We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic normal distribution, samples undergo sharp, discrete transitions, eventually forming distinct events of a desired distribution while progressively revealing finer structure. As this process is reversible, these transitions also occur in reverse, where intermediate states progressively merge, tracing a path back to the initial distribution. We demonstrate that these transitions can be detected as discontinuities in nth-order cross-fluctuations. For variance-preserving SDEs, we derive a closed-form for these cross-fluctuations that is efficiently computable for the reverse trajectory. We find that detecting these transitions directly boosts sampling efficiency, accelerates class-conditional and rare-class generation, and improves two zero-shot tasks-image classification and style transfer-without expensive grid search or retraining. We also show that this viewpoint unifies classical coupling and mixing from finite Markov chains with continuous dynamics while extending to stochastic SDEs and non Markovian samplers.

The variables of the low-level model (left) are divided into partitions (center) such that each low-level partition corresponds to a high level variable from the high-level model (right). The circles represent variables and the arrows represent causal dependencies. Blue circles are variables that are not being intervened on and red circles are variables that are being intervened on. Observe that a low-level causal dependence between partitions does not necessarily result in a high-level causal dependence between variables and that not every low-level intervention results in a high level intervention.

Gradient descent on log-sum-exp (LSE) objectives performs implicit expectation--maximization (EM): the gradient with respect to each component output equals its responsibility. The same theory predicts collapse without volume control analogous to the log-determinant in Gaussian mixture models. We instantiate the theory in a single-layer encoder with an LSE objective and InfoMax regularization for volume control. Experiments confirm the theory's predictions. The gradient--responsibility identity holds exactly; LSE alone collapses; variance prevents dead components; decorrelation prevents redundancy. The model exhibits EM-like optimization dynamics in which lower loss does not correspond to better features and adaptive optimizers offer no advantage. The resulting decoder-free model learns interpretable mixture components, confirming that implicit EM theory can prescribe architectures.

Typographic attacks exploit multi-modal systems by injecting text into images, leading to targeted misclassifications, malicious content generation and even Vision-Language Model jailbreaks. In this work, we analyze how CLIP vision encoders behave under typographic attacks, locating specialized attention heads in the latter half of the model's layers that causally extract and transmit typographic information to the cls token. Building on these insights, we introduce a method to defend CLIP models against typographic attacks by selectively ablating a typographic circuit, consisting of attention heads. Without requiring finetuning, our method improves performance by up to 19.6% on a typographic variant of ImageNet-100, while reducing standard ImageNet-100 accuracy by less than 1%. Notably, our training-free approach remains competitive with current state-of-the-art typographic defenses that rely on finetuning. To this end, we release a family of dyslexic CLIP models which are significantly more robust against typographic attacks. These models serve as suitable drop-in replacements for a broad range of safety-critical applications, where the risks of text-based manipulation outweigh the utility of text recognition.

The syntactic structures of sentences can be readily read-out from the activations of large language models (LLMs). However, the ``structural probes'' that have been developed to reveal this phenomenon are typically evaluated on an indiscriminate set of sentences. Consequently, it remains unclear whether structural and/or statistical factors systematically affect these syntactic representations. To address this issue, we conduct an in-depth analysis of structural probes on three controlled benchmarks. Our results are three-fold. First, structural probes are biased by a superficial property: the closer two words are in a sentence, the more likely structural probes will consider them as syntactically linked. Second, structural probes are challenged by linguistic properties: they poorly represent deep syntactic structures, and get interfered by interacting nouns or ungrammatical verb forms. Third, structural probes do not appear to be affected by the predictability of individual words. Overall, this work sheds light on the current challenges faced by structural probes. Providing a benchmark made of controlled stimuli to better evaluate their performance.

We investigate the generalization capabilities of small language models under two popular adaptation paradigms: few-shot prompting and supervised fine-tuning. While prompting is often favored for its parameter efficiency and flexibility, it remains unclear how robust this approach is in low-resource settings and under distributional shifts. This paper presents a comparative study of prompting and fine-tuning across task formats, prompt styles, and model scales, with a focus on their behavior in both in-distribution and out-of-distribution (OOD) settings. Beyond accuracy, we analyze the internal representations learned by each approach to assess the stability and abstraction of task-specific features. Our findings highlight critical differences in how small models internalize and generalize knowledge under different adaptation strategies. This work offers practical guidance for model selection in low-data regimes and contributes empirical insight into the ongoing debate over prompting versus fine-tuning. Code for the experiments is available at the following

This study investigates the internal reasoning mechanism of language models during symbolic multi-step reasoning, motivated by the question of whether chain-of-thought (CoT) outputs are faithful to the model's internals. Specifically, we inspect when they internally determine their answers, particularly before or after CoT begins, to determine whether models follow a post-hoc "think-to-talk" mode or a step-by-step "talk-to-think" mode of explanation. Through causal probing experiments in controlled arithmetic reasoning tasks, we found systematic internal reasoning patterns across models; for example, simple subproblems are solved before CoT begins, and more complicated multi-hop calculations are performed during CoT.

Many pretrained multilingual models exhibit cross-lingual transfer ability, which is often attributed to a learned language-neutral representation during pretraining. However, it remains unclear what factors contribute to the learning of a language-neutral representation, and whether the learned language-neutral representation suffices to facilitate cross-lingual transfer. We propose a synthetic task, Multilingual Othello (mOthello), as a testbed to delve into these two questions. We find that: (1) models trained with naive multilingual pretraining fail to learn a language-neutral representation across all input languages; (2) the introduction of "anchor tokens" (i.e., lexical items that are identical across languages) helps cross-lingual representation alignment; and (3) the learning of a language-neutral representation alone is not sufficient to facilitate cross-lingual transfer. Based on our findings, we propose a novel approach - multilingual pretraining with unified output space - that both induces the learning of language-neutral representation and facilitates cross-lingual transfer.

Joint embedding (JE) architectures have emerged as a promising avenue for acquiring transferable data representations. A key obstacle to using JE methods, however, is the inherent challenge of evaluating learned representations without access to a downstream task, and an annotated dataset. Without efficient and reliable evaluation, it is difficult to iterate on architectural and training choices for JE methods. In this paper, we introduce LiDAR (Linear Discriminant Analysis Rank), a metric designed to measure the quality of representations within JE architectures. Our metric addresses several shortcomings of recent approaches based on feature covariance rank by discriminating between informative and uninformative features. In essence, LiDAR quantifies the rank of the Linear Discriminant Analysis (LDA) matrix associated with the surrogate SSL task -- a measure that intuitively captures the information content as it pertains to solving the SSL task. We empirically demonstrate that LiDAR significantly surpasses naive rank based approaches in its predictive power of optimal hyperparameters. Our proposed criterion presents a more robust and intuitive means of assessing the quality of representations within JE architectures, which we hope facilitates broader adoption of these powerful techniques in various domains.