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Theory · Interpretability and Visualization

Siwei Wang, Yifei Shen, Haoran Sun, Shi Feng, Shang-Hua Teng, Li Dong, Yaru Hao, Wei Chen

Recent reinforcement learning (RL) methods have substantially enhanced the planning capabilities of Large Language Models (LLMs), yet the theoretical basis for their effectiveness remains elusive. In this work, we investigate RL's benefits and limitations through a tractable graph-based abstraction, focusing on policy gradient (PG) and Q-learning methods. Our theoretical analyses reveal that supervised fine-tuning (SFT) may introduce co-occurrence-based spurious solutions, whereas RL achieves correct planning primarily through exploration, underscoring exploration’s role in enabling better generalization. However, we also show that PG suffers from diversity collapse, where output diversity decreases during training and persists even after perfect accuracy is attained. By contrast, Q-learning provides two key advantages: off-policy learning and diversity preservation at convergence. We further demonstrate that careful reward design is necessary to prevent Q-value bias in Q-learning. Finally, applying our framework to the real-world planning benchmark Blocksworld, we confirm that these behaviors manifest in practice.

Zhiwang Zhou, Yuandong Pu, Xuming He, Yidi Liu, Yixin Chen, Junchao Gong, Xiang Zhuang, Wanghan Xu, Qinglong Cao, SHIXIANG TANG 等

Weather modeling requires both accurate prediction and mechanistic interpretation, yet existing methods treat these goals in isolation, separating generation from understanding. To address this gap, we present Omni-Weather, the first multimodal foundation model that unifies weather generation and understanding within a single architecture. Omni-Weather integrates a radar encoder for weather generation tasks, followed by unified processing using a shared self-attention mechanism. Moreover, we construct a Chain-of-Thought dataset for causal reasoning in weather generation, enabling interpretable outputs and improved perceptual quality. Extensive experiments show Omni-Weather achieves state-of-the-art performance in both weather generation and understanding. Our findings further indicate that generative and understanding tasks in the weather domain can mutually enhance each other. Omni-Weather also demonstrates the feasibility and value of unifying weather generation and understanding.

Applications · Neuroscience, Cognitive Science

Jiahe Li, Junru Chen, Fanqi Shen, Jialan Yang, Jada Li, Zhizhang Yuan, Baowen Cheng, Li Meng, Yang Yang

Enabling natural communication through brain–computer interfaces (BCIs) remains one of the most profound challenges in neuroscience and neurotechnology. While existing frameworks offer partial solutions, they are constrained by oversimplified semantic representations and a lack of interpretability. To overcome these limitations, we introduce **Semantic Intent Decoding(SID)**, a novel framework that translates neural activity into natural language by modeling meaning as a flexible set of compositional semantic units. SID is built on three core principles: semantic compositionality, continuity and expandability of semantic space, and fidelity in reconstruction. We present **BrainMosaic**, a deep learning architecture implementing SID. BrainMosaic decodes multiple semantic units from EEG/SEEG signals using set matching and then reconstructs coherent sentences through semantic-guided reconstruction. This approach moves beyond traditional pipelines that rely on fixed-class classification or unconstrained generation, enabling a more interpretable and expressive communication paradigm. Extensive experiments on multilingual EEG and clinical SEEG datasets demonstrate that SID and BrainMosaic offer substantial advantages over existing frameworks, paving the way for natural and effective BCI-mediated communication.

Fangyi Chen, Yaojie Shen, Lu Xu, Ye Yuan, Shu Zhang, Yulei Niu, Longyin Wen

Precise, object-aware control over visual content is essential for advanced image editing and compositional generation. Yet, most existing approaches operate on entire images holistically, limiting the ability to isolate and manipulate individual scene elements. In contrast, layered representations, where scenes are explicitly separated into objects, environmental context, and visual effects, provide a more intuitive and structured framework for interpreting and editing visual content. To bridge this gap and enable both compositional understanding and controllable editing, we introduce the Referring Layer Decomposition (RLD) task, which predicts complete RGBA layers from a single RGB image, conditioned on flexible user prompts, such as spatial inputs (e.g., points, boxes, masks), natural language descriptions, or combinations thereof. At the core is the RefLade, a large-scale dataset comprising 1.11M image–layer–prompt triplets produced by our scalable data engine, along with 100K manually curated, high-fidelity layers. Coupled with a perceptually grounded, human-preference-aligned automatic evaluation protocol, RefLade establishes RLD as a well-defined and benchmarkable research task. Building on this foundation, we present RefLayer, a simple baseline designed for prompt-conditioned layer decomposition, achieving high visual fidelity and semantic alignment. Extensive experiments show our approach enables effective training, reliable evaluation, and high-quality image decomposition, while exhibiting strong zero-shot generalization capabilities. The project will be released at https://yaojie-shen.github.io/project/RLD/

Reinforcement Learning · Everything Else

Ju-Hyun Kim, Seungki Min

We propose a sample-efficient Q-learning algorithm for reinforcement learning with the Conditional Value-at-Risk (CVaR) objective. Our algorithm is built upon predictive tail value function, a novel formulation of risk-sensitive action value, that admits a recursive structure as in the conventional risk-neutral Bellman equation. This structure enables the Q-learning algorithm to utilize the entire set of sample trajectories rather than relying only on worst-case outcomes, enhancing the sample efficiency. We further derive a Bellman optimality equation and a policy improvement theorem, which provide theoretical foundations of our algorithm and remedy inconsistencies that have existed in the literature. Empirical results demonstrate that our method consistently improves CVaR performance while maintaining stable and interpretable learning dynamics.

Computer Vision · Everything Else

Chenliang Zhou, Fangcheng Zhong, Weihao Xia, Albert Miao, Canberk Baykal, Cengiz Oztireli

We introduce the *Quartet of Diffusions*, a structure-aware point cloud generation framework that explicitly models part composition and symmetry. Unlike prior methods that treat shape generation as a holistic process or only support part composition, our approach leverages four coordinated diffusion models to learn distributions of global shape latents, symmetries, semantic parts, and their spatial assembly. This structured pipeline ensures guaranteed symmetry, coherent part placement, and diverse, high-quality outputs. By disentangling the generative process into interpretable components, our method supports fine-grained control over shape attributes, enabling targeted manipulation of individual parts while preserving global consistency. A central global latent further reinforces structural coherence across assembled parts. Our experiments show that the Quartet achieves state-of-the-art performance. To our best knowledge, this is the first 3D point cloud generation framework that fully integrates and enforces both symmetry and part priors throughout the generative process.

Fangyu Lei, Jinxiang Meng, Yiming Huang, Junjie zhao, Yitong Zhang, Jianwen Luo, Xin Zou, Ruiyi Yang, Wenbo Shi, Yan Gao 等

Real-world enterprise data intelligence workflows encompass data engineering that turns raw sources into analytical-ready tables and data analysis that convert those tables into decision-oriented insights. We introduce DAComp, a benchmark of 210 tasks that mirrors these complex workflows. Data engineering (DE) tasks require repository-level engineering on industrial schemas, including designing and building multi-stage SQL pipelines from scratch and evolving existing systems under evolving requirements. Data analysis (DA) tasks pose open-ended business problems that demand strategic planning, exploratory analysis through iterative coding, interpretation of intermediate results, and the synthesis of actionable recommendations. Engineering tasks are scored through execution-based, multi-metric evaluation. Open-ended tasks are assessed by a reliable, experimentally validated LLM-judge, which is guided by hierarchical, meticulously crafted rubrics. Our experiments reveal that even state-of-the-art agents falter on DAComp. Performance on DE tasks is particularly low, with success rates under 20\%, exposing a critical bottleneck in holistic pipeline orchestration, not merely code generation. Scores on DA tasks also average below 40\%, highlighting profound deficiencies in open-ended reasoning and demonstrating that engineering and analysis are distinct capabilities. By clearly diagnosing these limitations, DAComp provides a rigorous and realistic testbed to drive the development of truly capable autonomous data agents for enterprise settings. Our data and code are available at \url{da-comp.github.io}.

Applications · Time Series

Ziheng Peng, Shijie Ren, Xinyue Gu, Linxiao Yang, Xiting Wang, Liang Sun

While deep learning has achieved impressive performance in time series forecasting, it becomes increasingly crucial to understand its decision-making process for building trust in high-stakes scenarios. Existing interpretable models often provide only local and partial explanations, lacking the capability to reveal how heterogeneous and interacting input variables jointly shape the overall temporal patterns in the forecast curve. We propose ProtoTS, a novel interpretable forecasting framework that achieves both high accuracy and transparent decision-making through modeling prototypical temporal patterns. ProtoTS computes instance-prototype similarity based on a denoised representation that preserves abundant heterogeneous information. The prototypes are organized hierarchically to capture global temporal patterns with coarse prototypes while capturing finer-grained local variations with detailed prototypes, enabling expert steering and multi-level interpretability. Experiments on multiple realistic benchmarks, including a newly released LOF dataset, show that ProtoTS not only exceeds existing methods in forecast accuracy but also delivers expert-steerable interpretations for better model understanding and decision support. The source code is available at https://github.com/SKURA502/ProtoTS.

Leonardo Defilippis, Yizhou Xu, Julius Girardin, Vittorio Erba, Emanuele Troiani, Lenka Zdeborova, Bruno Loureiro, Florent Krzakala

Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and diagonal neural networks in the feature learning regime. Leveraging connections with matrix compressed sensing and LASSO, we derive a detailed phase diagram for the scaling exponents of the excess risk as a function of sample complexity and weight decay. This analysis uncovers crossovers between distinct scaling regimes and plateau behaviors, mirroring phenomena widely reported in the empirical neural scaling literature. Furthermore, we establish a precise link between these regimes and the spectral properties of the trained network weights, which we characterize in detail. As a consequence, we provide a theoretical validation of recent empirical observations connecting the emergence of power-law tails in the weight spectrum with network generalization performance, yielding an interpretation from first principles.

Deep Learning · Theory

Leonardo Defilippis, Yizhou Xu, Julius Girardin, Vittorio Erba, Emanuele Troiani, Lenka Zdeborova, Bruno Loureiro, Florent Krzakala

Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and diagonal neural networks in the feature learning regime. Leveraging connections with matrix compressed sensing and LASSO, we derive a detailed phase diagram for the scaling exponents of the excess risk as a function of sample complexity and weight decay. This analysis uncovers crossovers between distinct scaling regimes and plateau behaviors, mirroring phenomena widely reported in the empirical neural scaling literature. Furthermore, we establish a precise link between these regimes and the spectral properties of the trained network weights, which we characterize in detail. As a consequence, we provide a theoretical validation of recent empirical observations connecting the emergence of power-law tails in the weight spectrum with network generalization performance, yielding an interpretation from first principles.

Reinforcement Learning · Online

Hanyang Wang, Lu Wang, Chaoyun Zhang, Tianjun Mao, Si Qin, Qingwei Lin, Saravan Rajmohan, Dongmei Zhang

Traditional RLHF optimizes language models with coarse, scalar rewards that mask the fine-grained reasons behind success or failure, leading to slow, opaque learning. Recent work augments RL with textual critiques through prompting or reflection, improving interpretability but leaving model parameters untouched. We introduce **Text2Grad**, a reinforcement-learning paradigm that *turns free-form textual feedback into span-level gradients*. Given human (or programmatic) critiques, Text2Grad aligns each feedback phrase with the relevant token spans, converts these alignments into differentiable reward signals, and performs gradient updates that directly refine the offending portions of the model's policy. This yields precise, feedback-conditioned adjustments instead of global nudges. Text2Grad is realized through three components: (1) a high-quality feedback–annotation pipeline that pairs critiques with token spans; (2) a fine-grained reward model that predicts span-level reward on answers while generating explanatory critiques; and (3) a span-level policy optimizer that back-propagates *natural-language gradients*. Across summarization, code generation, and question answering, Text2Grad consistently surpasses scalar-reward RL and prompt-only baselines, providing both higher task metrics and richer interpretability. Our results suggest that natural-language feedback can serve not only as explanations, but also as actionable training signals for fine-grained alignment. The code for our method is available at *[https://github.com/microsoft/Text2Grad](https://github.com/microsoft/Text2Grad)*.

Social Aspects · Accountability, Transparency and Interpretability

Yongchao Long, Yingying Zhang, Xianbin Wen, Xian Wu, Yuxi Zhou, Shenda Hong

While Retrieval-Augmented Generation (RAG) enables large language models (LLMs) to generate contextually grounded responses, contextual faithfulness remains challenging as LLMs may not consistently trust provided context, leading to hallucinations that undermine reliability. We observe an inverse correlation between response copying degree and context-unfaithful hallucinations on RAGTruth, suggesting higher copying degrees reduce hallucinations by fostering genuine contextual belief. We propose Copy-Paste, a generation paradigm that directly embeds contextual fragments to ensure faithfulness, and instantiate it through CopyPasteLLM via two-stage high-copying preference training. We design three prompting methods to enhance copying degree, demonstrating that high-copying responses achieve superior contextual faithfulness and hallucination control. These approaches enable a fully automated pipeline that transforms generated responses into high-copying preference data for training CopyPasteLLM. On FaithEval, ConFiQA and PubMedQA, CopyPasteLLM achieves best performance in both counterfactual and original contexts, remarkably with 12.2\% to 24.5\% accuracy improvements on FaithEval over the best baseline, while requiring only 365 training samples—1/50th of baseline data. To elucidate CopyPasteLLM's effectiveness, we propose the Context-Parameter Copying Capturing algorithm. Interestingly, this reveals that CopyPasteLLM recalibrates reliance on internal parametric knowledge rather than external knowledge during generation. All codes are available at https://github.com/longyongchao/CopyPasteLLM

General Machine Learning · Everything Else

Spyros Rigas, Dhruv Verma, Georgios Alexandridis, Yixuan Wang

Kolmogorov–Arnold Networks (KANs) are a recently introduced neural architecture that replace fixed nonlinearities with trainable activation functions, offering enhanced flexibility and interpretability. While KANs have been applied successfully across scientific and machine learning tasks, their initialization strategies remain largely unexplored. In this work, we study initialization schemes for spline-based KANs, proposing two theory-driven approaches inspired by LeCun and Glorot, as well as an empirical power-law family with tunable exponents. Our evaluation combines large-scale grid searches on function fitting and forward PDE benchmarks, an analysis of training dynamics through the lens of the Neural Tangent Kernel, and evaluations on a subset of the Feynman dataset. Our findings indicate that the Glorot-inspired initialization significantly outperforms the baseline in parameter-rich models, while power-law initialization achieves the strongest performance overall, both across tasks and for architectures of varying size. This work underscores initialization as a key factor in KAN performance and introduces practical strategies to improve it.

Applications · Language, Speech and Dialog

Haipeng Luo, Huawen Feng, Qingfeng Sun, Can Xu, Kai Zheng, Yufei Wang, TAO YANG, Winston Hu, Yansong Tang

Large Reasoning Models (LRMs) like o3 and DeepSeek-R1 have achieved remarkable progress in natural language reasoning with long chain-of-thought. However, they remain computationally inefficient and struggle with accuracy when solving problems requiring complex mathematical operations. In this work, we present AgentMath, an agent framework that seamlessly integrates language models' reasoning capabilities with code interpreters' computational precision to efficiently tackle complex mathematical problems. Our approach introduces three key innovations: (1) An automated method that converts natural language chain-of-thought into structured tool-augmented trajectories, generating high-quality supervised fine-tuning (SFT) data to alleviate data scarcity; (2) A novel agentic reinforcement learning (RL) paradigm that dynamically interleaves natural language generation with real-time code execution. This enables models to autonomously learn optimal tool-use strategies through multi-round interactive feedback, while fostering emergent capabilities in code refinement and error correction; (3) An efficient training system incorporating innovative techniques, including request-level asynchronous rollout scheduling, agentic partial rollout, and prefix-aware weighted load balancing, achieving 4-5× speedup and making efficient RL training feasible on ultra-long sequences with scenarios with massive tool calls. Extensive evaluations show that AgentMath achieves state-of-the-art performance on challenging mathematical competition benchmarks including AIME24, AIME25, and HMMT25, substantially outperforming frontier open‑source models of comparable size. Specifically, AgentMath-30B-A3B attains 90.6\%, 86.4\%, and 73.8\% accuracy respectively, surpassing OpenAI-o3-mini and Claude-Opus-4.0-Thinking while remaining competitive with OpenAI-o3, Gemini-2.5-Pro, and DeepSeek-R1-671B-0528. These results validate the effectiveness of our approach and pave the way for building scalable mathematical reasoning agents.

Computer Vision · Image and Video Generation

Yongyuan Liang, Wei Chow, Feng Li, Ziqiao Ma, Xiyao Wang, Jiageng Mao, Jiuhai Chen, Jiatao Gu, Yue Wang, Furong Huang

Unified multimodal models (UMMs) have emerged as a powerful paradigm for seamlessly unifying text and image understanding and generation. However, prevailing evaluations treat these abilities in isolation, such that tasks with multimodal inputs and outputs are scored primarily through unimodal reasoning, i.e., textual benchmarks emphasize language-based reasoning, while visual benchmarks emphasize reasoning outcomes manifested in the pixels. We introduce ROVER to address this pressing need to test reciprocal cross-modal reasoning, the use of one modality to guide, verify, or refine outputs in the other, an ability central to the vision of unified multimodal intelligence. ROVER is a human-annotated benchmark that explicitly targets reciprocal cross-modal reasoning, which contains 1,312 tasks grounded in 1,876 images, spanning two complementary settings. Verbally-augmented reasoning for visual generation evaluates whether models can use verbal prompts and reasoning chains to guide faithful image synthesis. Visually-augmented reasoning for verbal generation evaluates whether models can generate intermediate visualizations that strengthen their own reasoning processes for question answering. Experiments on 17 unified models reveal two key findings: (i) Cross-modal reasoning determines visual generation quality, with interleaved models significantly outperforming non-interleaved ones; notably, combining strong unimodal models fails to achieve comparable reasoning. (ii) Models show dissociation between physical and symbolic reasoning: they succeed at interpreting perceptual concepts literally but fail to construct visual abstractions for symbolic tasks, where faulty reasoning harms performance. These results highlight reciprocal cross-modal reasoning as a critical frontier for enabling true omnimodal generation. Homepage: https://roverbench.github.io

Theory · Interpretability and Visualization

Yufa Zhou, Yixiao Wang, Xunjian Yin, Shuyan Zhou, Anru Zhang

We study how large language models (LLMs) "think" through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows---embedding trajectories evolving where logic goes. We disentangle logical structure from semantics by employing the same natural deduction propositions with varied semantic carriers, allowing us to test whether LLMs internalize logic beyond surface form. This perspective connects reasoning with geometric quantities such as position, velocity, and curvature, enabling formal analysis in representation and concept spaces. Our theory establishes: (1) LLM reasoning corresponds to smooth flows in representation space, and (2) logical statements act as local controllers of these flows' velocities. Using learned representation proxies, we design controlled experiments to visualize and quantify reasoning flows, providing empirical validation of our theoretical framework. Our findings indicate that training solely via next-token prediction can lead LLMs to internalize logical invariants as higher-order geometry in representation space, challenging the "stochastic parrot" argument. Experiments across Qwen and LLaMA model families further suggest the presence of a general, possibly universal, representational law underlying machine understanding and human linguistic regularities, largely independent of specific training recipes or model architectures. Our work serves as both a conceptual foundation and practical tools for studying reasoning phenomena, offering a new lens for interpretability and formal analysis of LLMs' behavior.

Applications · Genetics, Cell Biology, Health, etc

Tianwei Lin, Zhongwei Qiu, Wenqiao Zhang, Jiang Liu, Yihan Xie, Mingjian Gao, Zhenxuan Fan, Zhaocheng Li, Sijing Li, Zhongle Xie 等

Computed Tomography (CT) is one of the most widely used and diagnostically information-dense imaging modalities, covering critical organs such as the heart, lungs, liver, and colon. Clinical interpretation relies on both slice-driven local features (e.g., sub-centimeter nodules, lesion boundaries) and volume-driven spatial representations (e.g., tumor infiltration, inter-organ anatomical relations). However, existing Large Vision–Language Models (LVLMs) remain fragmented in CT slice versus volumetric understanding: slice-driven LVLMs show strong generalization but lack cross-slice spatial consistency, while volume-driven LVLMs explicitly capture volumetric semantics but suffer from coarse granularity and poor compatibility with slice inputs. The absence of a unified modeling paradigm constitutes a major bottleneck for the clinical translation of medical LVLMs. We present OmniCT, a powerful unified slice–volume LVLM for CT scenarios, which makes three contributions: (i) Spatial Consistency Enhancement (SCE): volumetric slice composition combined with tri-axial positional embedding that introduces volumetric consistency, and an MoE hybrid projection enables efficient slice–volume adaptation; (ii) Organ-level Semantic Enhancement (OSE): segmentation and ROI localization explicitly align anatomical regions, emphasizing lesion- and organ-level semantics; (iii) MedEval-CT: the largest slice–volume CT dataset and hybrid benchmark integrates comprehensive metrics for unified evaluation. OmniCT consistently outperforms existing methods with a substantial margin across diverse clinical tasks and satisfies both micro-level detail sensitivity and macro-level spatial reasoning. More importantly, it establishes a new paradigm for cross-modal medical imaging understanding. Our project is available at https://github.com/ZJU4HealthCare/OmniCT.

Optimization · Everything Else

Jiwan Chung, SAEJIN KIM, Yongrae Jo, Jaewoo Park, Dongjun Min, Youngjae Yu

Large language models (LLMs) operate as autoregressive predictors over discrete token vocabularies, a formulation that has enabled their adaptation far beyond natural language to vision, robotics, and multimodal reasoning. However, training against one-hot targets disregards metric relationships between tokens and limits effectiveness on tasks where distance is meaningful, such as numerical values, spatial coordinates, or quantized embeddings. We introduce DIST2Loss, a distance-aware objective for discrete autoregressive models that replaces one-hot targets with reward-weighted distributions derived from predefined token distances. DIST2Loss can be interpreted as the closed-form solution to entropy-regularized policy optimization with known per-token rewards, retaining the core mechanism of reinforcement learning while avoiding sampling, rollouts, and instability. Our experiments show that DIST2Loss improves data efficiency and downstream performance across diverse domains. It yields tighter bounding boxes in visual grounding, accelerates robotic manipulation by improving action learning, enhances reward modeling for LLM alignment, and strengthens vector-quantized image generation. These results demonstrate that distance-aware supervision offers a simple and general alternative to one-hot supervision for discrete autoregressive models.

Social Aspects · Accountability, Transparency and Interpretability

Yihong Chen, Xiangxiang Xu, Pontus Stenetorp, Sebastian Riedel, Luca Franceschi

Large language models are becoming general knowledge engines for diverse applications. However, their computations are deeply entangled after training, resisting modularization which complicates interpretability, auditing, and long-term maintenance. We introduce Jet Expansions, a framework for expanding computational graphs using jet operators that generalize truncated Taylor series. Our method systematically decomposes language models into explicit input-to-output computational paths and complementary remainders. This functional decomposition provides a principled, knife-like operator for cutting through entanglement in LLMs, enabling scalable model inspection. We demonstrate how Jet Expansions ground and subsume the popular interpretability technique Logit Lens, reveal a (super-)exponential path structure with respect to recursive residual depth, and support several interpretability applications, including sketching a transformer language model with $n$-gram statistics extracted from its computations and indexing model toxicity levels *without* curated benchmarks.

Seongyun Lee, Seungone Kim, Minju Seo, Yongrae Jo, Dongyoung Go, Hyeonbin Hwang, Jinho Park, Xiang Yue, Sean Welleck, Graham Neubig 等

Long chain-of-thought (CoT) is an essential ingredient in effective usage of modern large language models, but our understanding of the reasoning strategies underlying these capabilities remains limited. While some prior works have attempted to categorize CoTs using predefined strategy types, such approaches are constrained by human intuition and fail to capture the full diversity of model behaviors. In this work, we introduce the CoT Encyclopedia, a bottom-up framework for analyzing and steering model reasoning. Our method automatically extracts diverse reasoning criteria from model-generated CoTs, embeds them into a semantic space, clusters them into representative categories, and derives contrastive rubrics to interpret reasoning behavior. Human evaluations show that this framework produces more interpretable and comprehensive analyses than existing methods. Moreover, we show that this understanding translates into measurable improvements on both problem-solving and safety benchmarks. We can predict which strategy a model is likely to use and guide it toward more effective alternatives. Finally, we show that training data format (e.g., free-form vs. multiple-choice) impacts reasoning far more than data domain, highlighting the importance of format-aware model design. In short, the CoT Encyclopedia turns reasoning from a black box into a controllable asset, enabling LLMs that think more clearly, perform more reliably, and act more safely.