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Deep Learning · Self-Supervised Learning

Chung-Yiu Yau, Hoi To Wai, Parameswaran Raman, Soumajyoti Sarkar, Mingyi Hong

A key challenge in contrastive learning is to generate negative samples from a large sample set to contrast with positive samples, for learning better encoding of the data. These negative samples often follow a softmax distribution which are dynamically updated during the training process. However, sampling from this distribution is non-trivial due to the high computational costs in computing the partition function. In this paper, we propose an $\underline{\text{E}}$fficient $\underline{\text{M}}$arkov $\underline{\text{C}}$hain Monte Carlo negative sampling method for $\underline{\text{C}}$ontrastive learning (EMC$^2$). We follow the global contrastive learning loss as introduced in SogCLR, and propose EMC$^2$ which utilizes an adaptive Metropolis-Hastings subroutine to generate hardness-aware negative samples in an online fashion during the optimization. We prove that EMC$^2$ finds an $\mathcal{O}(1/\sqrt{T})$-stationary point of the global contrastive loss in $T$ iterations. Compared to prior works, EMC$^2$ is the first algorithm that exhibits global convergence (to stationarity) regardless of the choice of batch size while exhibiting low computation and memory cost. Numerical experiments validate that EMC$^2$ is effective with small batch training and achieves comparable or better performance than baseline algorithms. We report the results for pre-training image encoders on STL-10 and Imagenet-100.

Applications · Health

Xiangjian Jiang, Andrei Margeloiu, Nikola Simidjievski, Mateja Jamnik

Tabular biomedical data poses challenges in machine learning because it is often high-dimensional and typically low-sample-size (HDLSS). Previous research has attempted to address these challenges via local feature selection, but existing approaches often fail to achieve optimal performance due to their limitation in identifying globally important features and their susceptibility to the co-adaptation problem. In this paper, we propose ProtoGate, a prototype-based neural model for feature selection on HDLSS data. ProtoGate first selects instance-wise features via adaptively balancing global and local feature selection. Furthermore, ProtoGate employs a non-parametric prototype-based prediction mechanism to tackle the co-adaptation problem, ensuring the feature selection results and predictions are consistent with underlying data clusters. We conduct comprehensive experiments to evaluate the performance and interpretability of ProtoGate on synthetic and real-world datasets. The results show that ProtoGate generally outperforms state-of-the-art methods in prediction accuracy by a clear margin while providing high-fidelity feature selection and explainable predictions. Code is available at https://github.com/SilenceX12138/ProtoGate.

Social Aspects · Accountability, Transparency and Interpretability

Tom Bewley, Salim I. Amoukou, Saumitra Mishra, Daniele Magazzeni, Manuela Veloso

We introduce **T-CREx**, a novel model-agnostic method for local and global counterfactual explanation (CE), which summarises recourse options for both individuals and groups in the form of generalised rules. It leverages tree-based surrogate models to learn the counterfactual rules, alongside *metarules* denoting their regimes of optimality, providing both a global analysis of model behaviour and diverse recourse options for users. Experiments indicate that **T-CREx** achieves superior aggregate performance over existing rule-based baselines on a range of CE desiderata, while being orders of magnitude faster to run.

Deep Learning · Attention Mechanisms

Itamar Zimerman, Lior Wolf

Despite their dominance in modern DL and, especially, NLP domains, transformer architectures exhibit sub-optimal performance on long-range tasks compared to recent layers that are specifically designed for this purpose. In this work, drawing inspiration from key attributes of longrange layers, such as state-space layers, linear RNN layers, and global convolution layers, we demonstrate that minimal modifications to the transformer architecture can significantly enhance performance on the Long Range Arena (LRA) benchmark, thus narrowing the gap with these specialized layers. We identify that two key principles for long-range tasks are (i) incorporating an inductive bias towards smoothness, and (ii) locality. As we show, integrating these ideas into the attention mechanism improves results with a negligible amount of additional computation and without any additional trainable parameters. Our theory and experiments also shed light on the reasons for the inferior performance of transformers on long-range tasks and identify critical properties that are essential for successfully capturing long-range dependencies.

Miscellaneous Aspects of Machine Learning · Supervised Learning

Magzhan Gabidolla, Arman Zharmagambetov, Miguel Carreira-Perpinan

Important applications such as fraud or spam detection or churn prediction involve binary classification problems where the datasets are imbalanced and the cost of false positives greatly differs from the cost of false negatives. We focus on classification trees, in particular oblique trees, which subsume both the traditional axis-aligned trees and logistic regression, but are more accurate than both while providing interpretable models. Rather than using ROC curves, we advocate a loss based on minimizing the false negatives subject to a maximum false positive rate, which we prove to be equivalent to minimizing a weighted 0/1 loss. This yields a curve of classifiers that provably dominates the ROC curve, but is hard to optimize due to the 0/1 loss. We give the first algorithm that can iteratively update the tree parameters globally so that the weighted 0/1 loss decreases monotonically. Experiments on various datasets with class imbalance or class costs show this indeed dominates ROC-based classifiers and significantly improves over previous approaches to learn trees based on weighted purity criteria or over- or undersampling.

Deep Learning · Attention Mechanisms

Zhiyu Yao, Jian Wang, Haixu Wu, Jingdong Wang, Mingsheng Long

Vision Transformers (ViTs) excel in computer vision tasks due to their ability to capture global context among tokens. However, their quadratic complexity $\mathcal{O}(N^2D)$ in terms of token number $N$ and feature dimension $D$ limits practical use on mobile devices, necessitating more mobile-friendly ViTs with reduced latency. Multi-head linear-attention is emerging as a promising alternative with linear complexity $\mathcal{O}(NDd)$, where $d$ is the per-head dimension. Still, more compute is needed as $d$ gets large for model accuracy. Reducing $d$ improves mobile friendliness at the expense of excessive small heads weak at learning valuable subspaces, ultimately impeding model capability. To overcome this efficiency-capability dilemma, we propose a novel Mobile-Attention design with a head-competition mechanism empowered by information flow, which prevents overemphasis on less important subspaces upon trivial heads while preserving essential subspaces to ensure Transformer's capability. It enables linear-time complexity on mobile devices by supporting a small per-head dimension $d$ for mobile efficiency. By replacing the standard attention of ViTs with Mobile-Attention, our optimized ViTs achieved enhanced model capacity and competitive performance in a range of computer vision tasks. Specifically, we have achieved remarkable reductions in latency on the iPhone 12. Code is available at https://github.com/thuml/MobileAttention.

Probabilistic Methods · Variational Inference

Kaiwen Wu, Jacob Gardner

Stochastic natural gradient variational inference (NGVI) is a popular posterior inference method with applications in various probabilistic models. Despite its wide usage, little is known about the non-asymptotic convergence rate in the *stochastic* setting. We aim to lessen this gap and provide a better understanding. For conjugate likelihoods, we prove the first $\mathcal{O}(\frac{1}{T})$ non-asymptotic convergence rate of stochastic NGVI. The complexity is no worse than stochastic gradient descent (a.k.a. black-box variational inference) and the rate likely has better constant dependency that leads to faster convergence in practice. For non-conjugate likelihoods, we show that stochastic NGVI with the canonical parameterization implicitly optimizes a non-convex objective. Thus, a global convergence rate of $\mathcal{O}(\frac{1}{T})$ is unlikely without some significant new understanding of optimizing the ELBO using natural gradients.

Probabilistic Methods · Bayesian Models and Methods

Yasen Wang, Junlin Li, Zuogong Yue, Ye Yuan

As a well-known machine learning algorithm, sparse Bayesian learning (SBL) can find sparse representations in linearly probabilistic models by imposing a sparsity-promoting prior on model coefficients. However, classical SBL algorithms lack the essential theoretical guarantees of global convergence. To address this issue, we propose an iterative Min-Min optimization method to solve the marginal likelihood function (MLF) of SBL based on the concave-convex procedure. The method can optimize the hyperparameters related to both the prior and noise level analytically at each iteration by re-expressing MLF using auxiliary functions. Particularly, we demonstrate that the method globally converges to a local minimum or saddle point of MLF. With rigorous theoretical guarantees, the proposed novel SBL algorithm outperforms classical ones in finding sparse representations on simulation and real-world examples, ranging from sparse signal recovery to system identification and kernel regression.

Optimization · Zero-order and Black-box Optimization

Ruigang Wang, Krishnamurthy Dvijotham, Ian Manchester

This paper presents a new *bi-Lipschitz* invertible neural network, the BiLipNet, which has the ability to smoothly control both its *Lipschitzness* (output sensitivity to input perturbations) and *inverse Lipschitzness* (input distinguishability from different outputs). The second main contribution is a new scalar-output network, the PLNet, which is a composition of a BiLipNet and a quadratic potential. We show that PLNet satisfies the Polyak-Łojasiewicz condition and can be applied to learn non-convex surrogate losses with a unique and efficiently-computable global minimum. The central technical element in these networks is a novel invertible residual layer with certified strong monotonicity and Lipschitzness, which we compose with orthogonal layers to build the BiLipNet. The certification of these properties is based on incremental quadratic constraints, resulting in much tighter bounds than can be achieved with spectral normalization. Moreover, we formulate the calculation of the inverse of a BiLipNet -- and hence the minimum of a PLNet -- as a series of three-operator splitting problems, for which fast algorithms can be applied.

Theory · Online Learning and Bandits

Taira Tsuchiya, Shinji Ito, Junya Honda

Partial monitoring is a generic framework of online decision-making problems with limited feedback. To make decisions from such limited feedback, it is necessary to find an appropriate distribution for exploration. Recently, a powerful approach for this purpose, exploration by optimization (ExO), was proposed, which achieves optimal bounds in adversarial environments with follow-the-regularized-leader for a wide range of online decision-making problems. However, a naive application of ExO in stochastic environments significantly degrades regret bounds. To resolve this issue in locally observable games, we first establish a new framework and analysis for ExO with a hybrid regularizer. This development allows us to significantly improve existing regret bounds of best-of-both-worlds (BOBW) algorithms, which achieves nearly optimal bounds both in stochastic and adversarial environments. In particular, we derive a stochastic regret bound of $O(\sum_{a \neq a^*} k^2 m^2 \log T / \Delta_a)$, where $k$, $m$, and $T$ are the numbers of actions, observations and rounds, $a^*$ is an optimal action, and $\Delta_a$ is the suboptimality gap for action $a$. This bound is roughly $\Theta(k^2 \log T)$ times smaller than existing BOBW bounds. In addition, for globally observable games, we provide a new BOBW algorithm with the first $O(\log T)$ stochastic bound.

Deep Learning · Generative Models and Autoencoders

Tiago Silva, Luiz Carvalho, Amauri Souza, Samuel Kaski, Diego Mesquita

GFlowNets are a promising alternative to MCMC sampling for discrete compositional random variables. Training GFlowNets requires repeated evaluations of the unnormalized target distribution, or reward function. However, for large-scale posterior sampling, this may be prohibitive since it incurs traversing the data several times. Moreover, if the data are distributed across clients, employing standard GFlowNets leads to intensive client-server communication. To alleviate both these issues, we propose _embarrassingly parallel_ GFlowNet (EP-GFlowNet). EP-GFlowNet is a provably correct divide-and-conquer method to sample from product distributions of the form $R(\cdot) \propto R_1(\cdot) ... R_N(\cdot)$ --- e.g., in parallel or federated Bayes, where each $R_n$ is a local posterior defined on a data partition. First, in parallel, we train a local GFlowNet targeting each $R_n$ and send the resulting models to the server. Then, the server learns a global GFlowNet by enforcing our newly proposed _aggregating balance_ condition, requiring a single communication step. Importantly, EP-GFlowNets can also be applied to multi-objective optimization and model reuse. Our experiments illustrate the effectiveness of EP-GFlowNets on multiple tasks, including parallel Bayesian phylogenetics, multi-objective multiset and sequence generation, and federated Bayesian structure learning.

Optimization · Non-Convex

Zakhar Shumaylov, Jeremy Budd, Subhadip Mukherjee, Carola-Bibiane Schönlieb

Variational regularisation is the primary method for solving inverse problems, and recently there has been considerable work leveraging deeply learned regularisation for enhanced performance. However, few results exist addressing the convergence of such regularisation, particularly within the context of critical points as opposed to global minimisers. In this paper, we present a generalised formulation of convergent regularisation in terms of critical points, and show that this is achieved by a class of weakly convex regularisers. We prove convergence of the primal-dual hybrid gradient method for the associated variational problem, and, given a Kurdyka-Łojasiewicz condition, an $\mathcal{O}(\log{k}/k)$ ergodic convergence rate. Finally, applying this theory to learned regularisation, we prove universal approximation for input weakly convex neural networks (IWCNN), and show empirically that IWCNNs can lead to improved performance of learned adversarial regularisers for computed tomography (CT) reconstruction.

Aleksandr Podkopaev, Darren Xu, Kuang-chih Lee

Conformal prediction is a valuable tool for quantifying predictive uncertainty of machine learning models. However, its applicability relies on the assumption of data exchangeability, a condition which is often not met in real-world scenarios. In this paper, we consider the problem of adaptive conformal inference without any assumptions about the data generating process. Existing approaches for adaptive conformal inference are based on optimizing the pinball loss using variants of online gradient descent. A notable shortcoming of such approaches is in their explicit dependence on and sensitivity to the choice of the learning rates. In this paper, we propose a different approach for adaptive conformal inference that leverages parameter-free online convex optimization techniques. We prove that our method controls long-term miscoverage frequency at a nominal level and demonstrate its convincing empirical performance without any need of performing cumbersome parameter tuning.

Social Aspects · Trustworthy Machine Learning

Hongyi Peng, Han Yu, Xiaoli Tang, Xiaoxiao Li

Federated learning (FL) enables collaborative machine learning across distributed data owners, but data heterogeneity poses a challenge for model calibration. While prior work focused on improving accuracy for non-iid data, calibration remains under-explored. This study reveals existing FL aggregation approaches lead to sub-optimal calibration, and theoretical analysis shows despite constraining variance in clients’ label distributions, global calibration error is still asymptotically lower bounded. To address this, we propose a novel Federated Calibration (FedCal) approach, emphasizing both local and global calibration. It leverages client-specific scalers for local calibration to effectively correct output misalignment without sacrificing prediction accuracy. These scalers are then aggregated via weight averaging to generate a global scaler, minimizing the global calibration error. Extensive experiments demonstrate that FedCal significantly outperforms the best-performing baseline, reducing global calibration error by 47.66% on average.

Optimization · Convex

Konstantinos Oikonomidis, Emanuel Laude, Puya Latafat, Andreas Themelis, Panagiotis Patrinos

We show that adaptive proximal gradient methods for convex problems are not restricted to traditional Lipschitzian assumptions. Our analysis reveals that a class of linesearch-free methods is still convergent under mere local Hölder gradient continuity, covering in particular continuously differentiable semi-algebraic functions. To mitigate the lack of local Lipschitz continuity, popular approaches revolve around $\varepsilon$-oracles and/or linesearch procedures. In contrast, we exploit plain Hölder inequalities not entailing any approximation, all while retaining the linesearch-free nature of adaptive schemes. Furthermore, we prove full sequence convergence without prior knowledge of local Hölder constants nor of the order of Hölder continuity. Numerical experiments make comparisons with baseline methods on diverse tasks from machine learning covering both the locally and the globally Hölder setting.

Reinforcement Learning · Policy Search

Alessandro Montenegro, Marco Mussi, Alberto Maria Metelli, Matteo Papini

Policy gradient (PG) methods are successful approaches to deal with continuous reinforcement learning (RL) problems. They learn stochastic parametric (hyper)policies by either exploring in the space of actions or in the space of parameters. Stochastic controllers, however, are often undesirable from a practical perspective because of their lack of robustness, safety, and traceability. In common practice, stochastic (hyper)policies are learned only to deploy their deterministic version. In this paper, we make a step towards the theoretical understanding of this practice. After introducing a novel framework for modeling this scenario, we study the global convergence to the best deterministic policy, under (weak) gradient domination assumptions. Then, we illustrate how to tune the exploration level used for learning to optimize the trade-off between the sample complexity and the performance of the deployed deterministic policy. Finally, we quantitatively compare action-based and parameter-based exploration, giving a formal guise to intuitive results.

Optimization · Discrete and Combinatorial Optimization

Piyushi Manupriya, Pratik Kumar Jawanpuria, Karthik Gurumoorthy, Sakethanath Jagarlapudi, Bamdev Mishra

Unbalanced optimal transport (UOT) has recently gained much attention due to its flexible framework for handling un-normalized measures and its robustness properties. In this work, we explore learning (structured) sparse transport plans in the UOT setting, i.e., transport plans have an upper bound on the number of non-sparse entries in each column (structured sparse pattern) or in the whole plan (general sparse pattern). We propose novel sparsity-constrained UOT formulations building on the recently explored maximum mean discrepancy based UOT. We show that the proposed optimization problem is equivalent to the maximization of a weakly submodular function over a uniform matroid or a partition matroid. We develop efficient gradient-based discrete greedy algorithms and provide the corresponding theoretical guarantees. Empirically, we observe that our proposed greedy algorithms select a diverse support set and we illustrate the efficacy of the proposed approach in various applications.

Applications · Robotics

Yunhao Luo, Chen Sun, Josh Tenenbaum, Yilun Du

Effective motion planning in high dimensional spaces is a long-standing open problem in robotics. One class of traditional motion planning algorithms corresponds to potential-based motion planning. An advantage of potential based motion planning is composability -- different motion constraints can easily combined by adding corresponding potentials. However, constructing motion paths from potentials requires solving a global optimization across configuration space potential landscape, which is often prone to local minima. We propose a new approach towards learning potential based motion planning, where we train a neural network to capture and learn an easily optimizable potentials over motion planning trajectories. We illustrate the effectiveness of such approach, significantly outperforming both classical and recent learned motion planning approaches and avoiding issues with local minima. We further illustrate its inherent composability, enabling us to generalize to a multitude of different motion constraints. Project website at https://energy-based-model.github.io/potential-motion-plan.

Optimization · Non-Convex

Huikang Liu, Peng Wang, Longxiu Huang, Qing Qu, Laura Balzano

We study the problem of symmetric positive semi-definite low-rank matrix completion (MC) with deterministic entry-dependent sampling. In particular, we consider rectified linear unit (ReLU) sampling, where only positive entries are observed, as well as a generalization to threshold-based sampling. We first empirically demonstrate that the landscape of this MC problem is not globally benign: Gradient descent (GD) with random initialization will generally converge to stationary points that are not globally optimal. Nevertheless, we prove that when the matrix factor with a small rank satisfies mild assumptions, the nonconvex objective function is geodesically strongly convex on the quotient manifold in a neighborhood of a planted low-rank matrix. Moreover, we show that our assumptions are satisfied by a matrix factor with i.i.d. Gaussian entries. Finally, we develop a tailor-designed initialization for GD to solve our studied formulation, which empirically always achieves convergence to the global minima. We also conduct extensive experiments and compare MC methods, investigating convergence and completion performance with respect to initialization, noise level, dimension, and rank.

Optimization · Large Scale, Parallel and Distributed

Renpu Liu, Cong Shen, Jing Yang

Federated representation learning (FRL) is a popular personalized federated learning (FL) framework where clients work together to train a common representation while retaining their personalized heads. Existing studies, however, largely focus on the over-parameterized regime. In this paper, we make the initial efforts to investigate FRL in the under-parameterized regime, where the FL model is insufficient to express the variations in all ground-truth models. We propose a novel FRL algorithm FLUTE, and theoretically characterize its sample complexity and convergence rate for linear models in the under-parameterized regime. To the best of our knowledge, this is the first FRL algorithm with provable performance guarantees in this regime. FLUTE features a data-independent random initialization and a carefully designed objective function that aids the distillation of subspace spanned by the global optimal representation from the misaligned local representations. On the technical side, we bridge low-rank matrix approximation techniques with the FL analysis, which may be of broad interest. We also extend FLUTE beyond linear representations. Experimental results demonstrate that FLUTE outperforms state-of-the-art FRL solutions in both synthetic and real-world tasks.