Implicit Reasoning in Language Models

We study implicit reasoning, i.e. the ability to combine knowledge or rules within a single forward pass. While transformer-based large language models store substantial factual knowledge and rules, they often fail to compose this knowledge for implicit multi-hop reasoning, suggesting a lack of compositional generalization over their parametric knowledge. To address this limitation, we study recurrent-depth transformers, which enables iterative computation over the same transformer layers. We investigate two compositional generalization challenges under the implicit reasoning scenario: systematic generalization, i.e. combining knowledge that is never used for compositions during training, and depth extrapolation, i.e. generalizing from limited reasoning depth (e.g. training on up to 5-hop) to deeper compositions (e.g. 10-hop). Through controlled studies with models trained from scratch, we show that while vanilla transformers struggle with both generalization challenges, recurrent-depth transformers can effectively make such generalization. For systematic generalization, we find that this ability emerges through a three-stage grokking process, transitioning from memorization to in-distribution generalization and finally to systematic generalization, supported by mechanistic analysis. For depth extrapolation, we show that generalization beyond training depth can be unlocked by scaling inference-time recurrence, with more iterations enabling deeper reasoning. We further study how training strategies affect extrapolation, providing guidance on training recurrent-depth transformers, and identify a key limitation, overthinking, where excessive recurrence degrades predictions and limits generalization to very deep compositions.

The viability of chain-of-thought (CoT) monitoring hinges on models being unable to reason effectively in their latent representations. Yet little is known about the limits of such latent reasoning in LLMs. We test these limits by studying whether models can discover multi-step planning strategies without supervision on intermediate steps and execute them latently, within a single forward pass. Using graph path-finding tasks that precisely control the number of required latent planning steps, we uncover a striking limitation unresolved by massive scaling: tiny transformers trained from scratch discover strategies requiring up to three latent steps, fine-tuned GPT-4o and Qwen3-32B reach five, and GPT-5.4 attains seven under few-shot prompting. Although the maximum latent planning depth models can learn during training is five, the discovered strategy generalizes up to eight latent steps at test-time. This reveals a dissociation between the ability to discover a latent strategy under final-answer supervision alone and the ability to execute it once discovered. If similar limits hold more broadly, strategies requiring multiple coordinated latent planning steps may need to be explicitly taught or externalized, lending credence to CoT monitoring.

What makes writing "good" remains a persistent question in literary studies and computational linguistics. We present a two-study investigation of how reasoning-enabled LLMs evaluate literary quality. In Study 1, we construct a benchmark of 30 real texts spanning six quality tiers, from canonical literature to anonymous forum posts, and extract the model's implicit theory of quality from its reasoning traces. Across five DeepSeek replications, the model achieves 79.3% mean tier-classification accuracy. The traces reveal a consistent stated theory: the model values intentionality over correctness, prioritizing craft, depth, and distinctive voice. A familiarity experiment with style-matched but unrecognizable passages suggests that source recognition may inflate scores, although this is confounded by genuine quality differences between canonical originals and researcher-written pastiches. In Study 2, we probe this theory through systematic degradation of five canonical prose passages. We apply six manipulations - vocabulary simplification, rhythm flattening, imagery removal, voice genericization, structure simplification, and combined degradation - and reevaluate each version. Vocabulary simplification causes the smallest quality loss (0.41 +/- 0.46 points), far below structure (2.78) or voice (2.34) loss. Combined degradation is devastating (-5.64) but subadditive. An exploratory comparison with Qwen QwQ shows the same broad qualitative pattern. Together, these studies suggest that LLM judgments of writing quality are holistic, author-specific, and more sensitive to structural than lexical features, with implications for automated writing feedback and computational aesthetics.

Latent reasoning models (LRMs) have attracted significant research interest due to their low inference cost (relative to explicit reasoning models) and theoretical ability to explore multiple reasoning paths in parallel. However, these benefits come at the cost of reduced interpretability: LRMs are difficult to monitor because they do not reason in natural language. This paper presents an investigation into LRM interpretability by examining two state-of-the-art LRMs. First, we find that latent reasoning tokens are often unnecessary for LRMs' predictions; on logical reasoning datasets, LRMs can almost always produce the same final answers without using latent reasoning at all. This underutilization of reasoning tokens may partially explain why LRMs do not consistently outperform explicit reasoning methods and raises doubts about the stated role of these tokens in prior work. Second, we demonstrate that when latent reasoning tokens are necessary for performance, we can decode gold reasoning traces up to 65-93% of the time for correctly predicted instances. This suggests LRMs often implement the expected solution rather than an uninterpretable reasoning process. Finally, we present a method to decode a verified natural language reasoning trace from latent tokens without knowing a gold reasoning trace a priori, demonstrating that it is possible to find a verified trace for a majority of correct predictions but only a minority of incorrect predictions. Our findings highlight that current LRMs largely encode interpretable processes, and interpretability itself can be a signal of prediction correctness.

Large language models achieve strong performance on many language tasks, yet it remains unclear whether they integrate world knowledge with syntactic structure in a human-like, structure-sensitive way during ambiguity resolution. We test this question in Turkish prenominal relative-clause attachment ambiguities, where the same surface string permits high attachment (HA) or low attachment (LA). We construct ambiguous items that keep the syntactic configuration fixed and ensure both parses remain pragmatically possible, while graded event plausibility selectively favors High Attachment vs.\ Low Attachment. The contrasts are validated with independent norming ratings. In a speeded forced-choice comprehension experiment, humans show a large, correctly directed plausibility effect. We then evaluate Turkish and multilingual LLMs in a parallel preference-based setup that compares matched HA/LA continuations via mean per-token log-probability. Across models, plausibility-driven shifts are weak, unstable, or reversed. The results suggest that, in the tested models, plausibility information does not guide attachment preferences as reliably as it does in human judgments, and they highlight Turkish RC attachment as a useful cross-linguistic diagnostic beyond broad benchmarks.

Medical concept extraction from electronic health records underpins many downstream applications, yet remains challenging because medically meaningful concepts are frequently implied rather than explicitly stated in medical narratives. Existing benchmarks with human-annotated evidence spans underscore the importance of grounding extracted concepts in medical text. However, they predominantly focus on explicitly stated concepts instead of implicit concepts. We present MedicalBench, a benchmark for medical concept extraction with evidence grounding that evaluates implicit medical reasoning. MedicalBench formulates medical concept extraction as a verification task over medical note-concept pairs, coupled with sentence-level evidence identification. Built from MIMIC-IV discharge summaries and human-verified ICD-10 codes, the dataset is curated through a multi-stage large language model (LLM) triage pipeline followed by medical annotation and expert review. It deliberately includes implicit positives, semantically confusable negatives, and cases where LLM judgments disagree with medical expert assessments. We define two complementary evaluation tasks: (1) medical concept extraction and (2) sentence-level evidence retrieval, enabling assessment of both correctness and interpretability. Benchmarking state-of-the-art LLMs reveals that performance remains modest, highlighting the difficulty of extracting implicitly expressed concepts. We further show that performance is largely invariant to note length, indicating that MedicalBench isolates reasoning difficulty rather than superficial confounders. MedicalBench provides the first systematic benchmark for implicit, evidence-grounded medical concept extraction, offering a foundation for developing medical language models that can both identify medically relevant concepts and justify their predictions in a transparent and medically faithful manner.

Steering vectors offer a training-free mechanism for controlling reasoning behaviors in large language models, but constructing effective vectors requires identifying genuine behavioral signals in the model's hidden states. For behaviors that can be toggled via prompts, this is straightforward. However, many reasoning behaviors -- such as self-reflection -- emerge spontaneously and resist prompt-level control. Current methods detect these behaviors through keyword matching in chain-of-thought traces, implicitly assuming that every detected boundary encodes a genuine behavioral signal. We show that this assumption is overwhelmingly wrong: across 541 keyword-detected boundaries, 93.3% are behaviorally unstable, failing to reproduce the detected behavior under re-generation from the same prefix. We develop a probabilistic model that formalizes intrinsic reasoning behaviors as stochastic events with context-dependent trigger probabilities, and show that unstable boundaries dilute the steering signal. Guided by this analysis, we propose stability filtering, which retains only boundaries where the model consistently reproduces the target behavior. Combined with a content-subspace projection that removes residual question-specific noise, our method achieves 0.784 accuracy on MATH-500 (+5.0 over the strongest baseline). The resulting steering vectors transfer across models in the same architecture family without re-extraction, improving Nemotron-Research-Reasoning-1.5B (+5.0) and DeepScaleR-1.5B-Preview (+6.0). Code is available at https://github.com/zhmzm/stability-steering.

Latent space is rapidly emerging as a native substrate for language-based models. While modern systems are still commonly understood through explicit token-level generation, an increasing body of work shows that many critical internal processes are more naturally carried out in continuous latent space than in human-readable verbal traces. This shift is driven by the structural limitations of explicit-space computation, including linguistic redundancy, discretization bottlenecks, sequential inefficiency, and semantic loss. This survey aims to provide a unified and up-to-date landscape of latent space in language-based models. We organize the survey into five sequential perspectives: Foundation, Evolution, Mechanism, Ability, and Outlook. We begin by delineating the scope of latent space, distinguishing it from explicit or verbal space and from the latent spaces commonly studied in generative visual models. We then trace the field's evolution from early exploratory efforts to the current large-scale expansion. To organize the technical landscape, we examine existing work through the complementary lenses of mechanism and ability. From the perspective of Mechanism, we identify four major lines of development: Architecture, Representation, Computation, and Optimization. From the perspective of Ability, we show how latent space supports a broad capability spectrum spanning Reasoning, Planning, Modeling, Perception, Memory, Collaboration, and Embodiment. Beyond consolidation, we discuss the key open challenges, and outline promising directions for future research. We hope this survey serves not only as a reference for existing work, but also as a foundation for understanding latent space as a general computational and systems paradigm for next-generation intelligence.

We consider the question: when a large language reasoning model makes a choice, did it think first and then decide to, or decide first and then think? In this paper, we present evidence that detectable, early-encoded decisions shape chain-of-thought in reasoning models. Specifically, we show that a simple linear probe successfully decodes tool-calling decisions from pre-generation activations with very high confidence, and in some cases, even before a single reasoning token is produced. Activation steering supports this causally: perturbing the decision direction leads to inflated deliberation, and flips behavior in many examples (between 7 - 79% depending on model and benchmark). We also show through behavioral analysis that, when steering changes the decision, the chain-of-thought process often rationalizes the flip rather than resisting it. Together, these results suggest that reasoning models can encode action choices before they begin to deliberate in text.

Large language models have demonstrated impressive performance across many domains of mathematics and physics. One natural question is whether such models can support research in highly abstract theoretical fields such as quantum field theory and string theory. Evaluating this possibility faces an immediate challenge: correctness in these domains is layered, tacit, and fundamentally non-binary. Standard answer-matching metrics fail to capture whether intermediate conceptual steps are properly reconstructed or whether implicit structural constraints are respected. We construct a compact expert-curated dataset of twelve questions spanning core areas of quantum field theory and string theory, and introduce a five-level grading rubric separating statement correctness, key concept awareness, reasoning chain presence, tacit step reconstruction, and enrichment. Evaluating multiple contemporary LLMs, we observe near-ceiling performance on explicit derivations within stable conceptual frames, but systematic degradation when tasks require reconstruction of omitted reasoning steps or reorganization of representations under global consistency constraints. These failures are driven not only by missing intermediate steps, but by an instability in representation selection: models often fail to identify the correct conceptual framing required to resolve implicit tensions. We argue that highly abstract theoretical physics provides a uniquely sensitive lens on the epistemic limits of current evaluation paradigms.

Asked whether to walk or drive to a car wash 50 m away, most language models say walk, forgetting that the car has to be there. Such failures are usually measured by accuracy on questions where the hidden constraint applies. We show that this is misleading: a model can answer these questions correctly without reasoning about the constraint at all, simply by favoring the cautious option. We instead ask whether a model's decision changes when the constraint is removed. We test this at three levels of control: log-probability sweeps on open-weight models, a 500-prompt stress test, and CORE, a new human-validated benchmark of minimal constraint-present/constraint-absent pairs. The picture is consistent. The constraint nudges decisions rather than governing them. Models still miss presence constraints like the car wash, yet elsewhere they apply constraints that are not there. As a result, standard accuracy flatters all ten models we evaluate and reorders their ranking, and prompting fixes that look effective largely vanish under paired scoring. Claims about hidden-constraint reasoning need paired evidence.

I use the Pythia scaling suite (Biderman et al. 2023) to investigate if and how two well-known polarity illusions, the NPI illusion and the depth charge illusion, arise in LLMs. The NPI illusion becomes weaker and ultimately disappears as model size increases, while the depth charge illusion becomes stronger in larger models. The results have implications for human sentence processing: it may not be necessary to assume "rational inference" mechanisms that convert ill-formed sentences into well-formed ones to explain polarity illusions, given that LLMs cannot plausibly engage in this kind of reasoning, especially at the implicit level of next-token prediction. On the other hand, shallow, "good enough" processing and/or partial grammaticalization of prescriptively ungrammatical structures may both occur in LLMs. I propose a synthesis of different theoretical accounts that is rooted in the basic tenets of construction grammar.

Transformer-based language models excel at in-context learning (ICL), where they can adapt to new tasks based on contextual examples, without parameter updates. In a specific form of ICL, which we refer to as contextual recall, models pretrained on open-ended text leverage pairwise examples to recall specific facts in novel prompt formats. We investigate whether contextual recall emerges from pretraining alone, what finetuning is required, and what mechanisms drive the necessary representations. For this, we introduce a controlled synthetic framework where pretraining sequences consist of subject-grammar-attribute tuples, with attribute types tied to grammar statistics. We demonstrate that while such pretraining successfully yields factual knowledge, it is insufficient for contextual recall: models fail to implicitly infer attribute types when the grammar statistics are removed in ICL prompts. However, we show that finetuning on tasks requiring implicit inference, distinct from the ICL evaluation, using a subset of subjects, triggers the emergence of contextual recall across all subjects. This transition is accompanied by the formation of low-dimensional latent encodings of the shared attribute type. For mechanistic insight, we derive a construction for an attention-only transformer that replicates the transition from factual to contextual recall, corroborated by empirical validation.

Looped language models (LoopLMs) perform iterative latent computation to refine internal representations, offering an alternative to explicit chain-of-thought (CoT) reasoning. However, existing reinforcement learning (RL) paradigms primarily target output tokens, creating a structural mismatch with looped architectures whose reasoning unfolds implicitly. In this work, we propose LoopRPT, a reinforcement pre-training framework tailored for LoopLMs. By reframing next-token prediction as a next-token reasoning task, LoopRPT assigns reinforcement signals directly to latent steps using an EMA teacher reference and noisy latent rollouts. This formulation enables RL to directly shape intermediate representations, compressing effective reasoning into fewer iterations. We instantiate LoopRPT on Ouro across multiple model scales. Results show that LoopRPT improves per-step representation quality and achieves Pareto dominance in accuracy-computation trade-offs. Large gains on hard tokens indicate that LoopRPT enhances early-stage reasoning rather than merely encouraging premature exits. Our findings highlight reinforcement pre-training as a principled paradigm for learning efficient latent reasoning in LoopLMs.

Binary vulnerability analysis is increasingly performed by LLM-based agents in an iterative, multi-pass manner, with the model as the core decision-maker. However, how such systems organize exploration over hundreds of reasoning steps remains poorly understood, due to limited context windows and implicit token-level behaviors. We present the first large-scale, trace-level study showing that multi-pass LLM reasoning gives rise to structured, token-level implicit patterns. Analyzing 521 binaries with 99,563 reasoning steps, we identify four dominant patterns: early pruning, path-dependent lock-in, targeted backtracking, and knowledge-guided prioritization that emerge implicitly from reasoning traces. These token-level implicit patterns serve as an abstraction of LLM reasoning: instead of explicit control-flow or predefined heuristics, exploration is organized through implicit decisions regulating path selection, commitment, and revision. Our analysis shows these patterns form a stable, structured system with distinct temporal roles and measurable characteristics. Our results provide the first systematic characterization of LLM-driven binary analysis and a foundation for more reliable analysis systems.

The central challenge of reasoning-intensive retrieval lies in identifying implicitreasoning relationships between queries and documents, rather than superficial se-mantic or lexical similarity. The contrastive learning paradigm is fundamentallya static representation consolidation technique: during training, it encodes hier-archical relevance concepts into fixed geometric structures in the vector space,and at inference time it cannot dynamically adjust relevance judgments accord-ing to the specific reasoning demands of each query. Consequently, performancedegrades noticeably when vocabulary mismatch exists between queries and doc-uments or when implicit reasoning is required to establish relevance. This pa-per proposes Thought 1 (T1), a generative retrieval model that shifts relevancemodeling from static alignment to dynamic reasoning. On the query side, T1 dy-namically generates intermediate reasoning trajectories for each query to bridgeimplicit reasoning relationships and uses <embtoken> as a semantic aggregationpoint for the reasoning output. On the document side, it employs an instruction+ text + <embtoken> encoding format to support high-throughput indexing. Tointernalize dynamic reasoning capabilities into vector representations, we adopt athree-stage training curriculum and introduce GRPO in the third stage, enablingthe model to learn optimal derivation strategies for different queries through trial-and-error reinforcement learning. On the BRIGHT benchmark, T1-4B exhibitsstrong performance under the original query setting, outperforming larger modelstrained with contrastive learning overall, and achieving performance comparableto multi-stage retrieval pipelines. The results demonstrate that replacing static rep-resentation alignment with dynamic reasoning generation can effectively improvereasoning-intensive retrieval performance.

This paper proposes and argues for a counterintuitive thesis: the truly valuable capabilities of large language models (LLMs) reside precisely in the part that cannot be fully captured by human-readable discrete rules. The core argument is a proof by contradiction via expert system equivalence: if the full capabilities of an LLM could be described by a complete set of human-readable rules, then that rule set would be functionally equivalent to an expert system; but expert systems have been historically and empirically demonstrated to be strictly weaker than LLMs; therefore, a contradiction arises -- the capabilities of LLMs that exceed those of expert systems are exactly the capabilities that cannot be rule-encoded. This thesis is further supported by the Chinese philosophical concept of Wu (sudden insight through practice), the historical failure of expert systems, and a structural mismatch between human cognitive tools and complex systems. The paper discusses implications for interpretability research, AI safety, and scientific epistemology.

Token-level Chain-of-Thought (CoT) prompting has become a standard way to elicit multi-step reasoning in large language models (LLMs), especially for mathematical word problems. However, generating long intermediate traces increases output length and inference cost, and can be inefficient when the model could arrive at the correct answer without extensive verbalization. This has motivated latent-space reasoning approaches that shift computation into hidden representations and only emit a final answer. Yet, many latent reasoning methods depend on a fixed number of latent refinement steps at inference, adding another hyperparameter that must be tuned across models and datasets to balance accuracy and efficiency. We introduce AdaAnchor, a latent reasoning framework that performs silent iterative computation by refining a set of latent anchor vectors attached to the input. AdaAnchor further incorporates an adaptive halting mechanism that monitors anchor stability across iterations and terminates refinement once the anchor dynamics converge, allocating fewer steps to easier instances while reserving additional refinement steps for harder ones under a shared maximum-step budget. Our empirical evaluation across three mathematical word-problem benchmarks shows that AdaAnchor with adaptive halting yields accuracy gains of up to 5% over fixed-step latent refinement while reducing average latent refinement steps by 48-60% under the same maximum-step budget. Compared to standard reasoning baselines, AdaAnchor achieves large reductions in generated tokens (92-93%) by moving computation into silent latent refinement, offering a different accuracy-efficiency trade-off with substantially lower output-token usage.

Large language models (LLMs) achieve impressive scores on standard benchmarks yet routinely fail questions that any human would answer correctly in seconds. We introduce BrainBench, a benchmark of 100 brainteaser questions spanning 20 carefully designed categories, each targeting a specific commonsense reasoning failure mode in LLMs. Categories range from implicit physical constraints ("Should I walk or drive my rental car to the return lot?") to semantic scope tricks and default assumption hijacks. We evaluate eight frontier models -- four from the Claude family and four from the GPT family -- using a zero-shot protocol with 10 independent runs per question. The best model, Claude Opus 4.6 with extended thinking, achieves only 80.3% accuracy; the worst, GPT-4o, scores 39.7%. Even top-performing models exhibit a 6-16 percentage-point gap between accuracy and consistency, revealing stochastic reasoning. Cross-lingual evaluation in Chinese shows most models degrade by 2-8 percentage points, confirming that these failures reflect reasoning deficits rather than language-specific artifacts. BrainBench provides a fine-grained diagnostic tool for identifying where and why LLMs substitute surface heuristics for genuine commonsense reasoning.

We show that PLDR-LLMs pretrained at self-organized criticality exhibit reasoning at inference time. The characteristics of PLDR-LLM deductive outputs at criticality is similar to second-order phase transitions. At criticality, the correlation length diverges, and the deductive outputs attain a metastable steady state. The steady state behaviour suggests that deductive outputs learn representations equivalent to scaling functions, universality classes and renormalization groups from the training dataset, leading to generalization and reasoning capabilities in the process. We can then define an order parameter from the global statistics of the model's deductive output parameters at inference. The reasoning capabilities of a PLDR-LLM is better when its order parameter is close to zero at criticality. This observation is supported by the benchmark scores of the models trained at near-criticality and sub-criticality. Our results provide a self-contained explanation on how reasoning manifests in large language models, and the ability to reason can be quantified solely from global model parameter values of the deductive outputs at steady state, without any need for evaluation of curated benchmark datasets through inductive output for reasoning and comprehension.

Large language models (LLMs) tend to externalize their reasoning in their chain of thought, making the chain of thought a good target for monitoring. This is partially an inherent feature of the Transformer architecture: sufficiently long serial cognition must pass through the chain of thought (Korbak et al., 2025). We formalize this argument through the notion of opaque serial depth, given by the length of the longest computation that can be done without the use of interpretable intermediate steps like chain of thought. Given this formalization, we compute numeric upper bounds on the opaque serial depth of Gemma 3 models, as well as asymptotic results for additional architectures beyond standard LLMs. We also open-source an automated method that can calculate upper bounds on the opaque serial depth of arbitrary neural networks, and use it to demonstrate that Mixture-of-Experts models likely have lower depth than dense models. Overall, our results suggest that opaque serial depth is a useful tool for understanding the potential for models to do significant reasoning that is not externalized.

Large Language Models (LLMs) are increasingly deployed across diverse real-world applications and user communities. As such, it is crucial that these models remain both morally grounded and knowledge-aware. In this work, we uncover a critical limitation of current LLMs -- their tendency to prioritize moral reasoning over commonsense understanding. To investigate this phenomenon, we introduce CoMoral, a novel benchmark dataset containing commonsense contradictions embedded within moral dilemmas. Through extensive evaluation of ten LLMs across different model sizes, we find that existing models consistently struggle to identify such contradictions without prior signal. Furthermore, we observe a pervasive narrative focus bias, wherein LLMs more readily detect commonsense contradictions when they are attributed to a secondary character rather than the primary (narrator) character. Our comprehensive analysis underscores the need for enhanced reasoning-aware training to improve the commonsense robustness of large language models.

Chain-of-thought (CoT) prompting enables reasoning in language models but requires explicit verbalization of intermediate steps. Looped transformers offer an alternative by iteratively refining representations within hidden states. This parameter efficiency comes at a cost, as looped models lack the storage capacity of deeper models which use unique weights per layer. In this work, we investigate transformer models that feature both adaptive per-layer looping, where each transformer block learns to iterate its hidden state via a learned halting mechanism, and gated memory banks, that provide additional learned storage. We find that looping primarily benefits mathematical reasoning, while memory banks help recover performance on commonsense tasks compared to parameter and FLOP matched models. Combining both mechanisms yields a model that outperforms an iso-FLOP baseline, with three times the number of layers, across math benchmarks. Analysis of model internals reveals layer specialization: early layers learn to loop minimally and access memory sparingly, while later layers do both more heavily.

Real-world arguments in text and dialogues are normally enthymemes (i.e. some of their premises and/or claims are implicit). Natural language processing (NLP) methods for handling enthymemes can potentially identify enthymemes in text but they do not decode their underlying logic, whereas logic-based approaches for handling them assume a knowledgebase with sufficient formulae that can be used to decode them via abduction. There is therefore a lack of a systematic method for translating textual components of an enthymeme into a logical argument and generating the logical formulae required for their decoding, and thereby showing logical entailment. To address this, we propose a pipeline that integrates: (1) a large language model (LLM) to generate intermediate implicit premises based on the explicit premise and claim; (2) another LLM to translate the natural language into logical formulas; and (3) a neuro-symbolic reasoner based on a SAT solver to determine entailment. We evaluate our pipeline on two enthymeme datasets, demonstrating promising performance in selecting the correct implicit premise, as measured by precision, recall, F1-score, and accuracy.

Large language models (LLMs) achieve promising performance, yet their ability to reason remains poorly understood. Existing evaluations largely emphasize task-level accuracy, often conflating pattern matching with reasoning capability. We present X-RAY, an explainable reasoning analysis system that maps the LLM reasoning capability using calibrated, formally verified probes. We model reasoning capability as a function of extractable structure, operationalized through formal properties such as constraint interaction, reasoning depth, and solution-space geometry. X-Ray generates probes via formal tools with controlled structural variations, enabling precise isolation of incremental structural information through formal calibration and verification. We evaluate state-of-the-art LLMs on problems ranging from junior-level to advanced in mathematics, physics, and chemistry. Our analysis reveals a systematic asymmetry in LLM reasoning: models are relatively robust to constraint refinement, where additional conditions shrink an existing solution space, but degrade sharply under solution-space restructuring, where modifications alter the underlying structural form of the solution manifold. Moreover, calibrated formal probes differentiate models that appear indistinguishable on standard benchmarks and reveal failure modes that are structurally interpretable rather than opaque. Beyond evaluation, our framework is contamination-free and supports the training and testing of reasoning models.

Diffusion LLMs have been proposed as an alternative to autoregressive LLMs. Curiously, they are especially capable if the generation length, i.e., the number of tokens the model has to output, is set to a much higher value than the correct answer length, and the model pads its answer with end-of-sequence (EoS) tokens. We hypothesize that off-the-shelf masked diffusion LLMs use the representations of EoS tokens as additional computing capacity, which enhances their performance. We experiment with the diffusion models LLaDA1.5, LLaDA2.0-mini, and Dream-v0 on three reasoning tasks: Addition, Entity Tracking, and Sudoku. In a controlled prompting experiment, we confirm that adding EoS tokens improves the LLMs' performance. To further verify whether their representations are used for hidden computations, we perform a causal intervention and transfer the hidden states of the EoS tokens between generations, which increases the models' relative likelihood of outputting the counterfactual answer. The behavioral experiments and the causal interventions indicate that fully bidirectional masked diffusion LLMs can indeed perform latent reasoning in the representations of EoS tokens. Furthermore, we find that these results generalize beyond toy tasks and that providing the model with additional EoS tokens also improves performance on GSM8K and two-hop reasoning.

In-context learning enables large language models to perform novel tasks through few-shot demonstrations. However, demonstrations per se can naturally contain noise and conflicting examples, making this capability vulnerable. To understand how models process such conflicts, we study demonstration-dependent tasks requiring models to infer underlying patterns, a process we characterize as rule inference. We find that models suffer substantial performance degradation from a single demonstration with corrupted rule. This systematic misleading behavior motivates our investigation of how models process conflicting evidence internally. Using linear probes and logit lens analysis, we discover that under corruption models encode both correct and incorrect rules in intermediate layers but develop prediction confidence only in late layers, revealing a two-phase computational structure. We then identify attention heads for each phase underlying the reasoning failures: Vulnerability Heads in early-to-middle layers exhibit positional attention bias with high sensitivity to corruption, while Susceptible Heads in late layers significantly reduce support for correct predictions when exposed to the corrupted evidence. Targeted ablation validates our findings, with masking a small number of identified heads improving performance by over 10%.

LLMs have fundamentally transformed dense retrieval, upgrading backbones from discriminative encoders to generative architectures. However, a critical disconnect remains: while LLMs possess strong reasoning capabilities, current retrievers predominantly utilize them as static encoders, leaving their potential for complex reasoning unexplored. To address this, existing approaches typically adopt rewrite-then-retrieve pipelines to generate explicit CoT rationales before retrieval. However, this incurs prohibitive latency. In this paper, we propose LaSER, a novel self-distillation framework that internalizes explicit reasoning into the latent space of dense retrievers. Operating on a shared LLM backbone, LaSER introduces a dual-view training mechanism: an Explicit view that explicitly encodes ground-truth reasoning paths, and a Latent view that performs implicit latent thinking. To bridge the gap between these views, we design a multi-grained alignment strategy. Beyond standard output alignment, we introduce a trajectory alignment mechanism that synchronizes the intermediate latent states of the latent path with the semantic progression of the explicit reasoning segments. This allows the retriever to think silently and effectively without autoregressive text generation. Extensive experiments on both in-domain and out-of-domain reasoning-intensive benchmarks demonstrate that LaSER significantly outperforms state-of-the-art baselines. Furthermore, analyses across diverse backbones and model scales validate the robustness of our approach, confirming that our unified learning framework is essential for eliciting effective latent thinking. Our method successfully combines the reasoning depth of explicit CoT pipelines with the inference efficiency of standard dense retrievers.

Latent reasoning has been recently proposed as a reasoning paradigm and performs multi-step reasoning through generating steps in the latent space instead of the textual space. This paradigm enables reasoning beyond discrete language tokens by performing multi-step computation in continuous latent spaces. Although there have been numerous studies focusing on improving the performance of latent reasoning, its internal mechanisms remain not fully investigated. In this work, we conduct a comprehensive analysis of latent reasoning methods to better understand the role and behavior of latent representation in the process. We identify two key issues across latent reasoning methods with different levels of supervision. First, we observe pervasive shortcut behavior, where they achieve high accuracy without relying on latent reasoning. Second, we examine the hypothesis that latent reasoning supports BFS-like exploration in latent space, and find that while latent representations can encode multiple possibilities, the reasoning process does not faithfully implement structured search, but instead exhibits implicit pruning and compression. Finally, our findings reveal a trade-off associated with supervision strength: stronger supervision mitigates shortcut behavior but restricts the ability of latent representations to maintain diverse hypotheses, whereas weaker supervision allows richer latent representations at the cost of increased shortcut behavior.

Large language models consistently fail the "car wash problem," a viral reasoning benchmark requiring implicit physical constraint inference. We present a variable isolation study (n=20 per condition, 6 conditions, 120 total trials) examining which prompt architecture layers in a production system enable correct reasoning. Using Claude 3.5 Sonnet with controlled hyperparameters (temperature 0.7, top_p 1.0), we find that the STAR (Situation-Task-Action-Result) reasoning framework alone raises accuracy from 0% to 85% (p=0.001, Fisher's exact test, odds ratio 13.22). Adding user profile context via vector database retrieval provides a further 10 percentage point gain, while RAG context contributes an additional 5 percentage points, achieving 100% accuracy in the full-stack condition. These results suggest that structured reasoning scaffolds -- specifically, forced goal articulation before inference -- matter substantially more than context injection for implicit constraint reasoning tasks.