard neural network training and adds hyperparameter optimization to the procedure.

The settings of standard training can be controlled by passing train_loader, optimizer_cls, optimizer_kwargs, scheduler_cls, scheduler_kwargs, and n_epochs. The model should return logits, i.e., no softmax should be applied. With likelihood=Likelihood.CLASSIFICATION or Likelihood.REGRESSION, one can choose between categorical likelihood (CrossEntropyLoss) and Gaussian likelihood (MSELoss).

As in [1], we optimize prior precision and, for regression, observation noise using the marginal likelihood. The prior precision structure can be chosen as 'scalar', 'layerwise', or 'diagonal'. 'layerwise' is a good default and available to all Laplace approximations. lr_hyp is the step size of the Adam hyperparameter optimizer, n_hypersteps controls the number of steps for each estimated marginal likelihood, n_epochs_burnin controls how many epochs to skip marginal likelihood estimation, marglik_frequency controls how often to estimate the marginal likelihood (default of 1 re-estimates after every epoch, 5 would estimate every 5-th epoch).

References

[1] Immer, A., Bauer, M., Fortuin, V., Rätsch, G., Khan, EM. Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning. ICML 2021.

Parameters

model : torch.nn.Module
torch neural network model (needs to comply with Backend choice)
train_loader : DataLoader
pytorch dataloader that implements len(train_loader.dataset) to obtain number of data points
likelihood : str, default=Likelihood.CLASSIFICATION
Likelihood.CLASSIFICATION or Likelihood.REGRESSION
hessian_structure : {'diag', 'kron', 'full'}, default='kron'
structure of the Hessian approximation
backend : Backend, default=AsdlGGN
Curvature subclass, e.g. AsdlGGN/AsdlEF or BackPackGGN/BackPackEF
optimizer_cls : torch.optim.Optimizer, default=Adam
optimizer to use for optimizing the neural network parameters togeth with train_loader
optimizer_kwargs : dict, default=None
keyword arguments for optimizer_cls, for example to change learning rate or momentum
scheduler_cls : torch.optim.lr_scheduler._LRScheduler, default=None
optionally, a scheduler to use on the learning rate of the optimizer. scheduler.step() is called after every batch of the standard training.
scheduler_kwargs : dict, default=None
keyword arguments for scheduler_cls, e.g. lr_min for CosineAnnealingLR
n_epochs : int, default=300
number of epochs to train for
lr_hyp : float, default=0.1
Adam learning rate for hyperparameters
prior_structure : str, default='layerwise'
structure of the prior. one of ['scalar', 'layerwise', 'diag']
n_epochs_burnin : int default=0
how many epochs to train without estimating and differentiating marglik
n_hypersteps : int, default=10
how many steps to take on the hyperparameters when marglik is estimated
marglik_frequency : int
how often to estimate (and differentiate) the marginal likelihood marglik_frequency=1 would be every epoch, marglik_frequency=5 would be every 5 epochs.
prior_prec_init : float, default=1.0
initial prior precision
sigma_noise_init : float, default=1.0
initial observation noise (for regression only)
temperature : float, default=1.0
factor for the likelihood for 'overcounting' data. Might be required for data augmentation.
fix_sigma_noise : bool, default=False
if False, optimize observation noise via marglik otherwise use sigma_noise_init throughout. Only works for regression.
progress_bar : bool, default=False
whether to show a progress bar (updated per epoch) or not
enable_backprop : bool, default=False
make the returned Laplace instance backpropable—useful for e.g. Bayesian optimization.
dict_key_x : str, default='input_ids'
The dictionary key under which the input tensor x is stored. Only has effect when the model takes a MutableMapping as the input. Useful for Huggingface LLM models.
dict_key_y : str, default='labels'
The dictionary key under which the target tensor y is stored. Only has effect when the model takes a MutableMapping as the input. Useful for Huggingface LLM models.

Returns

lap : laplace.laplace
fit Laplace approximation with the best obtained marginal likelihood during training
model : torch.nn.Module
corresponding model with the MAP parameters
margliks : list
list of marginal likelihoods obtained during training (to monitor convergence)
losses : list
list of losses (log joints) obtained during training (to monitor convergence)

Classes

class BaseLaplace (model: nn.Module, likelihood: Likelihood | str, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, dict_key_x: str = 'input_ids', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, backend_kwargs: dict[str, Any] | None = None, asdl_fisher_kwargs: dict[str, Any] | None = None)

Baseclass for all Laplace approximations in this library.

Parameters

model : torch.nn.Module
 
likelihood : Likelihood or str in {'classification', 'regression', 'reward_modeling'}
determines the log likelihood Hessian approximation. In the case of 'reward_modeling', it fits Laplace using the classification likelihood, then does prediction as in regression likelihood. The model needs to be defined accordingly: The forward pass during training takes x.shape == (batch_size, 2, dim) with y.shape = (batch_size,). Meanwhile, during evaluation x.shape == (batch_size, dim). Note that 'reward_modeling' only supports KronLaplace and DiagLaplace.
sigma_noise : torch.Tensor or float, default=1
observation noise for the regression setting; must be 1 for classification
prior_precision : torch.Tensor or float, default=1
prior precision of a Gaussian prior (= weight decay); can be scalar, per-layer, or diagonal in the most general case
prior_mean : torch.Tensor or float, default=0
prior mean of a Gaussian prior, useful for continual learning
temperature : float, default=1
temperature of the likelihood; lower temperature leads to more concentrated posterior and vice versa.
enable_backprop : bool, default=False
whether to enable backprop to the input x through the Laplace predictive. Useful for e.g. Bayesian optimization.
dict_key_x : str, default='input_ids'
The dictionary key under which the input tensor x is stored. Only has effect when the model takes a MutableMapping as the input. Useful for Huggingface LLM models.
dict_key_y : str, default='labels'
The dictionary key under which the target tensor y is stored. Only has effect when the model takes a MutableMapping as the input. Useful for Huggingface LLM models.
backend : subclasses of CurvatureInterface
backend for access to curvature/Hessian approximations. Defaults to CurvlinopsGGN if None.
backend_kwargs : dict, default=None
arguments passed to the backend on initialization, for example to set the number of MC samples for stochastic approximations.
asdl_fisher_kwargs : dict, default=None
arguments passed to the ASDL backend specifically on initialization.

Subclasses

Instance variables

var backend : CurvatureInterface
var log_likelihood : torch.Tensor

Compute log likelihood on the training data after .fit() has been called. The log likelihood is computed on-demand based on the loss and, for example, the observation noise which makes it differentiable in the latter for iterative updates.

Returns

log_likelihood : torch.Tensor
 
var prior_precision_diag : torch.Tensor

Obtain the diagonal prior precision p_0 constructed from either a scalar, layer-wise, or diagonal prior precision.

Returns

prior_precision_diag : torch.Tensor
 
var prior_mean : torch.Tensor
var prior_precision : torch.Tensor
var sigma_noise : torch.Tensor

Methods

def fit(self, train_loader: DataLoader) ‑> None
def log_marginal_likelihood(self, prior_precision: torch.Tensor | None = None, sigma_noise: torch.Tensor | None = None) ‑> torch.Tensor
def predictive(self, x: torch.Tensor, pred_type: PredType | str, link_approx: LinkApprox | str, n_samples: int) ‑> torch.Tensor | tuple[torch.Tensor, torch.Tensor]
def optimize_prior_precision(self, pred_type: PredType | str, method: TuningMethod | str = TuningMethod.MARGLIK, n_steps: int = 100, lr: float = 0.1, init_prior_prec: float | torch.Tensor = 1.0, prior_structure: PriorStructure | str = PriorStructure.DIAG, val_loader: DataLoader | None = None, loss: torchmetrics.Metric | Callable[[torch.Tensor], torch.Tensor | float] | None = None, log_prior_prec_min: float = -4, log_prior_prec_max: float = 4, grid_size: int = 100, link_approx: LinkApprox | str = LinkApprox.PROBIT, n_samples: int = 100, verbose: bool = False, progress_bar: bool = False) ‑> None

Optimize the prior precision post-hoc using the method specified by the user.

Parameters

pred_type : PredType or str in {'glm', 'nn'}
type of posterior predictive, linearized GLM predictive or neural network sampling predictiv. The GLM predictive is consistent with the curvature approximations used here.
method : TuningMethod or str in {'marglik', 'gridsearch'}, default=PredType.MARGLIK
specifies how the prior precision should be optimized.
n_steps : int, default=100
the number of gradient descent steps to take.
lr : float, default=1e-1
the learning rate to use for gradient descent.
init_prior_prec : float or tensor, default=1.0
initial prior precision before the first optimization step.
prior_structure : PriorStructure or str in {'scalar', 'layerwise', 'diag'}, default=PriorStructure.SCALAR
if init_prior_prec is scalar, the prior precision is optimized with this structure. otherwise, the structure of init_prior_prec is maintained.
val_loader : torch.data.utils.DataLoader, default=None
DataLoader for the validation set; each iterate is a training batch (X, y).
loss : callable or torchmetrics.Metric, default=None
loss function to use for CV. If callable, the loss is computed offline (memory intensive). If torchmetrics.Metric, running loss is computed (efficient). The default depends on the likelihood: RunningNLLMetric() for classification and reward modeling, running MeanSquaredError() for regression.
log_prior_prec_min : float, default=-4
lower bound of gridsearch interval.
log_prior_prec_max : float, default=4
upper bound of gridsearch interval.
grid_size : int, default=100
number of values to consider inside the gridsearch interval.
link_approx : LinkApprox or str in {'mc', 'probit', 'bridge'}, default=LinkApprox.PROBIT
how to approximate the classification link function for the 'glm'. For pred_type='nn', only 'mc' is possible.
n_samples : int, default=100
number of samples for link_approx='mc'.
verbose : bool, default=False
if true, the optimized prior precision will be printed (can be a large tensor if the prior has a diagonal covariance).
progress_bar : bool, default=False
whether to show a progress bar; updated at every batch-Hessian computation. Useful for very large model and large amount of data, esp. when subset_of_weights='all'.
class ParametricLaplace (model: nn.Module, likelihood: Likelihood | str, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, dict_key_x: str = 'inputs_id', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, backend_kwargs: dict[str, Any] | None = None, asdl_fisher_kwargs: dict[str, Any] | None = None)

Parametric Laplace class.

Subclasses need to specify how the Hessian approximation is initialized, how to add up curvature over training data, how to sample from the Laplace approximation, and how to compute the functional variance.

A Laplace approximation is represented by a MAP which is given by the model parameter and a posterior precision or covariance specifying a Gaussian distribution \mathcal{N}(\theta_{MAP}, P^{-1}). The goal of this class is to compute the posterior precision P which sums as P = \sum_{n=1}^N \nabla^2_\theta \log p(\mathcal{D}_n \mid \theta) \vert_{\theta_{MAP}} + \nabla^2_\theta \log p(\theta) \vert_{\theta_{MAP}}. Every subclass implements different approximations to the log likelihood Hessians, for example, a diagonal one. The prior is assumed to be Gaussian and therefore we have a simple form for \nabla^2_\theta \log p(\theta) \vert_{\theta_{MAP}} = P_0 . In particular, we assume a scalar, layer-wise, or diagonal prior precision so that in all cases P_0 = \textrm{diag}(p_0) and the structure of p_0 can be varied.

Ancestors

Subclasses

Instance variables

var scatter : torch.Tensor

Computes the scatter, a term of the log marginal likelihood that corresponds to L-2 regularization: scatter = (\theta_{MAP} - \mu_0)^{T} P_0 (\theta_{MAP} - \mu_0) .

Returns

scatter : torch.Tensor
 
var log_det_prior_precision : torch.Tensor

Compute log determinant of the prior precision \log \det P_0

Returns

log_det : torch.Tensor
 
var log_det_posterior_precision : torch.Tensor

Compute log determinant of the posterior precision \log \det P which depends on the subclasses structure used for the Hessian approximation.

Returns

log_det : torch.Tensor
 
var log_det_ratio : torch.Tensor

Compute the log determinant ratio, a part of the log marginal likelihood. \log \frac{\det P}{\det P_0} = \log \det P - \log \det P_0

Returns

log_det_ratio : torch.Tensor
 
var posterior_precision : torch.Tensor

Compute or return the posterior precision P.

Returns

posterior_prec : torch.Tensor
 

Methods

def fit(self, train_loader: DataLoader, override: bool = True, progress_bar: bool = False) ‑> None

Fit the local Laplace approximation at the parameters of the model.

Parameters

train_loader : torch.data.utils.DataLoader
each iterate is a training batch, either (X, y) tensors or a dict-like object containing keys as expressed by self.dict_key_x and self.dict_key_y. train_loader.dataset needs to be set to access N, size of the data set.
override : bool, default=True
whether to initialize H, loss, and n_data again; setting to False is useful for online learning settings to accumulate a sequential posterior approximation.
progress_bar : bool, default=False
whether to show a progress bar; updated at every batch-Hessian computation. Useful for very large model and large amount of data, esp. when subset_of_weights='all'.
def square_norm(self, value) ‑> torch.Tensor

Compute the square norm under post. Precision with value-self.mean as 𝛥: \Delta^ op P \Delta Returns

square_form
 
def log_prob(self, value: torch.Tensor, normalized: bool = True) ‑> torch.Tensor

Compute the log probability under the (current) Laplace approximation.

Parameters

value : torch.Tensor
 
normalized : bool, default=True
whether to return log of a properly normalized Gaussian or just the terms that depend on value.

Returns

log_prob : torch.Tensor
 
def log_marginal_likelihood(self, prior_precision: torch.Tensor | None = None, sigma_noise: torch.Tensor | None = None) ‑> torch.Tensor

Compute the Laplace approximation to the log marginal likelihood subject to specific Hessian approximations that subclasses implement. Requires that the Laplace approximation has been fit before. The resulting torch.Tensor is differentiable in prior_precision and sigma_noise if these have gradients enabled. By passing prior_precision or sigma_noise, the current value is overwritten. This is useful for iterating on the log marginal likelihood.

Parameters

prior_precision : torch.Tensor, optional
prior precision if should be changed from current prior_precision value
sigma_noise : torch.Tensor, optional
observation noise standard deviation if should be changed

Returns

log_marglik : torch.Tensor
 
def predictive_samples(self, x: torch.Tensor | MutableMapping[str, torch.Tensor | Any], pred_type: PredType | str = PredType.GLM, n_samples: int = 100, diagonal_output: bool = False, generator: torch.Generator | None = None) ‑> torch.Tensor

Sample from the posterior predictive on input data x. Can be used, for example, for Thompson sampling.

Parameters

x : torch.Tensor or MutableMapping
input data (batch_size, input_shape)
pred_type : {'glm', 'nn'}, default='glm'
type of posterior predictive, linearized GLM predictive or neural network sampling predictive. The GLM predictive is consistent with the curvature approximations used here.
n_samples : int
number of samples
diagonal_output : bool
whether to use a diagonalized glm posterior predictive on the outputs. Only applies when pred_type='glm'.
generator : torch.Generator, optional
random number generator to control the samples (if sampling used)

Returns

samples : torch.Tensor
samples (n_samples, batch_size, output_shape)
def functional_variance(self, Js: torch.Tensor) ‑> torch.Tensor

Compute functional variance for the 'glm' predictive: f_var[i] = Js[i] @ P.inv() @ Js[i].T, which is a output x output predictive covariance matrix. Mathematically, we have for a single Jacobian \mathcal{J} = \nabla_\theta f(x;\theta)\vert_{\theta_{MAP}} the output covariance matrix \mathcal{J} P^{-1} \mathcal{J}^T .

Parameters

Js : torch.Tensor
Jacobians of model output wrt parameters (batch, outputs, parameters)

Returns

f_var : torch.Tensor
output covariance (batch, outputs, outputs)
def functional_covariance(self, Js: torch.Tensor) ‑> torch.Tensor

Compute functional covariance for the 'glm' predictive: f_cov = Js @ P.inv() @ Js.T, which is a batchoutput x batchoutput predictive covariance matrix.

This emulates the GP posterior covariance N([f(x1), …,f(xm)], Cov[f(x1), …, f(xm)]). Useful for joint predictions, such as in batched Bayesian optimization.

Parameters

Js : torch.Tensor
Jacobians of model output wrt parameters (batch*outputs, parameters)

Returns

f_cov : torch.Tensor
output covariance (batch*outputs, batch*outputs)
def sample(self, n_samples: int = 100, generator: torch.Generator | None = None) ‑> torch.Tensor

Sample from the Laplace posterior approximation, i.e., \theta \sim \mathcal{N}(\theta_{MAP}, P^{-1}).

Parameters

n_samples : int, default=100
number of samples
generator : torch.Generator, optional
random number generator to control the samples

Returns

samples : torch.Tensor
 
def state_dict(self) ‑> dict[str, typing.Any]
def load_state_dict(self, state_dict: dict[str, Any]) ‑> None

Inherited members

class FullLaplace (model: nn.Module, likelihood: Likelihood | str, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, dict_key_x: str = 'input_ids', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, backend_kwargs: dict[str, Any] | None = None)

Laplace approximation with full, i.e., dense, log likelihood Hessian approximation and hence posterior precision. Based on the chosen backend parameter, the full approximation can be, for example, a generalized Gauss-Newton matrix. Mathematically, we have P \in \mathbb{R}^{P \times P}. See BaseLaplace for the full interface.

Ancestors

Subclasses

Instance variables

var posterior_scale : torch.Tensor

Posterior scale (square root of the covariance), i.e., P^{-\frac{1}{2}}.

Returns

scale : torch.tensor
(parameters, parameters)
var posterior_covariance : torch.Tensor

Posterior covariance, i.e., P^{-1}.

Returns

covariance : torch.tensor
(parameters, parameters)
var posterior_precision : torch.Tensor

Posterior precision P.

Returns

precision : torch.tensor
(parameters, parameters)

Inherited members

class KronLaplace (model: nn.Module, likelihood: Likelihood | str, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, dict_key_x: str = 'inputs_id', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, damping: bool = False, backend_kwargs: dict[str, Any] | None = None, asdl_fisher_kwargs: dict[str, Any] | None = None)

Laplace approximation with Kronecker factored log likelihood Hessian approximation and hence posterior precision. Mathematically, we have for each parameter group, e.g., torch.nn.Module, that \P\approx Q \otimes H. See BaseLaplace for the full interface and see Kron and KronDecomposed for the structure of the Kronecker factors. Kron is used to aggregate factors by summing up and KronDecomposed is used to add the prior, a Hessian factor (e.g. temperature), and computing posterior covariances, marginal likelihood, etc. Damping can be enabled by setting damping=True.

Ancestors

Subclasses

Instance variables

var posterior_precision : KronDecomposed

Kronecker factored Posterior precision P.

Returns

precision : KronDecomposed
 
var prior_precision : torch.Tensor

Methods

def state_dict(self) ‑> dict[str, typing.Any]
def load_state_dict(self, state_dict: dict[str, Any])

Inherited members

class DiagLaplace (model: nn.Module, likelihood: Likelihood | str, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, dict_key_x: str = 'inputs_id', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, backend_kwargs: dict[str, Any] | None = None, asdl_fisher_kwargs: dict[str, Any] | None = None)

Laplace approximation with diagonal log likelihood Hessian approximation and hence posterior precision. Mathematically, we have P \approx \textrm{diag}(P). See BaseLaplace for the full interface.

Ancestors

Subclasses

Instance variables

var posterior_precision : torch.Tensor

Diagonal posterior precision p.

Returns

precision : torch.tensor
(parameters)
var posterior_scale : torch.Tensor

Diagonal posterior scale \sqrt{p^{-1}}.

Returns

precision : torch.tensor
(parameters)
var posterior_variance : torch.Tensor

Diagonal posterior variance p^{-1}.

Returns

precision : torch.tensor
(parameters)

Inherited members

class LowRankLaplace (model: nn.Module, likelihood: Likelihood | str, sigma_noise: float | torch.Tensor = 1, prior_precision: float | torch.Tensor = 1, prior_mean: float | torch.Tensor = 0, temperature: float = 1, enable_backprop: bool = False, dict_key_x: str = 'inputs_id', dict_key_y: str = 'labels', backend=laplace.curvature.asdfghjkl.AsdfghjklHessian, backend_kwargs: dict[str, Any] | None = None)

Laplace approximation with low-rank log likelihood Hessian (approximation). The low-rank matrix is represented by an eigendecomposition (vecs, values). Based on the chosen backend, either a true Hessian or, for example, GGN approximation could be used. The posterior precision is computed as P = V diag(l) V^T + P_0. To sample, compute the functional variance, and log determinant, algebraic tricks are usedto reduce the costs of inversion to the that of a K imes K matrix if we have a rank of K.

See BaseLaplace for the full interface.

Ancestors

Instance variables

var V : torch.Tensor
var Kinv : torch.Tensor
var posterior_precision : tuple[tuple[torch.Tensor, torch.Tensor], torch.Tensor]

Return correctly scaled posterior precision that would be constructed as H[0] @ diag(H[1]) @ H[0].T + self.prior_precision_diag.

Returns

H : tuple(eigenvectors, eigenvalues)
scaled self.H with temperature and loss factors.
prior_precision_diag : torch.Tensor
diagonal prior precision shape parameters to be added to H.

Inherited members

class LLLaplace (model: nn.Module, likelihood: Likelihood | str, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, feature_reduction: FeatureReduction | str | None = None, dict_key_x: str = 'inputs_id', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, last_layer_name: str | None = None, backend_kwargs: dict[str, Any] | None = None, asdl_fisher_kwargs: dict[str, Any] | None = None)

Baseclass for all last-layer Laplace approximations in this library. Subclasses specify the structure of the Hessian approximation. See BaseLaplace for the full interface.

A Laplace approximation is represented by a MAP which is given by the model parameter and a posterior precision or covariance specifying a Gaussian distribution \mathcal{N}(\theta_{MAP}, P^{-1}). Here, only the parameters of the last layer of the neural network are treated probabilistically. The goal of this class is to compute the posterior precision P which sums as P = \sum_{n=1}^N \nabla^2_\theta \log p(\mathcal{D}_n \mid \theta) \vert_{\theta_{MAP}} + \nabla^2_\theta \log p(\theta) \vert_{\theta_{MAP}}. Every subclass implements different approximations to the log likelihood Hessians, for example, a diagonal one. The prior is assumed to be Gaussian and therefore we have a simple form for \nabla^2_\theta \log p(\theta) \vert_{\theta_{MAP}} = P_0 . In particular, we assume a scalar or diagonal prior precision so that in all cases P_0 = \textrm{diag}(p_0) and the structure of p_0 can be varied.

Parameters

model : torch.nn.Module or FeatureExtractor
 
likelihood : Likelihood or {'classification', 'regression'}
determines the log likelihood Hessian approximation
sigma_noise : torch.Tensor or float, default=1
observation noise for the regression setting; must be 1 for classification
prior_precision : torch.Tensor or float, default=1
prior precision of a Gaussian prior (= weight decay); can be scalar, per-layer, or diagonal in the most general case
prior_mean : torch.Tensor or float, default=0
prior mean of a Gaussian prior, useful for continual learning
temperature : float, default=1
temperature of the likelihood; lower temperature leads to more concentrated posterior and vice versa.
enable_backprop : bool, default=False
whether to enable backprop to the input x through the Laplace predictive. Useful for e.g. Bayesian optimization.
feature_reduction : FeatureReduction or str, optional, default=None
when the last-layer features is a tensor of dim >= 3, this tells how to reduce it into a dim-2 tensor. E.g. in LLMs for non-language modeling problems, the penultultimate output is a tensor of shape (batch_size, seq_len, embd_dim). But the last layer maps (batch_size, embd_dim) to (batch_size, n_classes). Note: Make sure that this option faithfully reflects the reduction in the model definition. When inputting a string, available options are {'pick_first', 'pick_last', 'average'}.
dict_key_x : str, default='input_ids'
The dictionary key under which the input tensor x is stored. Only has effect when the model takes a MutableMapping as the input. Useful for Huggingface LLM models.
dict_key_y : str, default='labels'
The dictionary key under which the target tensor y is stored. Only has effect when the model takes a MutableMapping as the input. Useful for Huggingface LLM models.
backend : subclasses of CurvatureInterface
backend for access to curvature/Hessian approximations
last_layer_name : str, default=None
name of the model's last layer, if None it will be determined automatically
backend_kwargs : dict, default=None
arguments passed to the backend on initialization, for example to set the number of MC samples for stochastic approximations.

Ancestors

Subclasses

Instance variables

var prior_precision_diag : torch.Tensor

Obtain the diagonal prior precision p_0 constructed from either a scalar or diagonal prior precision.

Returns

prior_precision_diag : torch.Tensor
 

Methods

def fit(self, train_loader: DataLoader, override: bool = True, progress_bar: bool = False) ‑> None

Fit the local Laplace approximation at the parameters of the model.

Parameters

train_loader : torch.data.utils.DataLoader
each iterate is a training batch, either (X, y) tensors or a dict-like object containing keys as expressed by self.dict_key_x and self.dict_key_y. train_loader.dataset needs to be set to access N, size of the data set.
override : bool, default=True
whether to initialize H, loss, and n_data again; setting to False is useful for online learning settings to accumulate a sequential posterior approximation.
progress_bar : bool, default=False
 
def functional_variance_fast(self, X)

Should be overriden if there exists a trick to make this fast!

Parameters

X : torch.Tensor of shape (batch_size, input_dim)
 

Returns

f_var_diag : torch.Tensor of shape (batch_size, num_outputs)
Corresponding to the diagonal of the covariance matrix of the outputs
def state_dict(self) ‑> dict[str, typing.Any]
def load_state_dict(self, state_dict: dict[str, Any]) ‑> None

Inherited members

class FullLLLaplace (model: nn.Module, likelihood: Likelihood | str, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, feature_reduction: FeatureReduction | str | None = None, dict_key_x: str = 'inputs_id', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, last_layer_name: str | None = None, backend_kwargs: dict[str, Any] | None = None, asdl_fisher_kwargs: dict[str, Any] | None = None)

Last-layer Laplace approximation with full, i.e., dense, log likelihood Hessian approximation and hence posterior precision. Based on the chosen backend parameter, the full approximation can be, for example, a generalized Gauss-Newton matrix. Mathematically, we have P \in \mathbb{R}^{P \times P}. See FullLaplace, LLLaplace, and BaseLaplace for the full interface.

Ancestors

Inherited members

class KronLLLaplace (model: nn.Module, likelihood: Likelihood | str, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, feature_reduction: FeatureReduction | str | None = None, dict_key_x: str = 'inputs_id', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, last_layer_name: str | None = None, damping: bool = False, backend_kwargs: dict[str, Any] | None = None, asdl_fisher_kwargs: dict[str, Any] | None = None)

Last-layer Laplace approximation with Kronecker factored log likelihood Hessian approximation and hence posterior precision. Mathematically, we have for the last parameter group, i.e., torch.nn.Linear, that \P\approx Q \otimes H. See KronLaplace, LLLaplace, and BaseLaplace for the full interface and see Kron and KronDecomposed for the structure of the Kronecker factors. Kron is used to aggregate factors by summing up and KronDecomposed is used to add the prior, a Hessian factor (e.g. temperature), and computing posterior covariances, marginal likelihood, etc. Use of damping is possible by initializing or setting damping=True.

Ancestors

Inherited members

class DiagLLLaplace (model: nn.Module, likelihood: Likelihood | str, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, feature_reduction: FeatureReduction | str | None = None, dict_key_x: str = 'inputs_id', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, last_layer_name: str | None = None, backend_kwargs: dict[str, Any] | None = None, asdl_fisher_kwargs: dict[str, Any] | None = None)

Last-layer Laplace approximation with diagonal log likelihood Hessian approximation and hence posterior precision. Mathematically, we have P \approx \textrm{diag}(P). See DiagLaplace, LLLaplace, and BaseLaplace for the full interface.

Ancestors

Inherited members

class SubnetLaplace (model: nn.Module, likelihood: Likelihood | str, subnetwork_indices: torch.LongTensor, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, backend: Type[CurvatureInterface] | None = None, backend_kwargs: dict | None = None, asdl_fisher_kwargs: dict | None = None)

Class for subnetwork Laplace, which computes the Laplace approximation over just a subset of the model parameters (i.e. a subnetwork within the neural network), as proposed in [1]. Subnetwork Laplace can only be used with either a full or a diagonal Hessian approximation.

A Laplace approximation is represented by a MAP which is given by the model parameter and a posterior precision or covariance specifying a Gaussian distribution \mathcal{N}(\theta_{MAP}, P^{-1}). Here, only a subset of the model parameters (i.e. a subnetwork of the neural network) are treated probabilistically. The goal of this class is to compute the posterior precision P which sums as P = \sum_{n=1}^N \nabla^2_\theta \log p(\mathcal{D}_n \mid \theta) \vert_{\theta_{MAP}} + \nabla^2_\theta \log p(\theta) \vert_{\theta_{MAP}}. The prior is assumed to be Gaussian and therefore we have a simple form for \nabla^2_\theta \log p(\theta) \vert_{\theta_{MAP}} = P_0 . In particular, we assume a scalar or diagonal prior precision so that in all cases P_0 = \textrm{diag}(p_0) and the structure of p_0 can be varied.

The subnetwork Laplace approximation only supports a full, i.e., dense, log likelihood Hessian approximation and hence posterior precision. Based on the chosen backend parameter, the full approximation can be, for example, a generalized Gauss-Newton matrix. Mathematically, we have P \in \mathbb{R}^{P \times P}. See FullLaplace and BaseLaplace for the full interface.

References

[1] Daxberger, E., Nalisnick, E., Allingham, JU., Antorán, J., Hernández-Lobato, JM. Bayesian Deep Learning via Subnetwork Inference. ICML 2021.

Parameters

model : torch.nn.Module or FeatureExtractor
 
likelihood : {'classification', 'regression'}
determines the log likelihood Hessian approximation
subnetwork_indices : torch.LongTensor
indices of the vectorized model parameters (i.e. torch.nn.utils.parameters_to_vector(model.parameters())) that define the subnetwork to apply the Laplace approximation over
sigma_noise : torch.Tensor or float, default=1
observation noise for the regression setting; must be 1 for classification
prior_precision : torch.Tensor or float, default=1
prior precision of a Gaussian prior (= weight decay); can be scalar, per-layer, or diagonal in the most general case
prior_mean : torch.Tensor or float, default=0
prior mean of a Gaussian prior, useful for continual learning
temperature : float, default=1
temperature of the likelihood; lower temperature leads to more concentrated posterior and vice versa.
backend : subclasses of CurvatureInterface
backend for access to curvature/Hessian approximations
backend_kwargs : dict, default=None
arguments passed to the backend on initialization, for example to set the number of MC samples for stochastic approximations.

Ancestors

Subclasses

Instance variables

var prior_precision_diag : torch.Tensor

Obtain the diagonal prior precision p_0 constructed from either a scalar or diagonal prior precision.

Returns

prior_precision_diag : torch.Tensor
 
var mean_subnet : torch.Tensor

Methods

def assemble_full_samples(self, subnet_samples) ‑> torch.Tensor

Inherited members

class FullSubnetLaplace (model: nn.Module, likelihood: Likelihood | str, subnetwork_indices: torch.LongTensor, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, backend: Type[CurvatureInterface] | None = None, backend_kwargs: dict | None = None, asdl_fisher_kwargs: dict | None = None)

Subnetwork Laplace approximation with full, i.e., dense, log likelihood Hessian approximation and hence posterior precision. Based on the chosen backend parameter, the full approximation can be, for example, a generalized Gauss-Newton matrix. Mathematically, we have P \in \mathbb{R}^{P \times P}. See FullLaplace, SubnetLaplace, and BaseLaplace for the full interface.

Ancestors

Inherited members

class DiagSubnetLaplace (model: nn.Module, likelihood: Likelihood | str, subnetwork_indices: torch.LongTensor, sigma_noise: float | torch.Tensor = 1.0, prior_precision: float | torch.Tensor = 1.0, prior_mean: float | torch.Tensor = 0.0, temperature: float = 1.0, backend: Type[CurvatureInterface] | None = None, backend_kwargs: dict | None = None, asdl_fisher_kwargs: dict | None = None)

Subnetwork Laplace approximation with diagonal log likelihood Hessian approximation and hence posterior precision. Mathematically, we have P \approx \textrm{diag}(P). See DiagLaplace, SubnetLaplace, and BaseLaplace for the full interface.

Ancestors

Inherited members

class SubsetOfWeights (value, names=None, *, module=None, qualname=None, type=None, start=1)

An enumeration.

Ancestors

  • builtins.str
  • enum.Enum

Class variables

var ALL
var LAST_LAYER
var SUBNETWORK
class HessianStructure (value, names=None, *, module=None, qualname=None, type=None, start=1)

An enumeration.

Ancestors

  • builtins.str
  • enum.Enum

Class variables

var FULL
var KRON
var DIAG
var LOWRANK
class Likelihood (value, names=None, *, module=None, qualname=None, type=None, start=1)

An enumeration.

Ancestors

  • builtins.str
  • enum.Enum

Class variables

var REGRESSION
var CLASSIFICATION
var REWARD_MODELING
class PredType (value, names=None, *, module=None, qualname=None, type=None, start=1)

An enumeration.

Ancestors

  • builtins.str
  • enum.Enum

Class variables

var GLM
var NN
class LinkApprox (value, names=None, *, module=None, qualname=None, type=None, start=1)

An enumeration.

Ancestors

  • builtins.str
  • enum.Enum

Class variables

var MC
var PROBIT
var BRIDGE
var BRIDGE_NORM
class TuningMethod (value, names=None, *, module=None, qualname=None, type=None, start=1)

An enumeration.

Ancestors

  • builtins.str
  • enum.Enum

Class variables

var MARGLIK
var GRIDSEARCH
class PriorStructure (value, names=None, *, module=None, qualname=None, type=None, start=1)

An enumeration.

Ancestors

  • builtins.str
  • enum.Enum

Class variables

var SCALAR
var DIAG
var LAYERWISE