Skyler Wu

Skyler Wu, Eric Meng Shen, Charumathi Badrinath et al.

Chain-of-thought (CoT) prompting has been shown to empirically improve the accuracy of large language models (LLMs) on various question answering tasks. While understanding why CoT prompting is effective is crucial to ensuring that this phenomenon is a consequence of desired model behavior, little work has addressed this; nonetheless, such an understanding is a critical prerequisite for responsible model deployment. We address this question by leveraging gradient-based feature attribution methods which produce saliency scores that capture the influence of input tokens on model output. Specifically, we probe several open-source LLMs to investigate whether CoT prompting affects the relative importances they assign to particular input tokens. Our results indicate that while CoT prompting does not increase the magnitude of saliency scores attributed to semantically relevant tokens in the prompt compared to standard few-shot prompting, it increases the robustness of saliency scores to question perturbations and variations in model output.

Skyler Wu, Fred Lu, Edward Raff et al.

Convolutional layers have long served as the primary workhorse for image classification. Recently, an alternative to convolution was proposed using the Sharpened Cosine Similarity (SCS), which in theory may serve as a better feature detector. While multiple sources report promising results, there has not been to date a full-scale empirical analysis of neural network performance using these new layers. In our work, we explore SCS's parameter behavior and potential as a drop-in replacement for convolutions in multiple CNN architectures benchmarked on CIFAR-10. We find that while SCS may not yield significant increases in accuracy, it may learn more interpretable representations. We also find that, in some circumstances, SCS may confer a slight increase in adversarial robustness.

Skyler Wu, Aymen Echarghaoui

Fine-tuning is integral for aligning large language models (LLMs) with human preferences. Multiple-Reference Preference Optimization (MRPO) builds on Direct Preference Optimization (DPO) by fine-tuning LLMs on preference datasets while regularizing the policy towards a mixture of reference models to leverage their collective desirable properties. However, current methods for setting the reference weights are ad-hoc and statistically unsound, leading to unreliable performance. To address this, we introduce four new weighting strategies: two offline methods that leverage held-out validation signal; one online method that uses a sliding-window estimator to reduce overfitting; and an online method that treats reference weighting as a $K$-armed bandit via Thompson Sampling. Experiments using Qwen2.5-0.5B as the policy model and seven reference models from the Llama, Mistral, Qwen, Yi, and Phi families (0.5B-14B each) show that all 4 of our strategies outperform the current MRPO weighting methods on UltraFeedback and SafeRLHF in preference accuracy. More thought-provokingly, however, we find that single-reference DPO, using any of 6 out of 7 references, consistently outperforms all tested multiple-reference approaches -- calling into question the practical appeal of multiple-reference approaches.

Skyler Wu, Yash Nair, Emmanuel J. Candès

Exhaustively evaluating many large language models (LLMs) on a large suite of benchmarks is expensive. We cast benchmarking as finite-population inference and, under a fixed query budget, seek tight confidence intervals (CIs) for model accuracy with valid frequentist coverage. We propose Factorized Active Querying (FAQ), which (a) leverages historical information through a Bayesian factor model; (b) adaptively selects questions using a hybrid variance-reduction/active-learning sampling policy; and (c) maintains validity through Proactive Active Inference -- a finite-population extension of active inference (Zrnic & Candès, 2024) that enables direct question selection while preserving coverage. With negligible overhead cost, FAQ delivers up to $5\times$ effective sample size gains over strong baselines on two benchmark suites, across varying historical-data missingness levels: this means that it matches the CI width of uniform sampling while using up to $5\times$ fewer queries. We release our source code and our curated datasets to support reproducible evaluation and future research.

Skyler Wu, Fred Lu, Edward Raff et al.

Online learning methods, like the seminal Passive-Aggressive (PA) classifier, are still highly effective for high-dimensional streaming data, out-of-core processing, and other throughput-sensitive applications. Many such algorithms rely on fast adaptation to individual errors as a key to their convergence. While such algorithms enjoy low theoretical regret, in real-world deployment they can be sensitive to individual outliers that cause the algorithm to over-correct. When such outliers occur at the end of the data stream, this can cause the final solution to have unexpectedly low accuracy. We design a weighted reservoir sampling (WRS) approach to obtain a stable ensemble model from the sequence of solutions without requiring additional passes over the data, hold-out sets, or a growing amount of memory. Our key insight is that good solutions tend to be error-free for more iterations than bad solutions, and thus, the number of passive rounds provides an estimate of a solution's relative quality. Our reservoir thus contains $K$ previous intermediate weight vectors with high survival times. We demonstrate our WRS approach on the Passive-Aggressive Classifier (PAC) and First-Order Sparse Online Learning (FSOL), where our method consistently and significantly outperforms the unmodified approach. We show that the risk of the ensemble classifier is bounded with respect to the regret of the underlying online learning method.

Kyla Chasalow, Skyler Wu, Susan Murphy

Missing data in online reinforcement learning (RL) poses challenges compared to missing data in standard tabular data or in offline policy learning. The need to impute and act at each time step means that imputation cannot be put off until enough data exist to produce stable imputation models. It also means future data collection and learning depend on previous imputations. This paper proposes fully online imputation ensembles. We find that maintaining multiple imputation pathways may help balance the need to capture uncertainty under missingness and the need for efficiency in online settings. We consider multiple approaches for incorporating these pathways into learning and action selection. Using a Grid World experiment with various types of missingness, we provide preliminary evidence that multiple imputation pathways may be a useful framework for constructing simple and efficient online missing data RL methods.

Skyler Wu, Shihao Yang, S. C. Kou

In the era of AI, neural networks have become increasingly popular for modeling, inference, and prediction, largely due to their potential for universal approximation. With the proliferation of such deep learning models, a question arises: are leaner statistical methods still relevant? To shed insight on this question, we employ the mechanistic nonlinear ordinary differential equation (ODE) inverse problem as a testbed, using physics-informed neural network (PINN) as a representative of the deep learning paradigm and manifold-constrained Gaussian process inference (MAGI) as a representative of statistically principled methods. Through case studies involving the SEIR model from epidemiology and the Lorenz model from chaotic dynamics, we demonstrate that statistical methods are far from obsolete, especially when working with sparse and noisy observations. On tasks such as parameter inference and trajectory reconstruction, statistically principled methods consistently achieve lower bias and variance, while using far fewer parameters and requiring less hyperparameter tuning. Statistical methods can also decisively outperform deep learning models on out-of-sample future prediction, where the absence of relevant data often leads overparameterized models astray. Additionally, we find that statistically principled approaches are more robust to accumulation of numerical imprecision and can represent the underlying system more faithful to the true governing ODEs.

Skyler Wu

This work builds off the manifold-constrained Gaussian process inference (MAGI) method for Bayesian parameter inference and trajectory reconstruction of ODE-based dynamical systems, focusing primarily on sparse and noisy data conditions. First, we introduce Pilot MAGI (pMAGI), a novel methodological upgrade on the base MAGI method that confers significantly-improved numerical stability, parameter inference, and trajectory reconstruction. Second, we demonstrate, for the first time to our knowledge, how one can combine MAGI-based methods with dynamical systems theory to provide probabilistic classifications of whether a system is stable or chaotic. Third, we demonstrate how pMAGI performs favorably in many settings against much more computationally-expensive and overparameterized methods. Fourth, we introduce Pilot MAGI Sequential Prediction (PMSP), a novel method building upon pMAGI that allows one to predict the trajectory of ODE-based dynamical systems multiple time steps into the future, given only sparse and noisy observations. We show that PMSP can output accurate future predictions even on chaotic dynamical systems and significantly outperform PINN-based methods. Overall, we contribute to the literature two novel methods, pMAGI and PMSP, that serve as Bayesian, uncertainty-quantified competitors to the Physics-Informed Neural Network.