arXiv subjects

Laurence Aitchison

Publications and source records attributed to Laurence Aitchison.

At least 55 records · Page 3Linked to original sources

arXiv2024

Convolutional Deep Kernel Machines

Standard infinite-width limits of neural networks sacrifice the ability for intermediate layers to learn representations from data. Recent work (A theory of representation learning gives a deep generalisation of kernel methods, Yang et al. 2023) modified the Neural Network Gaussian Process (NNGP) limit of Bayesian neural networks so that representation learning is retained. Furthermore, they found that applying this modified limit to a deep Gaussian process gives a practical learning algorithm which they dubbed the deep kernel machine (DKM). However, they only considered the simplest possible setting: regression in small, fully connected networks with e.g. 10 input features. Here, we introduce convolutional deep kernel machines. This required us to develop a novel inter-domain inducing point approximation, as well as introducing and experimentally assessing a number of techniques not previously seen in DKMs, including analogues to batch normalisation, different likelihoods, and different types of top-layer. The resulting model trains in roughly 77 GPU hours, achieving around 99% test accuracy on MNIST, 72% on CIFAR-100, and 92.7% on CIFAR-10, which is SOTA for kernel methods.

stat.ML↗

arXiv2024

Bayesian Low-rank Adaptation for Large Language Models

Low-rank adaptation (LoRA) has emerged as a new paradigm for cost-efficient fine-tuning of large language models (LLMs). However, fine-tuned LLMs often become overconfident especially when fine-tuned on small datasets. Bayesian methods, with their inherent ability to estimate uncertainty, serve as potent tools to mitigate overconfidence and enhance calibration. In this work, we introduce Laplace-LoRA, which applies a Bayesian approach to the LoRA parameters. Specifically, Laplace-LoRA applies a Laplace approximation to the posterior over the LoRA parameters, considerably improving the calibration of fine-tuned LLMs.

cs.LG↗

arXiv2023

TouchSDF: A DeepSDF Approach for 3D Shape Reconstruction using Vision-Based Tactile Sensing

Humans rely on their visual and tactile senses to develop a comprehensive 3D understanding of their physical environment. Recently, there has been a growing interest in exploring and manipulating objects using data-driven approaches that utilise high-resolution vision-based tactile sensors. However, 3D shape reconstruction using tactile sensing has lagged behind visual shape reconstruction because of limitations in existing techniques, including the inability to generalise over unseen shapes, the absence of real-world testing, and limited expressive capacity imposed by discrete representations. To address these challenges, we propose TouchSDF, a Deep Learning approach for tactile 3D shape reconstruction that leverages the rich information provided by a vision-based tactile sensor and the expressivity of the implicit neural representation DeepSDF. Our technique consists of two components: (1) a Convolutional Neural Network that maps tactile images into local meshes representing the surface at the touch location, and (2) an implicit neural function that predicts a signed distance function to extract the desired 3D shape. This combination allows TouchSDF to reconstruct smooth and continuous 3D shapes from tactile inputs in simulation and real-world settings, opening up research avenues for robust 3D-aware representations and improved multimodal perception in robotics. Code and supplementary material are available at: https://touchsdf.github.io/

cs.CV↗

arXiv2023

Taylor TD-learning

Many reinforcement learning approaches rely on temporal-difference (TD) learning to learn a critic. However, TD-learning updates can be high variance. Here, we introduce a model-based RL framework, Taylor TD, which reduces this variance in continuous state-action settings. Taylor TD uses a first-order Taylor series expansion of TD updates. This expansion allows Taylor TD to analytically integrate over stochasticity in the action-choice, and some stochasticity in the state distribution for the initial state and action of each TD update. We include theoretical and empirical evidence that Taylor TD updates are indeed lower variance than standard TD updates. Additionally, we show Taylor TD has the same stable learning guarantees as standard TD-learning with linear function approximation under a reasonable assumption. Next, we combine Taylor TD with the TD3 algorithm, forming TaTD3. We show TaTD3 performs as well, if not better, than several state-of-the art model-free and model-based baseline algorithms on a set of standard benchmark tasks.

cs.LG↗

arXiv2023

LoRA ensembles for large language model fine-tuning

Finetuned LLMs often exhibit poor uncertainty quantification, manifesting as overconfidence, poor calibration, and unreliable prediction results on test data or out-of-distribution samples. One approach commonly used in vision for alleviating this issue is a deep ensemble, which constructs an ensemble by training the same model multiple times using different random initializations. However, there is a huge challenge to ensembling LLMs: the most effective LLMs are very, very large. Keeping a single LLM in memory is already challenging enough: keeping an ensemble of e.g. 5 LLMs in memory is impossible in many settings. To address these issues, we propose an ensemble approach using Low-Rank Adapters (LoRA), a parameter-efficient fine-tuning technique. Critically, these low-rank adapters represent a very small number of parameters, orders of magnitude less than the underlying pre-trained model. Thus, it is possible to construct large ensembles of LoRA adapters with almost the same computational overhead as using the original model. We find that LoRA ensembles, applied on its own or on top of pre-existing regularization techniques, gives consistent improvements in predictive accuracy and uncertainty quantification.

cs.LG↗

arXiv2023

InfoNCE is variational inference in a recognition parameterised model

Here, we show that the InfoNCE objective is equivalent to the ELBO in a new class of probabilistic generative model, the recognition parameterised model (RPM). When we learn the optimal prior, the RPM ELBO becomes equal to the mutual information (MI; up to a constant), establishing a connection to pre-existing self-supervised learning methods such as InfoNCE. However, practical InfoNCE methods do not use the MI as an objective; the MI is invariant to arbitrary invertible transformations, so using an MI objective can lead to highly entangled representations (Tschannen et al., 2019). Instead, the actual InfoNCE objective is a simplified lower bound on the MI which is loose even in the infinite sample limit. Thus, an objective that works (i.e. the actual InfoNCE objective) appears to be motivated as a loose bound on an objective that does not work (i.e. the true MI which gives arbitrarily entangled representations). We give an alternative motivation for the actual InfoNCE objective. In particular, we show that in the infinite sample limit, and for a particular choice of prior, the actual InfoNCE objective is equal to the ELBO (up to a constant); and the ELBO is equal to the marginal likelihood with a deterministic recognition model. Thus, we argue that our VAE perspective gives a better motivation for InfoNCE than MI, as the actual InfoNCE objective is only loosely bounded by the MI, but is equal to the ELBO/marginal likelihood (up to a constant).

stat.ML↗

arXiv2023

A theory of representation learning gives a deep generalisation of kernel methods

The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation learning. However, standard theoretical approaches (formally NNGPs) involving infinite width limits eliminate representation learning. We therefore develop a new infinite width limit, the Bayesian representation learning limit, that exhibits representation learning mirroring that in finite-width models, yet at the same time, retains some of the simplicity of standard infinite-width limits. In particular, we show that Deep Gaussian processes (DGPs) in the Bayesian representation learning limit have exactly multivariate Gaussian posteriors, and the posterior covariances can be obtained by optimizing an interpretable objective combining a log-likelihood to improve performance with a series of KL-divergences which keep the posteriors close to the prior. We confirm these results experimentally in wide but finite DGPs. Next, we introduce the possibility of using this limit and objective as a flexible, deep generalisation of kernel methods, that we call deep kernel machines (DKMs). Like most naive kernel methods, DKMs scale cubically in the number of datapoints. We therefore use methods from the Gaussian process inducing point literature to develop a sparse DKM that scales linearly in the number of datapoints. Finally, we extend these approaches to NNs (which have non-Gaussian posteriors) in the Appendices.

stat.ML↗

arXiv2023

An Improved Variational Approximate Posterior for the Deep Wishart Process

Deep kernel processes are a recently introduced class of deep Bayesian models that have the flexibility of neural networks, but work entirely with Gram matrices. They operate by alternately sampling a Gram matrix from a distribution over positive semi-definite matrices, and applying a deterministic transformation. When the distribution is chosen to be Wishart, the model is called a deep Wishart process (DWP). This particular model is of interest because its prior is equivalent to a deep Gaussian process (DGP) prior, but at the same time it is invariant to rotational symmetries, leading to a simpler posterior distribution. Practical inference in the DWP was made possible in recent work ("A variational approximate posterior for the deep Wishart process" Ober and Aitchison 2021a) where the authors used a generalisation of the Bartlett decomposition of the Wishart distribution as the variational approximate posterior. However, predictive performance in that paper was less impressive than one might expect, with the DWP only beating a DGP on a few of the UCI datasets used for comparison. In this paper, we show that further generalising their distribution to allow linear combinations of rows and columns in the Bartlett decomposition results in better predictive performance, while incurring negligible additional computation cost.

stat.ML↗

arXiv2023

Massively Parallel Reweighted Wake-Sleep

Reweighted wake-sleep (RWS) is a machine learning method for performing Bayesian inference in a very general class of models. RWS draws $K$ samples from an underlying approximate posterior, then uses importance weighting to provide a better estimate of the true posterior. RWS then updates its approximate posterior towards the importance-weighted estimate of the true posterior. However, recent work [Chattergee and Diaconis, 2018] indicates that the number of samples required for effective importance weighting is exponential in the number of latent variables. Attaining such a large number of importance samples is intractable in all but the smallest models. Here, we develop massively parallel RWS, which circumvents this issue by drawing $K$ samples of all $n$ latent variables, and individually reasoning about all $K^n$ possible combinations of samples. While reasoning about $K^n$ combinations might seem intractable, the required computations can be performed in polynomial time by exploiting conditional independencies in the generative model. We show considerable improvements over standard "global" RWS, which draws $K$ samples from the full joint.

cs.LG↗

arXiv2023

Robustness to corruption in pre-trained Bayesian neural networks

We develop ShiftMatch, a new training-data-dependent likelihood for robustness to corruption in Bayesian neural networks (BNNs). ShiftMatch is inspired by the training-data-dependent "EmpCov" priors from Izmailov et al. (2021a), and efficiently matches test-time spatial correlations to those at training time. Critically, ShiftMatch is designed to leave the neural network's training time likelihood unchanged, allowing it to use publicly available samples from pre-trained BNNs. Using pre-trained HMC samples, ShiftMatch gives strong performance improvements on CIFAR-10-C, outperforms EmpCov priors (though ShiftMatch uses extra information from a minibatch of corrupted test points), and is perhaps the first Bayesian method capable of convincingly outperforming plain deep ensembles.

cs.LG↗

arXiv2023

Decision trees compensate for model misspecification

The best-performing models in ML are not interpretable. If we can explain why they outperform, we may be able to replicate these mechanisms and obtain both interpretability and performance. One example are decision trees and their descendent gradient boosting machines (GBMs). These perform well in the presence of complex interactions, with tree depth governing the order of interactions. However, interactions cannot fully account for the depth of trees found in practice. We confirm 5 alternative hypotheses about the role of tree depth in performance in the absence of true interactions, and present results from experiments on a battery of datasets. Part of the success of tree models is due to their robustness to various forms of mis-specification. We present two methods for robust generalized linear models (GLMs) addressing the composite and mixed response scenarios.

stat.ML↗

arXiv2023

Imitating careful experts to avoid catastrophic events

RL is increasingly being used to control robotic systems that interact closely with humans. This interaction raises the problem of safe RL: how to ensure that a RL-controlled robotic system never, for instance, injures a human. This problem is especially challenging in rich, realistic settings where it is not even possible to clearly write down a reward function which incorporates these outcomes. In these circumstances, perhaps the only viable approach is based on IRL, which infers rewards from human demonstrations. However, IRL is massively underdetermined as many different rewards can lead to the same optimal policies; we show that this makes it difficult to distinguish catastrophic outcomes (such as injuring a human) from merely undesirable outcomes. Our key insight is that humans do display different behaviour when catastrophic outcomes are possible: they become much more careful. We incorporate carefulness signals into IRL, and find that they do indeed allow IRL to disambiguate undesirable from catastrophic outcomes, which is critical to ensuring safety in future real-world human-robot interactions.

cs.LG↗

arXiv2022

Machine learning emulation of a local-scale UK climate model

Climate change is causing the intensification of rainfall extremes. Precipitation projections with high spatial resolution are important for society to prepare for these changes, e.g. to model flooding impacts. Physics-based simulations for creating such projections are very computationally expensive. This work demonstrates the effectiveness of diffusion models, a form of deep generative models, for generating much more cheaply realistic high resolution rainfall samples for the UK conditioned on data from a low resolution simulation. We show for the first time a machine learning model that is able to produce realistic samples of high-resolution rainfall based on a physical model that resolves atmospheric convection, a key process behind extreme rainfall. By adding self-learnt, location-specific information to low resolution relative vorticity, quantiles and time-mean of the samples match well their counterparts from the high-resolution simulation.

physics.ao-ph↗

arXiv2022

Random initialisations performing above chance and how to find them

Neural networks trained with stochastic gradient descent (SGD) starting from different random initialisations typically find functionally very similar solutions, raising the question of whether there are meaningful differences between different SGD solutions. Entezari et al.\ recently conjectured that despite different initialisations, the solutions found by SGD lie in the same loss valley after taking into account the permutation invariance of neural networks. Concretely, they hypothesise that any two solutions found by SGD can be permuted such that the linear interpolation between their parameters forms a path without significant increases in loss. Here, we use a simple but powerful algorithm to find such permutations that allows us to obtain direct empirical evidence that the hypothesis is true in fully connected networks. Strikingly, we find that two networks already live in the same loss valley at the time of initialisation and averaging their random, but suitably permuted initialisation performs significantly above chance. In contrast, for convolutional architectures, our evidence suggests that the hypothesis does not hold. Especially in a large learning rate regime, SGD seems to discover diverse modes.

cs.LG↗

arXiv2022

What deep reinforcement learning tells us about human motor learning and vice-versa

Machine learning and specifically reinforcement learning (RL) has been extremely successful in helping us to understand neural decision making processes. However, RL's role in understanding other neural processes especially motor learning is much less well explored. To explore this connection, we investigated how recent deep RL methods correspond to the dominant motor learning framework in neuroscience, error-based learning. Error-based learning can be probed using a mirror reversal adaptation paradigm, where it produces distinctive qualitative predictions that are observed in humans. We therefore tested three major families of modern deep RL algorithm on a mirror reversal perturbation. Surprisingly, all of the algorithms failed to mimic human behaviour and indeed displayed qualitatively different behaviour from that predicted by error-based learning. To fill this gap, we introduce a novel deep RL algorithm: model-based deterministic policy gradients (MB-DPG). MB-DPG draws inspiration from error-based learning by explicitly relying on the observed outcome of actions. We show MB-DPG captures (human) error-based learning under mirror-reversal and rotational perturbation. Next, we demonstrate error-based learning in the form of MB-DPG learns faster than canonical model-free algorithms on complex arm-based reaching tasks, while being more robust to (forward) model misspecification than model-based RL. These findings highlight the gap between current deep RL methods and human motor adaptation and offer a route to closing this gap, facilitating future beneficial interaction between between the two fields.

q-bio.NC↗

arXiv2022

Bayesian Neural Network Priors Revisited

Isotropic Gaussian priors are the de facto standard for modern Bayesian neural network inference. However, it is unclear whether these priors accurately reflect our true beliefs about the weight distributions or give optimal performance. To find better priors, we study summary statistics of neural network weights in networks trained using stochastic gradient descent (SGD). We find that convolutional neural network (CNN) and ResNet weights display strong spatial correlations, while fully connected networks (FCNNs) display heavy-tailed weight distributions. We show that building these observations into priors can lead to improved performance on a variety of image classification datasets. Surprisingly, these priors mitigate the cold posterior effect in FCNNs, but slightly increase the cold posterior effect in ResNets.

stat.ML↗

arXiv2021

Data augmentation in Bayesian neural networks and the cold posterior effect

Bayesian neural networks that incorporate data augmentation implicitly use a ``randomly perturbed log-likelihood [which] does not have a clean interpretation as a valid likelihood function'' (Izmailov et al. 2021). Here, we provide several approaches to developing principled Bayesian neural networks incorporating data augmentation. We introduce a ``finite orbit'' setting which allows likelihoods to be computed exactly, and give tight multi-sample bounds in the more usual ``full orbit'' setting. These models cast light on the origin of the cold posterior effect. In particular, we find that the cold posterior effect persists even in these principled models incorporating data augmentation. This suggests that the cold posterior effect cannot be dismissed as an artifact of data augmentation using incorrect likelihoods.

stat.ML↗

arXiv2021

A variational approximate posterior for the deep Wishart process

Recent work introduced deep kernel processes as an entirely kernel-based alternative to NNs (Aitchison et al. 2020). Deep kernel processes flexibly learn good top-layer representations by alternately sampling the kernel from a distribution over positive semi-definite matrices and performing nonlinear transformations. A particular deep kernel process, the deep Wishart process (DWP), is of particular interest because its prior can be made equivalent to deep Gaussian process (DGP) priors for kernels that can be expressed entirely in terms of Gram matrices. However, inference in DWPs has not yet been possible due to the lack of sufficiently flexible distributions over positive semi-definite matrices. Here, we give a novel approach to obtaining flexible distributions over positive semi-definite matrices by generalising the Bartlett decomposition of the Wishart probability density. We use this new distribution to develop an approximate posterior for the DWP that includes dependency across layers. We develop a doubly-stochastic inducing-point inference scheme for the DWP and show experimentally that inference in the DWP can improve performance over doing inference in a DGP with the equivalent prior.

stat.ML↗