pwc-archive/papers-with-abstracts huggingface dataset:
Regularized Dikin Walks for Sampling Truncated Logconcave Measures, Mixed Isoperimetry and Beyond Worst-Case Analysis
Authors: Minhui Jiang, Yuansi Chen
Date: 2024-12-15 00:00:00

We study the problem of drawing samples from a logconcave distribution truncated on a polytope, motivated by computational challenges in Bayesian statistical models with indicator variables, such as probit regression. Building on interior point methods and the Dikin walk for sampling from uniform distributions, we analyze the mixing time of regularized Dikin walks. Our contributions are threefold. First, for a logconcave and log-smooth distribution with condition number $\kappa$, truncated on a polytope in $\mathbb{R}^n$ defined with $m$ linear constraints, we prove that the soft-threshold Dikin walk mixes in $\widetilde{O}((m+\kappa)n)$ iterations from a warm initialization. It improves upon prior work which required the polytope to be bounded and involved a bound dependent on the radius of the bounded region. Moreover, we introduce the regularized Dikin walk using Lewis weights for approximating the John ellipsoid. We show that it mixes in $\widetilde{O}((n^{2.5}+\kappa n)$. Second, we extend the mixing time guarantees mentioned above to weakly log-concave distributions truncated on polytopes, provided that they have a finite covariance matrix. Third, going beyond worst-case mixing time analysis, we demonstrate that soft-threshold Dikin walk can mix significantly faster when only a limited number of constraints intersect the high-probability mass of the distribution, improving the $\widetilde{O}((m+\kappa)n)$ upper bound to $\widetilde{O}(m + \kappa n)$. Additionally, per-iteration complexity of regularized Dikin walk and ways to generate a warm initialization are discussed to facilitate practical implementation.
Sequence-Level Leakage Risk of Training Data in Large Language Models
Authors: Trishita Tiwari, G. Edward Suh
Date: 2024-12-15 00:00:00
Tasks: Benchmarking

This work quantifies the risk of training data leakage from LLMs (Large Language Models) using sequence-level probabilities. Computing extraction probabilities for individual sequences provides finer-grained information than has been studied in prior benchmarking work. We re-analyze the effects of decoding schemes, model sizes, prefix lengths, partial sequence leakages, and token positions to uncover new insights that were not possible in previous works due to their choice of metrics. We perform this study on two pre-trained models, Llama and OPT, trained on the Common Crawl and The Pile respectively. We discover that 1) Extraction Rate, the predominant metric used in prior quantification work, underestimates the threat of leakage of training data in randomized LLMs by as much as 2.14X. 2) Although on average, larger models and longer prefixes can extract more data, this is not true for a substantial portion of individual sequences. 30.4-41.5% of our sequences are easier to extract with either shorter prefixes or smaller models. 3) Contrary to previous beliefs, partial leakage in commonly used decoding schemes like top-k and top-p is not easier than leaking verbatim training data. The aim of this work is to encourage the adoption of this metric for future work on quantification of training data extraction.
Semi-Implicit Neural Ordinary Differential Equations
Authors: Hong Zhang, Ying Liu, Romit Maulik
Date: 2024-12-15 00:00:00
Tasks: Graph Classification, Graph Learning

Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present a semi-implicit neural ODE approach that exploits the partitionable structure of the underlying dynamics. Our technique leads to an implicit neural network with significant computational advantages over existing approaches because of enhanced stability and efficient linear solves during time integration. We show that our approach outperforms existing approaches on a variety of applications including graph classification and learning complex dynamical systems. We also demonstrate that our approach can train challenging neural ODEs where both explicit methods and fully implicit methods are intractable.
How not to Stitch Representations to Measure Similarity: Task Loss Matching versus Direct Matching
Authors: András Balogh, Márk Jelasity
Date: 2024-12-15 00:00:00

Measuring the similarity of the internal representations of deep neural networks is an important and challenging problem. Model stitching has been proposed as a possible approach, where two half-networks are connected by mapping the output of the first half-network to the input of the second one. The representations are considered functionally similar if the resulting stitched network achieves good task-specific performance. The mapping is normally created by training an affine stitching layer on the task at hand while freezing the two half-networks, a method called task loss matching. Here, we argue that task loss matching may be very misleading as a similarity index. For example, it can indicate very high similarity between very distant layers, whose representations are known to have different functional properties. Moreover, it can indicate very distant layers to be more similar than architecturally corresponding layers. Even more surprisingly, when comparing layers within the same network, task loss matching often indicates that some layers are more similar to a layer than itself. We argue that the main reason behind these problems is that task loss matching tends to create out-of-distribution representations to improve task-specific performance. We demonstrate that direct matching (when the mapping minimizes the distance between the stitched representations) does not suffer from these problems. We compare task loss matching, direct matching, and well-known similarity indices such as CCA and CKA. We conclude that direct matching strikes a good balance between the structural and functional requirements for a good similarity index.
A Comparative Study on Dynamic Graph Embedding based on Mamba and Transformers
Authors: Ashish Parmanand Pandey, Alan John Varghese, Sarang Patil, Mengjia Xu
Date: 2024-12-15 00:00:00
Tasks: Computational Efficiency, Dynamic graph embedding, Graph Embedding, Graph Representation Learning, Link Prediction, Mamba, Representation Learning, State Space Models

Dynamic graph embedding has emerged as an important technique for modeling complex time-evolving networks across diverse domains. While transformer-based models have shown promise in capturing long-range dependencies in temporal graph data, they face scalability challenges due to quadratic computational complexity. This study presents a comparative analysis of dynamic graph embedding approaches using transformers and the recently proposed Mamba architecture, a state-space model with linear complexity. We introduce three novel models: TransformerG2G augment with graph convolutional networks, \mathcal{DG}-Mamba, and \mathcal{GDG}-Mamba with graph isomorphism network edge convolutions. Our experiments on multiple benchmark datasets demonstrate that Mamba-based models achieve comparable or superior performance to transformer-based approaches in link prediction tasks while offering significant computational efficiency gains on longer sequences. Notably, \mathcal{DG}-Mamba variants consistently outperform transformer-based models on datasets with high temporal variability, such as UCI, Bitcoin, and Reality Mining, while maintaining competitive performance on more stable graphs like SBM. We provide insights into the learned temporal dependencies through analysis of attention weights and state matrices, revealing the models' ability to capture complex temporal patterns. By effectively combining state-space models with graph neural networks, our work addresses key limitations of previous approaches and contributes to the growing body of research on efficient temporal graph representation learning. These findings offer promising directions for scaling dynamic graph embedding to larger, more complex real-world networks, potentially enabling new applications in areas such as social network analysis, financial modeling, and biological system dynamics.
Grassmannian Geometry Meets Dynamic Mode Decomposition in DMD-GEN: A New Metric for Mode Collapse in Time Series Generative Models
Authors: Amime Mohamed Aboussalah, Yassine Abbahaddou
Date: 2024-12-15 00:00:00
Tasks: Image Generation, Time Series

Generative models like Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) often fail to capture the full diversity of their training data, leading to mode collapse. While this issue is well-explored in image generation, it remains underinvestigated for time series data. We introduce a new definition of mode collapse specific to time series and propose a novel metric, DMD-GEN, to quantify its severity. Our metric utilizes Dynamic Mode Decomposition (DMD), a data-driven technique for identifying coherent spatiotemporal patterns, and employs Optimal Transport between DMD eigenvectors to assess discrepancies between the underlying dynamics of the original and generated data. This approach not only quantifies the preservation of essential dynamic characteristics but also provides interpretability by pinpointing which modes have collapsed. We validate DMD-GEN on both synthetic and real-world datasets using various generative models, including TimeGAN, TimeVAE, and DiffusionTS. The results demonstrate that DMD-GEN correlates well with traditional evaluation metrics for static data while offering the advantage of applicability to dynamic data. This work offers for the first time a definition of mode collapse for time series, improving understanding, and forming the basis of our tool for assessing and improving generative models in the time series domain.
Wearable Accelerometer Foundation Models for Health via Knowledge Distillation
Authors: Salar Abbaspourazad, Anshuman Mishra, Joseph Futoma, Andrew C. Miller, Ian Shapiro
Date: 2024-12-15 00:00:00
Tasks: Activity Recognition, cross-modal alignment, Heart Rate Variability, Knowledge Distillation, Photoplethysmography (PPG), Self-Supervised Learning

Modern wearable devices can conveniently record various biosignals in the many different environments of daily living, enabling a rich view of individual health. However, not all biosignals are the same: high-fidelity biosignals, such as photoplethysmogram (PPG), contain more physiological information, but require optical sensors with a high power footprint. Alternatively, a lower-fidelity biosignal such as accelerometry has a significantly smaller power footprint and is available in almost any wearable device. While accelerometry is widely used for activity recognition and fitness, it is less explored for health biomarkers and diagnosis. Here, we show that an accelerometry foundation model can predict a wide variety of health targets. To achieve improved performance, we distill representational knowledge from PPG encoders to accelerometery encoders using 20 million minutes of unlabeled data, collected from ~172K participants in the Apple Heart and Movement Study under informed consent. We observe strong cross-modal alignment on unseen data, e.g., 99.2% top-1 accuracy for retrieving PPG embeddings from accelerometry embeddings. We show that distilled accelerometry encoders have significantly more informative representations compared to self-supervised or supervised encoders trained directly on accelerometry data, observed by at least 23%-49% improved performance for predicting heart rate and heart rate variability. We also show that distilled accelerometry encoders are readily predictive of a wide array of downstream health targets, i.e., they are generalist foundation models. We believe accelerometry foundation models for health may unlock new opportunities for developing digital biomarkers from any wearable device.
Bayesian inference of mean velocity fields and turbulence models from flow MRI
Authors: A. Kontogiannis, P. Nair, M. Loecher, D. B. Ennis, A. Marsden, M. P. Juniper
Date: 2024-12-15 00:00:00
Tasks: Bayesian Inference

We solve a Bayesian inverse Reynolds-averaged Navier-Stokes (RANS) problem that assimilates mean flow data by jointly reconstructing the mean flow field and learning its unknown RANS parameters. We devise an algorithm that learns the most likely parameters of an algebraic effective viscosity model, and estimates their uncertainties, from mean flow data of a turbulent flow. We conduct a flow MRI experiment to obtain mean flow data of a confined turbulent jet in an idealized medical device known as the FDA (Food and Drug Administration) nozzle. The algorithm successfully reconstructs the mean flow field and learns the most likely turbulence model parameters without overfitting. The methodology accepts any turbulence model, be it algebraic (explicit) or multi-equation (implicit), as long as the model is differentiable, and naturally extends to unsteady turbulent flows.
Prediction-Enhanced Monte Carlo: A Machine Learning View on Control Variate
Authors: Fengpei Li, Haoxian Chen, Jiahe Lin, Arkin Gupta, Xiaowei Tan, Honglei Zhao, Gang Xu, Yuriy Nevmyvaka, Agostino Capponi, Henry Lam
Date: 2024-12-15 00:00:00
Tasks: Efficient Neural Network, Prediction

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations often become computationally prohibitive, especially for nested, multi-level, or path-dependent evaluations lacking effective variance reduction techniques. While machine learning (ML) surrogates appear as natural alternatives, naive replacements typically introduce unquantifiable biases. We address this challenge by introducing Prediction-Enhanced Monte Carlo (PEMC), a framework that leverages modern ML models as learned predictors, using cheap and parallelizable simulation as features, to output unbiased evaluation with reduced variance and runtime. PEMC can also be viewed as a "modernized" view of control variates, where we consider the overall computation-cost-aware variance reduction instead of per-replication reduction, while bypassing the closed-form mean function requirement and maintaining the advantageous unbiasedness and uncertainty quantifiability of Monte Carlo. We illustrate PEMC's broader efficacy and versatility through three examples: first, equity derivatives such as variance swaps under stochastic local volatility models; second, interest rate derivatives such as swaption pricing under the Heath-Jarrow-Morton (HJM) interest-rate model. Finally, we showcase PEMC in a socially significant context - ambulance dispatch and hospital load balancing - where accurate mortality rate estimates are key for ethically sensitive decision-making. Across these diverse scenarios, PEMC consistently reduces variance while preserving unbiasedness, highlighting its potential as a powerful enhancement to standard Monte Carlo baselines.
Are Expressive Models Truly Necessary for Offline RL?
Authors: Guan Wang, Haoyi Niu, Jianxiong Li, Li Jiang, Jianming Hu, Xianyuan Zhan
Date: 2024-12-15 00:00:00
Tasks: D4RL, Offline RL, Reinforcement Learning (RL)

Among various branches of offline reinforcement learning (RL) methods, goal-conditioned supervised learning (GCSL) has gained increasing popularity as it formulates the offline RL problem as a sequential modeling task, therefore bypassing the notoriously difficult credit assignment challenge of value learning in conventional RL paradigm. Sequential modeling, however, requires capturing accurate dynamics across long horizons in trajectory data to ensure reasonable policy performance. To meet this requirement, leveraging large, expressive models has become a popular choice in recent literature, which, however, comes at the cost of significantly increased computation and inference latency. Contradictory yet promising, we reveal that lightweight models as simple as shallow 2-layer MLPs, can also enjoy accurate dynamics consistency and significantly reduced sequential modeling errors against large expressive models by adopting a simple recursive planning scheme: recursively planning coarse-grained future sub-goals based on current and target information, and then executes the action with a goal-conditioned policy learned from data rela-beled with these sub-goal ground truths. We term our method Recursive Skip-Step Planning (RSP). Simple yet effective, RSP enjoys great efficiency improvements thanks to its lightweight structure, and substantially outperforms existing methods, reaching new SOTA performances on the D4RL benchmark, especially in multi-stage long-horizon tasks.
Wasserstein Bounds for generative diffusion models with Gaussian tail targets
Authors: Xixian Wang, Zhongjian Wang
Date: 2024-12-15 00:00:00

We present an estimate of the Wasserstein distance between the data distribution and the generation of score-based generative models, assuming an $\epsilon$-accurate approximation of the score and a Gaussian-type tail behavior of the data distribution. The complexity bound in dimension is $O(\sqrt{d})$, with a logarithmic constant. Such Gaussian tail assumption applies to the distribution of a compact support target with early stopping technique and the Bayesian posterior with a bounded observation operator. Corresponding convergence and complexity bounds are derived. The crux of the analysis lies in the Lipchitz bound of the score, which is related to the Hessian estimate of a viscous Hamilton-Jacobi equation (vHJ). This latter is demonstrated by employing a dimension independent kernel estimate. Consequently, our complexity bound scales linearly (up to a logarithmic constant) with the square root of the trace of the covariance operator, which relates to the invariant distribution of forward process. Our analysis also extends to the probabilistic flow ODE, as the sampling process.
Transformer-Based Bearing Fault Detection using Temporal Decomposition Attention Mechanism
Authors: Marzieh Mirzaeibonehkhater, Mohammad Ali Labbaf-Khaniki, Mohammad Manthouri
Date: 2024-12-15 00:00:00
Tasks: Fault Detection, Time Series

Bearing fault detection is a critical task in predictive maintenance, where accurate and timely fault identification can prevent costly downtime and equipment damage. Traditional attention mechanisms in Transformer neural networks often struggle to capture the complex temporal patterns in bearing vibration data, leading to suboptimal performance. To address this limitation, we propose a novel attention mechanism, Temporal Decomposition Attention (TDA), which combines temporal bias encoding with seasonal-trend decomposition to capture both long-term dependencies and periodic fluctuations in time series data. Additionally, we incorporate the Hull Exponential Moving Average (HEMA) for feature extraction, enabling the model to effectively capture meaningful characteristics from the data while reducing noise. Our approach integrates TDA into the Transformer architecture, allowing the model to focus separately on the trend and seasonal components of the data. Experimental results on the Case Western Reserve University (CWRU) bearing fault detection dataset demonstrate that our approach outperforms traditional attention mechanisms and achieves state-of-the-art performance in terms of accuracy and interpretability. The HEMA-Transformer-TDA model achieves an accuracy of 98.1%, with exceptional precision, recall, and F1-scores, demonstrating its effectiveness in bearing fault detection and its potential for application in other time series tasks with seasonal patterns or trends.
TrimLLM: Progressive Layer Dropping for Domain-Specific LLMs
Authors: Lanxiang Hu, Tajana Rosing, Hao Zhang
Date: 2024-12-15 00:00:00
Tasks: Model Compression, Quantization

Specializing large language models (LLMs) for local deployment in domain-specific use cases is necessary for strong performance while meeting latency and privacy constraints. However, conventional task-specific adaptation approaches do not show simultaneous memory saving and inference speedup at deployment time. Practical compression techniques like quantization and pruning require dedicated hardware or kernel support to achieve measured inference speedup. We develop TrimLLM based on the layer-wise specialization phenomenon we empirically observed and verified on contemporary LLMs. TrimLLM reduces the depth of LLMs via progressive layer dropping. We show it retains LLMs' capacity in specific domains and achieves inference speedup irrespective of hardware and deep learning frameworks. We evaluated TrimLLM on LLMs of various sizes for inference; models adapted on medical, legal, and financial datasets all demonstrate $2.1-5.7\times$ inference speedup on consumer GPUs and up to $3.1\times$ speedup on A100 when compared to state-of-the-art model compression algorithms, with no loss in accuracy at 50$\sim$60\% model compression ratio.
Learning Set Functions with Implicit Differentiation
Authors: Gözde Özcan, Chengzhi Shi, Stratis Ioannidis
Date: 2024-12-15 00:00:00
Tasks: Anomaly Detection, Product Recommendation, Variational Inference

Ou et al. (2022) introduce the problem of learning set functions from data generated by a so-called optimal subset oracle. Their approach approximates the underlying utility function with an energy-based model, whose parameters are estimated via mean-field variational inference. Ou et al. (2022) show this reduces to fixed point iterations; however, as the number of iterations increases, automatic differentiation quickly becomes computationally prohibitive due to the size of the Jacobians that are stacked during backpropagation. We address this challenge with implicit differentiation and examine the convergence conditions for the fixed-point iterations. We empirically demonstrate the efficiency of our method on synthetic and real-world subset selection applications including product recommendation, set anomaly detection and compound selection tasks.
Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networks
Authors: Cyrus Neary, Nathan Tsao, Ufuk Topcu
Date: 2024-12-15 00:00:00

We develop compositional learning algorithms for coupled dynamical systems. While deep learning has proven effective at modeling complex relationships from data, compositional couplings between system components typically introduce algebraic constraints on state variables, posing challenges to many existing data-driven approaches to modeling dynamical systems. Towards developing deep learning models for constrained dynamical systems, we introduce neural port-Hamiltonian differential algebraic equations (N-PHDAEs), which use neural networks to parametrize unknown terms in both the differential and algebraic components of a port-Hamiltonian DAE. To train these models, we propose an algorithm that uses automatic differentiation to perform index reduction, automatically transforming the neural DAE into an equivalent system of neural ordinary differential equations (N-ODEs), for which established model inference and backpropagation methods exist. The proposed compositional modeling framework and learning algorithms may be applied broadly to learn control-oriented models of dynamical systems in a variety of application areas, however, in this work, we focus on their application to the modeling of electrical networks. Experiments simulating the dynamics of nonlinear circuits exemplify the benefits of our approach: the proposed N-PHDAE model achieves an order of magnitude improvement in prediction accuracy and constraint satisfaction when compared to a baseline N-ODE over long prediction time horizons. We also validate the compositional capabilities of our approach through experiments on a simulated D.C. microgrid: we train individual N-PHDAE models for separate grid components, before coupling them to accurately predict the behavior of larger-scale networks.