Large-scale machine learning problems make the cost of hyperparameter tuning ever more prohibitive. This creates a need for algorithms that can tune themselves on-the-fly. We formalize the notion of *``tuning-free''* algorithms that can match the performance of optimally-tuned optimization algorithms up to polylogarithmic factors given only loose hints on the relevant problem parameters. We consider in particular algorithms that can match optimally-tuned Stochastic Gradient Descent (SGD). When the domain of optimization is bounded, we show tuning-free matching of SGD is possible and achieved by several existing algorithms. We prove that for the task of minimizing a convex and smooth or Lipschitz function over an unbounded domain, tuning-free optimization is impossible. We discuss conditions under which tuning-free optimization is possible even over unbounded domains. In particular, we show that the recently proposed DoG and DoWG algorithms are tuning-free when the noise distribution is sufficiently well-behaved. For the task of finding a stationary point of a smooth and potentially nonconvex function, we give a variant of SGD that matches the best-known high-probability convergence rate for tuned SGD at only an additional polylogarithmic cost. However, we also give an impossibility result that shows no algorithm can hope to match the optimal expected convergence rate for tuned SGD with high probability.
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Deep Learning
In-context learning, i.e., learning from context examples, is an impressive ability of Transformer. Training Transformers to possess this in-context learning skill is computationally intensive due to the occurrence of *learning plateaus*, which are periods within the training process where there is minimal or no enhancement in the model's in-context learning capability. To study the mechanism behind the learning plateaus, we conceptually separate a component within the model's internal representation that is exclusively affected by the model's weights. We call this the “weights component”, and the remainder is identified as the “context component”. By conducting meticulous and controlled experiments on synthetic tasks, we note that the persistence of learning plateaus correlates with compromised functionality of the weights component. Recognizing the impaired performance of the weights component as a fundamental behavior that drives learning plateaus, we have developed three strategies to expedite the learning of Transformers. The effectiveness of these strategies is further confirmed in natural language processing tasks. In conclusion, our research demonstrates the feasibility of cultivating a powerful in-context learning ability within AI systems in an eco-friendly manner.
Theory · Learning Theory
Neural tangent kernels (NTKs) provide a theoretical regime to analyze the learning and generalization behavior of over-parametrized neural networks. For a supervised learning task, the association between the eigenvectors of the NTK and given data (a concept referred to as alignment in this paper) can govern the rate of convergence of gradient descent, as well as generalization to unseen data. Building upon this concept and leveraging the structure of NTKs for graph neural networks (GNNs), we theoretically investigate NTKs and alignment, where our analysis reveals that optimizing the alignment translates to optimizing the graph representation or the graph shift operator (GSO) in a GNN. Our results further establish theoretical guarantees on the optimality of the alignment for a two-layer GNN and these guarantees are characterized by the graph shift operator being a function of the cross-covariance between the input and the output data. The theoretical insights drawn from the analysis of NTKs are validated by our experiments focused on a multi-variate time series prediction task for a publicly available dataset. Specifically, they demonstrate that GNN-based learning models that operate on the cross-covariance matrix indeed outperform those that operate on the covariance matrix estimated from only the input data.
Social Aspects · Fairness, Equity, Justice and Safety
In many predictive contexts (e.g., credit lending), true outcomes are only observed for samples that were positively classified in the past. These past observations, in turn, form training datasets for classifiers that make future predictions. However, such training datasets lack information about the outcomes of samples that were (incorrectly) negatively classified in the past and can lead to erroneous classifiers. We present an approach that trains a classifier using available data and comes with a family of exploration strategies to collect outcome data about subpopulations that otherwise would have been ignored. For any exploration strategy, the approach comes with guarantees that (1) all sub-populations are explored, (2) the fraction of false positives is bounded, and (3) the trained classifier converges to a "desired" classifier. The right exploration strategy is context-dependent; it can be chosen to improve learning guarantees and encode context-specific group fairness properties. Evaluation on real-world datasets shows that this approach consistently boosts the quality of collected outcome data and improves the fraction of true positives for all groups, with only a small reduction in predictive utility.
A Universal Transfer Theorem for Convex Optimization Algorithms Using Inexact First-order Oracles
PDF ↗Optimization · Convex
Given *any* algorithm for convex optimization that uses exact first-order information (i.e., function values and subgradients), we show how to use such an algorithm to solve the problem with access to *inexact* first-order information. This is done in a ``black-box'' manner without knowledge of the internal workings of the algorithm. This complements previous work that considers the performance of specific algorithms like (accelerated) gradient descent with inexact information. In particular, our results apply to a wider range of algorithms beyond variants of gradient descent, e.g., projection-free methods, cutting-plane methods, or any other first-order methods formulated in the future. Further, they also apply to algorithms that handle structured nonconvexities like mixed-integer decision variables.
Deep Learning · Graph Neural Networks
Current directed graph embedding methods build upon undirected techniques but often inadequately capture directed edge information, leading to challenges such as: (1) Suboptimal representations for nodes with low in/out-degrees, due to the insufficient neighbor interactions; (2) Limited inductive ability for representing new nodes post-training; (3) Narrow generalizability, as training is overly coupled with specific tasks. In response, we propose DUPLEX, an inductive framework for complex embeddings of directed graphs. It (1) leverages Hermitian adjacency matrix decomposition for comprehensive neighbor integration, (2) employs a dual GAT encoder for directional neighbor modeling, and (3) features two parameter-free decoders to decouple training from particular tasks. DUPLEX outperforms state-of-the-art models, especially for nodes with sparse connectivity, and demonstrates robust inductive capability and adaptability across various tasks. The code will be available upon publication.
Temporal difference (TD) learning algorithms with neural network function parameterization have well-established empirical success in many practical large-scale reinforcement learning tasks. However, theoretical understanding of these algorithms remains challenging due to the nonlinearity of the action-value approximation. In this paper, we develop an improved non-asymptotic analysis of the neural TD method with a general $L$-layer neural network. New proof techniques are developed and an improved new $\tilde{\mathcal{O}}(\epsilon^{-1})$ sample complexity is derived. To our best knowledge, this is the first finite-time analysis of neural TD that achieves an $\tilde{\mathcal{O}}(\epsilon^{-1})$ complexity under the Markovian sampling, as opposed to the best known $\tilde{\mathcal{O}}(\epsilon^{-2})$ complexity in the existing literature.
Probabilistic Methods · Gaussian Processes
Bayesian few-shot classification has been a focal point in the field of few-shot learning. This paper seamlessly integrates mirror descent-based variational inference into Gaussian process-based few-shot classification, addressing the challenge of non-conjugate inference. By leveraging non-Euclidean geometry, mirror descent achieves accelerated convergence by providing the steepest descent direction along the corresponding manifold. It also exhibits the parameterization invariance property concerning the variational distribution. Experimental results demonstrate competitive classification accuracy, improved uncertainty quantification, and faster convergence compared to baseline models. Additionally, we investigate the impact of hyperparameters and components. Code is publicly available at https://github.com/keanson/MD-BSFC.
Applications
Machine Learning (ML) has emerged as a promising alternative to numerical methods for physics-based simulation due to its flexibility and efficiency. Flood modeling is a key case study for ML-based simulation due to its relevance as a tool for supporting preventive and emergency measures to mitigate flood risks. However, the complexity of the topography or domain (ground elevation) and the sparsity of the time-evolving precipitations (external forcing) can be challenging for most existing ML approaches for simulating flooding processes in space and time. Another critical challenge is incorporating physics domain knowledge (hydraulics) into these data-driven models. This paper addresses these challenges by introducing a hydraulics-informed graph neural network for flood simulation. Given a (geographical) region and precipitation data, our model predicts water depths in an auto-regressive fashion. We propose a message-passing framework inspired by the conservation of momentum and mass expressed in the shallow-water equations, which describe the physical process of a flooding event. Empirical results on a dataset covering 9 regions and 7 historical precipitation events demonstrate that our model outperforms the best baseline, and can capture the propagation of water flow more effectively, especially at the very early stage of the flooding event when the amount of water in the domain is scarce. Differently from some of the most recent methods for ML-based simulation, which tend to work well only when the domain is a smooth surface (e.g., flat terrain), we show that our solution achieves accurate results for real ground elevation data.
Miscellaneous Aspects of Machine Learning · Causality
This study designs an adaptive experiment for efficiently estimating *average treatment effects* (ATEs). In each round of our adaptive experiment, an experimenter sequentially samples an experimental unit, assigns a treatment, and observes the corresponding outcome immediately. At the end of the experiment, the experimenter estimates an ATE using the gathered samples. The objective is to estimate the ATE with a smaller asymptotic variance. Existing studies have designed experiments that adaptively optimize the propensity score (treatment-assignment probability). As a generalization of such an approach, we propose optimizing the covariate density as well as the propensity score. First, we derive the efficient covariate density and propensity score that minimize the semiparametric efficiency bound and find that optimizing both covariate density and propensity score minimizes the semiparametric efficiency bound more effectively than optimizing only the propensity score. Next, we design an adaptive experiment using the efficient covariate density and propensity score sequentially estimated during the experiment. Lastly, we propose an ATE estimator whose asymptotic variance aligns with the minimized semiparametric efficiency bound.
Progressive Inference: Explaining Decoder-Only Sequence Classification Models Using Intermediate Predictions
PDF ↗Social Aspects · Trustworthy Machine Learning
This paper proposes Progressive inference--a framework to explain the predictions of decoder-only transformer models trained to perform sequence classification tasks. Our work is based on the insight that the classification head of a decoder-only model can be used to make intermediate predictions by evaluating them at different points in the input sequence. Due to the masked attention mechanism used in decoder-only models, these intermediate predictions only depend on the tokens seen before the inference point, allowing us to obtain the model's prediction on a masked input sub-sequence, with negligible computational overheads. We develop two methods to provide sub-sequence level attributions using this core insight. First, we propose Single Pass-Progressive Inference (SP-PI) to compute attributions by simply taking the difference between intermediate predictions. Second, we exploit a connection with Kernel SHAP to develop Multi Pass-Progressive Inference (MP-PI); this uses intermediate predictions from multiple masked versions of the input to compute higher-quality attributions that approximate SHAP values. We perform studies on several text classification datasets to demonstrate that our proposal provides better explanations compared to prior work, both in the single-pass and multi-pass settings.
Probabilistic Methods · Structure Learning
Representing uncertainty in causal discovery is a crucial component for experimental design, and more broadly, for safe and reliable causal decision making. Bayesian Causal Discovery (BCD) offers a principled approach to encapsulating this uncertainty. Unlike non-Bayesian causal discovery, which relies on a single estimated causal graph and model parameters for assessment, evaluating BCD presents challenges due to the nature of its inferred quantity – the posterior distribution. As a result, the research community has proposed various metrics to assess the quality of the approximate posterior. However, there is, to date, no consensus on the most suitable metric(s) for evaluation. In this work, we reexamine this question by dissecting various metrics and understanding their limitations. Through extensive empirical evaluation, we find that many existing metrics fail to exhibit a strong correlation with the quality of approximation to the true posterior, especially in scenarios with low sample sizes where BCD is most desirable. We highlight the suitability (or lack thereof) of these metrics under two distinct factors: the identifiability of the underlying causal model and the quantity of available data. Both factors affect the entropy of the true posterior, indicating that the current metrics are less fitting in settings of higher entropy. Our findings underline the importance of a more nuanced evaluation of new methods by taking into account the nature of the true posterior, as well as guide and motivate the development of new evaluation procedures for this challenge.
Deep Learning · Graph Neural Networks
$E(n)$-Equivariant Graph Neural Networks (EGNNs) are among the most widely used and successful models for representation learning on geometric graphs (e.g., 3D molecules). However, while the expressivity of EGNNs has been explored in terms of geometric variants of the Weisfeiler-Leman isomorphism test, characterizing their generalization capability remains open. In this work, we establish the first generalization bound for EGNNs. Our bound depicts a dependence on the weighted sum of logarithms of the spectral norms of the weight matrices (EGNN parameters). In addition, our main result reveals interesting novel insights: $i$) the spectral norms of the initial layers may impact generalization more than the final ones; $ii$) $\varepsilon$-normalization is beneficial to generalization --- confirming prior empirical evidence. We leverage these insights to introduce a spectral norm regularizer tailored to EGNNs. Experiments on real-world datasets substantiate our analysis, demonstrating a high correlation between theoretical and empirical generalization gaps and the effectiveness of the proposed regularization scheme.
Miscellaneous Aspects of Machine Learning · Kernel methods
While axis-aligned rules are known to induce an important inductive bias in machine learning models such as typical hard decision tree ensembles, theoretical understanding of the learning behavior is largely unrevealed due to the discrete nature of rules. To address this issue, we impose the axis-aligned constraint on soft trees, which relax the splitting process of decision trees and are trained using a gradient method, and present their Neural Tangent Kernel (NTK), which enables us to analytically describe the training behavior. We study two cases: imposing the axis-aligned constraint throughout the entire training process, and only at the initial state. Moreover, we extend the NTK framework to handle various tree architectures simultaneously, and prove that any axis-aligned non-oblivious tree ensemble can be transformed into axis-aligned oblivious tree ensembles with the same NTK. One can search for suitable tree architecture via Multiple Kernel Learning (MKL), and our numerical experiments show a variety of suitable features depending on the type of constraints. Our NTK analysis highlights both the theoretical and practical impacts of the axis-aligned constraint in tree ensemble learning.
Conformal prediction has shown impressive capacity in constructing statistically rigorous prediction sets for machine learning models with exchangeable data samples. The siloed datasets, coupled with the escalating privacy concerns related to local data sharing, have inspired recent innovations extending conformal prediction into federated environments with distributed data samples. However, this framework for distributed uncertainty quantification is susceptible to Byzantine failures. A minor subset of malicious clients can significantly compromise the practicality of coverage guarantees. To address this vulnerability, we introduce a novel framework Rob-FCP, which executes robust federated conformal prediction, effectively countering malicious clients capable of reporting arbitrary statistics with the conformal calibration process. We theoretically provide the conformal coverage bound of Rob-FCP in the Byzantine setting and show that the coverage of Rob-FCP is asymptotically close to the desired coverage level. We also propose a malicious client number estimator to tackle a more challenging setting where the number of malicious clients is unknown to the defender and theoretically shows its effectiveness. We empirically demonstrate the robustness of Rob-FCP against diverse proportions of malicious clients under a variety of Byzantine attacks on five standard benchmark and real-world healthcare datasets.
Reinforcement Learning · Batch/Offline
Decision Transformer-based decision-making agents have shown the ability to generalize across multiple tasks. However, their performance relies on massive data and computation. We argue that this inefficiency stems from the forgetting phenomenon, in which a model memorizes its behaviors in parameters throughout training. As a result, training on a new task may deteriorate the model's performance on previous tasks. In contrast to LLMs' implicit memory mechanism, the human brain utilizes distributed memory storage, which helps manage and organize multiple skills efficiently, mitigating the forgetting phenomenon. Inspired by this, we propose a working memory module to store, blend, and retrieve information for different downstream tasks. Evaluation results show that the proposed method improves training efficiency and generalization in Atari games and Meta-World object manipulation tasks. Moreover, we demonstrate that memory fine-tuning further enhances the adaptability of the proposed architecture.
Despite the impressive capabilities of large language models (LLMs) across diverse applications, they still suffer from trustworthiness issues, such as hallucinations and misalignments. Retrieval-augmented language models (RAG) have been proposed to enhance the credibility of generations by grounding external knowledge, but the theoretical understandings of their generation risks remains unexplored. In this paper, we answer: 1) whether RAG can indeed lead to low generation risks, 2) how to provide provable guarantees on the generation risks of RAG and vanilla LLMs, and 3) what sufficient conditions enable RAG models to reduce generation risks. We propose C-RAG, the first framework to certify generation risks for RAG models. Specifically, we provide conformal risk analysis for RAG models and certify an upper confidence bound of generation risks, which we refer to as conformal generation risk. We also provide theoretical guarantees on conformal generation risks for general bounded risk functions under test distribution shifts. We prove that RAG achieves a lower conformal generation risk than that of a single LLM when the quality of the retrieval model and transformer is non-trivial. Our intensive empirical results demonstrate the soundness and tightness of our conformal generation risk guarantees across four widely-used NLP datasets on four state-of-the-art retrieval models.
Deep Learning · Robustness
We introduce LaGTran, a novel framework that utilizes text supervision to guide robust transfer of discriminative knowledge from labeled source to unlabeled target data with domain gaps. While unsupervised adaptation methods have been established to address this problem, they show limitations in handling challenging domain shifts due to their exclusive operation within the pixel-space. Motivated by our observation that semantically richer text modality has more favorable transfer properties, we devise a transfer mechanism to use a source-trained text-classifier to generate predictions on the target text descriptions, and utilize these predictions as supervision for the corresponding images. Our approach driven by language guidance is surprisingly easy and simple, yet significantly outperforms all prior approaches on challenging datasets like GeoNet and DomainNet, validating its extreme effectiveness. To further extend the scope of our study beyond images, we introduce a new benchmark called Ego2Exo to study ego-exo transfer in videos and find that our language-aided approach LaGTran yields significant gains in this highly challenging and non-trivial transfer setting. Code, models, and proposed datasets are publicly available at https://tarun005.github.io/lagtran/.
Theory · Learning Theory
We provide an efficient replicable algorithm for the problem of learning large-margin halfspaces. Our results improve upon the algorithms provided by Impagliazzo, Lei, Pitassi, and Sorrell (STOC, 2022). We design the first dimension-independent replicable algorithm for this task which runs in polynomial time, is proper, and has strictly improved sample complexity compared to the one achieved by Impagliazzo et al. (STOC, 2022) with respect to all the relevant parameters. Moreover, our algorithm has sample complexity that is optimal with respect to the accuracy parameter $\epsilon$. Departing from the requirement of polynomial time algorithms, using the DP-to-Replicability reduction of Bun et al. (STOC 2023), we show how to obtain a replicable algorithm for large-margin halfspaces with improved sample complexity with respect to the margin parameter $\tau$, but running time doubly exponential in $1/\tau^2$ and worse sample complexity dependence on $\epsilon$ than our previous algorithm. We then design an improved algorithm with better sample complexity than both of our previous algorithms and running time exponential in $1/\tau^{2}.$
Social Aspects · Privacy-preserving Statistics and Machine Learning
In differentially private (DP) machine learning, the privacy guarantees of DP mechanisms are often reported and compared on the basis of a single $(\varepsilon, \delta)$-pair. This practice overlooks that DP guarantees can vary substantially even between mechanisms sharing a given $(\varepsilon, \delta)$, and potentially introduces privacy vulnerabilities which can remain undetected. This motivates the need for robust, rigorous methods for comparing DP guarantees in such cases. Here, we introduce the $\Delta$-divergence between mechanisms which quantifies the worst-case excess privacy vulnerability of choosing one mechanism over another in terms of $(\varepsilon, \delta)$, $f$-DP and in terms of a newly presented Bayesian interpretation. Moreover, as a generalisation of the Blackwell theorem, it is endowed with strong decision-theoretic foundations. Through application examples, we show that our techniques can facilitate informed decision-making and reveal gaps in the current understanding of privacy risks, as current practices in DP-SGD often result in choosing mechanisms with high excess privacy vulnerabilities.