This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a warm-start strategy to initialize the particles. To approximate the posterior score, we develop a Monte Carlo estimator in which particles are generated using Langevin dynamics, avoiding the heuristic approximations commonly used in prior work. The score governing the Langevin dynamics is learned from data, enabling the model to capture rich structural features of the underlying prior distribution. On the theoretical side, we provide non-asymptotic error bounds, showing that the method converges even for complex, multi-modal target posterior distributions. These bounds explicitly quantify the errors arising from posterior score estimation, the warm-start initialization, and the posterior sampling procedure. Our analysis further clarifies how the prior score-matching error and the condition number of the Bayesian inverse problem influence overall performance. Finally, we present numerical experiments demonstrating the effectiveness of the proposed method across a range of inverse problems.

The emergence of large language models (LLMs) has sparked much interest in creating LLM-based digital populations that can be applied to many applications such as social simulation, crowdsourcing, marketing, and recommendation systems. A digital population can reduce the cost of recruiting human participants and alleviate many concerns related to human subject study. However, research has found that most of the existing works rely solely on LLMs and could not sufficiently capture the accuracy and diversity of a real human population. To address this limitation, we propose CrowdLLM that integrates pretrained LLMs and generative models to enhance the diversity and fidelity of the digital population. We conduct theoretical analysis of CrowdLLM regarding its great potential in creating cost-effective, sufficiently representative, scalable digital populations that can match the quality of a real crowd. Comprehensive experiments are also conducted across multiple domains (e.g., crowdsourcing, voting, user rating) and simulation studies which demonstrate that CrowdLLM achieves promising performance in both accuracy and distributional fidelity to human data.

Classification of functional data where observations are curves or trajectories poses unique challenges, particularly under severe class imbalance. Traditional Random Forest algorithms, while robust for tabular data, often fail to capture the intrinsic structure of functional observations and struggle with minority class detection. This paper introduces Functional Random Forest with Adaptive Cost-Sensitive Splitting (FRF-ACS), a novel ensemble framework designed for imbalanced functional data classification. The proposed method leverages basis expansions and Functional Principal Component Analysis (FPCA) to represent curves efficiently, enabling trees to operate on low dimensional functional features. To address imbalance, we incorporate a dynamic cost sensitive splitting criterion that adjusts class weights locally at each node, combined with a hybrid sampling strategy integrating functional SMOTE and weighted bootstrapping. Additionally, curve specific similarity metrics replace traditional Euclidean measures to preserve functional characteristics during leaf assignment. Extensive experiments on synthetic and real world datasets including biomedical signals and sensor trajectories demonstrate that FRF-ACS significantly improves minority class recall and overall predictive performance compared to existing functional classifiers and imbalance handling techniques. This work provides a scalable, interpretable solution for high dimensional functional data analysis in domains where minority class detection is critical.

Abstract--We present a Fourier-enhanced recurrent neural network (RNN) for downscaling electrical loads. The model combines (i) a recurrent backbone driven by low-resolution inputs, (ii) explicit Fourier seasonal embeddings fused in latent space, and (iii) a self-attention layer that captures dependencies among high-resolution components within each period. Energy policy and infrastructure investment decisions require an integrated system-wide perspective that captures the interdependencies of supply, conversion, and end-use sectors, as well as feedback from macroeconomic, technology-cost, and policy drivers. Many such energy modeling systems exist [1], of which the National Energy Modeling System (NEMS), developed by the U.S. Energy Information Administration (EIA) [2], is widely used by policymakers and stakeholders for this very reason. However, as noted in the study of energy plant pollution studies provided by NEMS [3], using temporally and spatially averaged data may significantly miss essential features and pricing signals.

Kolmogorov-Arnold Networks (KANs) offer a promising path toward interpretable machine learning: their learnable activations can be studied individually, while collectively fitting complex data accurately. In practice, however, trained activations often lack symbolic fidelity, learning pathological decompositions with no meaningful correspondence to interpretable forms. We propose Softly Symbolified Kolmogorov-Arnold Networks (S2KAN), which integrate symbolic primitives directly into training. Each activation draws from a dictionary of symbolic and dense terms, with learnable gates that sparsify the representation. Crucially, this sparsification is differentiable, enabling end-to-end optimization, and is guided by a principled Minimum Description Length objective. When symbolic terms suffice, S2KAN discovers interpretable forms; when they do not, it gracefully degrades to dense splines. We demonstrate competitive or superior accuracy with substantially smaller models across symbolic benchmarks, dynamical systems forecasting, and real-world prediction tasks, and observe evidence of emergent self-sparsification even without regularization pressure.

Kolmogorov-Arnold Networks have emerged as interpretable alternatives to traditional multi-layer perceptrons. However, standard implementations lack principled uncertainty quantification capabilities essential for many scientific applications. We present a framework integrating sparse variational Gaussian process inference with the Kolmogorov-Arnold topology, enabling scalable Bayesian inference with computational complexity quasi-linear in sample size. Through analytic moment matching, we propagate uncertainty through deep additive structures while maintaining interpretability. We use three example studies to demonstrate the framework's ability to distinguish aleatoric from epistemic uncertainty: calibration of heteroscedastic measurement noise in fluid flow reconstruction, quantification of prediction confidence degradation in multi-step forecasting of advection-diffusion dynamics, and out-of-distribution detection in convolutional autoencoders. These results suggest Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KANs) is a promising architecture for uncertainty-aware learning in scientific machine learning.

Two pressing topics in the theory of deep learning are the interpretation of feature learning mechanisms and the determination of implicit bias of networks in the rich regime. Current theories of rich feature learning, often appear in the form of high-dimensional non-linear equations, which require computationally intensive numerical solutions. Given the many details that go into defining a deep learning problem, this complexity is a significant and often unavoidable challenge. Here, we propose a powerful heuristic route for predicting the data and width scales at which various patterns of feature learning emerge. This form of scale analysis is considerably simpler than exact theories and reproduces the scaling exponents of various known results. In addition, we make novel predictions on complex toy architectures, such as three-layer non-linear networks and attention heads, thus extending the scope of first-principle theories of deep learning.

We present CLAPS, a posterior-aware conformal regression method that pairs a Last-Layer Laplace Approximation with split-conformal calibration. From the resulting Gaussian posterior, CLAPS defines a simple two-sided posterior CDF score that aligns the conformity metric with the full predictive shape, not just a point estimate. This alignment yields narrower prediction intervals at the same target coverage, especially on small to medium tabular datasets where data are scarce and uncertainty modeling matters. We also provide a lightweight diagnostic suite that separates aleatoric and epistemic components and visualizes posterior behavior, helping practitioners understand why intervals shrink when they do. Across multiple benchmarks using the same MLP backbone, CLAPS consistently attains nominal coverage with improved efficiency and minimal overhead, offering a clear, practical upgrade to residual-based conformal baselines.

Self-supervised speech models have demonstrated impressive performance in speech processing, but their effectiveness on non-speech data remains underexplored. We study the transfer learning capabilities of such models on bioacoustic detection and classification tasks. We show that models such as HuBERT, WavLM, and XEUS can generate rich latent representations of animal sounds across taxa. We analyze the models properties with linear probing on time-averaged representations. We then extend the approach to account for the effect of time-wise information with other downstream architectures. Finally, we study the implication of frequency range and noise on performance. Notably, our results are competitive with fine-tuned bioacoustic pre-trained models and show the impact of noise-robust pre-training setups. These findings highlight the potential of speech-based self-supervised learning as an efficient framework for advancing bioacoustic research.

Directed fuzzing aims to find program inputs that lead to specified target program states. It has broad applications, such as debugging system crashes, confirming reported bugs, and generating exploits for potential vulnerabilities. This task is inherently challenging because target states are often deeply nested in the program, while the search space manifested by numerous possible program inputs is prohibitively large. Existing approaches rely on branch distances or manually-specified constraints to guide the search; however, the branches alone are often insufficient to precisely characterize progress toward reaching the target states, while the manually specified constraints are often tailored for specific bug types and thus difficult to generalize to diverse target states and programs. We present Locus, a novel framework to improve the efficiency of directed fuzzing. Our key insight is to synthesize predicates to capture fuzzing progress as semantically meaningful intermediate states, serving as milestones towards reaching the target states. When used to instrument the program under fuzzing, they can reject executions unlikely to reach the target states, while providing additional coverage guidance. To automate this task and generalize to diverse programs, Locus features an agentic framework with program analysis tools to synthesize and iteratively refine the candidate predicates, while ensuring the predicates strictly relax the target states to prevent false rejections via symbolic execution. Our evaluation shows that Locus substantially improves the efficiency of eight state-of-the-art fuzzers in discovering real-world vulnerabilities, achieving an average speedup of 41.6x. So far, Locus has found nine previously unpatched bugs, with three already acknowledged with draft patches.