36 accepted papers
A data mixture refers to how different data sources are combined to train large language models, and selecting an effective mixture is crucial for optimal downstream performance. Existing methods either conduct costly searches directly on the target model or rely on mixture scaling laws that fail to…
Data selection during supervised fine-tuning (SFT) can critically change the behavior of large language models (LLMs). Although existing work has studied the effect of selecting data based on heuristics such as perplexity, difficulty, or length, the reported findings are often inconsistent or contex…
This paper studies the complexity of finding an $\epsilon$-stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is strongly convex. Recent work proposed the first-order method, F${}^2$SA, achieving the $\tilde{\mathcal{O}}(\epsilo…
Reinforcement learning (RL) has emerged as a central paradigm for training large language models (LLMs) in reasoning tasks. Yet recent studies question RL’s ability to incentivize reasoning capacity beyond the base model. This raises a key challenge: how can RL be adapted to solve harder reasoning p…
Efficiently editing knowledge stored in Large Language Models (LLMs) enables model updates without large-scale training. One promising solution is Locate-and-Edit (L\&E), allowing simultaneous modifications of a massive number of factual knowledge. However, such editing may compromise the general ab…
Large Language Models (LLMs) are typically trained on data mixtures: most data come from web scrapes, while a small portion is curated from high-quality sources with dense domain-specific knowledge. In this paper, we show that when training LLMs on such data mixtures, knowledge acquisition from know…
Real world evolves in continuous time but computations are done from finite samples. Therefore, we study algorithms using finite observations in continuous-time linear dynamical systems. We first study the system identification problem, and propose a first non-asymptotic error analysis with finite o…
Chain-of-thought (CoT) significantly enhances the reasoning performance of large language models (LLM). While current theoretical studies often attribute this improvement to increased expressiveness and computational capacity, we argue that expressiveness is not the primary limitation in the LLM re…
This work studies the generalization error of gradient methods. More specifically, we focus on how training steps $T$ and step-size $\eta$ might affect generalization in smooth stochastic convex optimization (SCO) problems. Recent works show that in some cases longer training can hurt generalization…
Model merging offers an effective way to integrate the capabilities of multiple fine-tuned models. However, the performance degradation of the merged model remains a challenge, particularly when none or few data are available. This paper first highlights the necessity of domain-specific data for mod…
This paper studies second-order methods for convex-concave minimax optimization. Monteiro & Svaiter (2012) proposed a method to solve the problem with an optimal iteration complexity of $\mathcal{O}(\epsilon^{-3/2})$ to find an $\epsilon$-saddle point. However, it is unclear whether the computa…
Large language models (LLMs) exhibit remarkable task generalization, solving tasks they were never explicitly trained on with only a few demonstrations. This raises a fundamental question: When can learning from a small set of tasks generalize to a large task family? In this paper, we investigate t…
Given the rising popularity of AI-generated art and the associated copyright concerns, identifying whether an artwork was used to train a diffusion model is an important research topic. The work approaches this problem from the membership inference attack (MIA) perspective. We first identify the lim…
One explanation for the strong generalization ability of neural networks is implicit bias. Yet, the definition and mechanism of implicit bias in non-linear contexts remains little understood. In this work, we propose to characterize implicit bias by the count of connected regions in the input space…
In distributed deep learning with data parallelism, synchronizing gradients at each training step can cause a huge communication overhead, especially when many nodes work together to train large models. Local gradient methods, such as Local SGD, address this issue by allowing workers to compute lo…
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the approximate optimal value of such problems is not obtainable by first…
We study online control for continuous-time linear systems with finite sampling rates, where the objective is to design an online procedure that learns under non-stochastic noise and performs comparably to a fixed optimal linear controller. We present a novel two-level online algorithm, by integrat…
Reinforcement learning (RL) has exceeded human performance in many synthetic settings such as video games and Go. However, real-world deployment of end-to-end RL models is less common, as RL models can be very sensitive to perturbations in the environment. The robust Markov decision process (MDP) fr…
Fine-tuning large language models (LLM) can be costly. Parameter-efficient fine-tuning (PEFT) addresses the problems by training a fraction of the parameters, whose success reveals the expressiveness and flexibility of pretrained models. This paper studies the limit of PEFT, by further simplifying i…
Studies on benign overfitting provide insights for the success of overparameterized deep learning models. In this work, we examine whether overfitting is truly benign in real-world classification tasks. We start with the observation that a ResNet model overfits benignly on Cifar10 but not benignly o…
MCMC algorithms offer empirically efficient tools for sampling from a target distribution $\pi(x) \propto \exp(-V(x))$. However, on the theory side, MCMC algorithms suffer from slow mixing rate when $\pi(x)$ is non-log-concave. Our work examines this gap and shows that when Poincar\'e-style inequali…
In complex reinforcement learning (RL) problems, policies with similar rewards may have substantially different behaviors. It remains a fundamental challenge to optimize rewards while also discovering as many *diverse* strategies as possible, which can be crucial in many practical applications. Our…
Weight decay is a simple yet powerful regularization technique that has been very widely used in training of deep neural networks (DNNs). While weight decay has attracted much attention, previous studies fail to discover some overlooked pitfalls on large gradient norms resulted by weight decay. In t…
We study oracle complexity of gradient based methods for stochastic approximation problems. Though in many settings optimal algorithms and tight lower bounds are known for such problems, these optimal algorithms do not achieve the best performance when used in practice. We address this theory-practi…
We study the task of efficiently sampling from a Gibbs distribution $d \pi^* = e^{-h} d {\text{vol}}_g$ over a Riemannian manifold $M$ via (geometric) Langevin MCMC; this algorithm involves computing exponential maps in random Gaussian directions and is efficiently implementable in practice. The key…
This work examines the deep disconnect between existing theoretical analyses of gradient-based algorithms and the practice of training deep neural networks. Specifically, we provide numerical evidence that in large-scale neural network training (e.g., ImageNet + ResNet101, and WT103 + TransformerXL…
Most existing analyses of (stochastic) gradient descent rely on the condition that for $L$-smooth costs, the step size is less than $2/L$. However, many works have observed that in machine learning applications step sizes often do not fulfill this condition, yet (stochastic) gradient descent still c…
We provide a first-order oracle complexity lower bound for finding stationary points of min-max optimization problems where the objective function is smooth, nonconvex in the minimization variable, and strongly concave in the maximization variable. We establish a lower bound of $\Omega\left(\sqrt{\k…
The label shift problem refers to the supervised learning setting where the train and test label distributions do not match. Existing work addressing label shift usually assumes access to an unlabelled test sample. This sample may be used to estimate the test label distribution, and to then train a…
Exposure bias has been regarded as a central problem for auto-regressive language models (LM). It claims that teacher forcing would cause the test-time generation to be incrementally distorted due to the training-generation discrepancy. Although a lot of algorithms have been proposed to avoid teache…
Federated learning (FL) coordinates with numerous heterogeneous devices to collaboratively train a shared model while preserving user privacy. Despite its multiple advantages, FL faces new challenges. One challenge arises when devices drop out of the training process. In this case, the convergence o…
We study multi-objective reinforcement learning (RL) where an agent’s reward is represented as a vector. In settings where an agent competes against opponents, its performance is measured by the distance of its average return vector to a target set. We develop statistically and computationally effic…
We provide the first non-asymptotic analysis for finding stationary points of nonsmooth, nonconvex functions. In particular, we study the class of Hadamard semi-differentiable functions, perhaps the largest class of nonsmooth functions for which the chain rule of calculus holds. This class contains…
We provide a theoretical explanation for the effectiveness of gradient clipping in training deep neural networks. The key ingredient is a new smoothness condition derived from practical neural network training examples. We observe that gradient smoothness, a concept central to the analysis of first-…
While stochastic gradient descent (SGD) is still the de facto algorithm in deep learning, adaptive methods like Clipped SGD/Adam have been observed to outperform SGD across important tasks, such as attention models. The settings under which SGD performs poorly in comparison to adaptive methods are n…
We study gradient-based optimization methods obtained by directly discretizing a second-order ordinary differential equation (ODE) related to the continuous limit of Nesterov's accelerated gradient method. When the function is smooth enough, we show that acceleration can be achieved by a stable disc…