pwc-archive/papers-with-abstracts huggingface dataset:
Grokking and Generalization Collapse: Insights from \texttt{HTSR} theory
Authors: Hari K. Prakash, Charles H. Martin
Date: 2025-06-04 00:00:00

We study the well-known grokking phenomena in neural networks (NNs) using a 3-layer MLP trained on 1 k-sample subset of MNIST, with and without weight decay, and discover a novel third phase -- \emph{anti-grokking} -- that occurs very late in training and resembles but is distinct from the familiar \emph{pre-grokking} phases: test accuracy collapses while training accuracy stays perfect. This late-stage collapse is distinct, from the known pre-grokking and grokking phases, and is not detected by other proposed grokking progress measures. Leveraging Heavy-Tailed Self-Regularization HTSR through the open-source WeightWatcher tool, we show that the HTSR layer quality metric $\alpha$ alone delineates all three phases, whereas the best competing metrics detect only the first two. The \emph{anti-grokking} is revealed by training for $10^7$ and is invariably heralded by $\alpha < 2$ and the appearance of \emph{Correlation Traps} -- outlier singular values in the randomized layer weight matrices that make the layer weight matrix atypical and signal overfitting of the training set. Such traps are verified by visual inspection of the layer-wise empirical spectral densities, and by using Kolmogorov--Smirnov tests on randomized spectra. Comparative metrics, including activation sparsity, absolute weight entropy, circuit complexity, and $l^2$ weight norms track pre-grokking and grokking but fail to distinguish grokking from anti-grokking. This discovery provides a way to measure overfitting and generalization collapse without direct access to the test data. These results strengthen the claim that the \emph{HTSR} $\alpha$ provides universal layer-convergence target at $\alpha \approx 2$ and underscore the value of using the HTSR alpha $(\alpha)$ metric as a measure of generalization.
Orthogonal Gradient Descent Improves Neural Calibration
Authors: C. Evans Hedges
Date: 2025-06-04 00:00:00

We provide evidence that orthogonalizing gradients during training improves model calibration without sacrificing accuracy. On CIFAR-10 with 10% labeled data, $\perp$Grad matches SGD in accuracy but yields consistently improved calibration metrics such as lower test loss, reduced softmax overconfidence, and higher predictive entropy. These benefits persist under input corruption (CIFAR-10C) and extended training, where $\perp$Grad models degrade more gracefully than SGD-trained counterparts. $\perp$Grad is optimizer-agnostic, incurs minimal overhead, and works well with post-hoc calibration techniques like temperature scaling. Theoretically, we prove convergence of a simplified version of $\perp$Grad under mild assumptions and characterize its stationary points in positive homogeneous networks: $\perp$Grad converges to solutions where further loss reduction requires confidence scaling rather than decision boundary improvement.
Unsupervised Machine Learning for Scientific Discovery: Workflow and Best Practices
Authors: Andersen Chang, Tiffany M. Tang, Tarek M. Zikry, Genevera I. Allen
Date: 2025-06-05 00:00:00
Tasks: Astronomy, scientific discovery

Unsupervised machine learning is widely used to mine large, unlabeled datasets to make data-driven discoveries in critical domains such as climate science, biomedicine, astronomy, chemistry, and more. However, despite its widespread utilization, there is a lack of standardization in unsupervised learning workflows for making reliable and reproducible scientific discoveries. In this paper, we present a structured workflow for using unsupervised learning techniques in science. We highlight and discuss best practices starting with formulating validatable scientific questions, conducting robust data preparation and exploration, using a range of modeling techniques, performing rigorous validation by evaluating the stability and generalizability of unsupervised learning conclusions, and promoting effective communication and documentation of results to ensure reproducible scientific discoveries. To illustrate our proposed workflow, we present a case study from astronomy, seeking to refine globular clusters of Milky Way stars based upon their chemical composition. Our case study highlights the importance of validation and illustrates how the benefits of a carefully-designed workflow for unsupervised learning can advance scientific discovery.
Subjective Perspectives within Learned Representations Predict High-Impact Innovation
Authors: Likun Cao, Rui Pan, James Evans
Date: 2025-06-05 00:00:00
Tasks: Diversity, Large Language Model

Existing studies of innovation emphasize the power of social structures to shape innovation capacity. Emerging machine learning approaches, however, enable us to model innovators' personal perspectives and interpersonal innovation opportunities as a function of their prior trajectories of experience. We theorize then quantify subjective perspectives and innovation opportunities based on innovator positions within the geometric space of concepts inscribed by dynamic language representations. Using data on millions of scientists, inventors, writers, entrepreneurs, and Wikipedia contributors across the creative domains of science, technology, film, entrepreneurship, and Wikipedia, here we show that measured subjective perspectives anticipate what ideas individuals and groups creatively attend to and successfully combine in future. When perspective and background diversity are decomposed as the angular difference between collaborators' perspectives on their creation and between their experiences, the former consistently anticipates creative achievement while the latter portends its opposite, across all cases and time periods examined. We analyze a natural experiment and simulate creative collaborations between AI (large language model) agents designed with various perspective and background diversity, which are consistent with our observational findings. We explore mechanisms underlying these findings and identify how successful collaborators leverage common language to weave together diverse experience obtained through trajectories of prior work that converge to provoke one another and innovate. We explore the importance of these findings for team assembly and research policy.
On the Mechanism of Reasoning Pattern Selection in Reinforcement Learning for Language Models
Authors: Xingwu Chen, Tianle Li, Difan Zou
Date: 2025-06-05 00:00:00
Tasks: Instruction Following, Reinforcement Learning (RL)

Reinforcement learning (RL) has demonstrated remarkable success in enhancing model capabilities, including instruction-following, preference learning, and reasoning. Yet despite its empirical successes, the mechanisms by which RL improves reasoning abilities remain poorly understood. We present a systematic study of Reinforcement Learning with Verifiable Rewards (RLVR), showing that its primary benefit comes from optimizing the selection of existing reasoning patterns. Through extensive experiments, we demonstrate that RLVR-trained models preferentially adopt high-success-rate reasoning patterns while mostly maintaining stable performance on individual patterns. We further develop theoretical analyses on the convergence and training dynamics of RLVR based on a simplified question-reason-answer model. We study the gradient flow and show that RLVR can indeed find the solution that selects the reason pattern with the highest success rate. Besides, our theoretical results reveal two distinct regimes regarding the convergence of RLVR training: (1) rapid convergence for models with relatively strong initial reasoning capabilities versus (2) slower optimization dynamics for weaker models. Furthermore, we show that the slower optimization for weaker models can be mitigated by applying the supervised fine-tuning (SFT) before RLVR, when using a feasibly high-quality SFT dataset. We validate the theoretical findings through extensive experiments. This work advances our theoretical understanding of RL's role in LLM fine-tuning and offers insights for further enhancing reasoning capabilities.
Explicit Density Approximation for Neural Implicit Samplers Using a Bernstein-Based Convex Divergence
Authors: José Manuel de Frutos, Manuel A. Vázquez, Pablo M. Olmos, Joaquín Míguez
Date: 2025-06-05 00:00:00

Rank-based statistical metrics, such as the invariant statistical loss (ISL), have recently emerged as robust and practically effective tools for training implicit generative models. In this work, we introduce dual-ISL, a novel likelihood-free objective for training implicit generative models that interchanges the roles of the target and model distributions in the ISL framework, yielding a convex optimization problem in the space of model densities. We prove that the resulting rank-based discrepancy $d_K$ is i) continuous under weak convergence and with respect to the $L^1$ norm, and ii) convex in its first argument-properties not shared by classical divergences such as KL or Wasserstein distances. Building on this, we develop a theoretical framework that interprets $d_K$ as an $L^2$-projection of the density ratio $q = p/\tilde p$ onto a Bernstein polynomial basis, from which we derive exact bounds on the truncation error, precise convergence rates, and a closed-form expression for the truncated density approximation. We further extend our analysis to the multivariate setting via random one-dimensional projections, defining a sliced dual-ISL divergence that retains both convexity and continuity. We empirically show that these theoretical advantages translate into practical ones. Specifically, across several benchmarks dual-ISL converges more rapidly, delivers markedly smoother and more stable training, and more effectively prevents mode collapse than classical ISL and other leading implicit generative methods-while also providing an explicit density approximation.
Amortized variational transdimensional inference
Authors: Laurence Davies, Dan MacKinlay, Rafael Oliveira, Scott A. Sisson
Date: 2025-06-05 00:00:00
Tasks: Bayesian Inference, Bayesian Optimization, Variational Inference

The expressiveness of flow-based models combined with stochastic variational inference (SVI) has, in recent years, expanded the application of optimization-based Bayesian inference to include problems with complex data relationships. However, until now, SVI using flow-based models has been limited to problems of fixed dimension. We introduce CoSMIC, normalizing flows (COntextually-Specified Masking for Identity-mapped Components), an extension to neural autoregressive conditional normalizing flow architectures that enables using a single amortized variational density for inference over a transdimensional target distribution. We propose a combined stochastic variational transdimensional inference (VTI) approach to training CoSMIC flows using techniques from Bayesian optimization and Monte Carlo gradient estimation. Numerical experiments demonstrate the performance of VTI on challenging problems that scale to high-cardinality model spaces.
kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradients
Authors: Iosif Lytras, Sotirios Sabanis, Ying Zhang
Date: 2025-06-05 00:00:00

Motivated by applications in deep learning, where the global Lipschitz continuity condition is often not satisfied, we examine the problem of sampling from distributions with super-linearly growing log-gradients. We propose a novel tamed Langevin dynamics-based algorithm, called kTULA, to solve the aforementioned sampling problem, and provide a theoretical guarantee for its performance. More precisely, we establish a non-asymptotic convergence bound in Kullback-Leibler (KL) divergence with the best-known rate of convergence equal to $2-\overline{\epsilon}$, $\overline{\epsilon}>0$, which significantly improves relevant results in existing literature. This enables us to obtain an improved non-asymptotic error bound in Wasserstein-2 distance, which can be used to further derive a non-asymptotic guarantee for kTULA to solve the associated optimization problems. To illustrate the applicability of kTULA, we apply the proposed algorithm to the problem of sampling from a high-dimensional double-well potential distribution and to an optimization problem involving a neural network. We show that our main results can be used to provide theoretical guarantees for the performance of kTULA.
Unregularized limit of stochastic gradient method for Wasserstein distributionally robust optimization
Authors: Tam Le
Date: 2025-06-05 00:00:00

Distributionally robust optimization offers a compelling framework for model fitting in machine learning, as it systematically accounts for data uncertainty. Focusing on Wasserstein distributionally robust optimization, we investigate the regularized problem where entropic smoothing yields a sampling-based approximation of the original objective. We establish the convergence of the approximate gradient over a compact set, leading to the concentration of the regularized problem critical points onto the original problem critical set as regularization diminishes and the number of approximation samples increases. Finally, we deduce convergence guarantees for a projected stochastic gradient method. Our analysis covers a general machine learning situation with an unbounded sample space and mixed continuous-discrete data.
Towards Reasonable Concept Bottleneck Models
Authors: Nektarios Kalampalikis, Kavya Gupta, Georgi Vitanov, Isabel Valera
Date: 2025-06-05 00:00:00

In this paper, we propose $\textbf{C}$oncept $\textbf{REA}$soning $\textbf{M}$odels (CREAM), a novel family of Concept Bottleneck Models (CBMs) that: (i) explicitly encodes concept-concept (${\texttt{C-C}}$) and concept-task (${\texttt{C$\rightarrow$Y}}$) relationships to enforce a desired model reasoning; and (ii) use a regularized side-channel to achieve competitive task performance, while keeping high concept importance. Specifically, CREAM architecturally embeds (bi)directed concept-concept, and concept to task relationships specified by a human expert, while severing undesired information flows (e.g., to handle mutually exclusive concepts). Moreover, CREAM integrates a black-box side-channel that is regularized to encourage task predictions to be grounded in the relevant concepts, thereby utilizing the side-channel only when necessary to enhance performance. Our experiments show that: (i) CREAM mainly relies on concepts while achieving task performance on par with black-box models; and (ii) the embedded ${\texttt{C-C}}$ and ${\texttt{C$\rightarrow$Y}}$ relationships ease model interventions and mitigate concept leakage.
NIMO: a Nonlinear Interpretable MOdel
Authors: Shijian Xu, Marcello Massimo Negri, Volker Roth
Date: 2025-06-05 00:00:00
Tasks: model

Neural networks (NNs) have achieved tremendous success over the past decade, yet they are still extremely difficult to interpret. In contrast, linear models are less expressive but offer inherent interpretability. Linear coefficients are interpretable as the marginal effect of a feature on the prediction, assuming all other features are kept fixed. To combine the benefits of both approaches, we introduce NIMO (Nonlinear Interpretable MOdel). The key idea is to define a model where the NN is designed to learn nonlinear corrections to the linear model predictions, while also maintaining the original interpretability of the linear coefficients. Relevantly, we develop an optimization algorithm based on profile likelihood that elegantly allows for optimizing over the NN parameters while updating the linear coefficients analytically. By relying on adaptive ridge regression we can easily incorporate sparsity constraints as well. We show empirically that we can recover the underlying linear coefficients while significantly improving the predictive accuracy. Compared to other hybrid interpretable approaches, our model is the only one that actually maintains the same interpretability of linear coefficients as in linear models. We also achieve higher performance on various regression and classification settings.
UnHiPPO: Uncertainty-aware Initialization for State Space Models
Authors: Marten Lienen, Abdullah Saydemir, Stephan Günnemann
Date: 2025-06-05 00:00:00
Tasks: State Space Models

State space models are emerging as a dominant model class for sequence problems with many relying on the HiPPO framework to initialize their dynamics. However, HiPPO fundamentally assumes data to be noise-free; an assumption often violated in practice. We extend the HiPPO theory with measurement noise and derive an uncertainty-aware initialization for state space model dynamics. In our analysis, we interpret HiPPO as a linear stochastic control problem where the data enters as a noise-free control signal. We then reformulate the problem so that the data become noisy outputs of a latent system and arrive at an alternative dynamics initialization that infers the posterior of this latent system from the data without increasing runtime. Our experiments show that our initialization improves the resistance of state-space models to noise both at training and inference time. Find our implementation at https://cs.cit.tum.de/daml/unhippo.
Transformers Meet In-Context Learning: A Universal Approximation Theory
Authors: Gen Li, Yuchen Jiao, Yu Huang, Yuting Wei, Yuxin Chen
Date: 2025-06-05 00:00:00
Tasks: In-Context Learning

Modern large language models are capable of in-context learning, the ability to perform new tasks at inference time using only a handful of input-output examples in the prompt, without any fine-tuning or parameter updates. We develop a universal approximation theory to better understand how transformers enable in-context learning. For any class of functions (each representing a distinct task), we demonstrate how to construct a transformer that, without any further weight updates, can perform reliable prediction given only a few in-context examples. In contrast to much of the recent literature that frames transformers as algorithm approximators -- i.e., constructing transformers to emulate the iterations of optimization algorithms as a means to approximate solutions of learning problems -- our work adopts a fundamentally different approach rooted in universal function approximation. This alternative approach offers approximation guarantees that are not constrained by the effectiveness of the optimization algorithms being approximated, thereby extending far beyond convex problems and linear function classes. Our construction sheds light on how transformers can simultaneously learn general-purpose representations and adapt dynamically to in-context examples.
Sample Complexity and Representation Ability of Test-time Scaling Paradigms
Authors: Baihe Huang, Shanda Li, Tianhao Wu, Yiming Yang, Ameet Talwalkar, Kannan Ramchandran, Michael I. Jordan, Jiantao Jiao
Date: 2025-06-05 00:00:00

Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies -- such as self-consistency, best-of-$n$, and self-correction -- remains limited. In this work, we first establish a separation result between two repeated sampling strategies: self-consistency requires $\Theta(1/\Delta^2)$ samples to produce the correct answer, while best-of-$n$ only needs $\Theta(1/\Delta)$, where $\Delta < 1$ denotes the probability gap between the correct and second most likely answers. Next, we present an expressiveness result for the self-correction approach with verifier feedback: it enables Transformers to simulate online learning over a pool of experts at test time. Therefore, a single Transformer architecture can provably solve multiple tasks without prior knowledge of the specific task associated with a user query, extending the representation theory of Transformers from single-task to multi-task settings. Finally, we empirically validate our theoretical results, demonstrating the practical effectiveness of self-correction methods.
Heterogeneous Treatment Effect in Time-to-Event Outcomes: Harnessing Censored Data with Recursively Imputed Trees
Authors: Tomer Meir, Uri Shalit, Malka Gorfine
Date: 2025-02-03 00:00:00
Tasks: Causal Inference, Imputation

Tailoring treatments to individual needs is a central goal in fields such as medicine. A key step toward this goal is estimating Heterogeneous Treatment Effects (HTE) - the way treatments impact different subgroups. While crucial, HTE estimation is challenging with survival data, where time until an event (e.g., death) is key. Existing methods often assume complete observation, an assumption violated in survival data due to right-censoring, leading to bias and inefficiency. Cui et al. (2023) proposed a doubly-robust method for HTE estimation in survival data under no hidden confounders, combining a causal survival forest with an augmented inverse-censoring weighting estimator. However, we find it struggles under heavy censoring, which is common in rare-outcome problems such as Amyotrophic lateral sclerosis (ALS). Moreover, most current methods cannot handle instrumental variables, which are a crucial tool in the causal inference arsenal. We introduce Multiple Imputation for Survival Treatment Response (MISTR), a novel, general, and non-parametric method for estimating HTE in survival data. MISTR uses recursively imputed survival trees to handle censoring without directly modeling the censoring mechanism. Through extensive simulations and analysis of two real-world datasets-the AIDS Clinical Trials Group Protocol 175 and the Illinois unemployment dataset we show that MISTR outperforms prior methods under heavy censoring in the no-hidden-confounders setting, and extends to the instrumental variable setting. To our knowledge, MISTR is the first non-parametric approach for HTE estimation with unobserved confounders via instrumental variables.
Infinitesimal Higher-Order Spectral Variations in Rectangular Real Random Matrices
Authors: Róisín Luo
Date: 2025-06-04 00:00:00

We present a theoretical framework for deriving the general $n$-th order Fr\'echet derivatives of singular values in real rectangular matrices, by leveraging reduced resolvent operators from Kato's analytic perturbation theory for self-adjoint operators. Deriving closed-form expressions for higher-order derivatives of singular values is notoriously challenging through standard matrix-analysis techniques. To overcome this, we treat a real rectangular matrix as a compact operator on a finite-dimensional Hilbert space, and embed the rectangular matrix into a block self-adjoint operator so that non-symmetric perturbations are captured. Applying Kato's asymptotic eigenvalue expansion to this construction, we obtain a general, closed-form expression for the infinitesimal $n$-th order spectral variations. Specializing to $n=2$ and deploying on a Kronecker-product representation with matrix convention yield the Hessian of a singular value, not found in literature. By bridging abstract operator-theoretic perturbation theory with matrices, our framework equips researchers with a practical toolkit for higher-order spectral sensitivity studies in random matrix applications (e.g., adversarial perturbation in deep learning).