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Ernest K. Ryu

Publications and source records attributed to Ernest K. Ryu.

At least 37 records · Page 2Linked to original sources
arXiv2025

Clip-Low Increases Entropy and Clip-High Decreases Entropy in Reinforcement Learning of Large Language Models

Reinforcement learning with verifiable rewards (RLVR) has recently emerged as the leading approach for enhancing the reasoning capabilities of large language models (LLMs). However, RLVR is prone to entropy collapse, where the LLM quickly converges to a near-deterministic form, hindering exploration and progress during prolonged RL training. In this work, we reveal that the clipping mechanism in PPO and GRPO induces biases on entropy. Through theoretical and empirical analyses, we show that clip-low increases entropy, while clip-high decreases it. Further, under standard clipping parameters, the effect of clip-high dominates, resulting in an overall entropy reduction even when purely random rewards are provided to the RL algorithm. Our findings highlight an overlooked confounding factor in RLVR: independent of the reward signal, the clipping mechanism influences entropy, which in turn affects the reasoning behavior. Furthermore, our analysis demonstrates that clipping can be deliberately used to control entropy. Specifically, with a more aggressive clip-low value, one can increase entropy, promote exploration, and ultimately prevent entropy collapse in RLVR training.

cs.LG↗
arXiv2025

Task Diversity Shortens the ICL Plateau

In-context learning (ICL) describes a language model's ability to generate outputs based on a set of input demonstrations and a subsequent query. To understand this remarkable capability, researchers have studied simplified, stylized models. These studies have consistently observed long loss plateaus, during which models exhibit minimal improvement, followed by a sudden, rapid surge of learning. In this work, we reveal that training on multiple diverse ICL tasks simultaneously shortens the loss plateaus, making each task easier to learn. This finding is surprising as it contradicts the natural intuition that the combined complexity of multiple ICL tasks would lengthen the learning process, not shorten it. Our result suggests that the recent success in large-scale training of language models may be attributed not only to the richness of the data at scale but also to the easier optimization (training) induced by the diversity of natural language training data.

cs.LG↗
arXiv2025

Numerical Analysis of HiPPO-LegS ODE for Deep State Space Models

In deep learning, the recently introduced state space models utilize HiPPO (High-order Polynomial Projection Operators) memory units to approximate continuous-time trajectories of input functions using ordinary differential equations (ODEs), and these techniques have shown empirical success in capturing long-range dependencies in long input sequences. However, the mathematical foundations of these ODEs, particularly the singular HiPPO-LegS (Legendre Scaled) ODE, and their corresponding numerical discretizations remain unsettled. In this work, we fill this gap by establishing that HiPPO-LegS ODE is well-posed despite its singularity, albeit without the freedom of arbitrary initial conditions. Further, we establish convergence of the associated numerical discretization schemes for Riemann integrable input functions.

math.NA↗
arXiv2025

LoRA Training Provably Converges to a Low-Rank Global Minimum or It Fails Loudly (But it Probably Won't Fail)

Low-rank adaptation (LoRA) has become a standard approach for fine-tuning large foundation models. However, our theoretical understanding of LoRA remains limited as prior analyses of LoRA's training dynamics either rely on linearization arguments or consider highly simplified setups. In this work, we analyze the LoRA loss landscape without such restrictive assumptions. We define two regimes: a "special regime", which includes idealized setups where linearization arguments hold, and a "generic regime" representing more realistic setups where linearization arguments do not hold. In the generic regime, we show that LoRA training converges to a global minimizer with low rank and small magnitude, or a qualitatively distinct solution with high rank and large magnitude. Finally, we argue that the zero-initialization and weight decay in LoRA training induce an implicit bias toward the low-rank, small-magnitude region of the parameter space -- where global minima lie -- thus shedding light on why LoRA training usually succeeds in finding global minima.

cs.LG↗
arXiv2025

Deflated Dynamics Value Iteration

The Value Iteration (VI) algorithm is an iterative procedure to compute the value function of a Markov decision process, and is the basis of many reinforcement learning (RL) algorithms as well. As the error convergence rate of VI as a function of iteration $k$ is $O(γ^k)$, it is slow when the discount factor $γ$ is close to $1$. To accelerate the computation of the value function, we propose Deflated Dynamics Value Iteration (DDVI). DDVI uses matrix splitting and matrix deflation techniques to effectively remove (deflate) the top $s$ dominant eigen-structure of the transition matrix $\mathcal{P}^π$. We prove that this leads to a $\tilde{O}(γ^k |λ_{s+1}|^k)$ convergence rate, where $λ_{s+1}$is $(s+1)$-th largest eigenvalue of the dynamics matrix. We then extend DDVI to the RL setting and present Deflated Dynamics Temporal Difference (DDTD) algorithm. We empirically show the effectiveness of the proposed algorithms.

cs.LG↗
arXiv2025

Decomposing Complex Visual Comprehension into Atomic Visual Skills for Vision Language Models

Recent Vision-Language Models (VLMs) have demonstrated impressive multimodal comprehension and reasoning capabilities, yet they often struggle with trivially simple visual tasks. In this work, we focus on the domain of basic 2D Euclidean geometry and systematically categorize the fundamental, indivisible visual perception skills, which we refer to as atomic visual skills. We then introduce the Atomic Visual Skills Dataset (AVSD) for evaluating VLMs on the atomic visual skills. Using AVSD, we benchmark state-of-the-art VLMs and find that they struggle with these tasks, despite being trivial for adult humans. Our findings highlight the need for purpose-built datasets to train and evaluate VLMs on atomic, rather than composite, visual perception tasks.

cs.CV↗
arXiv2025

Accelerated Minimax Algorithms Flock Together

Several new accelerated methods in minimax optimization and fixed-point iterations have recently been discovered, and, interestingly, they rely on a mechanism distinct from Nesterov's momentum-based acceleration. In this work, we show that these accelerated algorithms exhibit what we call the merging path (MP) property; the trajectories of these algorithms merge quickly. Using this novel MP property, we establish point convergence of existing accelerated minimax algorithms and derive new state-of-the-art algorithms for the strongly-convex-strongly-concave setup and for the prox-grad setup.

math.OC↗
arXiv2025

Encryption-Friendly LLM Architecture

Large language models (LLMs) offer personalized responses based on user interactions, but this use case raises serious privacy concerns. Homomorphic encryption (HE) is a cryptographic protocol supporting arithmetic computations in encrypted states and provides a potential solution for privacy-preserving machine learning (PPML). However, the computational intensity of transformers poses challenges for applying HE to LLMs. In this work, we propose a modified HE-friendly transformer architecture with an emphasis on inference following personalized (private) fine-tuning. Utilizing LoRA fine-tuning and Gaussian kernels, we achieve significant computational speedups -- 6.94x for fine-tuning and 2.3x for inference -- while maintaining performance comparable to plaintext models. Our findings provide a viable proof of concept for offering privacy-preserving LLM services in areas where data protection is crucial. Our code is available on GitHub.

cs.CR↗
arXiv2025

Optimization Algorithm Design via Electric Circuits

We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose continuous-time dynamics converge to the solution of the optimization problem at hand. Then, the second stage is an automated, computer-assisted discretization of the continuous-time dynamics, yielding a provably convergent discrete-time algorithm. Our methodology recovers many classical (distributed) optimization algorithms and enables users to quickly design and explore a wide range of new algorithms with convergence guarantees.

math.OC↗
arXiv2024

Scaled Relative Graph of Normal Matrices

The Scaled Relative Graph (SRG) is a geometric tool that maps the action of a multi-valued nonlinear operator onto the 2D plane, used to analyze the convergence of a wide range of iterative methods. As the SRG includes the spectrum for linear operators, we can view the SRG as a generalization of the spectrum to multi-valued nonlinear operators. In this work, we further study the SRG of linear operators and characterize the SRG of block-diagonal and normal matrices.

math.NA↗
arXiv2024

Coordinate-Update Algorithms can Efficiently Detect Infeasible Optimization Problems

Coordinate update/descent algorithms are widely used in large-scale optimization due to their low per-iteration cost and scalability, but their behavior on infeasible or misspecified problems has not been much studied compared to the algorithms that use full updates. For coordinate-update methods to be as widely adopted to the extent so that they can be used as engines of general-purpose solvers, it is necessary to also understand their behavior under pathological problem instances. In this work, we show that the normalized iterates of randomized coordinate-update fixed-point iterations (RC-FPI) converge to the infimal displacement vector and use this result to design an efficient infeasibility detection method. We then extend the analysis to the setup where the coordinates are defined by non-orthonormal basis using the Friedrichs angle and then apply the machinery to decentralized optimization problems.

math.OC↗
arXiv2024

Simple Drop-in LoRA Conditioning on Attention Layers Will Improve Your Diffusion Model

Current state-of-the-art diffusion models employ U-Net architectures containing convolutional and (qkv) self-attention layers. The U-Net processes images while being conditioned on the time embedding input for each sampling step and the class or caption embedding input corresponding to the desired conditional generation. Such conditioning involves scale-and-shift operations to the convolutional layers but does not directly affect the attention layers. While these standard architectural choices are certainly effective, not conditioning the attention layers feels arbitrary and potentially suboptimal. In this work, we show that simply adding LoRA conditioning to the attention layers without changing or tuning the other parts of the U-Net architecture improves the image generation quality. For example, a drop-in addition of LoRA conditioning to EDM diffusion model yields FID scores of 1.91/1.75 for unconditional and class-conditional CIFAR-10 generation, improving upon the baseline of 1.97/1.79.

cs.CV↗
arXiv2024

Gradient-free Decoder Inversion in Latent Diffusion Models

In latent diffusion models (LDMs), denoising diffusion process efficiently takes place on latent space whose dimension is lower than that of pixel space. Decoder is typically used to transform the representation in latent space to that in pixel space. While a decoder is assumed to have an encoder as an accurate inverse, exact encoder-decoder pair rarely exists in practice even though applications often require precise inversion of decoder. Prior works for decoder inversion in LDMs employed gradient descent inspired by inversions of generative adversarial networks. However, gradient-based methods require larger GPU memory and longer computation time for larger latent space. For example, recent video LDMs can generate more than 16 frames, but GPUs with 24 GB memory can only perform gradient-based decoder inversion for 4 frames. Here, we propose an efficient gradient-free decoder inversion for LDMs, which can be applied to diverse latent models. Theoretical convergence property of our proposed inversion has been investigated not only for the forward step method, but also for the inertial Krasnoselskii-Mann (KM) iterations under mild assumption on cocoercivity that is satisfied by recent LDMs. Our proposed gradient-free method with Adam optimizer and learning rate scheduling significantly reduced computation time and memory usage over prior gradient-based methods and enabled efficient computation in applications such as noise-space watermarking while achieving comparable error levels.

cs.LG↗
arXiv2024

LoRA Training in the NTK Regime has No Spurious Local Minima

Low-rank adaptation (LoRA) has become the standard approach for parameter-efficient fine-tuning of large language models (LLM), but our theoretical understanding of LoRA has been limited. In this work, we theoretically analyze LoRA fine-tuning in the neural tangent kernel (NTK) regime with $N$ data points, showing: (i) full fine-tuning (without LoRA) admits a low-rank solution of rank $r\lesssim \sqrt{N}$; (ii) using LoRA with rank $r\gtrsim \sqrt{N}$ eliminates spurious local minima, allowing gradient descent to find the low-rank solutions; (iii) the low-rank solution found using LoRA generalizes well.

cs.LG↗
arXiv2024

Mirror Duality in Convex Optimization

While first-order optimization methods are usually designed to efficiently reduce the function value $f(x)$, there has been recent interest in methods efficiently reducing the magnitude of $\nabla f(x)$, and the findings show that the two types of methods exhibit a certain symmetry. In this work, we present mirror duality, a one-to-one correspondence between mirror-descent-type methods reducing function value and reducing gradient magnitude. Using mirror duality, we obtain the dual accelerated mirror descent (dual-AMD) method that efficiently reduces $ψ^*(\nabla f(x))$, where $ψ$ is a distance-generating function and $ψ^*$ quantifies the magnitude of $\nabla f(x)$. We then apply dual-AMD to efficiently reduce $\|\nabla f(\cdot) \|_q$ for $q\in [2,\infty)$ and to efficiently compute $\varepsilon$-approximate solutions of the optimal transport problem.

math.OC↗
arXiv2024

Optimal Acceleration for Minimax and Fixed-Point Problems is Not Unique

Recently, accelerated algorithms using the anchoring mechanism for minimax optimization and fixed-point problems have been proposed, and matching complexity lower bounds establish their optimality. In this work, we present the surprising observation that the optimal acceleration mechanism in minimax optimization and fixed-point problems is not unique. Our new algorithms achieve exactly the same worst-case convergence rates as existing anchor-based methods while using materially different acceleration mechanisms. Specifically, these new algorithms are dual to the prior anchor-based accelerated methods in the sense of H-duality. This finding opens a new avenue of research on accelerated algorithms since we now have a family of methods that empirically exhibit varied characteristics while having the same optimal worst-case guarantee.

math.OC↗
arXiv2024

Convergence Analyses of Davis-Yin Splitting via Scaled Relative Graphs

Davis-Yin splitting (DYS) has found a wide range of applications in optimization, but its linear rates of convergence have not been studied extensively. The scaled relative graph (SRG) simplifies the convergence analysis of operator splitting methods by mapping the action of the operator onto the complex plane, but the prior SRG theory did not fully apply to the DYS operator. In this work, we formalize an SRG theory for the DYS operator and use it to obtain tighter contraction factors.

math.OC↗