Sharpness-aware minimization (SAM) has emerged as a highly effective technique to improve model generalization, but its underlying principles are not fully understood. We investigate m-sharpness, where SAM performance improves monotonically as the micro-batch size for computing perturbations decreases, a phenomenon critical for distributed training yet lacking rigorous explanation. We leverage an extended Stochastic Differential Equation (SDE) framework and analyze stochastic gradient noise (SGN) to characterize the dynamics of SAM variants, including n-SAM and m-SAM. Our analysis reveals that stochastic perturbations induce an implicit variance-based sharpness regularization whose strength increases as m decreases. Motivated by this insight, we propose Reweighted SAM (RW-SAM), which employs sharpness-weighted sampling to mimic the generalization benefits of m-SAM while remaining parallelizable.

Despite Contrastive Language-Image Pre-training (CLIP)'s remarkable capability to retrieve content across modalities, a substantial modality gap persists in its feature space. Intriguingly, we discover that off-the-shelf MLLMs (Multimodal Large Language Models) demonstrate powerful inherent modality alignment properties. While recent MLLM-based retrievers with unified architectures partially mitigate this gap, their reliance on coarse modality alignment mechanisms fundamentally limits their potential. In this work, We introduce MAPLE (Modality-Aligned Preference Learning for Embeddings), a novel framework that leverages the finegrained alignment priors inherent in MLLM to guide cross-modal representation learning. MAPLE formulates the learning process as reinforcement learning with two key components: (1) Automatic preference data construction using off-theshelf MLLM, and (2) a new Relative Preference Alignment (RPA) loss, which adapts Direct Preference Optimization (DPO) to the embedding learning setting. Experimental results show that our preference-guided alignment achieves substantial gains in fine-grained cross-modal retrieval, underscoring its effectiveness in handling nuanced semantic distinctions.

Low-Rank Adaptation (LoRA) offers a cost-effective solution for fine-tuning large language models (LLMs), but it often produces overconfident predictions in datascarce few-shot settings. To address this issue, several classical statistical learning approaches have been repurposed for scalable uncertainty-aware LoRA fine-tuning. However, these approaches neglect how input characteristics affect the predictive uncertainty estimates. To address this limitation, we propose Contextual Low-Rank Adaptation (C-LoRA) as a novel uncertainty-aware and parameter efficient finetuning approach, by developing new lightweight LoRA modules contextualized to each input data sample to dynamically adapt uncertainty estimates. Incorporating data-driven contexts into the parameter posteriors, C-LoRA mitigates overfitting, achieves well-calibrated uncertainties, and yields robust predictions.

Learning object-level, structured representations is widely regarded as a key to better generalization in vision and underpins the design of next-generation Pre-trained Vision Models (PVMs). Mainstream Object-Centric Learning (OCL) methods adopt Slot Attention or its variants to iteratively aggregate objects' super-pixels into a fixed set of query feature vectors, termed slots. However, their reliance on a static slot count leads to an object being represented as multiple parts when the number of objects varies. We introduce MetaSlot, a plug-and-play Slot Attention variant that adapts to variable object counts. MetaSlot (i) maintains a codebook that holds prototypes of objects in a dataset by vector-quantizing the resulting slot representations; (ii) removes duplicate slots from the traditionally aggregated slots by quantizing them with the codebook; and (iii) injects progressively weaker noise into the Slot Attention iterations to accelerate and stabilize the aggregation. MetaSlot is a general Slot Attention variant that can be seamlessly integrated into existing OCL architectures. Across multiple public datasets and tasks-including object discovery and recognition-models equipped with MetaSlot achieve significant performance gains and markedly interpretable slot representations, compared with existing Slot Attention variants.

Denoiser models have become powerful tools for inverse problems, enabling the use of pretrained networks to approximate the score of a smoothed prior distribution. These models are often used in heuristic iterative schemes aimed at solving Maximum a Posteriori (MAP) optimisation problems, where the proximal operator of the negative log-prior plays a central role. In practice, this operator is intractable, and practitioners plug in a pretrained denoiser as a surrogate--despite the lack of general theoretical justification for this substitution. In this work, we show that a simple algorithm, closely related to several used in practice, provably converges to the proximal operator under a log-concavity assumption on the prior p. We show that this algorithm can be interpreted as a gradient descent on smoothed proximal objectives. Our analysis thus provides a theoretical foundation for a class of empirically successful but previously heuristic methods.

Transformers have emerged as a powerful neural network architecture capable of tackling a wide range of learning tasks. In this work, we provide a theoretical analysis of their ability to automatically extract structure from data in an unsupervised setting. In particular, we demonstrate their suitability for clustering when the input data is generated from a Gaussian mixture model. To this end, we study a simplified two-head attention layer and define a population risk whose minimization with unlabeled data drives the head parameters to align with the true mixture centroids. This phenomenon highlights the ability of attention-based layers to capture underlying distributional structure. We further examine an attention layer with key, query, and value matrices fixed to the identity, and show that, even without any trainable parameters, it can perform in-context quantization, revealing the surprising capacity of transformer-based methods to adapt dynamically to input-specific distributions.

Transformers have proven highly effective across various applications, especially in handling sequential data such as natural languages and time series. However, transformer models often lack clear interpretability, and the success of transformers has not been well understood in theory. In this paper, we study the capability and interpretability of transformers in learning a family of classic statistical models, namely random walks on circles. We theoretically demonstrate that, after training with gradient descent, a one-layer transformer model can achieve optimal accuracy in predicting random walks. Importantly, our analysis reveals that the trained model is interpretable: the trained softmax attention serves as a token selector, focusing on the direct parent state; subsequently, the value matrix executes a onestep probability transition to predict the location of the next state based on this parent state. We also show that certain edge cases not covered by our theory are indeed failure cases, demonstrating that our theoretical conditions are tight. By investigating these success and failure cases, it is revealed that gradient descent with small initialization may fail or struggle to converge to a good solution in certain simple tasks even beyond random walks. Experiments are conducted to support our theoretical findings.

Many emerging applications--such as adversarial training, AI alignment, and robust optimization--can be framed as zero-sum games between neural nets, with von Neumann-Nash equilibria (NE) capturing the desirable system behavior. While such games often involve non-convex non-concave objectives, empirical evidence shows that simple gradient methods frequently converge, suggesting a hidden geometric structure. In this paper, we provide a theoretical framework that explains this phenomenon through the lens of hidden convexity and overparameterization. We identify sufficient conditions--spanning initialization, training dynamics, and network width--that guarantee global convergence to a NE in a broad class of non-convex min-max games. To our knowledge, this is the first such result for games that involve two-layer neural networks. Technically, our approach is twofold: (a) we derive a novel path-length bound for the alternating gradient descent-ascent scheme in min-max games; and (b) we show that the reduction from a hidden convex-concave geometry to two-sided Polyak-Łojasiewicz (PL) min-max condition hold with high probability under overparameterization, using tools from random matrix theory.

We study whether visual embedding models capture continuous, ordinal attributes along linear directions, which we term rank axes. We define a model as rankable for an attribute if projecting embeddings onto such an axis preserves the attribute's order. Across 7 popular encoders and 9 datasets with attributes like age, crowd count, head pose, aesthetics, and recency, we find that many embeddings are inherently rankable. Surprisingly, a small number of samples, or even just two extreme examples, often suffice to recover meaningful rank axes, without full-scale supervision. These findings open up new use cases for image ranking in vector databases and motivate further study into the structure and learning of rankable embeddings.

Retraining a model using its own predictions together with the original, potentially noisy labels is a well-known strategy for improving the model's performance. While prior works have demonstrated the benefits of specific heuristic retraining schemes, the question of how to optimally combine the model's predictions and the provided labels remains largely open.