Haikang Deng

Nikhil Kandpal, Haikang Deng, Adam Roberts et al. · berkeley

The Internet contains a wealth of knowledge -- from the birthdays of historical figures to tutorials on how to code -- all of which may be learned by language models. However, while certain pieces of information are ubiquitous on the web, others appear extremely rarely. In this paper, we study the relationship between the knowledge memorized by large language models and the information in pre-training datasets scraped from the web. In particular, we show that a language model's ability to answer a fact-based question relates to how many documents associated with that question were seen during pre-training. We identify these relevant documents by entity linking pre-training datasets and counting documents that contain the same entities as a given question-answer pair. Our results demonstrate strong correlational and causal relationships between accuracy and relevant document count for numerous question answering datasets (e.g., TriviaQA), pre-training corpora (e.g., ROOTS), and model sizes (e.g., 176B parameters). Moreover, while larger models are better at learning long-tail knowledge, we estimate that today's models must be scaled by many orders of magnitude to reach competitive QA performance on questions with little support in the pre-training data. Finally, we show that retrieval-augmentation can reduce the dependence on relevant pre-training information, presenting a promising approach for capturing the long-tail.

Haikang Deng, Colin Raffel

While large language models have proven effective in a huge range of downstream applications, they often generate text that is problematic or lacks a desired attribute. In this paper, we introduce Reward-Augmented Decoding (RAD), a text generation procedure that uses a small unidirectional reward model to encourage a language model to generate text that has certain properties. Specifically, RAD uses the reward model to score generations as they are produced and rescales sampling probabilities to favor high-reward tokens. By using a unidirectional reward model, RAD can cache activations from prior generation steps to decrease computational overhead. Through experiments on generating non-toxic and sentiment-controlled text, we demonstrate that RAD performs best among methods that change only the generation procedure and matches the performance of state-of-the-art methods that involve re-training the language model. We further validate that RAD is effective on very large language models while incurring a minimal computational overhead.

Po-Nien Kung, Zhen Yang, Jeffrey Luo et al.

Large language models can exhibit emergent reasoning behaviors, often manifested as recurring lexical patterns (e.g., "wait," indicating verification). However, complex reasoning trajectories remain sparse in unconstrained sampling, and standard RL often fails to guarantee the acquisition of diverse reasoning behaviors. We propose a systematic discovery and reinforcement of diverse reasoning patterns through structured reasoning, a paradigm that requires targeted exploration of specific reasoning patterns during the RL process. To this end, we propose Ctrl-R, a framework for learning structured reasoning via tractable trajectory control that actively guides the rollout process, incentivizing the exploration of diverse reasoning patterns that are critical for complex problem-solving. The resulting behavior policy enables accurate importance-sampling estimation, supporting unbiased on-policy optimization. We further introduce a power-scaling factor on the importance-sampling weights, allowing the policy to selectively learn from exploratory, out-of-distribution trajectories while maintaining stable optimization. Experiments demonstrate that Ctrl-R enables effective exploration and internalization of previously unattainable reasoning patterns, yielding consistent improvements across language and vision-language models on mathematical reasoning tasks.

Alexander K Taylor, Junyi Zhang, Ethan Ji et al.

Automated theorem proving (ATP) benchmarks largely consist of problems formalized in MathLib, so current ATP training and evaluation are heavily biased toward MathLib's definitional framework. However, frontier mathematics is often exploratory and prototype-heavy, relying on bespoke constructions that deviate from standard libraries. In this work, we evaluate the robustness of current ATP systems when applied to a novel definitional framework, specifically examining the performance gap between standard library problems and bespoke mathematical constructions. We introduce TaoBench, an undergraduate-level benchmark derived from Terence Tao's Analysis I, which formalizes analysis by constructing core mathematical concepts from scratch, without relying on standard Mathlib definitions, as well as by mixing from-scratch and MathLib constructions. For fair evaluation, we build an agentic pipeline that automatically extracts a compilable, self-contained local environment for each problem. To isolate the effect of definitional frameworks, we additionally translate every problem into a mathematically equivalent Mathlib formulation, yielding paired TaoBench-Mathlib statements for direct comparison. While state-of-the-art ATP models perform capably within the MathLib framework, performance drops by an average of roughly 26% on the definitionally equivalent Tao formulation. This indicates that the main bottleneck is limited generalization across definitional frameworks rather than task difficulty. TaoBench thus highlights a gap between benchmark performance and applicability, and provides a concrete foundation for developing and testing provers better aligned with research mathematics.

Yihang Chen, Haikang Deng, Kaiqiao Han et al.

Chain-of-Thought (CoT) reasoning enhances large language models (LLMs) by decomposing complex problems into step-by-step solutions, improving performance on reasoning tasks. However, current CoT disclosure policies vary widely across different models in frontend visibility, API access, and pricing strategies, lacking a unified policy framework. This paper analyzes the dual-edged implications of full CoT disclosure: while it empowers small-model distillation, fosters trust, and enables error diagnosis, it also risks violating intellectual property, enabling misuse, and incurring operational costs. We propose a tiered-access policy framework that balances transparency, accountability, and security by tailoring CoT availability to academic, business, and general users through ethical licensing, structured reasoning outputs, and cross-tier safeguards. By harmonizing accessibility with ethical and operational considerations, this framework aims to advance responsible AI deployment while mitigating risks of misuse or misinterpretation.

Yu Zhou, Sohyun An, Haikang Deng et al.

Contact languages like English exhibit rich regional variations in the form of dialects, which are often used by dialect speakers interacting with generative models. However, can multimodal generative models effectively produce content given dialectal textual input? In this work, we study this question by constructing a new large-scale benchmark spanning six common English dialects. We work with dialect speakers to collect and verify over 4200 unique prompts and evaluate on 17 image and video generative models. Our automatic and human evaluation results show that current state-of-the-art multimodal generative models exhibit 32.26% to 48.17% performance degradation when a single dialect word is used in the prompt. Common mitigation methods such as fine-tuning and prompt rewriting can only improve dialect performance by small margins (< 7%), while potentially incurring significant performance degradation in Standard American English (SAE). To this end, we design a general encoder-based mitigation strategy for multimodal generative models. Our method teaches the model to recognize new dialect features while preserving SAE performance. Experiments on models such as Stable Diffusion 1.5 show that our method is able to simultaneously raise performance on five dialects to be on par with SAE (+34.4%), while incurring near zero cost to SAE performance.

Haikang Deng, Po-Nien Kung, Nanyun Peng

Large language models (LLMs) are increasingly adept at following instructions containing task descriptions to solve complex problems, such as mathematical reasoning and automatic evaluation (LLM-as-a-Judge). However, as prompts grow more complex, models often struggle to adhere to all instructions. This difficulty is especially common when instructive prompts intertwine reasoning directives -- specifying what the model should solve -- with rigid formatting requirements that dictate how the solution must be presented. The entanglement creates competing goals for the model, suggesting that more explicit separation of these two aspects could lead to improved performance. To this front, we introduce Deco-G, a decoding framework that explicitly decouples format adherence from task solving. Deco-G handles format compliance with a separate tractable probabilistic model (TPM), while prompts LLMs with only task instructions. At each decoding step, Deco-G combines next token probabilities from the LLM with the TPM calculated format compliance likelihood to form the output probability. To make this approach both practical and scalable for modern instruction-tuned LLMs, we introduce three key innovations: instruction-aware distillation, a flexible trie-building algorithm, and HMM state pruning for computational efficiency. We demonstrate the effectiveness of Deco-G across a wide range of tasks with diverse format requirements, including mathematical reasoning, LLM-as-a-judge, and event argument extraction. Overall, our approach yields 1.0% to 6.0% relative gain over regular prompting practice with guaranteed format compliance.