Test-time training (TTT) adapts a pretrained model to each prompt via parameter updates, improving accuracy under pretraining-to-test distribution shifts. Yet, its performance often suffers from instability and sensitivity to hyperparameters such as update steps and subspace. We explain this behavior through a decision-theoretic lens, treating TTT as implicit Bayesian inference in the kernel regime. Under a Gaussian process benchmark, we show that TTT reduces prediction error when updates are spectrally matched to the prompt's signal-to-noise ratio and aligned with query-relevant eigen-directions. This perspective underpins the following results: (1) we show when fixed update steps and subspaces fail under distribution shifts, motivating adaptive strategies; (2) we prove that selecting update steps via prompt evidence admits a PAC-Bayes guarantee against overfitting; and (3) we characterize the Bayes-optimal update subspace under a linear-Gaussian correction model, yielding a scoring rule for selecting Transformer blocks and heads. Our theory helps explain the empirical instability of TTT, taking a step toward principled guidance for when, how far, and which directions to adapt.

Detecting distributional differences between two independent samples is a fundamental problem in statistics and machine learning. Nonparametric two-sample testing provides a principled framework for determining whether two samples are drawn from the same underlying distribution, without assuming any specific parametric form for the distribution. In this study, we propose a new two-sample test statistic based on a newly introduced integral probability metric (IPM), using a specially designed parametric discriminator class with a single node of a neural network. We show that the resulting test statistic, called PReLU-IPM, is nonparametric and establish theoretical guarantees for the associated two-sample testing procedure, PReLU-TST, including its consistency and asymptotical equivalence to nonparametric IPM-based tests under regularity conditions. By analyzing multiple simulated and real benchmark datasets, we demonstrate that PReLU-TST achieves higher power across a range of alternatives or performs comparably to its competitors, for finite samples.

Sampling from complex, unnormalized probability densities is a fundamental challenge in Bayesian inference and probabilistic modeling. While Markov chain Monte Carlo (MCMC) methods provide asymptotic guarantees, they often suffer from slow mixing and high computational costs due to fixed or manually tuned trajectory lengths. In this work, we propose a novel framework that treats trajectory termination as a learnable component of the sampling dynamics. By framing MCMC within the theory of non-acyclic generative flow networks (GFlowNets), we train state-dependent neural classifiers to decide when a trajectory has reached a high-density region and should terminate. We theoretically establish the connection between optimal classifiers and the target density via detailed balance conditions and introduce a multilevel training scheme to facilitate exploration in complex geometries. Experimental results across various benchmark densities demonstrate that our approach significantly reduces average trajectory lengths while improving mode coverage and mixing compared to standard MCMC baselines.

A significant gap exists between theory and practice in deep learning. Generalization and approximation error bounds are often derived for simplified models or are too loose to be informative. Many rely on the manifold hypothesis and on geometric regularity such as intrinsic dimension, curvature, and reach. Progress requires insight into data-manifold geometry and suitable benchmarks, yet existing options are polarized: analytic manifolds with known geometry but limited applicability, or real-world datasets where geometry is only coarsely estimable. We introduce a benchmarking framework for studying data geometry. We repurpose and extend dSprites and COIL-20 with additional transformation dimensions and dense, axis-aligned sampling, and pair them with finite-difference estimators that recover curvature, reach, and volume at near-ground-truth accuracy in a regime where general-purpose estimators are unreliable or difficult to deploy. The framework is intended as a controlled testbed, useful as a calibration environment for geometric estimators and a sandbox for probing theoretical assumptions. To illustrate its use, we present two application studies, namely assessing the scaling behavior of the bounds of Genovese et al. and Fefferman et al., and tracking the layer-wise geometry of a $β$-VAE, highlighting the behavior of current bounds and the value of controlled benchmarks for guiding and validating future theory. A reference implementation is available at https://github.com/koulakis/manifold-microscope.

Simulation-based inference (SBI) of latent parameters is often hindered by simulator misspecification, the mismatch between simulated and real-world observations caused by inherent modeling simplifications. RoPE, the recent state-of-the-art for robust SBI, addresses this through optimal transport between learned representations of real and simulated observations, but requires ground-truth parameter calibration pairs that are typically unavailable in the very settings where SBI is needed. What practitioners do have is unstructured side-information such as regime labels, instruction text, and policy bulletins. We propose Misspecification-Aware Simulation-Based Inference (MA-SBI), a calibration-free framework that turns this side-channel into a posterior correction. A learned corrector maps side-channel text to an observation-space shift applied before any pre-trained amortized posterior, requiring no retraining and no parameter ground-truth. Our main theorem bounds achievable bias reduction by the mutual information between misspecification and side-channel, with a non-vacuous constant that extends to all sub-Gaussian noise via Donsker-Varadhan. On hide-the-calibration benchmarks, MA-SBI with text alone matches the oracle posterior across 10 seeds and two backbones (TOST equivalence), while RoPE given more data does not. The two approaches are complementary: where misspecification is structural and recoverable from parameter pairs, RoPE dominates, as the theory predicts. A stochastic variant improves posterior-predictive log-likelihood on real COVID and OxCGRT epidemiological data, and correctly leaves the posterior unchanged on a well-specified cognitive-science corpus.

We propose SCONE (Scalable, Contextualized, Offloaded, N-gram Embedding), a new method for extending input embedding layers to enhance language model performance. To avoid increased decoding costs, SCONE retains the original vocabulary while introducing embeddings for a set of frequent n-grams. These embeddings provide contextualized representation for each input token and are learned with a separate model during training. After training, embeddings are precomputed and stored in off-accelerator memory; during inference, querying them has minimal impact on latency due to the low complexity of embedding lookups. SCONE enables two new scaling strategies: increasing the number of n-gram embeddings and scaling the model used to learn them, both while maintaining fixed accelerator usage during inference (in terms of FLOPS and memory). We show that scaling both aspects enables a model with 1B accelerator-resident parameters to outperform a 1.9B-parameter baseline across diverse corpora, while using only about half the FLOPS and accelerator memory during inference.

Recent advancements in text-guided image editing have achieved notable success by leveraging natural language prompts for fine-grained semantic control. However, certain editing semantics are challenging to specify precisely using textual descriptions alone. A practical alternative involves learning editing semantics from paired source-target examples. Existing exemplar-based editing methods still rely on text prompts describing the change within paired examples or learning implicit text-based editing instructions. In this paper, we introduce PairEdit, a novel visual editing method designed to effectively learn complex editing semantics from a limited number of image pairs or even a single image pair, without using any textual guidance. We propose a target noise prediction that explicitly models semantic variations within paired images through a guidance direction term. Moreover, we introduce a content-preserving noise schedule to facilitate more effective semantic learning. We also propose optimizing distinct LoRAs to disentangle the learning of semantic variations from content. Extensive qualitative and quantitative evaluations demonstrate that PairEdit successfully learns intricate semantics while significantly improving content consistency compared to baseline methods.

Conventional representation learning methods learn a universal representation that primarily captures dominant semantics, which may not always align with customized downstream tasks. For instance, in animal habitat analysis, researchers prioritize scene-related features, whereas universal embeddings emphasize categorical semantics, leading to suboptimal results. As a solution, existing approaches resort to supervised fine-tuning, which however incurs high computational and annotation costs. In this paper, we propose Conditional Representation Learning (CRL), aiming to extract representations tailored to arbitrary user-specified criteria. Specifically, we reveal that the semantics of a space are determined by its basis, thereby enabling a set of descriptive words to approximate the basis for a customized feature space. Building upon this insight, given a user-specified criterion, CRL first employs a large language model (LLM) to generate descriptive texts to construct the semantic basis, then projects the image representation into this conditional feature space leveraging a vision-language model (VLM). The conditional representation better captures semantics for the specific criterion, which could be utilized for multiple customized tasks. Extensive experiments on classification and retrieval tasks demonstrate the superiority and generality of the proposed CRL.

Recent advances in large language models (LLMs) have yielded impressive performance on various tasks, yet they often depend on high-quality feedback that can be costly. Self-refinement methods attempt to leverage LLMs' internal evaluation mechanisms with minimal human supervision; however, these approaches frequently suffer from inherent biases and overconfidence, especially in domains where the models lack sufficient internal knowledge, resulting in performance degradation. As an initial step toward enhancing self-refinement for broader applications, we introduce an iterative refinement pipeline that employs the Unlabeled-Unlabeled learning framework to improve LLM-generated pseudo-labels for classification tasks.

We study metric distortion in distributed voting, where nvoters are partitioned into k groups, each selecting a local representative, and a final winner is chosen from these representatives (or from the entire set of candidates). This setting models systems like U.S. presidential elections, where state-level decisions determine the national outcome. We focus on four cost objectives from Anshelevich et al. [1]: avg-avg, avg-max, max-avg, and max-max. We present improved distortion bounds for both deterministic and randomized mechanisms, offering a near-complete characterization of distortion in this model. For deterministic mechanisms, we reduce the upper bound for avg-max from 11 to 7, establish a tight lower bound of 5 for max-avg (improving on 2+ 5), and tighten the upper bound for max-max from 5 to 3. For randomized mechanisms, we consider two settings: (i) only the second stage is randomized, and (ii) both stages may be randomized. In case (i), we prove tight bounds: 5 2/k for avg-avg, 3for avg-max and max-max, and 5for max-avg. In case (ii), we show tight bounds of 3 for max-avg and max-max, and nearly tight bounds for avg-avg and avg-max within [3 2/n, 3 2/(kn)]and [3 2/n, 3], respectively, where n denotes the largest group size.