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Deep Learning · Theory

Juno Kim, Tai Nakamaki, Taiji Suzuki

In-context learning (ICL) of large language models has proven to be a surprisingly effective method of learning a new task from only a few demonstrative examples. In this paper, we shed light on the efficacy of ICL from the viewpoint of statistical learning theory. We develop approximation and generalization error analyses for a transformer model composed of a deep neural network and one linear attention layer, pretrained on nonparametric regression tasks sampled from general function spaces including the Besov space and piecewise $\gamma$-smooth class. In particular, we show that sufficiently trained transformers can achieve -- and even improve upon -- the minimax optimal estimation risk in context by encoding the most relevant basis representations during pretraining. Our analysis extends to high-dimensional or sequential data and distinguishes the \emph{pretraining} and \emph{in-context} generalization gaps, establishing upper and lower bounds w.r.t. both the number of tasks and in-context examples. These findings shed light on the effectiveness of few-shot prompting and the roles of task diversity and representation learning for ICL.

Data-centric AI

Ju-Sheng Hong, Junwen Yao, Jonas Mueller, Jane-Ling Wang

Although the transformer architecture has come to dominate other models for text and image data, its application to irregularly-spaced longitudinal data has been limited. We introduce a variant of the transformer that enables it to more smoothly impute such functional data. We augment the vanilla transformer with a simple module we call SAND (self-attention on derivatives), which naturally encourages smoothness by modeling the sub-derivative of the imputed curve. On the theoretical front, we prove the number of hidden nodes required by a network with SAND to achieve an $\epsilon$ prediction error bound for functional imputation. Extensive experiments over various types of functional data demonstrate that transformers with SAND produce better imputations than both their standard counterparts as well as transformers augmented with alternative approaches to encode the inductive bias of smoothness. SAND also outperforms standard statistical methods for functional imputation like kernel smoothing and PACE.

Privacy

David Durfee

We provide a new algorithmic framework for differentially private estimation of general functions that adapts to the hardness of the underlying dataset. We build upon previous work that gives a paradigm for selecting an output through the exponential mechanism based upon closeness of the inverse to the underlying dataset, termed the inverse sensitivity mechanism. Our framework will slightly modify the closeness metric and instead give a simple and efficient application of the sparse vector technique. While the inverse sensitivity mechanism was shown to be instance optimal, it was only with respect to a class of unbiased mechanisms such that the most likely outcome matches the underlying data. We break this assumption in order to more naturally navigate the bias-variance tradeoff, which will also critically allow for extending our method to unbounded data. In consideration of this tradeoff, we provide theoretical guarantees and empirical validation that our technique will be particularly effective when the distances to the underlying dataset are asymmetric. This asymmetry is inherent to a range of important problems including fundamental statistics such as variance, as well as commonly used machine learning performance metrics for both classification and regression tasks. We efficiently instantiate our method in $O(n)$ time for these problems and empirically show that our techniques will give substantially improved differentially private estimations.

Probabilistic Methods

David Perera, Victor Letzelter, Theo Mariotte, Adrien Cortes, Mickael Chen, Slim Essid, Gaël Richard

We introduce Annealed Multiple Choice Learning (aMCL) which combines simulated annealing with MCL. MCL is a learning framework handling ambiguous tasks by predicting a small set of plausible hypotheses. These hypotheses are trained using the Winner-takes-all (WTA) scheme, which promotes the diversity of the predictions. However, this scheme may converge toward an arbitrarily suboptimal local minimum, due to the greedy nature of WTA. We overcome this limitation using annealing, which enhances the exploration of the hypothesis space during training. We leverage insights from statistical physics and information theory to provide a detailed description of the model training trajectory. Additionally, we validate our algorithm by extensive experiments on synthetic datasets, on the standard UCI benchmark, and on speech separation.

Theory · Statistics

Andrew Davison, S. Carlyle Morgan, Owen G. Ward

Embedding the nodes of a large network into an Euclidean space is a common objective in modernmachine learning, with a variety of tools available. These embeddings can then be used as features fortasks such as community detection/node clustering or link prediction, where they achieve state of the artperformance. With the exception of spectral clustering methods, there is little theoretical understandingfor commonly used approaches to learning embeddings. In this work we examine the theoreticalproperties of the embeddings learned by node2vec. Our main result shows that the use of k-meansclustering on the embedding vectors produced by node2vec gives weakly consistent community recoveryfor the nodes in (degree corrected) stochastic block models. We also discuss the use of these embeddingsfor node and link prediction tasks. We demonstrate this result empirically for bothreal and simulated networks, and examine how this relatesto other embedding tools for network data.

Neuroscience, Cognitive Science

Shihan Ma, Bo Hu, Tianyu Jia, Alexander Clarke, Blanka Zicher, Arnault Caillet, Dario Farina, Jose C Principe

The cortico-spinal neural pathway is fundamental for motor control and movement execution, and in humans it is typically studied using concurrent electroencephalography (EEG) and electromyography (EMG) recordings. However, current approaches for capturing high-level and contextual connectivity between these recordings have important limitations. Here, we present a novel application of statistical dependence estimators based on orthonormal decomposition of density ratios to model the relationship between cortical and muscle oscillations. Our method extends from traditional scalar-valued measures by learning eigenvalues, eigenfunctions, and projection spaces of density ratios from realizations of the signal, addressing the interpretability, scalability, and local temporal dependence of cortico-muscular connectivity. We experimentally demonstrate that eigenfunctions learned from cortico-muscular connectivity can accurately classify movements and subjects. Moreover, they reveal channel and temporal dependencies that confirm the activation of specific EEG channels during movement.

Probabilistic Methods · Monte Carlo and Sampling Methods

Luiz Chamon, Mohammad Reza Karimi Jaghargh, Anna Korba

This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem finds applications in, e.g., Bayesian inference, where it can constrain moments to evaluate counterfactual scenarios or enforce desiderata such as prediction fairness. Methods developed to handle support constraints, such as those based on mirror maps, barriers, and penalties, are not suited for this task. This work therefore relies on gradient descent-ascent dynamics in Wasserstein space to put forward a discrete-time primal-dual Langevin Monte Carlo algorithm (PD-LMC) that simultaneously constrains the target distribution and samples from it. We analyze the convergence of PD-LMC under standard assumptions on the target distribution and constraints, namely (strong) convexity and log-Sobolev inequalities. To do so, we bring classical optimization arguments for saddle-point algorithms to the geometry of Wasserstein space. We illustrate the relevance and effectiveness of PD-LMC in several applications.

Generative Models

Tianshi Wang, Qikai Yang, Ruijie Wang, Dachun Sun, Jinyang Li, Yizhuo Chen, Yigong Hu, Chaoqi Yang, Tomoyoshi Kimura, Denizhan Kara 等

Internet of Things (IoT) sensing models often suffer from overfitting due to data distribution shifts between training dataset and real-world scenarios. To address this, data augmentation techniques have been adopted to enhance model robustness by bolstering the diversity of synthetic samples within a defined vicinity of existing samples. This paper introduces a novel paradigm of data augmentation for IoT sensing signals by adding fine-grained control to generative models. We define a metric space with statistical metrics that capture the essential features of the short-time Fourier transformed (STFT) spectrograms of IoT sensing signals. These metrics serve as strong conditions for a generative model, enabling us to tailor the spectrogram characteristics in the time-frequency domain according to specific application needs. Furthermore, we propose a set of data augmentation techniques within this metric space to create new data samples. Our method is evaluated across various generative models, datasets, and downstream IoT sensing models. The results demonstrate that our approach surpasses the conventional transformation-based data augmentation techniques and prior generative data augmentation models.

Kai Liu, Zhihang Fu, Sheng Jin, Chao Chen, Ze Chen, Rongxin Jiang, Fan Zhou, Yaowu Chen, Jieping Ye

Detecting and rejecting unknown out-of-distribution (OOD) samples is critical for deployed neural networks to void unreliable predictions. In real-world scenarios, however, the efficacy of existing OOD detection methods is often impeded by the inherent imbalance of in-distribution (ID) data, which causes significant performance decline. Through statistical observations, we have identified two common challenges faced by different OOD detectors: misidentifying tail class ID samples as OOD, while erroneously predicting OOD samples as head class from ID. To explain this phenomenon, we introduce a generalized statistical framework, termed ImOOD, to formulate the OOD detection problem on imbalanced data distribution. Consequently, the theoretical analysis reveals that there exists a class-aware bias item between balanced and imbalanced OOD detection, which contributes to the performance gap. Building upon this finding, we present a unified training-time regularization technique to mitigate the bias and boost imbalanced OOD detectors across architecture designs. Our theoretically grounded method translates into consistent improvements on the representative CIFAR10-LT, CIFAR100-LT, and ImageNet-LT benchmarks against several state-of-the-art OOD detection ap- proaches. Code is available at https://github.com/alibaba/imood.

Time Series

Qinghua Liu, John Paparrizos

Time-series anomaly detection is a fundamental task across scientific fields and industries. However, the field has long faced the ``elephant in the room:'' critical issues including flawed datasets, biased evaluation measures, and inconsistent benchmarking practices that have remained largely ignored and unaddressed. We introduce the TSB-AD to systematically tackle these issues in the following three aspects: (i) Dataset Integrity: with 1070 high-quality time series from a diverse collection of 40 datasets (doubling the size of the largest collection and four times the number of existing curated datasets), we provide the first large-scale, heterogeneous, meticulously curated dataset that combines the effort of human perception and model interpretation; (ii) Measure Reliability: by revealing issues and biases in evaluation measures, we identify the most reliable and accurate measure, namely, VUS-PR for anomaly detection in time series to address concerns from the community; and (iii) Comprehensive Benchmarking: with a broad spectrum of 40 detection algorithms, from statistical methods to the latest foundation models, we perform a comprehensive evaluation that includes a thorough hyperparameter tuning and a unified setup for a fair and reproducible comparison. Our findings challenge the conventional wisdom regarding the superiority of advanced neural network architectures, revealing that simpler architectures and statistical methods often yield better performance. The promising performance of neural networks on multivariate cases and foundation models on point anomalies highlights the need for further advancements in these methods. We open-source the benchmark at https://github.com/TheDatumOrg/TSB-AD to promote further research.

Interpretability

Harvineet Singh, Fan Xia, Adarsh Subbaswamy, Alexej Gossmann, Jean Feng

Machine learning (ML) algorithms can often differ in performance across domains. Understanding why their performance differs is crucial for determining what types of interventions (e.g., algorithmic or operational) are most effective at closing the performance gaps. Aggregate decompositions express the total performance gap as the gap due to a shift in the feature distribution $p(X)$ plus the gap due to a shift in the outcome's conditional distribution $p(Y|X)$. While this coarse explanation is helpful for guiding root cause analyses, it provides limited details and can only suggest coarse fixes involving all variables in an ML system. Detailed decompositions quantify the importance of each variable to each term in the aggregate decomposition, which can provide a deeper understanding and suggest more targeted interventions. Although parametric methods exist for conducting a full hierarchical decomposition of an algorithm's performance gap at the aggregate and detailed levels, current nonparametric methods only cover parts of the hierarchy; many also require knowledge of the entire causal graph. We introduce a nonparametric hierarchical framework for explaining why the performance of an ML algorithm differs across domains, without requiring causal knowledge. Furthermore, we derive debiased, computationally-efficient estimators and statistical inference procedures to construct confidence intervals for the explanations.

Datasets and Benchmarks

Antonios Alexos, Junze Liu, Shashank Galla, Sean Hayes, Kshitij Bhardwaj, Alexander Schwartz, Monika Biener, Pierre Baldi, Satish Bukkapatnam, Suhas Bhandarkar

In the Inertial Confinement Fusion (ICF) process, roughly a 2mm spherical shell made of high-density carbon is used as a target for laser beams, which compress and heat it to energy levels needed for high fusion yield in nuclear fusion. These shells are polished meticulously to meet the standards for a fusion shot. However, the polishing of these shells involves multiple stages, with each stage taking several hours. To make sure that the polishing process is advancing in the right direction, we are able to measure the shell surface roughness. This measurement, however, is very labor-intensive, time-consuming, and requires a human operator. To help improve the polishing process we have released the first dataset to the public that consists of raw vibration signals with the corresponding polishing surface roughness changes. We show that this dataset can be used with a variety of neural network based methods for prediction of the change of polishing surface roughness, hence eliminating the need for the time-consuming manual process. This is the first dataset of its kind to be released in public and its use will allow the operator to make any necessary changes to the ICF polishing process for optimal results. This dataset contains the raw vibration data of multiple polishing runs with their extracted statistical features and the corresponding surface roughness values. Additionally, to generalize the prediction models to different polishing conditions, we also apply domain adaptation techniques to improve prediction accuracy for conditions unseen by the trained model. The dataset is available in \url{https://junzeliu.github.io/Diamond-Polishing-Dataset/}.

Multimodal Models

Adriel Saporta, Aahlad Manas Puli, Mark Goldstein, Rajesh Ranganath

Contrastive learning methods, such as CLIP, leverage naturally paired data—for example, images and their corresponding text captions—to learn general representations that transfer efficiently to downstream tasks. While such approaches are generally applied to two modalities, domains such as robotics, healthcare, and video need to support many types of data at once. We show that the pairwise application of CLIP fails to capture joint information between modalities, thereby limiting the quality of the learned representations. To address this issue, we present Symile, a simple contrastive learning approach that captures higher-order information between any number of modalities. Symile provides a flexible, architecture-agnostic objective for learning modality-specific representations. To develop Symile's objective, we derive a lower bound on total correlation, and show that Symile representations for any set of modalities form a sufficient statistic for predicting the remaining modalities. Symile outperforms pairwise CLIP, even with modalities missing in the data, on cross-modal classification and retrieval across several experiments including on an original multilingual dataset of 33M image, text and audio samples and a clinical dataset of chest X-rays, electrocardiograms, and laboratory measurements. All datasets and code used in this work are publicly available at https://github.com/rajesh-lab/symile.

Datasets and Benchmarks

Aoran Wang, Tsz Pan Tong, Andrzej Mizera, Jun Pang

Understanding complex dynamical systems begins with identifying their topological structures, which expose the organization of the systems. This requires robust structural inference methods that can deduce structure from observed behavior. However, existing methods are often domain-specific and lack a standardized, objective comparison framework. We address this gap by benchmarking 13 structural inference methods from various disciplines on simulations representing two types of dynamics and 11 interaction graph models, supplemented by a biological experimental dataset to mirror real-world application. We evaluated the methods for accuracy, scalability, robustness, and sensitivity to graph properties. Our findings indicate that deep learning methods excel with multi-dimensional data, while classical statistics and information theory based approaches are notably accurate and robust. Additionally, performance correlates positively with the graph's average shortest path length. This benchmark should aid researchers in selecting suitable methods for their specific needs and stimulate further methodological innovation.

Time Series

Seunghan Lee, Kibok Lee, Taeyoung Park

Advances in diffusion models for generative artificial intelligence have recently propagated to the time series (TS) domain, demonstrating state-of-the-art performance on various tasks. However, prior works on TS diffusion models often borrow the framework of existing works proposed in other domains without considering the characteristics of TS data, leading to suboptimal performance. In this work, wepropose Adaptive Noise schedule for Time series diffusion models (ANT), which automatically predetermines proper noise schedules for given TS datasets based on their statistics representing non-stationarity. Our intuition is that an optimal noise schedule should satisfy the following desiderata: 1) It linearly reduces the non-stationarity of TS data so that all diffusion steps are equally meaningful, 2) the data is corrupted to the random noise at the final step, and 3) the number of steps is sufficiently large. The proposed method is practical for use in that it eliminates the necessity of finding the optimal noise schedule with a small additional cost to compute the statistics for given datasets, which can be done offline before training. We validate the effectiveness of our method across various tasks, including TS forecasting, refinement, and generation, on datasets from diverse domains. Code is available at this repository: https://github.com/seunghan96/ANT.

Deep Learning · Everything Else

Hai Vy Nguyen, Fabrice Gamboa, Reda CHHAIBI, Sixin Zhang, Serge Gratton, Thierry Giaccone

We measure the out-of-domain uncertainty in the prediction of Neural Networks using a statistical notion called "Lens Depth'' (LD) combined with Fermat Distance, which is able to capture precisely the "depth'' of a point with respect to a distribution in feature space, without any distributional assumption. Our method also has no trainable parameter. The method is applied directly in the feature space at test time and does not intervene in training process. As such, it does not impact the performance of the original model. The proposed method gives excellent qualitative results on toy datasets and can give competitive or better uncertainty estimation on standard deep learning datasets compared to strong baseline methods.

Language · Knowledge

Xiao Zhang, Miao Li, Ji Wu

Pretrained language models can encode a large amount of knowledge and utilize it for various reasoning tasks, yet they can still struggle to learn novel factual knowledge effectively from finetuning on limited textual demonstrations. In this work, we show that the reason for this deficiency is that language models are biased to learn word co-occurrence statistics instead of true factual associations. We identify the differences between two forms of knowledge representation in language models: knowledge in the form of co-occurrence statistics is encoded in the middle layers of the transformer model and does not generalize well to reasoning scenarios beyond simple question answering, while true factual associations are encoded in the lower layers and can be freely utilized in various reasoning tasks. Based on these observations, we propose two strategies to improve the learning of factual associations in language models. We show that training on text with implicit rather than explicit factual associations can force the model to learn factual associations instead of co-occurrence statistics, significantly improving the generalization of newly learned knowledge. We also propose a simple training method to actively forget the learned co-occurrence statistics, which unblocks and enhances the learning of factual associations when training on plain narrative text. On both synthetic and real-world corpora, the two proposed strategies improve the generalization of the knowledge learned during finetuning to reasoning scenarios such as indirect and multi-hop question answering.

Optimization · Non-Convex

Zih-Syuan Huang, Ching-pei Lee

We propose a Regularized Adaptive Momentum Dual Averaging (RAMDA) algorithm for training structured neural networks. Similar to existing regularized adaptive methods, the subproblem for computing the update direction of RAMDA involves a nonsmooth regularizer and a diagonal preconditioner, and therefore does not possess a closed-form solution in general. We thus also carefully devise an implementable inexactness condition that retains convergence guarantees similar to the exact versions, and propose a companion efficient solver for the subproblems of both RAMDA and existing methods to make them practically feasible. We leverage the theory of manifold identification in variational analysis to show that, even in the presence of such inexactness, the iterates of RAMDA attain the ideal structure induced by the regularizer at the stationary point of asymptotic convergence. This structure is locally optimal near the point of convergence, so RAMDA is guaranteed to obtain the best structure possible among all methods converging to the same point, making it the first regularized adaptive method outputting models that possess outstanding predictive performance while being (locally) optimally structured. Extensive numerical experiments in large-scale modern computer vision, language modeling, and speech tasks show that the proposed RAMDA is efficient and consistently outperforms state of the art for training structured neural network. Implementation of our algorithm is available at https://www.github.com/ismoptgroup/RAMDA.

Statistical Methods

Xinyi Li, Shan Yu, Yueying Wang, Guannan Wang, Li Wang, Ming-Jun Lai

In recent years, there has been an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient smoothing tool based on multivariate splines over the triangulation to extract the underlying signal and build up a 3D solid model from the point cloud. The proposed method can denoise or deblur the point cloud effectively, provide a multi-resolution reconstruction of the actual signal, and handle sparse and irregularly distributed point clouds to recover the underlying trajectory. In addition, our method provides a natural way of numerosity data reduction. We establish the theoretical guarantees of the proposed method, including the convergence rate and asymptotic normality of the estimator, and show that the convergence rate achieves optimal nonparametric convergence. We also introduce a bootstrap method to quantify the uncertainty of the estimators. Through extensive simulation studies and a real data example, we demonstrate the superiority of the proposed method over traditional smoothing methods in terms of estimation accuracy and efficiency of data reduction.

Theory · Statistics

Fan Chen, Dylan J Foster, Yanjun Han, Jian Qian, Alexander Rakhlin, Yunbei Xu

We develop a unifying framework for information-theoretic lower bound in statistical estimation and interactive decision making. Classical lower bound techniques---such as Fano's method, Le Cam's method, and Assouad's lemma---are central to the study of minimax risk in statistical estimation, yet are insufficient to provide tight lower bounds for \emph{interactive decision making} algorithms that collect data interactively (e.g., algorithms for bandits and reinforcement learning). Recent work of Foster et al. provides minimax lower bounds for interactive decision making using seemingly different analysis techniques from the classical methods. These results---which are proven using a complexity measure known as the \emph{Decision-Estimation Coefficient} (DEC)---capture difficulties unique to interactive learning, yet do not recover the tightest known lower bounds for passive estimation. We propose a unified view of these distinct methodologies through a new lower bound approach called \emph{interactive Fano method}. As an application, we introduce a novel complexity measure, the \emph{Fractional Covering Number}, which facilitates the new lower bounds for interactive decision making that extend the DEC methodology by incorporating the complexity of estimation. Using the fractional covering number, we (i) provide a unified characterization of learnability for \emph{any} stochastic bandit problem, (ii) close the remaining gap between the upper and lower bounds in Foster et al. (up to polynomial factors) for any interactive decision making problem in which the underlying model class is convex.