Orthogonal Finetuning Made Scalable

Orthogonal finetuning (OFT) offers highly parameter-efficient adaptation while preventing catastrophic forgetting, but its high runtime and memory demands limit practical deployment. We identify the core computational bottleneck in OFT as its weight-centric implementation, which relies on costly matrix-matrix multiplications with cubic complexity. To overcome this, we propose OFTv2, an input-centric reformulation that instead uses matrix-vector multiplications (i.e., matrix-free computation), reducing the computational cost to quadratic. We further introduce the Cayley-Neumann parameterization, an efficient orthogonal parameterization that approximates the matrix inversion in Cayley transform via a truncated Neumann series. These modifications allow OFTv2 to achieve up to 10x faster training and 3x lower GPU memory usage without compromising performance. In addition, we extend OFTv2 to support finetuning quantized foundation models and show that it outperforms the popular QLoRA in training stability, efficiency, and memory usage.

Flipping Against All Odds: Reducing LLM Coin Flip Bias via Verbalized Rejection Sampling

Large language models (LLMs) can often accurately describe probability distributions using natural language, yet they still struggle to generate faithful samples from them. This mismatch limits their use in tasks requiring reliable stochasticity, such as Monte Carlo methods, agent-based simulations, and randomized decision-making. We investigate this gap between knowledge and sampling in the context of Bernoulli distributions. We introduce Verbalized Rejection Sampling (VRS), a natural-language adaptation of classical rejection sampling that prompts the LLM to reason about and accept or reject proposed samples. Despite relying on the same Bernoulli mechanism internally, VRS substantially reduces sampling bias across models. We provide theoretical analysis showing that, under mild assumptions, VRS improves over direct sampling, with gains attributable to both the algorithm and prompt design. More broadly, our results show how classical probabilistic tools can be verbalized and embedded into LLM workflows to improve reliability, without requiring access to model internals or heavy prompt engineering.

Reparameterized LLM Training via Orthogonal Equivalence Transformation

While large language models (LLMs) are driving the rapid advancement of artificial intelligence, effectively and reliably training these large models remains one of the field's most significant challenges. To address this challenge, we propose POET, a novel reParameterized training algorithm that uses Orthogonal Equivalence Transformation to optimize neurons. Specifically, POET reparameterizes each neuron with two learnable orthogonal matrices and a fixed random weight matrix. Because of its provable preservation of spectral properties of weight matrices, POET can stably optimize the objective function with improved generalization. We further develop efficient approximations that make POET flexible and scalable for training large-scale neural networks. Extensive experiments validate the effectiveness and scalability of POET in training LLMs.

FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models

Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising 5,560 formally verified problems spanning from high-school Olympiad challenges to undergraduate-level theorems across diverse domains (e.g., algebra, applied mathematics, calculus, number theory, and discrete mathematics). To mitigate the inefficiency of manual formalization, we introduce a novel human-in-the-loop autoformalization pipeline that integrates: (1) specialized large language models (LLMs) for statement autoformalization, (2) multi-LLM semantic verification, and (3) negation-based disproof filtering strategies using off-the-shelf LLM-based provers. This approach reduces expert annotation costs by retaining 72.09% of statements before manual verification while ensuring fidelity to the original natural-language problems. Our evaluation of state-of-the-art LLM-based theorem provers reveals significant limitations: even the strongest models achieve only 16.46% success rate under practical sampling budgets, exhibiting pronounced domain bias (e.g., excelling in algebra but failing in calculus) and over-reliance on simplified automation tactics. Notably, we identify a counterintuitive inverse relationship between natural-language solution guidance and proof success in chain-of-thought reasoning scenarios, suggesting that human-written informal reasoning introduces noise rather than clarity in the formal reasoning settings. We believe that FormalMATH provides a robust benchmark for benchmarking formal mathematical reasoning.

Generating Symbolic World Models via Test-time Scaling of Large Language Models

Solving complex planning problems requires Large Language Models (LLMs) to explicitly model the state transition to avoid rule violations, comply with constraints, and ensure optimality-a task hindered by the inherent ambiguity of natural language. To overcome such ambiguity, Planning Domain Definition Language (PDDL) is leveraged as a planning abstraction that enables precise and formal state descriptions. With PDDL, we can generate a symbolic world model where classic searching algorithms, such as A*, can be seamlessly applied to find optimal plans. However, directly generating PDDL domains with current LLMs remains an open challenge due to the lack of PDDL training data. To address this challenge, we propose to scale up the test-time computation of LLMs to enhance their PDDL reasoning capabilities, thereby enabling the generation of high-quality PDDL domains. Specifically, we introduce a simple yet effective algorithm, which first employs a Best-of-N sampling approach to improve the quality of the initial solution and then refines the solution in a fine-grained manner with verbalized machine learning. Our method outperforms o1-mini by a considerable margin in the generation of PDDL domain, achieving over 50% success rate on two tasks (i.e., generating PDDL domains from natural language description or PDDL problems). This is done without requiring additional training. By taking advantage of PDDL as state abstraction, our method is able to outperform current state-of-the-art methods on almost all competition-level planning tasks.

SepLLM: Accelerate Large Language Models by Compressing One Segment into One Separator

Large Language Models (LLMs) have exhibited exceptional performance across a spectrum of natural language processing tasks. However, their substantial sizes pose considerable challenges, particularly in computational demands and inference speed, due to their quadratic complexity. In this work, we have identified a key pattern: certain seemingly meaningless special tokens (i.e., separators) contribute disproportionately to attention scores compared to semantically meaningful tokens. This observation suggests that information of the segments between these separator tokens can be effectively condensed into the separator tokens themselves without significant information loss. Guided by this insight, we introduce SepLLM, a plug-and-play framework that accelerates inference by compressing these segments and eliminating redundant tokens. Additionally, we implement efficient kernels for training acceleration. Experimental results across training-free, training-from-scratch, and post-training settings demonstrate SepLLM's effectiveness. Notably, using the Llama-3-8B backbone, SepLLM achieves over 50% reduction in KV cache on the GSM8K-CoT benchmark while maintaining comparable performance. Furthermore, in streaming settings, SepLLM effectively processes sequences of up to 4 million tokens or more while maintaining consistent language modeling capabilities.

Efficient Diversity-Preserving Diffusion Alignment via Gradient-Informed GFlowNets

While one commonly trains large diffusion models by collecting datasets on target downstream tasks, it is often desired to align and finetune pretrained diffusion models on some reward functions that are either designed by experts or learned from small-scale datasets. Existing methods for finetuning diffusion models typically suffer from lack of diversity in generated samples, lack of prior preservation, and/or slow convergence in finetuning. Inspired by recent successes in generative flow networks (GFlowNets), a class of probabilistic models that sample with the unnormalized density of a reward function, we propose a novel GFlowNet method dubbed Nabla-GFlowNet (abbreviated as $\nabla$-GFlowNet), the first GFlowNet method that leverages the rich signal in reward gradients, together with an objective called $\nabla$-DB plus its variant residual $\nabla$-DB designed for prior-preserving diffusion alignment. We show that our proposed method achieves fast yet diversity- and prior-preserving alignment of Stable Diffusion, a large-scale text-conditioned image diffusion model, on different realistic reward functions.

VERA: Explainable Video Anomaly Detection via Verbalized Learning of Vision-Language Models

The rapid advancement of vision-language models (VLMs) has established a new paradigm in video anomaly detection (VAD): leveraging VLMs to simultaneously detect anomalies and provide comprehendible explanations for the decisions. Existing work in this direction often assumes the complex reasoning required for VAD exceeds the capabilities of pretrained VLMs. Consequently, these approaches either incorporate specialized reasoning modules during inference or rely on instruction tuning datasets through additional training to adapt VLMs for VAD. However, such strategies often incur substantial computational costs or data annotation overhead. To address these challenges in explainable VAD, we introduce a verbalized learning framework named VERA that enables VLMs to perform VAD without model parameter modifications. Specifically, VERA automatically decomposes the complex reasoning required for VAD into reflections on simpler, more focused guiding questions capturing distinct abnormal patterns. It treats these reflective questions as learnable parameters and optimizes them through data-driven verbal interactions between learner and optimizer VLMs, using coarsely labeled training data. During inference, VERA embeds the learned questions into model prompts to guide VLMs in generating segment-level anomaly scores, which are then refined into frame-level scores via the fusion of scene and temporal contexts. Experimental results on challenging benchmarks demonstrate that the learned questions of VERA are highly adaptable, significantly improving both detection performance and explainability of VLMs for VAD.

Manifold-Constrained Nucleus-Level Denoising Diffusion Model for Structure-Based Drug Design

Artificial intelligence models have shown great potential in structure-based drug design, generating ligands with high binding affinities. However, existing models have often overlooked a crucial physical constraint: atoms must maintain a minimum pairwise distance to avoid separation violation, a phenomenon governed by the balance of attractive and repulsive forces. To mitigate such separation violations, we propose NucleusDiff. It models the interactions between atomic nuclei and their surrounding electron clouds by enforcing the distance constraint between the nuclei and manifolds. We quantitatively evaluate NucleusDiff using the CrossDocked2020 dataset and a COVID-19 therapeutic target, demonstrating that NucleusDiff reduces violation rate by up to 100.00% and enhances binding affinity by up to 22.16%, surpassing state-of-the-art models for structure-based drug design. We also provide qualitative analysis through manifold sampling, visually confirming the effectiveness of NucleusDiff in reducing separation violations and improving binding affinities.

Can Large Language Models Understand Symbolic Graphics Programs?

Assessing the capabilities of large language models (LLMs) is often challenging, in part, because it is hard to find tasks to which they have not been exposed during training. We take one step to address this challenge by turning to a new task: focusing on symbolic graphics programs, which are a popular representation for graphics content that procedurally generates visual data. LLMs have shown exciting promise towards program synthesis, but do they understand symbolic graphics programs? Unlike conventional programs, symbolic graphics programs can be translated to graphics content. Here, we characterize an LLM's understanding of symbolic programs in terms of their ability to answer questions related to the graphics content. This task is challenging as the questions are difficult to answer from the symbolic programs alone -- yet, they would be easy to answer from the corresponding graphics content as we verify through a human experiment. To understand symbolic programs, LLMs may need to possess the ability to imagine how the corresponding graphics content would look without directly accessing the rendered visual content. We use this task to evaluate LLMs by creating a large benchmark for the semantic understanding of symbolic graphics programs. This benchmark is built via program-graphics correspondence, hence requiring minimal human efforts. We evaluate current LLMs on our benchmark to elucidate a preliminary assessment of their ability to reason about visual scenes from programs. We find that this task distinguishes existing LLMs and models considered good at reasoning perform better. Lastly, we introduce Symbolic Instruction Tuning (SIT) to improve this ability. Specifically, we query GPT4-o with questions and images generated by symbolic programs. Such data are then used to finetune an LLM. We also find that SIT data can improve the general instruction following ability of LLMs.