With the pervasive deployment of Machine Learning (ML) models in real-world applications, verifying and auditing properties of ML models have become a central concern. In this work, we focus on three properties: robustness, individual fairness, and group fairness. We discuss two approaches for auditing ML model properties: estimation with and without reconstruction of the target model under audit. Though the first approach is studied in the literature, the second approach remains unexplored. For this purpose, we develop a new framework that quantifies different properties in terms of the Fourier coefficients of the ML model under audit but does not parametrically reconstruct it. We propose the Active Fourier Auditor (AFA), which queries sample points according to the Fourier coefficients of the ML model, and further estimates the properties. We derive high probability error bounds on AFA's estimates, along with the worst-case lower bounds on the sample complexity to audit them. Numerically we demonstrate on multiple datasets and models that AFA is more accurate and sample-efficient to estimate the properties of interest than the baselines.

Multi-agent reinforcement learning (MARL) presents unique challenges as agents learn strategies through experiences. Gradient-based methods are often sensitive to hyperparameter selection and initial random seed variations. Concurrently, significant advances have been made in solving Variational Inequalities (VIs) which include equilibrium-finding problems particularly in addressing the non-converging rotational dynamics that impede convergence of traditional gradient based optimization methods. This paper explores the potential of leveraging VI-based techniques to improve MARL training. Specifically, we study the performance of VI method namely, Nested-Lookahead VI (nLA-VI) and Extragradient (EG) in enhancing the multi-agent deep deterministic policy gradient (MADDPG) algorithm. We present a VI reformulation of the actor-critic algorithm for both single- and multi-agent settings. We introduce three algorithms that use nLA-VI, EG, and a combination of both, named LA-MADDPG, EG-MADDPG, and LA-EG-MADDPG, respectively. Our empirical results demonstrate that these VI-based approaches yield significant performance improvements in benchmark environments, such as the zero-sum games: rock-paper-scissors and matching pennies, where equilibrium strategies can be quantitatively assessed, and the Multi-Agent Particle Environment: Predator prey benchmark, where VI-based methods also yield balanced participation of agents from the same team.

The heterogeneity of neurological and mental health disorders has been a key confound to disease understanding, treatment development and outcome prediction, as patient populations are thought to include multiple disease pathways that selectively respond to treatment (Kapur et al., 2012). These challenges are reflected in poor treatment outcomes; for instance, in depression, approximately only 40% of patients remit after first-line antidepressant treatment or psychotherapy (Amick et al., 2015; Cuijpers et al., 2014; Fava and Davidson, 1996; Trivedi et al., 2006). Diagnostic categories in psychiatry have historically been defined based on signs and symptoms, prioritising diagnostic agreement between clinicians, rather than underlying biological mechanisms (Freedman et al., 2013; Robins and Guze, 1970). Resultingly, the usefulness of supervised machine learning methods as diagnostic tools for mental health disorders (i.e., classifying patients vs. healthy controls) is questionable, as they may simply inherit the flaws of current diagnostic categories. Additional challenges in neurological and mental health disorders are comorbidity (i.e., individuals with one disorder often develop another disorder during their lifespan) and that different disorders can share similar symptoms (Kessler et al., 2005). To address the limitations of current diagnostic categories in psychiatry, the National Institute of Mental Health launched the Research Domain Criteria framework (RDoC) in 2009 (https://www.nimh.nih.gov/research/ 2 research-funded-by-nimh/rdoc) as an attempt to move beyond diagnostic categories and ground psychiatry within neurobiological constructs that combine multiple levels of measures or sources of information (Insel et al., 2010). Multivariate methods, such as Canonical Correlation Analysis (CCA) and related methods, that do not rely on the diagnostic categories, have been widely used to uncover latent disease dimensions capturing associations between brain imaging and non-imaging data (e.g., self-report questionnaires, cognitive tests and genetics). The identified latent dimensions provide information on how a set of non-imaging features (e.g.

Attention layers are the core component of transformers, the current state-of-the-art neural network architecture. However, \softmaxx-based attention puts transformers' trainability at risk. Even \textit{at initialisation}, the propagation of signals and gradients through the random network can be pathological, resulting in known issues such as (i) vanishing/exploding gradients and (ii) \textit{rank collapse}, i.e. when all tokens converge to a single representation \textit{with depth}. This paper examines signal propagation in \textit{attention-only} transformers from a random matrix perspective, illuminating the origin of such issues, as well as unveiling a new phenomenon -- (iii) rank collapse \textit{in width}. Modelling \softmaxx-based attention at initialisation with Random Markov matrices, our theoretical analysis reveals that a \textit{spectral gap} between the two largest singular values of the attention matrix causes (iii), which, in turn, exacerbates (i) and (ii). Building on this insight, we propose a novel, yet simple, practical solution to resolve rank collapse in width by removing the spectral gap. Moreover, we validate our findings and discuss the training benefits of the proposed fix through experiments that also motivate a revision of some of the default parameter scaling. Our attention model accurately describes the standard key-query attention in a single-layer transformer, making this work a significant first step towards a better understanding of the initialisation dynamics in the multi-layer case.

The phenomenon of benign overfitting, where a trained neural network perfectly fits noisy training data but still achieves near-optimal test performance, has been extensively studied in recent years for linear models and fully-connected/convolutional networks. In this work, we study benign overfitting in a single-head softmax attention model, which is the fundamental building block of Transformers. We prove that under appropriate conditions, the model exhibits benign overfitting in a classification setting already after two steps of gradient descent. Moreover, we show conditions where a minimum-norm/maximum-margin interpolator exhibits benign overfitting. We study how the overfitting behavior depends on the signal-to-noise ratio (SNR) of the data distribution, namely, the ratio between norms of signal and noise tokens, and prove that a sufficiently large SNR is both necessary and sufficient for benign overfitting.

Training a large set of machine learning algorithms to convergence in order to select the best-performing algorithm for a dataset is computationally wasteful. Moreover, in a budget-limited scenario, it is crucial to carefully select an algorithm candidate and allocate a budget for training it, ensuring that the limited budget is optimally distributed to favor the most promising candidates. Casting this problem as a Markov Decision Process, we propose a novel framework in which an agent must select in the process of learning the most promising algorithm without waiting until it is fully trained. At each time step, given an observation of partial learning curves of algorithms, the agent must decide whether to allocate resources to further train the most promising algorithm (exploitation), to wake up another algorithm previously put to sleep, or to start training a new algorithm (exploration). In addition, our framework allows the agent to meta-learn from learning curves on past datasets along with dataset meta-features and algorithm hyperparameters. By incorporating meta-learning, we aim to avoid myopic decisions based solely on premature learning curves on the dataset at hand. We introduce two benchmarks of learning curves that served in international competitions at WCCI'22 and AutoML-conf'22, of which we analyze the results. Our findings show that both meta-learning and the progression of learning curves enhance the algorithm selection process, as evidenced by methods of winning teams and our DDQN baseline, compared to heuristic baselines or a random search. Interestingly, our cost-effective baseline, which selects the best-performing algorithm w.r.t. a small budget, can perform decently when learning curves do not intersect frequently.

Understanding the training dynamics of deep learning models is perhaps a necessary step toward demystifying the effectiveness of these models. In particular, how do training data from different classes gradually become separable in their feature spaces when training neural networks using stochastic gradient descent? As a crucial ingredient in our modeling strategy, each SDE contains a drift term that reflects the impact of backpropagation at an input on the features of all samples. Our main finding uncovers a sharp phase transition phenomenon regarding the intra-class impact: if the SDEs are locally elastic in the sense that the impact is more significant on samples from the same class as the input, the features of training data become linearly separable---meaning vanishing training loss; otherwise, the features are not separable, no matter how long the training time is. In the presence of local elasticity, moreover, an analysis of our SDEs shows the emergence of a simple geometric structure called neural collapse of the features.

In this paper, we comprehensively reveal the learning dynamics of normalized neural network using Stochastic Gradient Descent (with momentum) and Weight Decay (WD), named as Spherical Motion Dynamics (SMD). Most related works focus on studying behavior of effective learning rate" inequilibrium" state, i.e. assuming weight norm remains unchanged. However, their discussion on why this equilibrium can be reached is either absent or less convincing. Our work directly explores the cause of equilibrium, as a special state of SMD. Specifically, 1) we introduce the assumptions that can lead to equilibrium state in SMD, and prove equilibrium can be reached in a linear rate regime under given assumptions; 2) we propose angular update" as a substitute for effective learning rate to depict the state of SMD, and derive the theoretical value of angular update in equilibrium state; 3) we verify our assumptions and theoretical results on various large-scale computer vision tasks including ImageNet and MSCOCO with standard settings. Experiment results show our theoretical findings agree well with empirical observations.

The present paper develops a novel aggregated gradient approach for distributed machine learning that adaptively compresses the gradient communication. The key idea is to first quantize the computed gradients, and then skip less informative quantized gradient communications by reusing outdated gradients. Quantizing and skipping result in'lazy' worker-server communications, which justifies the term Lazily Aggregated Quantized gradient that is henceforth abbreviated as LAQ. Our LAQ can provably attain the same linear convergence rate as the gradient descent in the strongly convex case, while effecting major savings in the communication overhead both in transmitted bits as well as in communication rounds. Empirically, experiments with real data corroborate a significant communication reduction compared to existing gradient- and stochastic gradient-based algorithms.

We consider the problem of learning the best-fitting single neuron as measured by the expected square loss \E_{(x,y)\sim \mathcal{D}}[(\sigma(w \top x)-y) 2] over some unknown joint distribution \mathcal{D} by using gradient descent to minimize the empirical risk induced by a set of i.i.d. The activation function \sigma is an arbitrary Lipschitz and non-decreasing function, making the optimization problem nonconvex and nonsmooth in general, and covers typical neural network activation functions and inverse link functions in the generalized linear model setting. In the agnostic PAC learning setting, where no assumption on the relationship between the labels y and the input x is made, if the optimal population risk is \mathsf{OPT}, we show that gradient descent achieves population risk O(\mathsf{OPT}) \eps in polynomial time and sample complexity when \sigma is strictly increasing. When labels take the form y \sigma(v \top x) \xi for zero-mean sub-Gaussian noise \xi, we show that the population risk guarantees for gradient descent improve to \mathsf{OPT} \eps . Our sample complexity and runtime guarantees are (almost) dimension independent, and when \sigma is strictly increasing, require no distributional assumptions beyond boundedness.