arXiv subjects

Danqi Chen

Publications and source records attributed to Danqi Chen.

At least 19 recordsLinked to original sources

arXiv2026

Hubs or Fringes: Pretraining Data Selection via Web Graph Centrality

The performance of modern language models depends critically on pretraining data composition. Yet existing data selection methods rely on auxiliary classifiers for document scoring or mixture optimization, adding computational overhead and dependence on labeled data. We propose WebGraphMix, a lightweight data selection framework that computes structural centrality scores over the Common Crawl host-level web graph and uses them to vary the proportion of central versus peripheral documents in the pretraining mixture. We hypothesize that central hosts expose models to reusable abstractions, while peripheral hosts encode specialized, long-tail knowledge. WebGraphMix computes centrality scores efficiently at web scale, requiring no model training, labeled data, or downstream supervision. We integrate WebGraphMix into the DataComp-LM pipeline and train models at 400M and 1B parameter scales with 8B and 28B tokens respectively, evaluating on 23 tasks ranging from factual knowledge to symbolic reasoning. Our experiments show that central and peripheral web regions encode complementary capabilities. Mixture combining both at a ratio of 1:1 achieves 41.4% on average, compared to 39.8% for uniform sampling. Combining structural scores with document-level quality classifier scores further improves performance to 43.8%. These findings demonstrate that web graph topology is a meaningful axis for pretraining data curation, capturing information that is largely orthogonal to existing content-based approaches.

cs.CL↗

arXiv2026

Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement

We introduce Goedel-Architect, an agentic framework for formal theorem proving in Lean 4 centered on blueprint generation and refinement. A blueprint is a dependency graph of definitions and lemmas that builds up to the main theorem. First, Goedel-Architect generates a blueprint of formally stated definitions and lemmas, along with declared dependencies. This blueprint is optionally guided by a natural language proof. Then, a tool-equipped Lean prover component closes each open lemma node in parallel using relevant dependencies. Failed lemmas in turn drive refinement of the global blueprint. This strategy contrasts with other mainstream approaches which use recursive lemma decomposition, and can inefficiently loop on dead-end strategies. Using the open-weight DeepSeek-V4-Flash (284B-A13B) as the backbone, Goedel-Architect attains 99.2% pass@1 on MiniF2F-test and 75.6% pass@1 on PutnamBench. With an optional natural-language proof seeding the initial blueprint on the harder problems, we additionally close the remaining two MiniF2F-test problems (reaching 100%), lift PutnamBench to 88.8% (597/672), and solve 4/6 on IMO 2025, 11/12 on Putnam 2025, and 3/6 on USAMO 2026. This represents state-of-the-art performance for an open-source pipeline at a price point up to 500x less than comparable open-source pipelines.

cs.AI↗

arXiv2026

The tau functions of the constrained CKP hierarchy

The CKP hierarchy is one important sub-hierarchy of the KP hierarchy, which is quite special due to its tau function. Here we construct the tau functions for the constrained CKP hierarchy $(L^k)_{<0}=\sum_{i=1}^{m}\big(q_{1,i}\partial^{-1}q_{2,i}-(-1)^kq_{2,i}\partial^{-1}q_{1,i}\big)$ with $k$ being odd or even positive integer by using the CKP Darboux transformations.

nlin.SI↗

arXiv2026

Odysseus: Scaling VLMs to 100+ Turn Decision-Making in Games via Reinforcement Learning

Given the rapidly growing capabilities of vision-language models (VLMs), extending them to interactive decision-making tasks such as video games has emerged as a promising frontier. However, existing approaches either rely on large-scale supervised fine-tuning (SFT) on human trajectories or apply reinforcement learning (RL) only in relatively short-horizon settings (typically around 20--30 turns). In this work, we study RL-based training of VLMs for long-horizon decision-making in Super Mario Land, a visually grounded environment requiring 100+ turns of interaction with coordinated perception, reasoning, and action. We begin with a systematic investigation of key algorithmic components and propose an adapted variant of PPO with a lightweight turn-level critic, which substantially improves training stability and sample efficiency over critic-free methods such as GRPO and Reinforce++. We further show that pretrained VLMs provide strong action priors, significantly improving sample efficiency during RL training and reducing the need for manual design choices such as action engineering, compared to classical deep RL trained from scratch. Building on these insights, we introduce Odysseus, an open training framework for VLM agents, achieving substantial gains across multiple levels of the game and at least 3 times average game progresses than frontier models. Moreover, the trained models exhibit consistent improvements under both in-game and cross-game generalization settings, while maintaining general-domain capabilities. Overall, our results identify key ingredients for making RL stable and effective in long-horizon, multi-modal settings, and provide practical guidance for developing VLMs as embodied agents.

cs.LG↗

arXiv2026

Agentic Aggregation for Parallel Scaling of Long-Horizon Agentic Tasks

We study parallel test-time scaling for long-horizon agentic tasks such as agentic search and deep research, where multiple rollouts are generated in parallel and aggregated into a final response. While such scaling has proven effective for chain-of-thought reasoning, agentic tasks pose unique challenges: trajectories are long, multi-turn, and tool-augmented, and outputs are often open-ended. Aggregating only final answers discards rich information from trajectories, while concatenating all trajectories exceeds the model's context window. To address this, we propose AggAgent, an aggregation agent that treats parallel trajectories as an environment. We equip it with lightweight tools to inspect candidate solutions and search across trajectories, enabling it to navigate and synthesize information on demand. Across six benchmarks and three model families (GLM-4.7, Qwen3.5, MiniMax-M2.5), AggAgent outperforms all existing aggregation methods-by up to 5.3% absolute on average and 10.3% on two deep research tasks-while adding minimal overhead, as the aggregation cost remains bounded by a single agentic rollout. Our findings establish agentic aggregation as an effective and cost-efficient approach to parallel test-time scaling.

cs.CL↗

arXiv2026

Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision

Current post-training methods in verifiable settings fall into two categories. Reinforcement learning (RLVR) relies on binary rewards, which are broadly applicable and powerful, but provide only sparse supervision during training. Distillation provides dense token-level supervision, typically obtained from an external teacher or using high-quality demonstrations. Collecting such supervision can be costly or unavailable. We propose Self-Distillation Zero (SD-Zero), a method that is substantially more training sample-efficient than RL and does not require an external teacher or high-quality demonstrations. SD-Zero trains a single model to play two roles: a Generator, which produces an initial response, and a Reviser, which conditions on that response and its binary reward to produce an improved response. We then perform on-policy self-distillation to distill the reviser into the generator, using the reviser's token distributions conditioned on the generator's response and its reward as supervision. In effect, SD-Zero trains the model to transform binary rewards into dense token-level self-supervision. On math and code reasoning benchmarks with Qwen3-4B-Instruct and Olmo-3-7B-Instruct, SD-Zero improves performance by at least 10% over the base models and outperforms strong baselines, including Rejection Fine-Tuning (RFT), GRPO, and Self-Distillation Fine-Tuning (SDFT), under the same question set and training sample budget. Extensive ablation studies show two novel characteristics of our proposed algorithm: (a) token-level self-localization, where the reviser can identify the key tokens that need to be revised in the generator's response based on reward, and (b) iterative self-evolution, where the improving ability to revise answers can be distilled back into generation performance with regular teacher synchronization. Code: https://github.com/princeton-pli/Self-Distillation-Zero.

cs.CL↗

arXiv2026

Vero: An Open RL Recipe for General Visual Reasoning

What does it take to build a visual reasoner that works across charts, science, spatial understanding, and open-ended tasks? The strongest vision-language models (VLMs) suggest that broad visual reasoning is within reach, yet their closed data and reinforcement learning (RL) pipelines make their gains difficult to study, reproduce, or extend. We introduce Vero, a family of fully open VLMs that match or exceed existing open-weight models across diverse visual reasoning tasks. We scale RL data and rewards across six broad task categories, constructing Vero-600K, a 600K-sample dataset from 59 datasets, and designing task-routed rewards that handle heterogeneous answers. Across VeroEval, our 30-benchmark suite, Vero-600K outperforms existing RL datasets under controlled comparisons. Applied to five starting models, Vero variants gain 2.9-5.4 points on average over their initial models. Notably, Vero-Qwen3I-8B, trained on the Instruct model, surpasses Qwen3-VL-8B-Thinking by 3.8 points on average without additional distillation. Systematic ablations reveal that different task categories elicit distinct reasoning patterns and that broad gains depend on learning them jointly rather than in isolation. All data, code, and models are publicly available.

cs.CV↗

arXiv2026

DySCO: Dynamic Attention-Scaling Decoding for Long-Context Language Models

Understanding and reasoning over long contexts is a crucial capability for language models (LMs). Although recent models support increasingly long context windows, their accuracy often deteriorates as input length grows. In practice, models often struggle to keep attention aligned with the most relevant context throughout decoding. In this work, we propose DYSCO, a novel decoding algorithm for improving long-context reasoning. DYSCO leverages retrieval heads--a subset of attention heads specialized for longcontext retrieval--to identify task-relevant tokens at each decoding step and explicitly up-weight them. By doing so, DYSCO dynamically adjusts attention during generation to better utilize relevant context. The method is training-free and can be applied directly to any off-the-shelf LMs. Across multiple instruction-tuned and reasoning models, DYSCO consistently improves performance on challenging long-context reasoning benchmarks, yielding relative gains of up to 25% on MRCR and LongBenchV2 at 128K context length with modest additional compute. Further analysis highlights the importance of both dynamic attention rescaling and retrievalhead guided selection for the effectiveness of the method, while providing interpretability insights into decoding-time attention behavior. Our code is available at https://github.com/princeton-pli/DySCO.

cs.CL↗

arXiv2025

Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting

Adapting language models (LMs) to new tasks via post-training carries the risk of degrading existing capabilities -- a phenomenon classically known as catastrophic forgetting. In this paper, toward identifying guidelines for mitigating this phenomenon, we systematically compare the forgetting patterns of two widely adopted post-training methods: supervised fine-tuning (SFT) and reinforcement learning (RL). Our experiments reveal a consistent trend across LM families (Llama, Qwen) and tasks (instruction following, general knowledge, and arithmetic reasoning): RL leads to less forgetting than SFT while achieving comparable or higher target task performance. To investigate the cause for this difference, we consider a simplified setting in which the LM is modeled as a mixture of two distributions, one corresponding to prior knowledge and the other to the target task. We identify that the mode-seeking nature of RL, which stems from its use of on-policy data, enables keeping prior knowledge intact when learning the target task. We then verify this insight by demonstrating that the use on-policy data underlies the robustness of RL to forgetting in practical settings, as opposed to other algorithmic choices such as the KL regularization or advantage estimation. Lastly, as a practical implication, our results highlight the potential of mitigating forgetting using approximately on-policy data, which can be substantially more efficient to obtain than fully on-policy data.

cs.LG↗

arXiv2025

Lost in the Maze: Overcoming Context Limitations in Long-Horizon Agentic Search

Long-horizon agentic search requires iteratively exploring the web over long trajectories and synthesizing information across many sources, enabling powerful applications like deep research systems. In this work, we show that popular agentic search frameworks struggle to scale to long trajectories primarily due to context limitations--they accumulate long, noisy content, hit context window and tool budgets, or stop early. We therefore introduce SLIM (Simple Lightweight Information Management), a simple framework that separates retrieval into distinct search and browse tools, and periodically summarizes the trajectory, keeping context concise while enabling longer, more focused searches. Across a wide range of long-horizon tasks, SLIM achieves comparable performance at substantially lower cost and far fewer tool calls than strong open-source frameworks with both proprietary and open-weight models, including RL-trained models for deep research. Specifically, with o3 as the base model, SLIM achieves 56% on BrowseComp and 33% on HLE, outperforming all open-source frameworks by 8 and 6 absolute points, respectively, while incurring 4-6x fewer tool calls. With GLM-4.7 Flash, SLIM achieves 10 points improvement over the next best open-source framework, Search-o1, on BrowseComp using a third of the cost. To systematically understand failure modes in long-horizon agentic search, we develop an automated fine-grained trajectory analysis pipeline and error taxonomy, and find that SLIM exhibits significantly fewer hallucinations than prior systems. We hope our analysis framework and simple tool design inform future long-horizon agents.

cs.CL↗

arXiv2025

Extracting Rule-based Descriptions of Attention Features in Transformers

Mechanistic interpretability strives to explain model behavior in terms of bottom-up primitives. The leading paradigm is to express hidden states as a sparse linear combination of basis vectors, called features. However, this only identifies which text sequences (exemplars) activate which features; the actual interpretation of features requires subjective inspection of these exemplars. This paper advocates for a different solution: rule-based descriptions that match token patterns in the input and correspondingly increase or decrease the likelihood of specific output tokens. Specifically, we extract rule-based descriptions of SAE features trained on the outputs of attention layers. While prior work treats the attention layers as an opaque box, we describe how it may naturally be expressed in terms of interactions between input and output features, of which we study three types: (1) skip-gram rules of the form "[Canadian city]... speaks --> English", (2) absence rules of the form "[Montreal]... speaks -/-> English," and (3) counting rules that toggle only when the count of a word exceeds a certain value or the count of another word. Absence and counting rules are not readily discovered by inspection of exemplars, where manual and automatic descriptions often identify misleading or incomplete explanations. We then describe a simple approach to extract these types of rules automatically from a transformer, and apply it to GPT-2 small. We find that a majority of features may be described well with around 100 skip-gram rules, though absence rules are abundant even as early as the first layer (in over a fourth of features). We also isolate a few examples of counting rules. This paper lays the groundwork for future research into rule-based descriptions of features by defining them, showing how they may be extracted, and providing a preliminary taxonomy of some of the behaviors they represent.

cs.CL↗

arXiv2025

Language Models that Think, Chat Better

Reinforcement learning with verifiable rewards (RLVR) trains language models to use long chain-of-thought reasoning (CoT) in domains like mathematics and code with rule-based verifiers. However, long CoT learned through RLVR does not generalize well to open-ended tasks -- such as writing essay outlines or making meal plans -- where humans reason routinely. This paper establishes the benefits of long CoT for general-purpose chat capabilities and introduces RL with Model-rewarded Thinking (RLMT)1, which pushes RLVR beyond verifiable domains. Using diverse real-world prompts, RLMT requires LMs to generate long CoT reasoning before responding, and optimizes them with online RL against a preference-based reward model used in RLHF. Across 40 training runs on Llama-3.1-8B and Qwen-2.5-7B (both base and instruct) and multiple optimization algorithms (DPO, PPO, and GRPO), RLMT consistently outperforms standard RLHF pipelines. This includes substantial gains of 3-7 points on three chat benchmarks (AlpacaEval2, WildBench, and ArenaHardV2), along with 1-3 point improvements on other tasks like creative writing and general knowledge. RLMT can also be applied directly to base models without an SFT stage, akin to DeepSeek-R1-Zero. Remarkably, with only 7K prompts, Llama-3.1-8B base trained with our RLMT recipe outperforms Llama-3.1-8B-Instruct post-trained with a complex multi-staged pipeline with 25M+ examples. We close with qualitative and quantitative analyses of how trained models plan their responses. Our results rethink the post-training pipeline and call upon future work to understand and employ thinking more broadly.

cs.CL↗

arXiv2025

Statutory Construction and Interpretation for Artificial Intelligence

AI systems are increasingly governed by natural language principles, yet a key challenge arising from reliance on language remains underexplored: interpretive ambiguity. As in legal systems, ambiguity arises both from how these principles are written and how they are applied. But while legal systems use institutional safeguards to manage such ambiguity, such as transparent appellate review policing interpretive constraints, AI alignment pipelines offer no comparable protections. Different interpretations of the same rule can lead to inconsistent or unstable model behavior. Drawing on legal theory, we identify key gaps in current alignment pipelines by examining how legal systems constrain ambiguity at both the rule creation and rule application steps. We then propose a computational framework that mirrors two legal mechanisms: (1) a rule refinement pipeline that minimizes interpretive disagreement by revising ambiguous rules (analogous to agency rulemaking or iterative legislative action), and (2) prompt-based interpretive constraints that reduce inconsistency in rule application (analogous to legal canons that guide judicial discretion). We evaluate our framework on a 5,000-scenario subset of the WildChat dataset and show that both interventions significantly improve judgment consistency across a panel of reasonable interpreters. Our approach offers a first step toward systematically managing interpretive ambiguity, an essential step for building more robust, law-following AI systems.

cs.CL↗

arXiv2025

Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction

We introduce Goedel-Prover-V2, a series of open-source language models that set a new state-of-the-art in automated theorem proving. Built on the standard expert iteration and reinforcement learning pipeline, our approach incorporates three key innovations: (1) Scaffolded data synthesis: We generate synthetic tasks of increasing difficulty to train the model to master increasingly complex theorems; (2) Verifier-guided self-correction: We enable the model to iteratively revise its proofs by leveraging feedback from the Lean compiler; (3) Model averaging: We merge model checkpoints to mitigate the decrease in model output diversity in later stages of training. Our small model, Goedel-Prover-V2-8B, reaches 84.6% pass@32 on MiniF2F and outperforms DeepSeek-Prover-V2-671B under the same metric, despite being 80X smaller. Our flagship model, Goedel-Prover-V2-32B, achieves 88.1% on MiniF2F at pass@32 in standard mode and 90.4% in self-correction mode, outperforming prior SOTA by a large margin. Additionally, our flagship model solves 86 problems on PutnamBench at pass@184, securing the first place among open-source models on the leaderboard, surpassing DeepSeek-Prover-V2-671B's record of solving 47 problems by pass@1024 with a significantly smaller model size and compute budget. At the time of its release (July-August 2025), Goedel-Prover-V2 achieves the strongest overall performance among all open-source theorem provers. It also ranks among the top-performing models--including closed-source systems with publicly reported performance--under a constrained test-time compute budget. Our models, code, and data are released at https://github.com/Goedel-LM/Goedel-Prover-V2.

cs.LG↗

arXiv2025

Cache Me If You Can: How Many KVs Do You Need for Effective Long-Context LMs?

Language models handle increasingly long contexts for tasks such as book summarization, but this leads to growing memory costs for the key-value (KV) cache. Many prior works have proposed ways of discarding KVs from memory, but their approaches are tailored to favorable settings, obscuring caveats like high peak memory and performance degradation, and a fair comparison between methods is difficult. In this paper, we propose the *KV footprint* as a unified metric, which accounts for both the amount of KV entries stored and their lifespan in memory. We evaluate methods based on the smallest footprint they attain while preserving performance in both long-context understanding and generation, with context lengths of up to 128K tokens. This metric reveals the high peak memory of prior KV eviction methods. One class of methods -- *post-fill eviction* -- has a high footprint due to being incompatible with eviction during pre-filling. We adapt these methods to be able to evict KVs during pre-filling, achieving substantially lower KV footprints. We then turn to *recency eviction* methods, wherein we propose PruLong, an end-to-end optimization method for learning which attention heads need to retain the full KV cache and which do not. PruLong saves memory while preserving long-context performance, achieving 12% smaller KV footprint than prior methods while retaining performance in challenging recall tasks. Our paper clarifies the complex tangle of long-context inference methods and paves the way for future development to minimize the KV footprint.

cs.CL↗

arXiv2025

Query-Focused Retrieval Heads Improve Long-Context Reasoning and Re-ranking

Recent work has identified retrieval heads, a subset of attention heads responsible for retrieving salient information in long-context language models (LMs), as measured by their copy-paste behavior in Needlein-a-Haystack tasks. In this paper, we introduce QRHead (Query-Focused Retrieval Head), an improved set of attention heads that enhance retrieval from long context. We identify QRHead by aggregating attention scores with respect to the input query, using a handful of examples from real-world tasks (e.g., long-context QA). We further introduce QRRetriever, an efficient and effective retriever that uses the accumulated attention mass of QRHead as retrieval scores. We use QRRetriever for long-context reasoning by selecting the most relevant parts with the highest retrieval scores. On multi-hop reasoning tasks LongMemEval and CLIPPER, this yields over 10% performance gains over full context and outperforms strong dense retrievers. We also evaluate QRRetriever as a re-ranker on the BEIR benchmark and find that it achieves strong zero-shot performance, outperforming other LLM-based re-rankers such as RankGPT. Further analysis shows that both the query-context attention scoring and task selection are crucial for identifying QRHead with strong downstream utility. Overall, our work contributes a general-purpose retriever and offers interpretability insights into the long-context capabilities of LMs.

cs.CL↗

arXiv2025

Precise Information Control in Long-Form Text Generation

A central challenge in language models (LMs) is faithfulness hallucination: the generation of information unsubstantiated by input context. To study this problem, we propose Precise Information Control (PIC), a new task formulation that requires models to generate long-form outputs grounded in a provided set of short self-contained statements, without adding any unsupported ones. PIC includes a full setting that tests a model's ability to include exactly all input claims, and a partial setting that requires the model to selectively incorporate only relevant claims. We present PIC-Bench, a benchmark of eight long-form generation tasks (e.g., summarization, biography generation) adapted to the PIC setting, where LMs are supplied with well-formed, verifiable input claims. Our evaluation of a range of open and proprietary LMs on PIC-Bench reveals that, surprisingly, state-of-the-art LMs still hallucinate against user-provided input in over 70% of generations. To alleviate this lack of faithfulness, we introduce a post-training framework that uses a weakly supervised preference data construction method to train an 8B PIC-LM with stronger PIC ability--improving from 69.1% to 91.0% F1 in the full PIC setting. When integrated into end-to-end factual generation pipelines, PIC-LM improves exact match recall by 17.1% on ambiguous QA with retrieval, and factual precision by 30.5% on a birthplace fact-checking task, underscoring the potential of precisely grounded generation.

cs.CL↗

arXiv2025

The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training language models (LMs) on reasoning tasks that elicit emergent long chains of thought (CoTs). Unlike supervised learning, it updates the model using both correct and incorrect samples via policy gradients. To better understand its mechanism, we decompose the learning signal into reinforcing correct responses and penalizing incorrect ones, referred to as Positive and Negative Sample Reinforcement (PSR and NSR), respectively. We train Qwen2.5-Math-7B, Qwen3-4B and Llama-3.1-8B-Instruct on a mathematical reasoning dataset and uncover a surprising result: training with only negative samples -- without reinforcing correct responses -- can be highly effective: it consistently improves performance over the base model across the entire Pass@$k$ spectrum $k$ up to 256), often matching or surpassing PPO and GRPO. In contrast, reinforcing only correct responses improves Pass@1 but degrades performance at higher $k$, due to reduced diversity. These inference-scaling trends highlight that solely penalizing incorrect responses may contribute more to performance than previously recognized. Through gradient analysis, we show that NSR works by suppressing incorrect generations and redistributing probability mass toward other plausible candidates, guided by the model's prior beliefs. It refines the model's existing knowledge rather than introducing entirely new behaviors. Building on this insight, we propose a simple variant of the RL objective that upweights NSR, and show that it consistently improves overall Pass@$k$ performance on MATH, AIME 2025, and AMC23. Our code is available at https://github.com/TianHongZXY/RLVR-Decomposed.

cs.CL↗