Related papers: Accelerating LMO-Based Optimization via Implicit G…

Vision-language models (VLMs) such as CLIP demonstrate strong performance but struggle when adapted to downstream tasks. Prompt learning has emerged as an efficient and effective strategy to adapt VLMs while preserving their pre-trained…

Stochastic trajectory optimization methods like STOMP enable planning with non-differentiable costs, offering substantial flexibility over gradient-based approaches. We show that STOMP implicitly minimizes the KL divergence from a Boltzmann…

Prompt engineering plays a critical role in adapting large language models (LLMs) to complex reasoning and labeling tasks without the need for extensive fine-tuning. In this paper, we propose a novel prompt optimization pipeline for frame…

We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold. First, we propose a new evolution equation in the set of…

As large language models (LLMs) scale to billions of parameters, full-parameter fine-tuning becomes compute- and memory-prohibitive. Parameter-efficient fine-tuning (PEFT) mitigates this issue by updating only a small set of task-specific…

Memory-efficient optimization is critical for training increasingly large language models (LLMs). A popular strategy involves gradient low-rank projection, storing only the projected optimizer states, with GaLore being a representative…

The incremental gradient method is a prominent algorithm for minimizing a finite sum of smooth convex functions, used in many contexts including large-scale data processing applications and distributed optimization over networks. It is a…

Gradient orthogonalization is a simple strategy that shows great utility in speeding up gradient descent. The Muon optimizer (Jordan, Jin, et al., 2024) combines gradient orthogonalization with first-order momentum and achieves significant…

Recent progress in Large Language Model (LLM) reasoning is increasingly driven by the refinement of post-training loss functions and alignment strategies. However, standard Reinforcement Learning (RL) paradigms like Group Relative Policy…

Low-Rank Adaptation (LoRA) is a crucial method for efficiently fine-tuning large language models (LLMs), with its effectiveness influenced by two key factors: rank selection and weight initialization. While numerous LoRA variants have been…

Stochastic gradient-based descent (SGD), have long been central to training large language models (LLMs). However, their effectiveness is increasingly being questioned, particularly in large-scale applications where empirical evidence…

Recently, large language models (LLMs) have notably positioned them as capable tools for addressing complex optimization challenges. Despite this recognition, a predominant limitation of existing LLM-based optimization methods is their…

In distributed and federated learning algorithms, communication overhead is often reduced by performing multiple local updates between communication rounds. However, due to data heterogeneity across nodes and the local gradient noise within…

In this work, we study the classical distributed optimization problem over digraphs, where the objective function is a sum of smooth local functions. Inspired by the implicit tracking mechanism proposed in our earlier work, we develop a…

In this paper, we consider the general non-oblivious stochastic optimization where the underlying stochasticity may change during the optimization procedure and depends on the point at which the function is evaluated. We develop Stochastic…

The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex…

This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based…

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT…

Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally…

Recently, latent reasoning has been introduced into large language models (LLMs) to leverage rich information within a continuous space. However, without stochastic sampling, these methods inevitably collapse to deterministic inference,…