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Authors:Jesse Hoogland, George Wang, Matthew Farrugia-Roberts, Liam Carroll, Susan Wei, Daniel Murfet

Abstract:We show that in-context learning emerges in transformers in discrete developmental stages, when they are trained on either language modeling or linear regression tasks. We introduce two methods for detecting the milestones that separate these stages, by probing the geometry of the population loss in both parameter space and function space. We study the stages revealed by these new methods using a range of behavioral and structural metrics to establish their validity.

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Abstract:Fair machine learning aims to prevent discrimination against individuals or sub-populations based on sensitive attributes such as gender and race. In recent years, causal inference methods have been increasingly used in fair machine learning to measure unfairness by causal effects. However, current methods assume that the true causal graph is given, which is often not true in real-world applications. To address this limitation, this paper proposes a framework for achieving causal fairness based on the notion of interventions when the true causal graph is partially known. The proposed approach involves modeling fair prediction using a Partially Directed Acyclic Graph (PDAG), specifically, a class of causal DAGs that can be learned from observational data combined with domain knowledge. The PDAG is used to measure causal fairness, and a constrained optimization problem is formulated to balance between fairness and accuracy. Results on both simulated and real-world datasets demonstrate the effectiveness of this method.

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Abstract:We investigate phase transitions in a Toy Model of Superposition (TMS) using Singular Learning Theory (SLT). We derive a closed formula for the theoretical loss and, in the case of two hidden dimensions, discover that regular $k$-gons are critical points. We present supporting theory indicating that the local learning coefficient (a geometric invariant) of these $k$-gons determines phase transitions in the Bayesian posterior as a function of training sample size. We then show empirically that the same $k$-gon critical points also determine the behavior of SGD training. The picture that emerges adds evidence to the conjecture that the SGD learning trajectory is subject to a sequential learning mechanism. Specifically, we find that the learning process in TMS, be it through SGD or Bayesian learning, can be characterized by a journey through parameter space from regions of high loss and low complexity to regions of low loss and high complexity.

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Abstract:Deep neural networks (DNN) are singular statistical models which exhibit complex degeneracies. In this work, we illustrate how a quantity known as the \emph{learning coefficient} introduced in singular learning theory quantifies precisely the degree of degeneracy in deep neural networks. Importantly, we will demonstrate that degeneracy in DNN cannot be accounted for by simply counting the number of "flat" directions. We propose a computationally scalable approximation of a localized version of the learning coefficient using stochastic gradient Langevin dynamics. To validate our approach, we demonstrate its accuracy in low-dimensional models with known theoretical values. Importantly, the local learning coefficient can correctly recover the ordering of degeneracy between various parameter regions of interest. An experiment on MNIST shows the local learning coefficient can reveal the inductive bias of stochastic opitmizers for more or less degenerate critical points.

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Abstract:The ADMANI datasets (annotated digital mammograms and associated non-image datasets) from the Transforming Breast Cancer Screening with AI programme (BRAIx) run by BreastScreen Victoria in Australia are multi-centre, large scale, clinically curated, real-world databases. The datasets are expected to aid in the development of clinically relevant Artificial Intelligence (AI) algorithms for breast cancer detection, early diagnosis, and other applications. To ensure high data quality, technical outliers must be removed before any downstream algorithm development. As a first step, we randomly select 30,000 individual mammograms and use Convolutional Variational Autoencoder (CVAE), a deep generative neural network, to detect outliers. CVAE is expected to detect all sorts of outliers, although its detection performance differs among different types of outliers. Traditional image processing techniques such as erosion and pectoral muscle analysis can compensate for the poor performance of CVAE in certain outlier types. We identify seven types of technical outliers: implant, pacemaker, cardiac loop recorder, improper radiography, atypical lesion/calcification, incorrect exposure parameter and improper placement. The outlier recall rate for the test set is 61% if CVAE, erosion and pectoral muscle analysis each select the top 1% images ranked in ascending or descending order according to image outlier score under each detection method, and 83% if each selects the top 5% images. This study offers an overview of technical outliers in the ADMANI dataset and suggests future directions to improve outlier detection effectiveness.

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Abstract:In this work, we advocate for the importance of singular learning theory (SLT) as it pertains to the theory and practice of variational inference in Bayesian neural networks (BNNs). To begin, using SLT, we lay to rest some of the confusion surrounding discrepancies between downstream predictive performance measured via e.g., the test log predictive density, and the variational objective. Next, we use the SLT-corrected asymptotic form for singular posterior distributions to inform the design of the variational family itself. Specifically, we build upon the idealized variational family introduced in \citet{bhattacharya_evidence_2020} which is theoretically appealing but practically intractable. Our proposal takes shape as a normalizing flow where the base distribution is a carefully-initialized generalized gamma. We conduct experiments comparing this to the canonical Gaussian base distribution and show improvements in terms of variational free energy and variational generalization error.

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Abstract:Fair machine learning aims to avoid treating individuals or sub-populations unfavourably based on \textit{sensitive attributes}, such as gender and race. Those methods in fair machine learning that are built on causal inference ascertain discrimination and bias through causal effects. Though causality-based fair learning is attracting increasing attention, current methods assume the true causal graph is fully known. This paper proposes a general method to achieve the notion of counterfactual fairness when the true causal graph is unknown. To be able to select features that lead to counterfactual fairness, we derive the conditions and algorithms to identify ancestral relations between variables on a \textit{Partially Directed Acyclic Graph (PDAG)}, specifically, a class of causal DAGs that can be learned from observational data combined with domain knowledge. Interestingly, we find that counterfactual fairness can be achieved as if the true causal graph were fully known, when specific background knowledge is provided: the sensitive attributes do not have ancestors in the causal graph. Results on both simulated and real-world datasets demonstrate the effectiveness of our method.

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Abstract:In singular models, the optimal set of parameters forms an analytic set with singularities and classical statistical inference cannot be applied to such models. This is significant for deep learning as neural networks are singular and thus "dividing" by the determinant of the Hessian or employing the Laplace approximation are not appropriate. Despite its potential for addressing fundamental issues in deep learning, singular learning theory appears to have made little inroads into the developing canon of deep learning theory. Via a mix of theory and experiment, we present an invitation to singular learning theory as a vehicle for understanding deep learning and suggest important future work to make singular learning theory directly applicable to how deep learning is performed in practice.

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Abstract:Mitigating bias in machine learning is a challenging task, due in large part to the presence of competing objectives. Namely, a fair algorithm often comes at the cost of lower predictive accuracy, and vice versa, a highly predictive algorithm may be one that incurs high bias. This work presents a methodology for estimating the fairness-accuracy Pareto front of a fully-connected feedforward neural network, for any accuracy measure and any fairness measure. Our experiments firstly reveal that for training data already exhibiting disparities, a newly introduced causal notion of fairness may be capable of traversing a greater part of the fairness-accuracy space, relative to more standard measures such as demographic parity and conditional parity. The experiments also reveal that tools from multi-objective optimisation are crucial in efficiently estimating the Pareto front (i.e., by finding more non-dominated points), relative to other sensible but ad-hoc approaches. Finally, the work serves to highlight possible synergy between deep learning and multi-objective optimisation. Given that deep learning is increasingly deployed in real-world decision making, the Pareto front can provide a formal way to reason about inherent conflicts.

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Abstract:Biofouling is the accumulation of organisms on surfaces immersed in water. It is of particular concern to the international shipping industry because fouling increases the drag on vessels as they move through the water, resulting in higher fuel costs, and presents a biosecurity risk by providing a pathway for marine non-indigenous species (NIS) to establish in new areas. There is growing interest within jurisdictions to strengthen biofouling risk-management regulations, but it is expensive to conduct in-water inspections and assess the collected data to determine the biofouling state of vessel hulls. Machine learning is well suited to tackle the latter challenge, and here we apply so-called deep learning to automate the classification of images from in-water inspections for the presence and severity of biofouling. We combined images collected from in-water surveys conducted by the Australian Department of Agriculture, Water and the Environment, the New Zealand Ministry for Primary Industries and the California State Lands Commission, and annotated them using the Amazon Mechanical Turk (MTurk) crowdsourcing platform. We compared the annotations from three biofouling experts on a 120-sample subset of these images, and found that for two tasks, identifying images containing fouling, and identifying images containing heavy fouling, they showed 89% agreement (95% CI: 87-92%). It was found that the MTurk labelling approach achieved similar agreement with experts, which we defined as performing at most 5% worse than experts (p=0.004-0.020). Our deep learning model trained with the MTurk annotations also showed reasonable performance in comparison to expert agreement, although at a lower significance level (p=0.071-0.093). We also demonstrate that significantly better performance than expert agreement can be achieved if a classifier with high recall or precision was required.

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