Enmao Diao, Ganghua Wang, Jiawei Zhan et al. · pku
In recent years, deep network pruning has attracted significant attention in order to enable the rapid deployment of AI into small devices with computation and memory constraints. Pruning is often achieved by dropping redundant weights, neurons, or layers of a deep network while attempting to retain a comparable test performance. Many deep pruning algorithms have been proposed with impressive empirical success. However, existing approaches lack a quantifiable measure to estimate the compressibility of a sub-network during each pruning iteration and thus may under-prune or over-prune the model. In this work, we propose PQ Index (PQI) to measure the potential compressibility of deep neural networks and use this to develop a Sparsity-informed Adaptive Pruning (SAP) algorithm. Our extensive experiments corroborate the hypothesis that for a generic pruning procedure, PQI decreases first when a large model is being effectively regularized and then increases when its compressibility reaches a limit that appears to correspond to the beginning of underfitting. Subsequently, PQI decreases again when the model collapse and significant deterioration in the performance of the model start to occur. Additionally, our experiments demonstrate that the proposed adaptive pruning algorithm with proper choice of hyper-parameters is superior to the iterative pruning algorithms such as the lottery ticket-based pruning methods, in terms of both compression efficiency and robustness.
Sindri Magnusson, Chinwendu Enyioha, Kathryn Heal et al.
Typical coordination schemes for future power grids require two-way communications. Since the number of end power-consuming devices is large, the bandwidth requirements for such two-way communication schemes may be prohibitive. Motivated by this observation, we study distributed coordination schemes that require only one-way limited communications. In particular, we investigate how dual descent distributed optimization algorithm can be employed in power networks using one-way communication. In this iterative algorithm, system coordinators broadcast coordinating (or pricing) signals to the users/devices who update power consumption based on the received signal. Then system coordinators update the coordinating signals based on the physical measurement of the aggregate power usage. We provide conditions to guarantee the feasibility of the aggregated power usage at each iteration so as to avoid blackout. Furthermore, we prove the convergence of algorithms under these conditions, and establish its rate of convergence. We illustrate the performance of our algorithms using numerical simulations. These results show that one-way limited communication may be viable for coordinating/operating the future smart grids.
We consider the problem of sparse phase retrieval, where a $k$-sparse signal ${\bf x} \in {\mathbb R}^n \textrm{ (or } {\mathbb C}^n\textrm{)}$ is measured as ${\bf y} = |{\bf Ax}|,$ where ${\bf A} \in {\mathbb R}^{m \times n} \textrm{ (or } {\mathbb C}^{m \times n}\textrm{ respectively)}$ is a measurement matrix and $|\cdot|$ is the element-wise absolute value. For a real signal and a real measurement matrix ${\bf A}$, we show that $m = 2k$ measurements are necessary and sufficient to recover ${\bf x}$ uniquely. For complex signal ${\bf x} \in {\mathbb C}^n$ and ${\bf A} \in {\mathbb C}^{m \times n}$, we show that $m = 4k-2$ phaseless measurements are sufficient to recover ${\bf x}$. It is known that the multiplying constant $4$ in $m = 4k-2$ cannot be improved.
Chinwendu Enyioha, Sindri Magnusson, Kathryn Heal et al.
As independent service providers shift from conventional energy to renewable energy sources, the power distribution system will likely experience increasingly significant fluctuation in supply, given the uncertain and intermittent nature of renewable sources like wind and solar energy. These fluctuations in power generation, coupled with time-varying consumer demands of electricity and the massive scale of power distribution networks present the need to not only design real-time decentralized power allocation algorithms, but also characterize how effective they are given fast-changing consumer demands and power generation capacities. In this paper, we present an Online Decentralized Dual Descent (OD3) power allocation algorithm and determine (in the worst case) how much of observed social welfare and price volatility can be explained by fluctuations in generation capacity and consumer demand. Convergence properties and performance guarantees of the OD3 algorithm are analyzed by characterizing the difference between the online decision and the optimal decision. The theoretical results in the paper are validated and illustrated by numerical experiments using real data.
Classical quickest change detection algorithms require modeling pre-change and post-change distributions. Such an approach may not be feasible for various machine learning models because of the complexity of computing the explicit distributions. Additionally, these methods may suffer from a lack of robustness to model mismatch and noise. This paper develops a new variant of the classical Cumulative Sum (CUSUM) algorithm for the quickest change detection. This variant is based on Fisher divergence and the Hyvärinen score and is called the Score-based CUSUM (SCUSUM) algorithm. The SCUSUM algorithm allows the applications of change detection for unnormalized statistical models, i.e., models for which the probability density function contains an unknown normalization constant. The asymptotic optimality of the proposed algorithm is investigated by deriving expressions for average detection delay and the mean running time to a false alarm. Numerical results are provided to demonstrate the performance of the proposed algorithm.
Shyam Venkatasubramanian, Sandeep Gogineni, Bosung Kang et al.
Leveraging the advanced functionalities of modern radio frequency (RF) modeling and simulation tools, specifically designed for adaptive radar processing applications, this paper presents a data-driven approach to improve accuracy in radar target localization post adaptive radar detection. To this end, we generate a large number of radar returns by randomly placing targets of variable strengths in a predefined area, using RFView, a high-fidelity, site-specific, RF modeling & simulation tool. We produce heatmap tensors from the radar returns, in range, azimuth [and Doppler], of the normalized adaptive matched filter (NAMF) test statistic. We then train a regression convolutional neural network (CNN) to estimate target locations from these heatmap tensors, and we compare the target localization accuracy of this approach with that of peak-finding and local search methods. This empirical study shows that our regression CNN achieves a considerable improvement in target location estimation accuracy. The regression CNN offers significant gains and reasonable accuracy even at signal-to-clutter-plus-noise ratio (SCNR) regimes that are close to the breakdown threshold SCNR of the NAMF. We also study the robustness of our trained CNN to mismatches in the radar data, where the CNN is tested on heatmap tensors collected from areas that it was not trained on. We show that our CNN can be made robust to mismatches in the radar data through few-shot learning, using a relatively small number of new training samples.
Understanding multivariate dependencies in both the bulk and the tails of a distribution is an important problem for many applications, such as ensuring algorithms are robust to observations that are infrequent but have devastating effects. Archimax copulas are a family of distributions endowed with a precise representation that allows simultaneous modeling of the bulk and the tails of a distribution. Rather than separating the two as is typically done in practice, incorporating additional information from the bulk may improve inference of the tails, where observations are limited. Building on the stochastic representation of Archimax copulas, we develop a non-parametric inference method and sampling algorithm. Our proposed methods, to the best of our knowledge, are the first that allow for highly flexible and scalable inference and sampling algorithms, enabling the increased use of Archimax copulas in practical settings. We experimentally compare to state-of-the-art density modeling techniques, and the results suggest that the proposed method effectively extrapolates to the tails while scaling to higher dimensional data. Our findings suggest that the proposed algorithms can be used in a variety of applications where understanding the interplay between the bulk and the tails of a distribution is necessary, such as healthcare and safety.
This work considers the problem of transferring causal knowledge between tasks for Individual Treatment Effect (ITE) estimation. To this end, we theoretically assess the feasibility of transferring ITE knowledge and present a practical framework for efficient transfer. A lower bound is introduced on the ITE error of the target task to demonstrate that ITE knowledge transfer is challenging due to the absence of counterfactual information. Nevertheless, we establish generalization upper bounds on the counterfactual loss and ITE error of the target task, demonstrating the feasibility of ITE knowledge transfer. Subsequently, we introduce a framework with a new Causal Inference Task Affinity (CITA) measure for ITE knowledge transfer. Specifically, we use CITA to find the closest source task to the target task and utilize it for ITE knowledge transfer. Empirical studies are provided, demonstrating the efficacy of the proposed method. We observe that ITE knowledge transfer can significantly (up to 95%) reduce the amount of data required for ITE estimation.
Although reinforcement learning (RL) is considered the gold standard for policy design, it may not always provide a robust solution in various scenarios. This can result in severe performance degradation when the environment is exposed to potential disturbances. Adversarial training using a two-player max-min game has been proven effective in enhancing the robustness of RL agents. In this work, we extend the two-player game by introducing an adversarial herd, which involves a group of adversaries, in order to address ($\textit{i}$) the difficulty of the inner optimization problem, and ($\textit{ii}$) the potential over pessimism caused by the selection of a candidate adversary set that may include unlikely scenarios. We first prove that adversarial herds can efficiently approximate the inner optimization problem. Then we address the second issue by replacing the worst-case performance in the inner optimization with the average performance over the worst-$k$ adversaries. We evaluate the proposed method on multiple MuJoCo environments. Experimental results demonstrate that our approach consistently generates more robust policies.
Computational experiments are exploited in finding a well-designed processing path to optimize material structures for desired properties. This requires understanding the interplay between the processing-(micro)structure-property linkages using a multi-scale approach that connects the macro-scale (process parameters) to meso (homogenized properties) and micro (crystallographic texture) scales. Due to the nature of the problem's multi-scale modeling setup, possible processing path choices could grow exponentially as the decision tree becomes deeper, and the traditional simulators' speed reaches a critical computational threshold. To lessen the computational burden for predicting microstructural evolution under given loading conditions, we develop a neural network (NN)-based method with physics-infused constraints. The NN aims to learn the evolution of microstructures under each elementary process. Our method is effective and robust in finding optimal processing paths. In this study, our NN-based method is applied to maximize the homogenized stiffness of a Copper microstructure, and it is found to be 686 times faster while achieving 0.053% error in the resulting homogenized stiffness compared to the traditional finite element simulator on a 10-process experiment.
Unsupervised domain adaptation (UDA) is a technique used to transfer knowledge from a labeled source domain to a different but related unlabeled target domain. While many UDA methods have shown success in the past, they often assume that the source and target domains must have identical class label distributions, which can limit their effectiveness in real-world scenarios. To address this limitation, we propose a novel generalization bound that reweights source classification error by aligning source and target sub-domains. We prove that our proposed generalization bound is at least as strong as existing bounds under realistic assumptions, and we empirically show that it is much stronger on real-world data. We then propose an algorithm to minimize this novel generalization bound. We demonstrate by numerical experiments that this approach improves performance in shifted class distribution scenarios compared to state-of-the-art methods.
Causal mediation analysis (CMA) is a powerful method to dissect the total effect of a treatment into direct and mediated effects within the potential outcome framework. This is important in many scientific applications to identify the underlying mechanisms of a treatment effect. However, in many scientific applications the mediator is unobserved, but there may exist related measurements. For example, we may want to identify how changes in brain activity or structure mediate an antidepressant's effect on behavior, but we may only have access to electrophysiological or imaging brain measurements. To date, most CMA methods assume that the mediator is one-dimensional and observable, which oversimplifies such real-world scenarios. To overcome this limitation, we introduce a CMA framework that can handle complex and indirectly observed mediators based on the identifiable variational autoencoder (iVAE) architecture. We prove that the true joint distribution over observed and latent variables is identifiable with the proposed method. Additionally, our framework captures a disentangled representation of the indirectly observed mediator and yields accurate estimation of the direct and mediated effects in synthetic and semi-synthetic experiments, providing evidence of its potential utility in real-world applications.
We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.
Transformers have demonstrated remarkable efficacy in forecasting time series data. However, their extensive dependence on self-attention mechanisms demands significant computational resources, thereby limiting their practical applicability across diverse tasks, especially in multimodal problems. In this work, we propose a new architecture, called perceiver-CDF, for modeling cumulative distribution functions (CDF) of time series data. Our approach combines the perceiver architecture with a copula-based attention mechanism tailored for multimodal time series prediction. By leveraging the perceiver, our model efficiently transforms high-dimensional and multimodal data into a compact latent space, thereby significantly reducing computational demands. Subsequently, we implement a copula-based attention mechanism to construct the joint distribution of missing data for prediction. Further, we propose an output variance testing mechanism to effectively mitigate error propagation during prediction. To enhance efficiency and reduce complexity, we introduce midpoint inference for the local attention mechanism. This enables the model to efficiently capture dependencies within nearby imputed samples without considering all previous samples. The experiments on the unimodal and multimodal benchmarks consistently demonstrate a 20% improvement over state-of-the-art methods while utilizing less than half of the computational resources.
Shyam Venkatasubramanian, Sandeep Gogineni, Bosung Kang et al.
Recent works exploring data-driven approaches to classical problems in adaptive radar have demonstrated promising results pertaining to the task of radar target localization. Via the use of space-time adaptive processing (STAP) techniques and convolutional neural networks, these data-driven approaches to target localization have helped benchmark the performance of neural networks for matched scenarios. However, the thorough bridging of these topics across mismatched scenarios still remains an open problem. As such, in this work, we augment our data-driven approach to radar target localization by performing a subspace perturbation analysis, which allows us to benchmark the localization accuracy of our proposed deep learning framework across mismatched scenarios. To evaluate this framework, we generate comprehensive datasets by randomly placing targets of variable strengths in mismatched constrained areas via RFView, a high-fidelity, site-specific modeling and simulation tool. For the radar returns from these constrained areas, we generate heatmap tensors in range, azimuth, and elevation using the normalized adaptive matched filter (NAMF) test statistic. We estimate target locations from these heatmap tensors using a convolutional neural network, and demonstrate that the predictive performance of our framework in the presence of mismatches can be predetermined.
Discrete diffusion language models have emerged as a competitive alternative to auto-regressive language models, but training them efficiently under limited parameter and memory budgets remains challenging. Modern architectures are predominantly based on a full-vocabulary token prediction layer, which accounts for a substantial fraction of model parameters (e.g., more than 20% in small scale DiT-style designs) and often dominates peak GPU memory usage. This leads to inefficient use of both parameters and memory under constrained training resources. To address this issue, we revisit the necessity of explicit full-vocabulary prediction, and instead exploit the inherent structure among tokens to build a tree-structured diffusion language model. Specifically, we model the diffusion process with intermediate latent states corresponding to a token's ancestor nodes in a pre-constructed vocabulary tree. This tree-structured factorization exponentially reduces the classification dimensionality, makes the prediction head negligible in size, and enables reallocation of parameters to deepen the attention blocks. Empirically, under the same parameter budget, our method reduces peak GPU memory usage by half while matching the perplexity performance of state-of-the-art discrete diffusion language models.
Understanding treatment effects in extreme regimes is important for characterizing risks associated with different interventions. This is hindered by the unavailability of counterfactual outcomes and the rarity and difficulty of collecting extreme data in practice. To address this issue, we propose a new framework based on extreme value theory for estimating treatment effects in extreme regimes. We quantify these effects using variations in tail decay rates of potential outcomes in the presence and absence of treatments. We establish algorithms for calculating these quantities and develop related theoretical results. We demonstrate the efficacy of our approach on various standard synthetic and semi-synthetic datasets.
Federated Learning (FL) is a collaborative machine learning framework that allows multiple users to train models utilizing their local data in a distributed manner. However, considerable statistical heterogeneity in local data across devices often leads to suboptimal model performance compared with independently and identically distributed (IID) data scenarios. In this paper, we introduce DynamicFL, a new FL framework that investigates the trade-offs between global model performance and communication costs for two widely adopted FL methods: Federated Stochastic Gradient Descent (FedSGD) and Federated Averaging (FedAvg). Our approach allocates diverse communication resources to clients based on their data statistical heterogeneity, considering communication resource constraints, and attains substantial performance enhancements compared to uniform communication resource allocation. Notably, our method bridges the gap between FedSGD and FedAvg, providing a flexible framework leveraging communication heterogeneity to address statistical heterogeneity in FL. Through extensive experiments, we demonstrate that DynamicFL surpasses current state-of-the-art methods with up to a 10% increase in model accuracy, demonstrating its adaptability and effectiveness in tackling data statistical heterogeneity challenges.
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often necessary to compute the solutions or a function of the solutions to a parametric PDE in multiple scenarios corresponding to different parameters of this PDE. This process often requires resolving the PDEs from scratch, which is time-consuming. To better employ existing simulations for the PDEs, we propose a framework for finding solutions to parabolic PDEs across different scenarios by meta-learning an underlying base distribution. We build upon this base distribution to propose a method for computing solutions to parametric PDEs under different parameter settings. Finally, we illustrate the application of the proposed methods through extensive experiments in generative modeling, stochastic control, and finance. The empirical results suggest that the proposed approach improves generalization to solving PDEs under new parameter regimes.
Off-policy evaluation (OPE) is important for closing the gap between offline training and evaluation of reinforcement learning (RL), by estimating performance and/or rank of target (evaluation) policies using offline trajectories only. It can improve the safety and efficiency of data collection and policy testing procedures in situations where online deployments are expensive, such as healthcare. However, existing OPE methods fall short in estimating human feedback (HF) signals, as HF may be conditioned over multiple underlying factors and is only sparsely available; as opposed to the agent-defined environmental rewards (used in policy optimization), which are usually determined over parametric functions or distributions. Consequently, the nature of HF signals makes extrapolating accurate OPE estimations to be challenging. To resolve this, we introduce an OPE for HF (OPEHF) framework that revives existing OPE methods in order to accurately evaluate the HF signals. Specifically, we develop an immediate human reward (IHR) reconstruction approach, regularized by environmental knowledge distilled in a latent space that captures the underlying dynamics of state transitions as well as issuing HF signals. Our approach has been tested over two real-world experiments, adaptive in-vivo neurostimulation and intelligent tutoring, as well as in a simulation environment (visual Q&A). Results show that our approach significantly improves the performance toward estimating HF signals accurately, compared to directly applying (variants of) existing OPE methods.
We address the problem of quickest change detection in Markov processes with unknown transition kernels. The key idea is to learn the conditional score $\nabla_{\mathbf{y}} \log p(\mathbf{y}|\mathbf{x})$ directly from sample pairs $( \mathbf{x},\mathbf{y})$, where both $\mathbf{x}$ and $\mathbf{y}$ are high-dimensional data generated by the same transition kernel. In this way, we avoid explicit likelihood evaluation and provide a practical way to learn the transition dynamics. Based on this estimation, we develop a score-based CUSUM procedure that uses conditional Hyvarinen score differences to detect changes in the kernel. To ensure bounded increments, we propose a truncated version of the statistic. With Hoeffding's inequality for uniformly ergodic Markov processes, we prove exponential lower bounds on the mean time to false alarm. We also prove asymptotic upper bounds on detection delay. These results give both theoretical guarantees and practical feasibility for score-based detection in high-dimensional Markov models.
One of the most significant challenges in Conditional Average Treatment Effect (CATE) estimation is the statistical discrepancy between distinct treatment groups. To address this issue, we propose a model-agnostic data augmentation method for CATE estimation. First, we derive regret bounds for general data augmentation methods suggesting that a small imputation error may be necessary for accurate CATE estimation. Inspired by this idea, we propose a contrastive learning approach that reliably imputes missing potential outcomes for a selected subset of individuals formed using a similarity measure. We augment the original dataset with these reliable imputations to reduce the discrepancy between different treatment groups while inducing minimal imputation error. The augmented dataset can subsequently be employed to train standard CATE estimation models. We provide both theoretical guarantees and extensive numerical studies demonstrating the effectiveness of our approach in improving the accuracy and robustness of numerous CATE estimation models.
The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions built from spatial Poisson point processes. While powerful, these models are only asymptotically valid for large samples. However, since extreme data is by definition scarce, the potential for model misspecification error is inherent to these applications, thus DRO estimators are natural. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. We study both tractable convex formulations for some problems of interest (e.g. CVaR) and more general neural network based estimators. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques. Additionally, the proposed method is applied to a real data set of financial returns for comparison to a previous analysis. We established the proposed model as a novel formulation in the multivariate EVT domain, and innovative with respect to performance when compared to relevant alternate proposals.
We develop a novel generative model to simulate vehicle health and forecast faults, conditioned on practical operational considerations. The model, trained on data from the US Army's Predictive Logistics program, aims to support predictive maintenance. It forecasts faults far enough in advance to execute a maintenance intervention before a breakdown occurs. The model incorporates real-world factors that affect vehicle health. It also allows us to understand the vehicle's condition by analyzing operating data, and characterizing each vehicle into discrete states. Importantly, the model predicts the time to first fault with high accuracy. We compare its performance to other models and demonstrate its successful training.
Shyam Venkatasubramanian, Ali Pezeshki, Vahid Tarokh
We introduce a new approach to processing complex-valued data using DNNs consisting of parallel real-valued subnetworks with coupled outputs. Our proposed class of architectures, referred to as Steinmetz Neural Networks, incorporates multi-view learning to construct more interpretable representations in the latent space. Moreover, we present the Analytic Neural Network, which incorporates a consistency penalty that encourages analytic signal representations in the latent space of the Steinmetz neural network. This penalty enforces a deterministic and orthogonal relationship between the real and imaginary components. Using an information-theoretic construction, we demonstrate that the generalization gap upper bound posited by the analytic neural network is lower than that of the general class of Steinmetz neural networks. Our numerical experiments depict the improved performance and robustness to additive noise, afforded by our proposed networks on benchmark datasets and synthetic examples.
Shyam Venkatasubramanian, Ahmed Aloui, Vahid Tarokh
Advancing loss function design is pivotal for optimizing neural network training and performance. This work introduces Random Linear Projections (RLP) loss, a novel approach that enhances training efficiency by leveraging geometric relationships within the data. Distinct from traditional loss functions that target minimizing pointwise errors, RLP loss operates by minimizing the distance between sets of hyperplanes connecting fixed-size subsets of feature-prediction pairs and feature-label pairs. Our empirical evaluations, conducted across benchmark datasets and synthetic examples, demonstrate that neural networks trained with RLP loss outperform those trained with traditional loss functions, achieving improved performance with fewer data samples, and exhibiting greater robustness to additive noise. We provide theoretical analysis supporting our empirical findings.
McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical description of the behavior of an infinite number of interacting particles by imposing a dependence on the particle density. As such, we study the influence of explicitly including distributional information in the parameterization of the SDE. We propose a series of semi-parametric methods for representing MV-SDEs, and corresponding estimators for inferring parameters from data based on the properties of the MV-SDE. We analyze the characteristics of the different architectures and estimators, and consider their applicability in relevant machine learning problems. We empirically compare the performance of the different architectures and estimators on real and synthetic datasets for time series and probabilistic modeling. The results suggest that explicitly including distributional dependence in the parameterization of the SDE is effective in modeling temporal data with interaction under an exchangeability assumption while maintaining strong performance for standard Itô-SDEs due to the richer class of probability flows associated with MV-SDEs.
In this paper, we introduce a new approach for integrating score-based models with the Metropolis-Hastings algorithm. While traditional score-based diffusion models excel in accurately learning the score function from data points, they lack an energy function, making the Metropolis-Hastings adjustment step inaccessible. Consequently, the unadjusted Langevin algorithm is often used for sampling using estimated score functions. The lack of an energy function then prevents the application of the Metropolis-adjusted Langevin algorithm and other Metropolis-Hastings methods, limiting the wealth of other algorithms developed that use acceptance functions. We address this limitation by introducing a new loss function based on the \emph{detailed balance condition}, allowing the estimation of the Metropolis-Hastings acceptance probabilities given a learned score function. We demonstrate the effectiveness of the proposed method for various scenarios, including sampling from heavy-tail distributions.
Accelerating model convergence in resource-constrained environments is essential for fast and efficient neural network training. This work presents learn2mix, a new training strategy that adaptively adjusts class proportions within batches, focusing on classes with higher error rates. Unlike classical training methods that use static class proportions, learn2mix continually adapts class proportions during training, leading to faster convergence. Empirical evaluations on benchmark datasets show that neural networks trained with learn2mix converge faster than those trained with existing approaches, achieving improved results for classification, regression, and reconstruction tasks under limited training resources and with imbalanced classes. Our empirical findings are supported by theoretical analysis.
Regularizing continual learning techniques is important for anticipating algorithmic behavior under new realizations of data. We introduce a new approach to continual learning by imposing the properties of a parabolic partial differential equation (PDE) to regularize the expected behavior of the loss over time. This class of parabolic PDEs has a number of favorable properties that allow us to analyze the error incurred through forgetting and the error induced through generalization. Specifically, we do this through imposing boundary conditions where the boundary is given by a memory buffer. By using the memory buffer as a boundary, we can enforce long term dependencies by bounding the expected error by the boundary loss. Finally, we illustrate the empirical performance of the method on a series of continual learning tasks.
A primary function of back-propagation is to compute both the gradient of hidden representations and parameters for optimization with gradient descent. Training large models requires high computational costs due to their vast parameter sizes. While Parameter-Efficient Fine-Tuning (PEFT) methods aim to train smaller auxiliary models to save computational space, they still present computational overheads, especially in Fine-Tuning as a Service (FTaaS) for numerous users. We introduce Collaborative Adaptation (ColA) with Gradient Learning (GL), a parameter-free, model-agnostic fine-tuning approach that decouples the computation of the gradient of hidden representations and parameters. In comparison to PEFT methods, ColA facilitates more cost-effective FTaaS by offloading the computation of the gradient to low-cost devices. We also provide a theoretical analysis of ColA and experimentally demonstrate that ColA can perform on par or better than existing PEFT methods on various benchmarks.
Regularizing neural networks is important for anticipating model behavior in regions of the data space that are not well represented. In this work, we propose a regularization technique for enforcing a level of smoothness in the mapping between the data input space and the loss value. We specify the level of regularity by requiring that the loss of the network satisfies an elliptic operator over the data domain. To do this, we modify the usual empirical risk minimization objective such that we instead minimize a new objective that satisfies an elliptic operator over points within the domain. This allows us to use existing theory on elliptic operators to anticipate the behavior of the error for points outside the training set. We propose a tractable computational method that approximates the behavior of the elliptic operator while being computationally efficient. Finally, we analyze the properties of the proposed regularization to understand the performance on common problems of distribution shift and group imbalance. Numerical experiments confirm the utility of the proposed regularization technique.
Large language models (LLMs) have recently demonstrated impressive capabilities across a range of reasoning and generation tasks. However, research studies have shown that LLMs lack the ability to identify causal relationships, a fundamental cornerstone of human intelligence. We first conduct an exploratory investigation of LLMs' behavior when asked to perform a causal-discovery task and find that they mostly rely on the semantic meaning of variable names, ignoring the observation data. This is unsurprising, given that LLMs were never trained to process structural datasets. To first tackle this challenge, we prompt the LLMs with the outputs of established causal discovery algorithms designed for observational datasets. These algorithm outputs effectively serve as the sufficient statistics of the observation data. However, quite surprisingly, we find that prompting the LLMs with these sufficient statistics decreases the LLMs' performance in causal discovery. To address this current limitation, we propose CARE, a framework that enhances LLMs' causal-reasoning ability by teaching them to effectively utilize the outputs of established causal-discovery algorithms through supervised fine-tuning. Experimental results show that a finetuned Qwen2.5-1.5B model produced by CARE significantly outperforms both traditional causal-discovery algorithms and state-of-the-art LLMs with over a thousand times more parameters, demonstrating effective utilization of its own knowledge and the external algorithmic clues.
Solving Inductive Logic Programming (ILP) problems with neural networks is a key challenge in Neural-Symbolic Ar- tificial Intelligence (AI). While most research has focused on designing novel network architectures for individual prob- lems, less effort has been devoted to exploring new learning paradigms involving a sequence of problems. In this work, we investigate lifelong learning ILP, which leverages the com- positional and transferable nature of logic rules for efficient learning of new problems. We introduce a compositional framework, demonstrating how logic rules acquired from ear- lier tasks can be efficiently reused in subsequent ones, leading to improved scalability and performance. We formalize our approach and empirically evaluate it on sequences of tasks. Experimental results validate the feasibility and advantages of this paradigm, opening new directions for continual learn- ing in Neural-Symbolic AI.
David Fenwick, Navid NaderiAlizadeh, Vahid Tarokh et al.
Protocol optimization is critical in Computed Tomography (CT) to achieve high diagnostic image quality while minimizing radiation dose. However, due to the complex interdependencies among CT acquisition and reconstruction parameters, traditional optimization methods rely on exhaustive testing of combinations of these parameters, which is often impractical. This study introduces a novel methodology that combines virtual imaging tools with reinforcement learning to optimize CT protocols more efficiently. Human models with liver lesions were imaged using a validated CT simulator and reconstructed with a novel CT reconstruction toolkit. The optimization parameter space included tube voltage, tube current, reconstruction kernel, slice thickness, and pixel size. The optimization process was performed using a Proximal Policy Optimization (PPO) agent, which was trained to maximize an image quality objective, specifically the detectability index (d') of liver lesions in the reconstructed images. Optimization performance was compared against an exhaustive search performed on a supercomputer. The proposed reinforcement learning approach achieved the global maximum d' across test cases while requiring 79.7% fewer steps than the exhaustive search, demonstrating both accuracy and computational efficiency. The proposed framework is flexible and can accommodate various image quality objectives. The findings highlight the potential of integrating virtual imaging tools with reinforcement learning for CT protocol management.
We study a broad class of assortment optimization problems in an offline and data-driven setting. In such problems, a firm lacks prior knowledge of the underlying choice model, and aims to determine an optimal assortment based on historical customer choice data. The combinatorial nature of assortment optimization often results in insufficient data coverage, posing a significant challenge in designing provably effective solutions. To address this, we introduce a novel Pessimistic Assortment Optimization (PASTA) framework that leverages the principle of pessimism to achieve optimal expected revenue under general choice models. Notably, PASTA requires only that the offline data distribution contains an optimal assortment, rather than providing the full coverage of all feasible assortments. Theoretically, we establish the first finite-sample regret bounds for offline assortment optimization across several widely used choice models, including the multinomial logit and nested logit models. Additionally, we derive a minimax regret lower bound, proving that PASTA is minimax optimal in terms of sample and model complexity. Numerical experiments further demonstrate that our method outperforms existing baseline approaches.
One of the major challenges in estimating conditional potential outcomes and conditional average treatment effects (CATE) is the presence of hidden confounders. Since testing for hidden confounders cannot be accomplished only with observational data, conditional unconfoundedness is commonly assumed in the literature of CATE estimation. Nevertheless, under this assumption, CATE estimation can be significantly biased due to the effects of unobserved confounders. In this work, we consider the case where in addition to a potentially large observational dataset, a small dataset from a randomized controlled trial (RCT) is available. Notably, we make no assumptions on the existence of any covariate information for the RCT dataset, we only require the outcomes to be observed. We propose a CATE estimation method based on a pseudo-confounder generator and a CATE model that aligns the learned potential outcomes from the observational data with those observed from the RCT. Our method is applicable to many practical scenarios of interest, particularly those where privacy is a concern (e.g., medical applications). Extensive numerical experiments are provided demonstrating the effectiveness of our approach for both synthetic and real-world datasets.
In-Context Learning (ICL) allows Large Language Models (LLMs) to adapt to new tasks with just a few examples, but their predictions often suffer from systematic biases, leading to unstable performances in classification. While calibration techniques are proposed to mitigate these biases, we show that, in the logit space, many of these methods are equivalent to merely shifting the LLM's decision boundary without having the ability to alter its orientation. This proves inadequate when biases cause the LLM to be severely misdirected. To address these limitations and provide a unifying framework, we propose Supervised Calibration (SC), a loss-minimization based framework which learns an optimal, per-class affine transformation of the LLM's predictive probabilities in the logit space without requiring external data beyond the context. By using a more expressive functional class, SC not only subsumes many existing calibration methods in ICL as special cases, but also enables the ability to alter and even completely reverse the orientation of the LLM's decision boundary. Furthermore, SC's loss-based nature facilitates the seamless integration of two purpose-built regularization techniques: context-invariance and directional trust-region. The former is designed to tackle the instability issue in ICL, while the latter controls the degree of calibration. Finally, SC delivers state-of-the-art performance over calibration baselines in the 4-shot, 8-shot, and 16-shot settings across all nine datasets for Mistral-7B-Instruct-v0.3, LLaMA-2-7B-chat, and Qwen2-7B-Instruct.
Optimization techniques have become increasingly critical due to the ever-growing model complexity and data scale. In particular, teleportation has emerged as a promising approach, which accelerates convergence of gradient descent-based methods by navigating within the loss invariant level set to identify parameters with advantageous geometric properties. Existing teleportation algorithms have primarily demonstrated their effectiveness in optimizing Multi-Layer Perceptrons (MLPs), but their extension to more advanced architectures, such as Convolutional Neural Networks (CNNs) and Transformers, remains challenging. Moreover, they often impose significant computational demands, limiting their applicability to complex architectures. To this end, we introduce an algorithm that projects the gradient of the teleportation objective function onto the input null space, effectively preserving the teleportation within the loss invariant level set and reducing computational cost. Our approach is readily generalizable from MLPs to CNNs, transformers, and potentially other advanced architectures. We validate the effectiveness of our algorithm across various benchmark datasets and optimizers, demonstrating its broad applicability.
Time series forecasting has recently achieved significant progress with multi-scale models to address the heterogeneity between long and short range patterns. Despite their state-of-the-art performance, we identify two potential areas for improvement. First, the variates of the multivariate time series are processed independently. Moreover, the multi-scale (long and short range) representations are learned separately by two independent models without communication. In light of these concerns, we propose State Space Transformer with cross-attention (S2TX). S2TX employs a cross-attention mechanism to integrate a Mamba model for extracting long-range cross-variate context and a Transformer model with local window attention to capture short-range representations. By cross-attending to the global context, the Transformer model further facilitates variate-level interactions as well as local/global communications. Comprehensive experiments on seven classic long-short range time-series forecasting benchmark datasets demonstrate that S2TX can achieve highly robust SOTA results while maintaining a low memory footprint.
William N. Caballero, Matthew LaRosa, Alexander Fisher et al.
The multivariate Gaussian distribution underpins myriad operations-research, decision-analytic, and machine-learning models (e.g., Bayesian optimization, Gaussian influence diagrams, and variational autoencoders). However, despite recent advances in adversarial machine learning (AML), inference for Gaussian models in the presence of an adversary is notably understudied. Therefore, we consider a self-interested attacker who wishes to disrupt a decisionmaker's conditional inference and subsequent actions by corrupting a set of evidentiary variables. To avoid detection, the attacker also desires the attack to appear plausible wherein plausibility is determined by the density of the corrupted evidence. We consider white- and grey-box settings such that the attacker has complete and incomplete knowledge about the decisionmaker's underlying multivariate Gaussian distribution, respectively. Select instances are shown to reduce to quadratic and stochastic quadratic programs, and structural properties are derived to inform solution methods. We assess the impact and efficacy of these attacks in three examples, including, real estate evaluation, interest rate estimation and signals processing. Each example leverages an alternative underlying model, thereby highlighting the attacks' broad applicability. Through these applications, we also juxtapose the behavior of the white- and grey-box attacks to understand how uncertainty and structure affect attacker behavior.
Arman Adibi, Sanjeev Kulkarni, H. Vincent Poor et al.
This paper addresses the problem of detecting changes when only unnormalized pre- and post-change distributions are accessible. This situation happens in many scenarios in physics such as in ferromagnetism, crystallography, magneto-hydrodynamics, and thermodynamics, where the energy models are difficult to normalize. Our approach is based on the estimation of the Cumulative Sum (CUSUM) statistics, which is known to produce optimal performance. We first present an intuitively appealing approximation method. Unfortunately, this produces a biased estimator of the CUSUM statistics and may cause performance degradation. We then propose the Log-Partition Approximation Cumulative Sum (LPA-CUSUM) algorithm based on thermodynamic integration (TI) in order to estimate the log-ratio of normalizing constants of pre- and post-change distributions. It is proved that this approach gives an unbiased estimate of the log-partition function and the CUSUM statistics, and leads to an asymptotically optimal performance. Moreover, we derive a relationship between the required sample size for thermodynamic integration and the desired detection delay performance, offering guidelines for practical parameter selection. Numerical studies are provided demonstrating the efficacy of our approach.
Shyam Venkatasubramanian, Bosung Kang, Ali Pezeshki et al.
We present a large-scale dataset called RASPNet for radar adaptive signal processing (RASP) applications to support the development of data-driven models within the adaptive radar community. RASPNet exceeds 16 TB in size and comprises 100 realistic scenarios compiled over a variety of topographies and land types across the contiguous United States. For each scenario, RASPNet comprises 10,000 clutter realizations from an airborne radar setting, which can be used to benchmark radar and complex-valued learning algorithms. RASPNet intends to fill a prominent gap in the availability of a large-scale, realistic dataset that standardizes the evaluation of RASP techniques and complex-valued neural networks. We outline its construction, organization, and several applications, including a transfer learning example to demonstrate how RASPNet can be used for real-world adaptive radar scenarios.
The main challenge in continual learning for generative models is to effectively learn new target modes with limited samples while preserving previously learned ones. To this end, we introduce a new continual learning approach for conditional generative adversarial networks by leveraging a mode-affinity score specifically designed for generative modeling. First, the generator produces samples of existing modes for subsequent replay. The discriminator is then used to compute the mode similarity measure, which identifies a set of closest existing modes to the target. Subsequently, a label for the target mode is generated and given as a weighted average of the labels within this set. We extend the continual learning model by training it on the target data with the newly-generated label, while performing memory replay to mitigate the risk of catastrophic forgetting. Experimental results on benchmark datasets demonstrate the gains of our continual learning approach over the state-of-the-art methods, even when using fewer training samples.
We propose a new structured pruning framework for compressing Deep Neural Networks (DNNs) with skip connections, based on measuring the statistical dependency of hidden layers and predicted outputs. The dependence measure defined by the energy statistics of hidden layers serves as a model-free measure of information between the feature maps and the output of the network. The estimated dependence measure is subsequently used to prune a collection of redundant and uninformative layers. Model-freeness of our measure guarantees that no parametric assumptions on the feature map distribution are required, making it computationally appealing for very high dimensional feature space in DNNs. Extensive numerical experiments on various architectures show the efficacy of the proposed pruning approach with competitive performance to state-of-the-art methods.
Shyam Venkatasubramanian, Chayut Wongkamthong, Mohammadreza Soltani et al.
Using an amalgamation of techniques from classical radar, computer vision, and deep learning, we characterize our ongoing data-driven approach to space-time adaptive processing (STAP) radar. We generate a rich example dataset of received radar signals by randomly placing targets of variable strengths in a predetermined region using RFView, a site-specific radio frequency modeling and simulation tool developed by ISL Inc. For each data sample within this region, we generate heatmap tensors in range, azimuth, and elevation of the output power of a minimum variance distortionless response (MVDR) beamformer, which can be replaced with a desired test statistic. These heatmap tensors can be thought of as stacked images, and in an airborne scenario, the moving radar creates a sequence of these time-indexed image stacks, resembling a video. Our goal is to use these images and videos to detect targets and estimate their locations, a procedure reminiscent of computer vision algorithms for object detection$-$namely, the Faster Region-Based Convolutional Neural Network (Faster R-CNN). The Faster R-CNN consists of a proposal generating network for determining regions of interest (ROI), a regression network for positioning anchor boxes around targets, and an object classification algorithm; it is developed and optimized for natural images. Our ongoing research will develop analogous tools for heatmap images of radar data. In this regard, we will generate a large, representative adaptive radar signal processing database for training and testing, analogous in spirit to the COCO dataset for natural images. As a preliminary example, we present a regression network in this paper for estimating target locations to demonstrate the feasibility of and significant improvements provided by our data-driven approach.
Juncheng Dong, Suya Wu, Mohammadreza Sultani et al.
Recently Reinforcement Learning (RL) has been applied as an anti-adversarial remedy in wireless communication networks. However, studying the RL-based approaches from the adversary's perspective has received little attention. Additionally, RL-based approaches in an anti-adversary or adversarial paradigm mostly consider single-channel communication (either channel selection or single channel power control), while multi-channel communication is more common in practice. In this paper, we propose a multi-agent adversary system (MAAS) for modeling and analyzing adversaries in a wireless communication scenario by careful design of the reward function under realistic communication scenarios. In particular, by modeling the adversaries as learning agents, we show that the proposed MAAS is able to successfully choose the transmitted channel(s) and their respective allocated power(s) without any prior knowledge of the sender strategy. Compared to the single-agent adversary (SAA), multi-agents in MAAS can achieve significant reduction in signal-to-noise ratio (SINR) under the same power constraints and partial observability, while providing improved stability and a more efficient learning process. Moreover, through empirical studies we show that the results in simulation are close to the ones in communication in reality, a conclusion that is pivotal to the validity of performance of agents evaluated in simulations.
Mohammadreza Momenifar, Enmao Diao, Vahid Tarokh et al.
Analyzing large-scale data from simulations of turbulent flows is memory intensive, requiring significant resources. This major challenge highlights the need for data compression techniques. In this study, we apply a physics-informed Deep Learning technique based on vector quantization to generate a discrete, low-dimensional representation of data from simulations of three-dimensional turbulent flows. The deep learning framework is composed of convolutional layers and incorporates physical constraints on the flow, such as preserving incompressibility and global statistical characteristics of the velocity gradients. The accuracy of the model is assessed using statistical, comparison-based similarity and physics-based metrics. The training data set is produced from Direct Numerical Simulation of an incompressible, statistically stationary, isotropic turbulent flow. The performance of this lossy data compression scheme is evaluated not only with unseen data from the stationary, isotropic turbulent flow, but also with data from decaying isotropic turbulence, and a Taylor-Green vortex flow. Defining the compression ratio (CR) as the ratio of original data size to the compressed one, the results show that our model based on vector quantization can offer CR $=85$ with a mean square error (MSE) of $O(10^{-3})$, and predictions that faithfully reproduce the statistics of the flow, except at the very smallest scales where there is some loss. Compared to the recent study based on a conventional autoencoder where compression is performed in a continuous space, our model improves the CR by more than $30$ percent, and reduces the MSE by an order of magnitude. Our compression model is an attractive solution for situations where fast, high quality and low-overhead encoding and decoding of large data are required.
Mohammadreza Momenifar, Enmao Diao, Vahid Tarokh et al.
We use a data-driven approach to model a three-dimensional turbulent flow using cutting-edge Deep Learning techniques. The deep learning framework incorporates physical constraints on the flow, such as preserving incompressibility and global statistical invariants of velocity gradient tensor. The accuracy of the model is assessed using statistical and physics-based metrics. The data set comes from Direct Numerical Simulation of an incompressible, statistically stationary, isotropic turbulent flow in a cubic box. Since the size of the dataset is memory intensive, we first generate a low-dimensional representation of the velocity data, and then pass it to a sequence prediction network that learns the spatial and temporal correlations of the underlying data. The dimensionality reduction is performed via extraction using Vector-Quantized Autoencoder (VQ-AE), which learns the discrete latent variables. For the sequence forecasting, the idea of Transformer architecture from natural language processing is used, and its performance compared against more standard Recurrent Networks (such as Convolutional LSTM). These architectures are designed and trained to perform a sequence to sequence multi-class classification task in which they take an input sequence with a fixed length (k) and predict a sequence with a fixed length (p), representing the future time instants of the flow. Our results for the short-term predictions show that the accuracy of results for both models deteriorates across predicted snapshots due to autoregressive nature of the predictions. Based on our diagnostics tests, the trained Conv-Transformer model outperforms the Conv-LSTM one and can accurately, both quantitatively and qualitatively, retain the large scales and capture well the inertial scales of flow but fails at recovering the small and intermittent fluid motions.
Numerous physical systems are described by ordinary or partial differential equations whose solutions are given by holomorphic or meromorphic functions in the complex domain. In many cases, only the magnitude of these functions are observed on various points on the purely imaginary jw-axis since coherent measurement of their phases is often expensive. However, it is desirable to retrieve the lost phases from the magnitudes when possible. To this end, we propose a physics-infused deep neural network based on the Blaschke products for phase retrieval. Inspired by the Helson and Sarason Theorem, we recover coefficients of a rational function of Blaschke products using a Blaschke Product Neural Network (BPNN), based upon the magnitude observations as input. The resulting rational function is then used for phase retrieval. We compare the BPNN to conventional deep neural networks (NNs) on several phase retrieval problems, comprising both synthetic and contemporary real-world problems (e.g., metamaterials for which data collection requires substantial expertise and is time consuming). On each phase retrieval problem, we compare against a population of conventional NNs of varying size and hyperparameter settings. Even without any hyper-parameter search, we find that BPNNs consistently outperform the population of optimized NNs in scarce data scenarios, and do so despite being much smaller models. The results can in turn be applied to calculate the refractive index of metamaterials, which is an important problem in emerging areas of material science.