Emergent Symbolic Mechanisms Support Abstract Reasoning in Large Language Models

Many recent studies have found evidence for emergent reasoning capabilities in large language models, but debate persists concerning the robustness of these capabilities, and the extent to which they depend on structured reasoning mechanisms. To shed light on these issues, we perform a comprehensive study of the internal mechanisms that support abstract rule induction in an open-source language model (Llama3-70B). We identify an emergent symbolic architecture that implements abstract reasoning via a series of three computations. In early layers, symbol abstraction heads convert input tokens to abstract variables based on the relations between those tokens. In intermediate layers, symbolic induction heads perform sequence induction over these abstract variables. Finally, in later layers, retrieval heads predict the next token by retrieving the value associated with the predicted abstract variable. These results point toward a resolution of the longstanding debate between symbolic and neural network approaches, suggesting that emergent reasoning in neural networks depends on the emergence of symbolic mechanisms.

DISC: Dynamic Decomposition Improves LLM Inference Scaling

Many inference scaling methods work by breaking a problem into smaller steps (or groups of tokens), then sampling and choosing the best next step. However, these steps and their sizes are usually predetermined based on human intuition or domain knowledge. This paper introduces dynamic decomposition, a method that automatically and adaptively splits solution and reasoning traces into steps during inference. This approach improves computational efficiency by focusing more resources on difficult steps, breaking them down further and prioritizing their sampling. Experiments on coding and math benchmarks (APPS, MATH, and LiveCodeBench) show that dynamic decomposition performs better than static methods, which rely on fixed steps like token-level, sentence-level, or single-step decompositions. These results suggest that dynamic decomposition can enhance many inference scaling techniques.

Diffusion-Sharpening: Fine-tuning Diffusion Models with Denoising Trajectory Sharpening

We propose Diffusion-Sharpening, a fine-tuning approach that enhances downstream alignment by optimizing sampling trajectories. Existing RL-based fine-tuning methods focus on single training timesteps and neglect trajectory-level alignment, while recent sampling trajectory optimization methods incur significant inference NFE costs. Diffusion-Sharpening overcomes this by using a path integral framework to select optimal trajectories during training, leveraging reward feedback, and amortizing inference costs. Our method demonstrates superior training efficiency with faster convergence, and best inference efficiency without requiring additional NFEs. Extensive experiments show that Diffusion-Sharpening outperforms RL-based fine-tuning methods (e.g., Diffusion-DPO) and sampling trajectory optimization methods (e.g., Inference Scaling) across diverse metrics including text alignment, compositional capabilities, and human preferences, offering a scalable and efficient solution for future diffusion model fine-tuning. Code: https://github.com/Gen-Verse/Diffusion-Sharpening

Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models

Training-free guidance enables controlled generation in diffusion and flow models, but most existing methods assume differentiable objectives and rely on gradients. This work focuses on training-free guidance addressing challenges from non-differentiable objectives and discrete data distributions. We propose an algorithmic framework TreeG: Tree Search-Based Path Steering Guidance, applicable to both continuous and discrete settings in diffusion and flow models. TreeG offers a unified perspective on training-free guidance: proposing candidates for the next step, evaluating candidates, and selecting the best to move forward, enhanced by a tree search mechanism over active paths or parallelizing exploration. We comprehensively investigate the design space of TreeG over the candidate proposal module and the evaluation function, instantiating TreeG into three novel algorithms. Our experiments show that TreeG consistently outperforms the top guidance baselines in symbolic music generation, small molecule generation, and enhancer DNA design, all of which involve non-differentiable challenges. Additionally, we identify an inference-time scaling law showing TreeG's scalability in inference-time computation.

A First-order Generative Bilevel Optimization Framework for Diffusion Models

Diffusion models, which iteratively denoise data samples to synthesize high-quality outputs, have achieved empirical success across domains. However, optimizing these models for downstream tasks often involves nested bilevel structures, such as tuning hyperparameters for fine-tuning tasks or noise schedules in training dynamics, where traditional bilevel methods fail due to the infinite-dimensional probability space and prohibitive sampling costs. We formalize this challenge as a generative bilevel optimization problem and address two key scenarios: (1) fine-tuning pre-trained models via an inference-only lower-level solver paired with a sample-efficient gradient estimator for the upper level, and (2) training diffusion models from scratch with noise schedule optimization by reparameterizing the lower-level problem and designing a computationally tractable gradient estimator. Our first-order bilevel framework overcomes the incompatibility of conventional bilevel methods with diffusion processes, offering theoretical grounding and computational practicality. Experiments demonstrate that our method outperforms existing fine-tuning and hyperparameter search baselines.

MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations

Large language models have demonstrated impressive performance on challenging mathematical reasoning tasks, which has triggered the discussion of whether the performance is achieved by true reasoning capability or memorization. To investigate this question, prior work has constructed mathematical benchmarks when questions undergo simple perturbations -- modifications that still preserve the underlying reasoning patterns of the solutions. However, no work has explored hard perturbations, which fundamentally change the nature of the problem so that the original solution steps do not apply. To bridge the gap, we construct MATH-P-Simple and MATH-P-Hard via simple perturbation and hard perturbation, respectively. Each consists of 279 perturbed math problems derived from level-5 (hardest) problems in the MATH dataset (Hendrycksmath et. al., 2021). We observe significant performance drops on MATH-P-Hard across various models, including o1-mini (-16.49%) and gemini-2.0-flash-thinking (-12.9%). We also raise concerns about a novel form of memorization where models blindly apply learned problem-solving skills without assessing their applicability to modified contexts. This issue is amplified when using original problems for in-context learning. We call for research efforts to address this challenge, which is critical for developing more robust and reliable reasoning models.

ReasonFlux: Hierarchical LLM Reasoning via Scaling Thought Templates

We present that hierarchical LLM reasoning via scaling thought templates can effectively optimize the reasoning search space and outperform the mathematical reasoning capabilities of powerful LLMs like OpenAI o1-preview and DeepSeek V3. We train our ReasonFlux-32B model with only 8 GPUs and introduces three innovations: (i) a structured and generic thought template library, containing around 500 high-level thought templates capable of generalizing to similar or relevant reasoning problems; (ii) performing hierarchical reinforcement learning on a sequence of thought templates instead of long CoTs, optimizing a base LLM to plan out an optimal template trajectory for gradually handling complex problems; (iii) a brand new inference scaling system that enables hierarchical LLM reasoning by adaptively scaling thought templates at inference time. With a template trajectory containing sequential thought templates, our ReasonFlux-32B significantly advances math reasoning capabilities to state-of-the-art levels. Notably, on the MATH benchmark, it achieves an accuracy of 91.2% and surpasses o1-preview by 6.7%. On the USA Math Olympiad (AIME) benchmark, ReasonFlux-32B solves an average of 56.7% of problems, surpassing o1-preview and DeepSeek-V3 by 27% and 45%, respectively. Code: https://github.com/Gen-Verse/ReasonFlux

ScoreFlow: Mastering LLM Agent Workflows via Score-based Preference Optimization

Recent research has leveraged large language model multi-agent systems for complex problem-solving while trying to reduce the manual effort required to build them, driving the development of automated agent workflow optimization methods. However, existing methods remain inflexible due to representational limitations, a lack of adaptability, and poor scalability when relying on discrete optimization techniques. We address these challenges with ScoreFlow, a simple yet high-performance framework that leverages efficient gradient-based optimization in a continuous space. ScoreFlow incorporates Score-DPO, a novel variant of the direct preference optimization method that accounts for quantitative feedback. Across six benchmarks spanning question answering, coding, and mathematical reasoning, ScoreFlow achieves an 8.2% improvement over existing baselines. Moreover, it empowers smaller models to outperform larger ones with lower inference costs. Project: https://github.com/Gen-Verse/ScoreFlow

RTLMarker: Protecting LLM-Generated RTL Copyright via a Hardware Watermarking Framework

Recent advances of large language models in the field of Verilog generation have raised several ethical and security concerns, such as code copyright protection and dissemination of malicious code. Researchers have employed watermarking techniques to identify codes generated by large language models. However, the existing watermarking works fail to protect RTL code copyright due to the significant syntactic and semantic differences between RTL code and software code in languages such as Python. This paper proposes a hardware watermarking framework RTLMarker that embeds watermarks into RTL code and deeper into the synthesized netlist. We propose a set of rule-based Verilog code transformations , ensuring the watermarked RTL code's syntactic and semantic correctness. In addition, we consider an inherent tradeoff between watermark transparency and watermark effectiveness and jointly optimize them. The results demonstrate RTLMarker's superiority over the baseline in RTL code watermarking.

On the Statistical Complexity for Offline and Low-Adaptive Reinforcement Learning with Structures

This article reviews the recent advances on the statistical foundation of reinforcement learning (RL) in the offline and low-adaptive settings. We will start by arguing why offline RL is the appropriate model for almost any real-life ML problems, even if they have nothing to do with the recent AI breakthroughs that use RL. Then we will zoom into two fundamental problems of offline RL: offline policy evaluation (OPE) and offline policy learning (OPL). It may be surprising to people that tight bounds for these problems were not known even for tabular and linear cases until recently. We delineate the differences between worst-case minimax bounds and instance-dependent bounds. We also cover key algorithmic ideas and proof techniques behind near-optimal instance-dependent methods in OPE and OPL. Finally, we discuss the limitations of offline RL and review a burgeoning problem of \emph{low-adaptive exploration} which addresses these limitations by providing a sweet middle ground between offline and online RL.