Efficient Weight-Space Laplace-Gaussian Filtering and Smoothing for Sequential Deep Learning

Efficiently learning a sequence of related tasks, such as in continual learning, poses a significant challenge for neural nets due to the delicate trade-off between catastrophic forgetting and loss of plasticity. We address this challenge with a grounded framework for sequentially learning related tasks based on Bayesian inference. Specifically, we treat the model's parameters as a nonlinear Gaussian state-space model and perform efficient inference using Gaussian filtering and smoothing. This general formalism subsumes existing continual learning approaches, while also offering a clearer conceptual understanding of its components. Leveraging Laplace approximations during filtering, we construct Gaussian posterior measures on the weight space of a neural network for each task. We use it as an efficient regularizer by exploiting the structure of the generalized Gauss-Newton matrix (GGN) to construct diagonal plus low-rank approximations. The dynamics model allows targeted control of the learning process and the incorporation of domain-specific knowledge, such as modeling the type of shift between tasks. Additionally, using Bayesian approximate smoothing can enhance the performance of task-specific models without needing to re-access any data.

Uncertainty-Guided Optimization on Large Language Model Search Trees

Beam search is a standard tree search algorithm when it comes to finding sequences of maximum likelihood, for example, in the decoding processes of large language models. However, it is myopic since it does not take the whole path from the root to a leaf into account. Moreover, it is agnostic to prior knowledge available about the process: For example, it does not consider that the objective being maximized is a likelihood and thereby has specific properties, like being bound in the unit interval. Taking a probabilistic approach, we define a prior belief over the LLMs' transition probabilities and obtain a posterior belief over the most promising paths in each iteration. These beliefs are helpful to define a non-myopic Bayesian-optimization-like acquisition function that allows for a more data-efficient exploration scheme than standard beam search. We discuss how to select the prior and demonstrate in on- and off-model experiments with recent large language models, including Llama-2-7b, that our method achieves higher efficiency than beam search: Our method achieves the same or a higher likelihood while expanding fewer nodes than beam search.

A Critical Look At Tokenwise Reward-Guided Text Generation

Large language models (LLMs) can significantly be improved by aligning to human preferences -- the so-called reinforcement learning from human feedback (RLHF). However, the cost of fine-tuning an LLM is prohibitive for many users. Due to their ability to bypass LLM finetuning, tokenwise reward-guided text generation (RGTG) methods have recently been proposed. They use a reward model trained on full sequences to score partial sequences during a tokenwise decoding, in a bid to steer the generation towards sequences with high rewards. However, these methods have so far been only heuristically motivated and poorly analyzed. In this work, we show that reward models trained on full sequences are not compatible with scoring partial sequences. To alleviate this issue, we propose to explicitly train a Bradley-Terry reward model on partial sequences, and autoregressively sample from the implied tokenwise policy during decoding time. We study the property of this reward model and the implied policy. In particular, we show that this policy is proportional to the ratio of two distinct RLHF policies. We show that our simple approach outperforms previous RGTG methods and achieves similar performance as strong offline baselines but without large-scale LLM finetuning.

How Useful is Intermittent, Asynchronous Expert Feedback for Bayesian Optimization?

Bayesian optimization (BO) is an integral part of automated scientific discovery -- the so-called self-driving lab -- where human inputs are ideally minimal or at least non-blocking. However, scientists often have strong intuition, and thus human feedback is still useful. Nevertheless, prior works in enhancing BO with expert feedback, such as by incorporating it in an offline or online but blocking (arrives at each BO iteration) manner, are incompatible with the spirit of self-driving labs. In this work, we study whether a small amount of randomly arriving expert feedback that is being incorporated in a non-blocking manner can improve a BO campaign. To this end, we run an additional, independent computing thread on top of the BO loop to handle the feedback-gathering process. The gathered feedback is used to learn a Bayesian preference model that can readily be incorporated into the BO thread, to steer its exploration-exploitation process. Experiments on toy and chemistry datasets suggest that even just a few intermittent, asynchronous expert feedback can be useful for improving or constraining BO. This can especially be useful for its implication in improving self-driving labs, e.g. making them more data-efficient and less costly.

A Sober Look at LLMs for Material Discovery: Are They Actually Good for Bayesian Optimization Over Molecules?

Automation is one of the cornerstones of contemporary material discovery. Bayesian optimization (BO) is an essential part of such workflows, enabling scientists to leverage prior domain knowledge into efficient exploration of a large molecular space. While such prior knowledge can take many forms, there has been significant fanfare around the ancillary scientific knowledge encapsulated in large language models (LLMs). However, existing work thus far has only explored LLMs for heuristic materials searches. Indeed, recent work obtains the uncertainty estimate -- an integral part of BO -- from point-estimated, non-Bayesian LLMs. In this work, we study the question of whether LLMs are actually useful to accelerate principled Bayesian optimization in the molecular space. We take a sober, dispassionate stance in answering this question. This is done by carefully (i) viewing LLMs as fixed feature extractors for standard but principled BO surrogate models and by (ii) leveraging parameter-efficient finetuning methods and Bayesian neural networks to obtain the posterior of the LLM surrogate. Our extensive experiments with real-world chemistry problems show that LLMs can be useful for BO over molecules, but only if they have been pretrained or finetuned with domain-specific data.

Position Paper: Bayesian Deep Learning in the Age of Large-Scale AI

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

Structured Inverse-Free Natural Gradient: Memory-Efficient & Numerically-Stable KFAC for Large Neural Nets

Second-order methods for deep learning -- such as KFAC -- can be useful for neural net training. However, they are often memory-inefficient and numerically unstable for low-precision training since their preconditioning Kronecker factors are dense, and require high-precision matrix inversion or decomposition. Consequently, such methods are not widely used for training large neural networks such as transformer-based models. We address these two issues by (i) formulating an inverse-free update of KFAC and (ii) imposing structures in each of the Kronecker factors, resulting in a method we term structured inverse-free natural gradient descent (SINGD). On large modern neural networks, we show that, in contrast to KFAC, SINGD is memory efficient and numerically robust, and often outperforms AdamW even in half precision. Hence, our work closes a gap between first-order and second-order methods in modern low precision training for large neural nets.

Preventing Arbitrarily High Confidence on Far-Away Data in Point-Estimated Discriminative Neural Networks

Discriminatively trained, deterministic neural networks are the de facto choice for classification problems. However, even though they achieve state-of-the-art results on in-domain test sets, they tend to be overconfident on out-of-distribution (OOD) data. For instance, ReLU networks -- a popular class of neural network architectures -- have been shown to almost always yield high confidence predictions when the test data are far away from the training set, even when they are trained with OOD data. We overcome this problem by adding a term to the output of the neural network that corresponds to the logit of an extra class, that we design to dominate the logits of the original classes as we move away from the training data.This technique provably prevents arbitrarily high confidence on far-away test data while maintaining a simple discriminative point-estimate training. Evaluation on various benchmarks demonstrates strong performance against competitive baselines on both far-away and realistic OOD data.

On the Disconnect Between Theory and Practice of Overparametrized Neural Networks

The infinite-width limit of neural networks (NNs) has garnered significant attention as a theoretical framework for analyzing the behavior of large-scale, overparametrized networks. By approaching infinite width, NNs effectively converge to a linear model with features characterized by the neural tangent kernel (NTK). This establishes a connection between NNs and kernel methods, the latter of which are well understood. Based on this link, theoretical benefits and algorithmic improvements have been hypothesized and empirically demonstrated in synthetic architectures. These advantages include faster optimization, reliable uncertainty quantification and improved continual learning. However, current results quantifying the rate of convergence to the kernel regime suggest that exploiting these benefits requires architectures that are orders of magnitude wider than they are deep. This assumption raises concerns that practically relevant architectures do not exhibit behavior as predicted via the NTK. In this work, we empirically investigate whether the limiting regime either describes the behavior of large-width architectures used in practice or is informative for algorithmic improvements. Our empirical results demonstrate that this is not the case in optimization, uncertainty quantification or continual learning. This observed disconnect between theory and practice calls into question the practical relevance of the infinite-width limit.

Promises and Pitfalls of the Linearized Laplace in Bayesian Optimization

The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. It is theoretically compelling since it can be seen as a Gaussian process posterior with the mean function given by the neural network's maximum-a-posteriori predictive function and the covariance function induced by the empirical neural tangent kernel. However, while its efficacy has been studied in large-scale tasks like image classification, it has not been studied in sequential decision-making problems like Bayesian optimization where Gaussian processes -- with simple mean functions and kernels such as the radial basis function -- are the de-facto surrogate models. In this work, we study the usefulness of the LLA in Bayesian optimization and highlight its strong performance and flexibility. However, we also present some pitfalls that might arise and a potential problem with the LLA when the search space is unbounded.