27 accepted papers
Molecular dynamics (MD) simulations underpin modern computational drug discovery, materials science, and biochemistry. Recent machine learning models provide high-fidelity MD predictions without the need for repeated quantum-mechanical force calculations, enabling significant speedups over conventio…
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with deep learning models promises fast solvers and new perspecti…
Neural rough differential equations (NRDEs) learn continuous-time dynamics from irregularly sampled sequences by encoding the input path with signature features, providing robustness to discretisation and sampling irregularity. However, existing NRDEs implicitly rely on algebraic identities that can…
Training large language models (LLMs) typically relies on adaptive optimizers such as Adam, which introduce extra operations and require significant more memory to maintain first- and second-order moments than SGD. While recent works such as GaLore, Fira and APOLLO have proposed state-compressed var…
One crucial factor behind the success of deep learning lies in the implicit bias induced by noise inherent in gradient-based training algorithms. Motivated by empirical observations that training with noisy labels improves model generalization, we delve into the underlying mechanisms behind stochast
Recent curriculum techniques in the post-training stage of LLMs have been empirically observed to outperform non-curriculum approaches in improving reasoning performance, yet a principled understanding of their effectiveness and limitations remains incomplete. To bridge this gap, we develop an abstr…
Message-passing neural networks (MPNNs) often suffer from an information bottleneck when capturing long-range dependencies, leading to the oversquashing (OSQ) phenomenon. Alongside spatial connectivity enrichment (e.g., rewiring), recent studies have shown that spectral filtering can yield strong lo…
Although unified MLLMs aim to unify generation and understanding, they are considered to exhibit an internal gap, with understanding outperforming generation. Through large‑scale evaluation across multiple MLLMs and tasks, we confirm the widespread non‑unification of MLLMs, and demonstrate that it i…
Supervised learning relies on high-quality labeled data, but obtaining such data through human annotation is both expensive and time-consuming. Recent work explores using large language models (LLMs) for annotation, but LLM-generated labels still fall short of human-level quality. To address this pr…
Despite the remarkable success of diffusion models (DMs) in data generation, they exhibit specific failure cases with unsatisfactory outputs. We focus on one such limitation: the ability of DMs to learn hidden rules between image features. Specifically, for image data with dependent features ($\math…
Graph Neural Networks (GNNs) are proficient in graph representation learning and achieve promising performance on versatile tasks such as node classification and link prediction. Usually, a comprehensive hyperparameter tuning is essential for fully unlocking GNN's top performance, especially for com…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian manifold structure and performing optimization intrinsically on t…
Gradient-based optimization methods have shown remarkable empirical success, yet their theoretical generalization properties remain only partially understood. In this paper, we establish a generalization bound for gradient flow that aligns with the classical Rademacher complexity bounds for kernel m…
The capacity of deep learning models is often large enough to both learn the underlying statistical signal and overfit to noise in the training set. This noise memorization can be harmful especially for data with a low signal-to-noise ratio (SNR), leading to poor generalization. Inspired by prior ob…
The predominant success of diffusion models in generative modeling has spurred significant interest in understanding their theoretical foundations. In this work, we propose a feature learning framework aimed at analyzing and comparing the training dynamics of diffusion models with those of tradition…
The Adam optimizer is widely used for transformer optimization in practice, which makes understanding the underlying optimization mechanisms an important problem. However, due to the Adam's complexity, theoretical analysis of how it optimizes transformers remains a challenging task. Fortunately, Si…
Deep learning with noisy labels presents significant challenges. In this work, we theoretically characterize the role of label noise from a feature learning perspective. Specifically, we consider a signal-noise data distribution, where each sample comprises a label-dependent signal and label-indepen…
In-context learning (ICL) has garnered significant attention for its ability to grasp functions/tasks from demonstrations. Recent studies suggest the presence of a latent **task/function vector** in LLMs during ICL. Merullo et al. (2024) showed that LLMs leverage this vector alongside the residual s…
Graph Neural Networks (GNNs) have emerged as fundamental tools for a wide range of prediction tasks on graph-structured data. Recent studies have drawn analogies between GNN feature propagation and diffusion processes, which can be interpreted as dynamical systems. In this paper, we delve deeper int…
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian manifolds. We present several hypergradient estimation strategie…
Multi-modal contrastive learning with language supervision has presented a paradigm shift in modern machine learning. By pre-training on a web-scale dataset, multi-modal contrastive learning can learn high-quality representations that exhibit impressive robustness and transferability. Despite its em…
Transformer-based large language models (LLMs) have displayed remarkable creative prowess and emergence capabilities. Existing empirical studies have revealed a strong connection between these LLMs' impressive emergence abilities and their in-context learning (ICL) capacity, allowing them to solve n…
Many machine learning applications are naturally formulated as optimization problems on Riemannian manifolds. The main idea behind Riemannian optimization is to maintain the feasibility of the variables while moving along a descent direction on the manifold. This results in updating all the variable…
Large language models (LLMs) have shown impressive capabilities across various tasks. However, training LLMs from scratch requires significant computational power and extensive memory capacity. Recent studies have explored low-rank structures on weights for efficient fine-tuning in terms of paramete…
In this paper, we propose a convergence acceleration scheme for general Riemannian optimization problems by extrapolating iterates on manifolds. We show that when the iterates are generated from the Riemannian gradient descent method, the scheme achieves the optimal convergence rate asymptotically a…
In this paper, we comparatively analyze the Bures-Wasserstein (BW) geometry with the popular Affine-Invariant (AI) geometry for Riemannian optimization on the symmetric positive definite (SPD) matrix manifold. Our study begins with an observation that the BW metric has a linear dependence on SPD mat…
We propose a stochastic recursive momentum method for Riemannian non-convex optimization that achieves a nearly-optimal complexity to find epsilon-approximate solution with one sample. The new algorithm requires one-sample gradient evaluations per iteration and does not require restarting with a lar…