Traveling Salesman-Based Token Ordering Improves Stability in Homomorphically Encrypted Language Models

As users increasingly interact with large language models (LLMs) using private information, secure and encrypted communication becomes essential. Homomorphic encryption (HE) provides a principled solution by enabling computation directly on encrypted data. Although prior work has explored aspects of running LLMs under HE, the challenge of text generation, particularly next-token prediction, has received limited attention and remains a key obstacle to practical encrypted interaction. In this work, we propose a TSP-based token reordering strategy to address the difficulties of encrypted text generation, together with a post-processing step that further reduces approximation error. Theoretical analysis and experimental results demonstrate that our method prevents collapse, improves coherence in generated text, and preserves data privacy throughout. Overall, our contributions advance the feasibility of practical and privacy-preserving LLM inference.

STORK: Improving the Fidelity of Mid-NFE Sampling for Diffusion and Flow Matching Models

Diffusion models (DMs) have demonstrated remarkable performance in high-fidelity image and video generation. Because high-quality generations with DMs typically require a large number of function evaluations (NFEs), resulting in slow sampling, there has been extensive research successfully reducing the NFE to a small range (<10) while maintaining acceptable image quality. However, many practical applications, such as those involving Stable Diffusion 3.5, FLUX, and SANA, commonly operate in the mid-NFE regime (20-50 NFE) to achieve superior results, and, despite the practical relevance, research on the effective sampling within this mid-NFE regime remains underexplored. In this work, we propose a novel, training-free, and structure-independent DM ODE solver called the Stabilized Taylor Orthogonal Runge--Kutta (STORK) method, based on a class of stiff ODE solvers with a Taylor expansion adaptation. Unlike prior work such as DPM-Solver, which is dependent on the semi-linear structure of the DM ODE, STORK is applicable to any DM sampling, including noise-based and flow matching-based models. Within the 20-50 NFE range, STORK achieves improved generation quality, as measured by FID scores, across unconditional pixel-level generation and conditional latent-space generation tasks using models like Stable Diffusion 3.5 and SANA. Code is available at https://github.com/ZT220501/STORK.

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.

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.

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 unexplored. 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, and by establishing convergence of the associated numerical discretization schemes for Riemann-integrable input functions.

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.

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.

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.

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.

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 $O(\gamma^k)$, it is slow when the discount factor $\gamma$ 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 $\mathcal{P}^{\pi}$. We prove that this leads to a $\tilde{O}(\gamma^k |\lambda_{s+1}|^k)$ convergence rate, where $\lambda_{s+1}$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.