Hidden States

SpeechLLMs have shown strong potential for emotion recognition, yet they read the predicted emotion off a generative decoder not suited for classification: it can emit labels outside the target set and favors frequent classes. We propose a discriminative adaptation that reads the final prompt token's hidden state through a classification head, producing a label in one forward pass without modifying the backbone. Because this readout starts from the hidden state the model would otherwise decode, it gives a controlled comparison of generative and discriminative inference in an otherwise identical speechLLM. We keep the head a single linear layer, trading little accuracy for interpretability: each emotion becomes one direction in the LLM output token space, revealing associated tokens. On IEMOCAP, across two speechLLM architectures, it improves Macro F1 and removes hallucinations, with largest gains on realistic ASR transcripts. Our analysis reveals that these emotion directions encode indirect associations mirroring biases in web-scale text.

Masked diffusion language models (dLLMs) generate text by iteratively denoising masked tokens with bidirectional attention. Extending reasoning across generation chunks normally requires keeping earlier generated text in context. We ask whether a dLLM can instead continue reasoning after that text is cleared, using only a fixed-size carried state. We implement this state as a small number of register tokens: dedicated fixed-position tokens whose continuous hidden states are trained to carry reasoning progress across generation chunks. We post-train dLLMs to decode a chunk of text, clear it while preserving the register values, and continue decoding from the prompt and carried state. In our main comparisons on LLaDA and Dream, registers outperform discrete-text carry on every benchmark, with gains of up to 8.5 points on math and 19.5 points on code. Registers are especially effective for bounded code generation, where correct programs usually span several chunks. Finally, registers can be further refined with reinforcement learning on long-horizon reasoning tasks.

Existing bias auditing methods typically rely on model outputs, requiring costly benchmarks or judge models and potentially missing internal shifts that never appear in generated text. We propose a reference-based method that audits bias in hidden-state representations across related model variants, for example before and after fine-tuning. Because fine-tuning reshapes representation geometry, absolute hidden states are not directly comparable, so we encode each sentence by its similarities to a fixed set of anchor sentences, yielding relative representations in a shared comparison space. There we measure how target groups shift in their association with positive and negative attributes, a quantity we call the Representational Bias Shift $ΔB$. Across three model families and the WildGuardMix, DecodingTrust and ToxiGen benchmarks, $ΔB$ correlates with output-level bias change in 15 of the 18 settings we test, reaching $|r| = 0.84$ ($p < 0.001$) under full fine-tuning and becoming more model-dependent under parameter-efficient adaptation. Thresholding $ΔB$ detects checkpoints whose bias increased with ROC AUC between $0.65$ and $0.99$, and on WildGuardMix and DecodingTrust it separates them better than a SEAT-based baseline for all three families. $ΔB$ is also stable under changes to the anchor set, attribute sets and target templates. Our method requires no task-specific evaluation data and audits a model in about three minutes, using $3$-$50\times$ less compute than the output-level benchmarks considered here. We view it as complementary to output-based auditing rather than a replacement for it.

Reading a transformer's internal states in token space is easy to do and hard to trust: a logit lens on a single hidden state is dominated, at intermediate layers, by the generic tokens the model would predict for almost any input. We read the difference instead. Subtracting two closely matched prompts' hidden states and projecting through the unembedding cancels the shared component and surfaces what separates them, an operation equivalent to reading a RepE/ActAdd steering vector through a logit lens. Built into a training-free tracer that reads at every position, sub-layer, and head and averages over designed baselines, it traces a compound- noun MLP->attention chain in Phi-2, confirmed there by activation patching, with the same distinction recovered across three architectures by readout and probe rather than by patching; it reads what retrieval surfaces for real versus fictional entities, and reads metaphor as a set of domain-to-domain mappings rather than a single figurativity feature. A cross-seed control marks the boundary: across five networks differing only in initialization, the same distinction surfaces as almost entirely different tokens (top-10 overlap 0.08). What a computation looks like in token space is network-specific; the distinction it draws is not

Linear classifiers trained on hidden states of a large language model (LLM), linear probes, can flag factual errors from a single forward pass. Geometrically, that implies that true and false statements separate along a stable direction in hidden state space, i.e., the truth direction. Prior work disagrees on whether this generalises across input shifts, but the disagreement is hard to interpret because cross-dataset probe transfer experiments confound several kinds of input change at once. We isolate three such variables in medical question-answering (QA): writing style (register), domain (medical specialty), and corpus (dataset). We build a benchmark using 500 MedQA entries, each rewritten into four styles (textbook, patient, clinical note, colloquial), annotated with clinical specialty, and grouped with two other exam corpora, MedMCQA and MMLU-medical, for cross-dataset evaluation. Probing four open-weight LLMs (2--8B), we find that the truth direction is largely robust to writing style (mean $Δ_\text{register} \approx 0.10$ AUROC on held-out facts) and to medical specialty ($Δ_\text{specialty} \approx 0.03$), but degrades unevenly across corpora: by $0.12$ AUROC on MMLU-medical and by $0.21$ on MedMCQA, roughly twice the register gap. The register result replicates with a second generator and carries over to human-written patient questions. The truth direction is therefore largely stable within the medical domain but breaks under some corpus shifts, and question format does not explain the break, which suggests that the signal a linear probe recovers is partly bound to dataset structure rather than to medical knowledge alone.

Large language models often answer the same multiple-choice question inconsistently when it is posed under support-oriented and elimination-oriented framings. We investigate whether these discrepancies arise from different internal representations induced by the two framings. We introduce a dual-framing protocol with minimally varied prompts that use either support- or elimination-oriented framing while keeping the evaluation target fixed. To probe the internal computation, we append an untrained special token, [STATE], and treat its residual-stream activation as an intervention interface. Across both models, the two framings induce separable [STATE] activations concentrated in intermediate layers. Swapping these activations between paired prompts systematically changes predictions and improves cross-framing agreement, providing intervention-based evidence that the activations are behaviorally relevant. Beyond instance-level substitution, mean-difference steering directions derived from the dual-framing contrast exhibit more bounded layer-wise responses than matched contrastive activation addition directions under the evaluated protocol.

Local learning methods offer an alternative to end-to-end backpropagation, but their unstructured local objectives can produce weak feature learning in deep networks. We study whether the order of hidden-state optimization can address this limitation. We propose a boundary-first inference schedule that partitions a model into chunks, first coordinates hidden states at chunk boundaries, and then refines representations within each chunk. We instantiate this schedule in predictive coding networks (PCNs), a local-learning framework in which hidden activities and prediction errors are explicitly exposed during inference. On CIFAR-10, the resulting boundary-first predictive-coding instantiation improves accuracy over standard predictive coding by $9.77\%$ under a standard parametrization and by $5.51\%$ under a $μ$-parametrization. Diagnostic analyses further show more non-trivial early-layer updates, lower initial-to-final CKA, and more diverse layerwise gradients, consistent with stronger feature learning. These results support boundary-first, chunk-based inference as a practical design principle for predictive-coding training and motivate its study in broader local-learning systems.

The Jacobian Lens (J-lens) is a recent tool for interpreting LLMs. It reads a hidden state as a ranked list of vocabulary tokens, leaving multi-token concepts without a representation of their own. The original J-lens work addresses this limitation with Template Lens, which precomputes vectors for a fixed phrase vocabulary, and Oracle Lens, which fine-tunes components to propose phrases and reconstruct phrase vectors. We ask whether multi-token concepts and their vectors can instead be recovered directly from J-lens and the frozen model. We find that the first token of a multi-token concept is about as readable as a single-token concept. Given the correct first token and source prompt, the frozen model recovers the second token in 88.3% of two-token cases. We show that a vector for the complete concept can be recovered from subsequent hidden states in a single forward pass. We therefore use J-lens to propose first tokens and let the frozen model complete candidate concepts. We then recover a vector for each candidate and score it alongside the complete vocabulary. Across 496 multi-hop clozes on Gemma-3-12B-IT, Llama-3.1-8B, and Qwen3-14B, our method achieves an average $\mathrm{Rank@}10$ of 43.1%, compared with 27.6% for Template Lens. Without the J-lens clue, performance drops to 21.6%, showing that the first-token clue substantially improves readout. Causal concept swaps using the recovered vectors achieve an average $\mathrm{succ}@10$ of 61.4%, compared with 26.2% for Template Lens under the same intervention. These results show that first-token clues can guide multi-token concept recovery, while subsequent hidden states provide vectors for readout and intervention.

Video world models are increasingly used as simulators, yet visual fidelity alone does not show that a model maintains the hidden state of the world. We examine this gap with an action-conditioned video Shell Game, a visual analog of $S_5$ state tracking that decouples visual rendering from compositing the hidden state underneath. Bidirectional and autoregressive Transformers, Mamba, and linear attention restricted to nonnegative transition eigenvalues all fit the training horizon of 5 swaps and then fall toward chance on longer swap chains (extrapolation) while still rendering plausible video with additional denoising steps providing no benefit. The pixel-based diffusion target never supervises the unseen hidden state, so the generated frames cannot carry it and the state has to live inside the architecture rather than in the tokens. For a Transformer, that architectural state is only an append-only KV cache, so the model has to re-derive the hidden arrangement from the whole history at every chunk. We find two mechanisms that do extrapolate, and both carry a state across chunks and revise it in place. Linear attention succeeds once its transition eigenvalues may be negative, and TTT with a nonlinear fast weight succeeds by updating the feature map through which it reads its own state. We further examine harder cases in dynamic world exploration tasks, and discuss the broader implications for building stateful video world models.

When visual evidence is occluded or chaotic, models should abstain. In this paper, we show that Vision-Language Models (VLMs) can internally distinguish when abstention is required, but fail to express it anyway. We introduce TRAPSBench, a procedurally generated video benchmark of 1,404 matched physics pairs in which a single targeted change renders the outcome undeterminable from the visual evidence. Furthermore, we introduce Penalized Epistemic Calibration Score (PECS), a new robust metric that requires models to both answer correctly when the outcome is knowable, and abstain when the outcome is not. Across 16 VLMs spanning five families, spontaneous restraint is poor: the best PECS is 0.292. The bottleneck is expression, not perception: linear probes decode answerability from hidden states at up to 0.91 AUROC across physics domains; steering a single-layer void direction causally induces or suppresses abstention. Our results replicate across three open-weight families (Qwen, Gemma, LLaVA). The failure is also more pronounced in visual than textual uncertainty: models detect textual impossibility about 4x more readily than missing visual evidence. Closing this representation--output gap likely requires output-stage interventions.

Lens methods interpret large language models (LLMs) by mapping intermediate activations to the output vocabulary, revealing how next-token predictions develop through the network. Trained lenses remain expensive: affine-translator parameters grow quadratically with model width, while exact, full-vocabulary Kullback--Leibler (KL) training dominates memory. Consequently, prior trained lenses have been applied to models of at most 20B parameters and remain tied to particular component types. We present OmniLens, which applies a single lens family to any model-width activation, whether residual stream, attention, or MLP, and combines two independent scaling techniques. First, low-rank translators make per-lens parameter growth linear in model width and reduce trainable parameters by up to 98.4%. Second, Subset-KL materializes only selected vocabulary logits: its Top-k mode cuts peak training memory by up to 70%, while its importance-sampled variant retains unbiased stochastic gradients for the full KL. These savings enable a dense ensemble of 482 lenses for LLaMA-3.3-70B, providing 6x the coverage of a residual-stream design at the same depth. Model-wide coverage then reveals what single-component lenses cannot: the components where a behavior is most visible need not be those where intervention is most effective, and the most effective interventions lie outside the attention heads examined by prior lens studies. Across three case studies (prompt-injection detection, multi-hop memory injection, and toxicity localization), OmniLens reproduces key published results at substantially lower cost.

Diffusion language models (DLMs) iteratively refine a sequence, allowing earlier predictions to be revised as context evolves. This rollback capability distinguishes them from irreversible autoregressive generation, but makes inference costly. Every denoising update alters the global context, forcing both prompt and response states to be recomputed even though only response tokens are revisable. Key-value (KV) caching could reduce this cost, yet conventional caching assumes immutable historical states and is therefore difficult to reconcile with rollback. In this paper, we introduce Adaptive Reuse of Cached Hidden States for Efficient Rollback (Archer), a training-free KV caching method for rollback-capable DLMs. Archer asymmetrically keeps the mutable response synchronized with the current hypothesis while reusing prompt K/V within a bounded state neighborhood. Although prompt representations also change under bidirectional attention, their token identities remain fixed; bounded reuse therefore amortizes repeated prompt computation without caching mutable response states. It also delays feedback from tentative tokens, reducing premature reinforcement of transient high-confidence errors and giving rollback more opportunity to correct them. Our analysis characterizes prompt reuse as a reversibility-aligned cache boundary, bounds its state-dependent approximation error, and gives a decoder-margin condition for preserving full-refresh decisions. Existing DLM acceleration often trades quality for speed. Archer shifts this frontier, attaining the best mean performance of 33.63% together with a 2.57x mean speedup on the main suite. Across evaluated settings, it improves Pass@1 by up to 3.05 points and reaches up to 2.95x speedup. Controlled analyses connect the quality gain to delayed prompt feedback and validate state-aware refresh. Our code is available at https://github.com/Hxnng/Archer.

Large language models (LLMs) can generate fluent and useful responses but remain prone to hallucinations. We introduce Prompt Embedding Probes (PEP), a white-box method for answer-level hallucination detection from the hidden states of a frozen LLM. PEP extends standard linear probes by augmenting the input with a small number of learnable prompt embeddings. We evaluate PEP on TriviaQA, GSM8K, and MedQA using Qwen3 models at multiple scales. PEP improves hidden-state-based detection over standard linear probes in the main in-distribution setting. We further evaluate PEP for pre-generation prediction, cross-model transfer, and out-of-distribution generalization. PEP remains effective in the pre-generation and cross-model settings, whereas robust cross-dataset transfer remains difficult. These results show that prompt-based adaptation can strengthen hidden-state probing while keeping the backbone frozen and adding only a small number of trainable parameters.

Deployed vision-language systems often gate their answers on confidence, making confidence robustness relevant to oversight. We study confidence readouts under white-box, image-only attacks constrained to preserve the generated answer byte-identically. Under a reachability assumption, an unmovable readout cannot outperform the answer-string accuracy prior, whose pooled value is 0.617. Independently of that assumption, a uniform amplitude certificate below a measurable threshold guarantees adversarial discrimination above the same floor. Across four vision-language models, three visual question answering benchmarks, five deployed confidence channels and two defense estimators, direct or surrogate-aimed attacks produce itemwise feasible perturbations that refute this uniform certificate in all 84 estimator-by-cell combinations. Coordinated correctness-label-aware attacks drive adversarial discrimination to or below the answer-string floor in all sixty deployed-channel cells, including all fifty-nine that begin above it. Hidden-state interventions and an open-ended text-model activation-space replication show that comparable confidence movement can be induced at the representation level rather than only through adversarial images. None of four tested defense families establishes a robust alternative under the specific evaluation applied to it. In a confidence-gated simulation, a coordinated token-probability attack transferred to a hidden-state gate causes up to 84.8% of previously rejected wrong answers to become accepted. After reweighting to each benchmark's natural correctness prevalence, accepted accuracy falls below the no-gate baseline in eight of twelve cells under transfer and all twelve under a direct gate-aimed attack. Under the studied threat model and budget, confidence is therefore an integrity-sensitive rather than intrinsically robust oversight signal.

Despite the remarkable progress of large vision language models (LVLMs), object hallucination remains a fundamental challenge that hinders their trustworthy deployment. A key finding motivates our work: real and hallucinated object tokens are clearly separable in hidden representations, yet this separability is largely lost at the language-modeling (LM) head. We propose TruthLens, a self-evaluation framework that teaches the LM head to expose a per-object truthfulness signal without any auxiliary model or additional inference cost. Concretely, a rarely-used special token is repurposed as a reference token. For each object-token position, we extract the log-probability assigned to this special token by the LM head, and define its difference from a predefined constant as the truthfulness score. The model is then fine-tuned with an MSE objective that drives scores toward 1 for real objects and 0 for hallucinated ones, while a divergence constraint preserves the original generation capability. Despite being trained on only a limited set of object categories, TruthLens generalizes effectively to benchmarks with substantially larger label spaces. Extensive experiments across multiple LVLMs demonstrate state-of-the-art performance; notably, on Qwen2.5-VL-7B, TruthLens outperforms the previous best method on MS-COCO by over 17% in AUROC. Our code is available at https://github.com/wyqstan/TruthLens.

Large language model agents derive much of their capability from tool use. Existing research on tool use has largely focused on selecting the right tool and orchestrating the order of calls. However, correctly filling the parameters of a tool call is equally critical for successful execution and has received far less attention. In domains such as cloud networking, even frontier models correctly complete fewer than half of tool calls. Inspired by recent analyses showing that LLM hidden states encode rich information about model predictions, we discover that while the model generates a parameter value, its hidden state contains a strong correctness signal: a simple linear probe can accurately predict whether the value will be correct. Based on this observation, we propose a unified probe-guided framework with two complementary approaches: probe-filtered bootstrapped training (PBT), which uses the probe to filter reliable self-generated calls for fine-tuning, and probe-guided reranking (PGR), which uses the probe to select better candidates during inference. To support systematic evaluation, we release ParamBench, a benchmark built from real cloud-network APIs that categorizes every instance into five difficulty levels according to parameter nesting depth, cross-parameter dependencies, and the reasoning required to derive values from earlier calls. Extensive experiments across 5 open models on ParamBench and 6 external benchmarks demonstrate that our method substantially improves parameter generation, raising the average exact match from 19.7% to 59.6%.

Large language model (LLM) agents increasingly operate over long interaction histories, where effective reasoning requires identifying and exploiting task-relevant evidence distributed across past observations and actions. However, useful information encoded in previously computed representations is often underutilized during subsequent generation. We propose \textbf{TransMem}, a lightweight inference-time parametric memory module that transforms sparse historical hidden states from a frozen LLM backbone into reusable memory representations. TransMem uses a lightweight gating network to dynamically apply the latent intervention to the current hidden states, without repeatedly encoding the preceding context. To learn transferable memory utilization rather than task-specific knowledge, we introduce evidence-conditioned self-distillation. A memory-augmented student processes the full context and matches the predictive distribution of an evidence-only teacher that shares the same frozen backbone. Experiments on LoCoMo, HotpotQA, and MemoryAgentBench demonstrate consistent improvements across different model architectures and scales. TransMem yields gains of 11.58--29.25 $F_1$ on LoCoMo and 10.20--13.03 $F_1$ on HotpotQA, while improving the average MemoryAgentBench accuracy from 29.54% to 40.00%. These results establish sparse historical hidden states as an effective and efficient memory substrate for long-context LLM agents. Our code is available at https://github.com/Haodong-Lei-Ray/TransMem.

What do a language model's hidden states say about the organization of a single text? From one forward pass, without training, we score every token position on two properties. The aggregator measures whether the position consolidates the whole text into a stable configuration. The differentiator, whether other tokens are transiently carried into its subspace as the model reads: metaphor in its root sense, transport. Constants were frozen on one discovery text; every other is confirmatory. The aggregator is not, in the classic sense, an information measure, nor a measure of salience. Across three unrelated models, as a signifier repeats, its surprisal and its attention drain while its aggregator score holds: the channel marks a token's place in the text. That this tracks a reading rests on independent ground truth: an engineered register the aggregator follows across its boundaries (6/6 cells), and a psychoanalyst's marking of clinical transcripts, fixed before the instrument existed, in 34/36 cells, with a graded increment above lexical controls and dissociations no type-level measure reproduces. A transfer test gives the result its shape: the model whose token structure travels with lexical type reads the singular discourse worst, and in a matched base/instruct pair tuning raises fidelity without moving type-transfer. Structural value is a property of a token's place in this text, not of its vector alone: a relational rather than essentialist reading of hidden states, operationalizing theory that predated the instrument.

Identical language-model answers can arise from hidden states that support different future computations, so current-answer probes do not establish a reusable internal interface. We introduce forked futures: future operations are sampled only after a prefix state has formed, and states are compared through the response distributions induced by those operations. This yields an empirical causal quotient over hidden states without requiring researcher-specified latent labels. Shared, Local, Mixture, and Distributed interfaces then compete under prequential causal description length subject to future-signature fidelity and matched capacity constraints. In the two detailed model evaluations, Shared has the lowest held-out description length, with gains of 0.216 nats on Qwen2.5-1.5B and 0.294 nats on Llama-3-8B, while maintaining tightly clustered mean future-signature distortion; a five-backbone sweep preserves the positive direction of Sharedness Gain. The figure-aligned transplantation analysis gives Shared the strongest joint target-correctness, locality, copy-preservation, and composite profile, and API-aligned paths mediate 0.749 of the target effect versus 0.150 for matched null paths. In the blind four-class model-organism test, 14/16 architectures are recovered, with one observed non-Shared to Shared error among 12 non-Shared organisms. These results support an economical reusable causal interface within the tested operation banks, while keeping the claim explicitly conditional on the candidate architectures, interventions, and held-out futures.

The same diagnostic result can support or challenge one causal claim yet fail to address another when the claims concern different populations, outcomes, estimands, pathways, or identifying assumptions. When the evidence and target vary together, a correct answer may reflect favorable or adverse wording, lexical overlap, or a familiar diagnostic pattern rather than matching the evidence to the causal question. We introduce paired prompts that repeat the same diagnostic evidence verbatim while changing the causal target. Each prompt is labeled Favors, Challenges, Unresolved, or Wrong Target according to how the evidence bears on the causal question. A pair is recovered only when both prompts are classified correctly. Using linear readouts trained on a separate development set, we analyze the final-token hidden state from the penultimate transformer block of Qwen2.5-7B-Instruct, Qwen3-8B, and Llama-3.1-8B-Instruct. On the 49-pair primary benchmark spanning nine diagnostic families, balanced accuracy ranges from 0.654 to 0.659 and 18-21 pairs are recovered. Two independent human reviewers assigned the same label to 95 of the 98 prompts (96.9%). Across checkpoints, balanced accuracy and complete-pair recovery exceed permutation nulls that preserve development scenario groups. In Qwen2.5, full-prompt balanced accuracy exceeds both restricted inputs, with paired-bootstrap intervals for both differences above zero. Readouts trained without development examples from the evaluated diagnostic family recover 21 pairs, including at least one in each of the nine families. The hidden-state readout exceeds a linear classifier on answer-option logits and text baselines in balanced accuracy and recovered pairs. These results show that the hidden state contains linearly decodable information about whether diagnostic evidence favors, challenges, or fails to address the causal target.

Transformer language models are usually analyzed through vector geometry, yet ordered context and rotary position encoding introduce explicit phase structure into query-key interactions. This paper develops a bounded spectral framework for examining rotary phase alignment, hidden-state continuity, and semantic drift without treating language models as literal physical wave systems. It first identifies ordered hidden-state sequences, rather than vocabulary indices, as valid domains for spectral decomposition. It then derives the Rotary Position Embedding (RoPE) attention score as a sum of magnitude-weighted cosine terms and proves a local stability lemma: uniformly bounded phase displacement limits degradation of the corresponding pre-softmax score. To extend phase analysis beyond native RoPE coordinates, the paper defines complex modal coordinates over fixed orthonormal direction pairs and introduces a weighted coherence functional for hidden-state trajectories. These constructions support a strict distinction between representational continuity and execution-boundary admissibility. Internal coherence may describe preservation of task-relevant relations, but it cannot authorize a consequential transition. Positioned against existing geometric, spectral, phase-modulation, representation-analysis, and mechanistic-interpretability accounts, the framework contributes a theoretical and methodological program for determining when spectral structure explains continuity and when governance must remain an external predicate over execution.

Mechanistic interpretability has largely focused on language models and deterministic toy tasks. Much less is known about how sequence models internally represent latent stochastic dynamics under noisy, partially observed observations. We study this question in a controlled multivariate stochastic volatility setting, where models observe only returns while the ground-truth latent volatility state is known to the researcher. This setting provides a useful benchmark for mechanistic interpretability under partial observability: the latent state is hidden from the model but directly available for evaluation. Across architectures, losses, and output heads, we find evidence for a two-stage computation. Hidden representations encode substantial information about the next latent volatility state, and the output head maps this representation to squared return forecasts. Furthermore, in Transformers, latent-state decodability emerges at identifiable architectural stages whose location depends on the volatility period. In long-cycle regimes, this computation simplifies into an explicit latent-state filter consisting of a learned linear projection followed by $\ell^2$ normalization. Output-head replacement further shows that part of the degradation under noisy MSE training arises from readout misalignment rather than representation failure. These results suggest that stochastic volatility models provide a useful benchmark for mechanistic interpretability under noisy latent dynamics and partial observability.

Large Language Models can produce fluent text that is false, unsupported by the available evidence, or inconsistent with information that appears to be internally represented by the model. We study hallucination detection from the geometry of hidden activations and introduce the D-Score, a simple spectral statistic computed from a single forward pass. For a fixed model, layer, and tolerance parameter, the D-Score counts how many singular directions of the hidden activation matrix have singular values that remain close to the leading one. We use this quantity as a hallucination score, classifying an input text as hallucinated when its D-Score is larger than a pre-defined quantity. The motivation is that, when a model processes a text that conflicts with information available in its own internal state, the hidden representation may encode both the asserted content and some form of counter-evidence, uncertainty, correction, or lack of support; this can make the hidden trajectory spread across additional singular directions. We formalize this intuition through a lightweight spectral argument and evaluate the resulting detector on FAVA-Annotation and RAGTruth. The experiments indicate that the D-Score is a strong hidden-state signal for hallucination detection, while requiring no external verifier, no retrieval step, and no multiple generations.

Manipulating objects with hidden internal state, such as a latched microwave, forces a robot to probe before it can act. Yet a robot that has solved an instance once re-runs the same probes whenever it encounters that instance again, because existing cross-episode memories target task success and organize reuse around states, not the object or the cost of re-exploring it. We present Instance-Oriented Memory (IOM), an object-centric framework that amortizes this exploration: from a single encounter that uncovers the hidden state, whether or not it succeeds, IOM records a short procedure for manipulating that instance, keys it on the object's identifiable features, and injects it as a soft bias on a procedure-conditioned policy. A later encounter recognizes the object and recalls its procedure instead of re-exploring. We instantiate this distillation with an off-the-shelf vision-language model (VLM) that parses each encounter into the procedure without task-specific training. Across four articulated-object tasks, two in simulation (microwave, door) and two on a real robot (bottle, cabinet), an oracle procedure memory cuts manipulation operations by 16-30% over re-exploration at non-regressing success, and the VLM instantiation recovers 69-88% of that saving out of the box. Because the procedure is a soft bias on a feedback-driven policy, an incorrect memory is recovered from rather than obeyed: success holds even when a retrieved procedure is wrong, as for $\approx$12% of door instances. Across all tasks the benefit is purely one of efficiency: success never regresses, and on the real robot even improves. Code will be released upon acceptance.

Chain-of-thought prompting improves language-model reasoning by carrying intermediate states across successive computation steps. However, relying on natural language as the only recurrent interface is overly restrictive, since many transient computations do not need to be fully verbalized. Existing latent-reasoning methods remove this constraint by recurrently propagating continuous hidden states. However, these methods pass a dense hidden vector as a whole, without an explicit mechanism for selecting and organizing the information needed by the next reasoning step. This motivates an intermediate interface that remains linguistically grounded without requiring a decoded sentence. We introduce \textbf{J-CoT}, a recurrent reasoning framework built on \emph{J-space}, a vocabulary-indexed coordinate system within the model's hidden representations. Within each cycle, the model computes in its full hidden space. At the cycle boundary, J-CoT expresses the intermediate state as vocabulary-indexed coefficients, carries these coefficients forward as a \emph{J-thought}, and maps them back into the model's hidden representation for the next cycle. J-CoT therefore requires neither a fluent intermediate rationale nor recurrence over the complete hidden state. Under matched backbone and inference settings, J-CoT-Zero matches or exceeds the strongest evaluated latent-reasoning baseline on every benchmark, while J-CoT-Train obtains the highest score across the evaluated mathematical, scientific, coding, and structured path-reasoning tasks.

Large language models can answer scientific questions, yet a correct output does not reveal whether the model represents or uses the governing physics. Here, using three open-weight Gemma 4 models (google/gemma-4-E4B-it, google/gemma-4-12B-it, google/gemma-4-31B-it) we identify three experimentally separable signatures of materials-science mechanism information: selective concept readability, relational encoding of qualitative constitutive orientation, and causal, context-dependent control of constrained engineering answers. We combine matched direct and Jacobian vocabulary readouts, option-free state geometry, a 60-law counterfactual benchmark and causal interventions. In 50 held-out materials descriptions, three independently fitted Jacobian lenses reproduced concept ranks, and target-free word sets from both readouts enabled blinded identification of 9 of 10 mechanism families. A separate 72-prompt benchmark produced mechanism-specific hidden-state neighborhoods, but an exact graph audit showed that this apparent physical organization was equally explained by numerical comparison. We therefore compared otherwise identical prompts in which only the direction of the physical input was reversed, asking whether the resulting hidden-state movement followed the supplied constitutive law. These state transformations ordered direct, physically neutral and inverse laws across 60 frozen relations and correctly oriented 39 of 40 directional laws, whereas lexical controls were near chance. Bidirectional interventions shifted answer probabilities toward or away from the physically appropriate outcome across all 12 matched cases, while counterfactual state patches transferred opposing decision signals across mechanisms and answer formats. Physical relationships were therefore more visible in controlled state changes than in absolute states alone.

Reinforcement learning is conventionally divided into model-based and model-free methods. In this taxonomy, model-based methods perform lookahead planning over a learned world model, whereas model-free methods learn a reactive state-action mapping. Recent work, however, has shown that planning can emerge from model-free reinforcement learning alone. The conditions under which this behavior emerges from a pure reward-maximization objective have so far remained unclear. In this paper, we present evidence that, in the observed cases, the hidden-state structure of the neural architecture is the deciding factor. We find that a network of relational hidden states, each anchored to an environment state and exchanging messages along learned relations, acquires a planning mechanism. These hidden states recover the environment's transition structure in their learned relations, and improve the policy at decision time by planning over the learned graph. In a matched control agent that must additionally discover which cells represent which states, no such binding arises, and no planning follows from it. We argue that this explains the observed phenomenon of emergent planning in model-free reinforcement learning and raises the question of how common such emergent planning might be more generally. Finally, we hypothesize that the discovered mechanism could describe how planning emerges from pure reward maximization in the human brain through a neural architectural prior.

Bürger et al.\ (2024) demonstrated that truth representations in large language models are universal across statement polarity but reside within a multidimensional subspace. The truth value of a statement is linearly readable from a residual stream of language model, but it is not clear how much of that representation fits on a single direction, which component builds it, or what it is made of. We conducted a study based on these questions, with one instrument: a training-free axis, the dominant direction of the singular value decomposition (SVD) of hidden-state differences over true/false minimal pairs, identified without labels up to one global sign. Extensive evaluation across 14 models from 6 diverse architectural families (including MoE), read and extract at cost $O(d)$ per token. We close with a pre-registered prediction on whether the arrangement extends to categories whose truth is computed rather than retrieved.

Hallucinations and artificial text in LLM-generated outputs often appear as distributional deviations between prompt and response hidden-state distributions. Since prompts or retrieved contexts typically serve as reference samples and responses as query samples, with major differences in length, these asymmetries motivate the use of change test statistics that treat the two samples differently. We consider an asymmetric two-sample test ASK-NN based on the directed k-nearest-neighbor graph. Our statistic counts reference points whose nearest neighbor in the pooled sample is also a reference point. Under the permutation null, it admits an exact finite-sample conditional mean and variance; we further establish asymptotic normality and consistency under fixed alternatives. ASK-NN is computationally effective and easy to implement. Empirically, it is competitive with kernel and graph-based baselines on synthetic benchmarks, artificial-text detection, and LLM hallucination detection from token-level hidden states.

We study Dynamical System Autoencoders (DSAE) for LiDAR point-cloud classification using spatial coordinates and Product Coefficient feature augmentations. The experiments compare separately trained DSAE architectures at encoder depths $K=1,\ldots,5$ and evaluate the resulting hidden representations with Random Forest, kNN, and a majority-class Dummy baseline. The main finding is a hidden-state collapse at $K=5$. For both xyz and xyz plus Product Coefficient inputs, the hidden-state standard deviation falls to the order of $10^{-5}$, while all three classifiers attain the same macro F1 score of $0.224688$. We prove that between-class hidden scatter is bounded by total hidden scatter, which in turn is controlled by the reported hidden-state variance. Thus a nearly constant hidden representation cannot retain substantial class-separating structure. Product Coefficients neither improve pre-collapse macro F1 nor prevent the $K=5$ collapse in the present DSAE setting. These results identify large-depth representation collapse as a concrete failure mode for DSAE LiDAR classification.

Alignment faking is dangerous because a model can appear compliant under monitoring while preserving behavior it would reveal when unmonitored. When no scratchpad is visible, behavior alone cannot distinguish strategic from genuine compliance. We ask whether hidden states reveal what outputs hide. We run a 13-model sweep for naturally-emerging faking, then probe and steer hidden states on the two models that fake. Natural faking appears only in Qwen3-32B (+18.2pp) and Llama-3.1-8B (+24.4pp at n=10, p<10^-15), while explicit scratchpad self-reports are rare (a Claude Opus 4 judge flags faking reasoning in 1.4% of Qwen and 0.0% of Llama compliant scratchpads). Both fakers show an asymmetric refusal residue: monitored compliance shifts toward refusal (d=0.32 Qwen, d=0.33 Llama, both p<0.0001), while refusal representations do not move (p=1.00). Per-sample detection is model-conditional. Under leakage-free leave-one-query-out probing, detection survives on Llama (AUROC 0.87) but collapses to chance on Qwen (0.43), and cross-model transfer is null. Steering over 2,000 runs barely changes compliance (|h|<0.08), so the detected direction can flag faking but does not by itself control it. Standard residualized probing leaks across folds and reaches AUROC 0.63 on a control where no faking can occur; naive linear probes reach a meaningless AUROC 1.0; and conventional MLPs overstate detectability by 0.2-0.3 AUROC. For future alignment-faking detection work, we release a five-control measurement framework: multi-token extraction, refuse-vs-refuse confound checks, per-fold residualization, leave-one-query-out evaluation, and orthogonality-constrained probing.

Large language models (LLMs) in financial applications fail most consequentially when they are confidently wrong. Hedged, uncertain answers invite scrutiny, whereas confident errors silently degrade downstream decisions without warning. We ask how reliably such confidently wrong answers, or confident hallucinations, can be detected from a model's internal activations, and whether those activations carry information beyond its observable outputs. We train linear probes on the residual stream and evaluate them on two established question-answering (QA) benchmarks built from real filings, FinQA and TAT-QA. Behavioral confidence is measured as the agreement among eight resampled answers to the same question, and probe effectiveness is compared against baselines, such as token log-probabilities and the model's own True/False self-assessment of its answer. Our findings show that among confident answers, those for which all eight resamples agree, 15-23% are wrong on FinQA. There the probes have a significant advantage over baseline methods in detecting hallucinations, holding 0.68-0.77 AUROC while the best baselines fall to 0.55-0.63, across Qwen3-8B, Llama-3.1-8B, and Gemma-2-9B. Our results suggest that probing can be a cost-effective triage mechanism for routing LLM answers to human review and quality control procedures in high-stakes financial applications.

Reasoning failures in large language models (LLMs) are usually evaluated from final answers, but a wrong answer does not reveal why the model failed. The same incorrect output may reflect missing capability, an unstable reasoning trajectory, or a failure to activate a reasoning state that is already available in the frozen model. Existing prompting and benchmark-based evaluation methods mostly operate at the output level, while generic activation-steering methods typically apply global directions without diagnosing which examples require intervention. In this paper, we introduce SPARK, which uses hidden-state response to diagnose whether a model internally enters an effective reasoning state and to guide lightweight test-time steering. The key observation is that raw hidden-state susceptibility is strongly confounded by prompt length, especially in programmatic and algorithmic reasoning where harder serialized instances naturally become longer. SPARK therefore uses length-controlled susceptibility to separate input-scale effects from residual reasoning activation, and combines this signal with cross-layer coordination to select reasoning-active anchors and under-activated hard examples. We use FRONTIER-4.5K as a controlled programmatic reasoning suite for latent profiling and difficulty-aware analysis, and evaluate SPARK-Steering on GSM8K and MATH-500 with forward-only benchmark profiling. Our method improves Qwen3 series models consistently; on MATH-500, accuracy rises from 82.0% to 84.6% for Qwen3-4B and from 82.4% to 85.6% for Qwen3-8B. These results suggest that susceptibility can serve not only as a diagnostic signal for reasoning failures, but also as a practical guide for targeted test-time intervention.

State-of-the-art code models achieve impressive performance, yet the extent to which they internally encode type information remains poorly understood. We probe the residual streams of pretrained code models for internal type representations using a parallel dataset of Java and Python code examples. Our results show that cross-lingual type representations emerge even from untyped code. Moreover, we test whether hidden states linearly encode the result type implied by typed function application by training probes on one language to infer argument and result types in the other. Finally, we find that this structure is partly robust to lexical perturbations and cross-language syntactic variations. To the best of our knowledge, prior work on interpretability of code models has not directly targeted formal type semantics or cross-lingual type representations. We release our code and datasets.

Large Language Models (LLMs) store factual knowledge and domain-specific patterns implicitly in dense Transformer parameters, making knowledge expansion costly through pretraining, fine-tuning, retrieval augmentation, or longer contexts. Engram-style memory offers a compact hidden-state injection pathway, but existing GPU-resident designs often rely on hash-based compression, causing unrelated phrases to collide in shared slots and weakening phrase-level semantic fidelity. We present TF-Engram, a train-free Engram system that constructs phrase-specific semantic memory offline from external corpora, stores large memory tables across a GPU--DRAM--SSD hierarchy, and uses Early-Exit Guided Predictive Prefetching to hide external-memory latency during autoregressive decoding. On Qwen3-0.6B, TF-Engram improves the average downstream score from 57.6 to 59.4, outperforming both the frozen backbone and a parameter-matched LoRA baseline. System evaluation shows that large TF-Engram tables can be built with moderate offline cost, SSD-backed storage substantially reduces GPU memory demand, and predictive prefetching recovers much of the throughput loss caused by external memory access. These results demonstrate that static phrase memory can be integrated into LLM inference as a scalable, train-free, and low-overhead system component.

A common method for the representation and analysis of time-series data is the hidden Markov model (HMM), where each observation is associated with a hidden state that evolves over time. However, many real-world systems are influenced by multiple independent factors, which are more naturally represented by factorial hidden Markov models (fHMM), where several hidden Markov chains jointly generate the observed data. Although an fHMM provides a richer and more realistic representation of many real-world systems, it can be reformulated as an equivalent HMM, but with a significantly larger state-space, leading to a severe increase in computational cost. In particular, the forward filtering algorithm, which is central to evaluation, decoding, and estimation tasks, becomes prohibitively expensive even for small systems. This work focuses on developing scalable methods for time-series analysis using tensor algebra to exploit the multidimensional structure of fHMM directly, without constructing intermediate HMM representations. Our novel filtering approach significantly improves computational performance and enables the efficient analysis of large systems and datasets, extending the scope of fHMM and providing a practical framework for data intensive applications.

Deep neural networks often contain substantial hidden-state redundancy, but most compression methods operate directly on weights, neurons, or quantised representations without explicitly characterising the dynamical role of internal states. This paper proposes a controllability-observability framework for empirical state-order reduction of deep neural networks. By viewing a trained network as a depth-indexed nonlinear dynamical system, we construct data-driven reachability, observability, and balanced Gramians from hidden-state snapshots and output Jacobians. The resulting A/B/C tests estimate layer-wise reachable, observable, and jointly reachable--observable ranks. These ranks are then used not only as diagnostic measures of hidden-state redundancy, but also as actual compressed layer widths for realised reduced networks. Experiments on MNIST and CIFAR-10 compare the proposed balanced realisation against projection-based reduction, unstructured pruning, structured pruning, low-rank SVD, dynamic INT8 quantisation, and linear baselines. On MNIST, a four-layer SiLU DNN is reduced from state order 1024 to 277, giving 72.95% state compression and 73.48% parameter compression, while maintaining 95.45% accuracy compared with 96.60% for the full model. On CIFAR-10, a larger SiLU DNN is reduced from state order 4608 to 1339, giving 70.94% state compression and 83.09% parameter compression, while preserving accuracy from 54.45% to 54.44% and reducing CUDA inference latency by approximately 3X. The results show that balanced reachable-observable ranks provide a principled empirical minimal-realisation criterion for designing compact neural architectures with little or no loss in accuracy.

Diffusion architectures now encompass convolutional UNets as well as transformer-based designs such as Diffusion Transformers (DiTs), inspired by Vision Transformers (ViTs), yet the effects of structured geometric perturbations within these architectures remain poorly understood. We study this question through a unified framework that applies reflection-based elements of the dihedral group to intermediate hidden states as controlled internal interventions, contrasting geometrically consistent and inconsistent variants. Using activation-level diagnostics, including Self-Consistency Shift (SCS), Activation Mass Scatter (AMS), and Drift, we analyze feature stability and geometric drift. We find that consistent transformations improve stability, while inconsistent ones induce predictable, architecture-specific failures. In the main Stable Diffusion 2.1 U-Net study, we evaluate seven intervention modes over three seeds and complement the internal diagnostics with image-level FID, KID, CLIP score, and LPIPS diversity. Taken together with supporting ViT and controlled DiT analyses, these results establish geometric consistency as a key principle for stable hidden-state interventions in spatially structured vision and diffusion models.

This work studies the hidden-state inversion problem: recovering the original input token sequence of a decoder-only language model from its last-layer hidden states. Rather than treating inversion as a one-shot reconstruction, we study it as a continuous embedding-space optimisation in which a soft proxy is driven towards the leaked target without any hard-token projection during the search, and a token is committed only once, at the end of the inner loop. This design choice has two consequences which are the main focus of this paper. First, keeping the optimisation entirely in continuous space exposes a rich set of internal signals: rank trajectories of the ground-truth token, per-position loss curves, and a discrete loss measured at commit time. Second, the discrete loss allows assessing the correctness of recovery via cumulative discrete loss. We further analyse which tokens break the reconstructions and find a sharp categorical asymmetry: space-prefixed, high-frequency function words in dense regions of the embedding matrix dominate the failures, while content-bearing tokens are recovered almost perfectly. On 10-token C4 prompts the exact-match rate rises from 66.9% to 97.5% (mean similarity 0.994) as the candidate window is widened, confirming that most errors are recoverable near-misses rather than genuine ambiguities. A comparison with the released SIPIT reference situates these findings: per-step hard projection is faster, but the continuous formulation is what makes the optimisation observable and its failures detectable. The results show that last-layer hidden states of GPT-2 are as sensitive as the original text.

Large language models achieve strong performance on many reasoning tasks when allowed to externalize intermediate steps as Chain-of-Thought (CoT). However, many questions require the model to internalize the multi-step reasoning within a single forward pass before generating the answer. We study this challenge through two-hop reasoning, a representative task where the model must compose multiple pieces of parametric knowledge within a single forward pass. Standard non-recurrent Transformers suffer from a depth-local storage problem: facts learned in earlier layers are unavailable where second-hop retrieval happens. We found that Looped Transformers mitigate this issue by reusing the same memory, but still generalize imperfectly. We show that the remaining bottleneck is representational. In the two-hop reasoning task, the first loop often makes the correct bridge entity nearly perfectly decodable, yet the corresponding hidden state remains poorly aligned with the bridge token embedding. Surprisingly, an easy training-free realignment intervention nearly closes the generalization gap. Building upon this insight, we propose DiscoLoop, a looping architecture whose recurrence carries both a discrete embedding channel and a continuous hidden-state channel. DiscoLoop achieves near-perfect accuracy with substantially fewer training steps across symbolic and synthetic-language multi-hop reasoning tasks. When applied to real-world pretraining, DiscoLoop attains lower training loss and stronger benchmark performance than looped-transformer baselines, suggesting that the mixed-channel design transfers to practical language modeling.

Hallucination remains one of the central obstacles to deploying medical LLMs. Yet, even when hallucination can be detected, it is still unclear whether the internal representations associated with it can be used for control rather than detection alone. Using four open-source models across a suite of medical question-answering datasets, we show that a simple, carefully conditioned probe can reliably detect hallucination, with AUROC scores between 0.77 and 0.86 in our case. We further show that this signal is distributed and redundant rather than narrowly localized. Systematically selected neurons outperform random neurons only at very small subset sizes, whereas random subsets of a few hundred neurons recover nearly the full signal, and low-dimensional random projections preserve most of the detection performance. Beyond detection, we test whether this representation is causally actionable. Across 16 model--dataset combinations, our results reveal a sharp gap between decodability and controllability. The same internal structure that makes hallucination easy to detect does not translate into reliable neuron-level control. These findings show that medical hallucination seems to be readily visible in internal activations, but not easily corrected by steering the neurons most associated with it. More broadly, our results suggest that hallucination mitigation is not simply a matter of identifying the right neurons, and point to a deeper separation between what representations reveal and what they allow us to change.

LLM agents can share more than text. In some systems, an agent can send a short visible message while also passing its full KV-cache state to another model. This hidden state can help the final model combine evidence from several agents, but it is also hard to inspect. A visible message may look harmless even if the hidden state has been changed. We study this problem in a multi-agent question-answering setup. Specialists each see part of the evidence, send a short commitment, and pass full KV-cache state to a coordinator. In clean runs, this latent collaboration improves over a matched text-only version. On transformed HiddenBench with Qwen3-4B, it reaches EM/F1 of 0.338/0.486, compared with 0.231/0.369 for text collaboration. Qwen3-8B and HotPotQA runs show the same direction of improvement. The problem appears when one specialist is malicious. Some false visible commitments can steer answers. More seriously, changing the hidden KV state can collapse performance even when the visible commitment still looks plausible. A verifier that checks only text misses this failure mode. Simple magnitude checks catch some obvious corruptions, but adaptive attacks can evade them while still damaging the final answer. The most reliable fix we find is not to guess whether hidden state looks normal, but to protect it in transport. We implement an HMAC-SHA256 manifest that binds the specialist, session, model, visible commitment, tensor metadata, and payload digest. It accepts all 774 honest replayed payloads and rejects all 295 recorded tampered payloads. The main lesson is that full-KV latent memory can be useful, but it should be treated as a security-sensitive object, not as ordinary internal model state.

World models can predict future physical states, but prediction accuracy alone does not explain how physical information is organized and used inside their latent dynamics. We introduce a controlled diagnostic protocol for studying event-conditioned latent physical structure in passive object-state world models. The protocol tests whether hidden representations encode event-regime information, whether event contexts reweight non-exclusive physical field readouts, and whether field-aligned representational components have functional consequences for prediction. Using a balanced controlled-generator dataset with free-motion, collision, and occlusion events, we evaluate recurrent, attention-based, and latent state-space transition models under a fixed-horizon forecasting setup. The models learn useful predictive dynamics and their hidden states support reliable event-regime readout. Event contexts systematically reweight kinematic, contact, and object-permanence field readouts: free motion is kinematic-dominant, collision combines kinematic and contact structure, and occlusion combines motion-related and object-permanence structure. Time-aligned and directional-consistency analyses further show phase-related shifts in field emphasis. Finally, fixed-horizon projection causal field effect (CFE) shows that suppressing field-aligned directions can degrade event-relevant prediction, with strongest evidence for contact-aligned structure in collision-contact windows and more qualified evidence for object-permanence-aligned structure in hard-occlusion hidden windows. These results support event-conditioned organization and fixed-horizon functional sensitivity of latent physical fields, while not implying explicit physical modules, isolated causal circuits, or context-invariant sliding-window generalization.

Ill-posed questions, including ambiguous, underspecified, or contradictory queries, may admit no valid answer or multiple plausible answers, posing a challenge for large language models (LLMs). Existing approaches largely analyze ill-posedness through model outputs and often focus on specific subclasses. We investigate whether diverse sources of ill-posedness can be represented within a unified topology of LLM internal states and whether this structure can be used to steer response behavior. We model the contextual hidden states of prompt tokens at each transformer layer as a point cloud and characterize its geometry using finite zero-dimensional persistent homology. Each layer is summarized by three compact descriptors: mean finite lifetime, normalized lifetime entropy, and largest-lifetime concentration. Concatenating these descriptors across layers yields a topology representation of the question. We further introduce topology-conditioned activation steering, which retrieves topologically similar examples and constructs query-specific activation interventions that encourage source-aware clarification or abstention. Across three open-weight LLMs, topology features consistently outperform prompt-based and pooled-hidden-state baselines for ill-posedness classification, improving average accuracy from $67.4\%$ to $78.9\%$ on AmbigQA, from $79.9\%$ to $88.5\%$ on SituatedQA, and from $57.6\%$ to $69.6\%$ on CLAMBER 9-way classification. Topology-conditioned steering increases the average total acceptable response rate from $61.4\%$ to $70.6\%$ and grounded acceptable responses from $11.9\%$ to $16.4\%$. These results show that persistent homology provides both an interpretable representation of ill-posedness and an effective mechanism for targeted response steering.

Long-horizon LLM agents can fail quietly: they settle on one reading of the evidence early, then spend the rest of the run defending it. We call this premature commitment. Final-answer scoring misses the failure mode because it sees only the answer, not whether the process has already collapsed to a stable path. We define representational commitment as cross-run hidden-state convergence at a fixed reasoning step, and use it as an early diagnostic of trajectory consistency. On Llama-3.1-70B running ReAct on HotpotQA, step-4 hidden-state similarity predicts downstream behavioral consistency (r = -0.35, partial r = -0.45), with a localized temporal and layer-wise signature. The signal replicates across Qwen-2.5-72B and Phi-3-14B, and on StrategyQA (r = -0.83). It does not track correctness: committed-wrong and committed-correct questions are not separable in activation similarity. That boundary is central to the claim. Commitment tells us whether an agent has settled, not whether it is right. A runtime monitor detects inconsistent trajectories from hidden states at AUROC up to 0.97 (0.85--0.88 under a stricter split), and a prompting intervention cuts behavioral variance by 28% against a token-matched control while leaving accuracy statistically unchanged. We also test whether the signal can route self-consistency compute; on a harder benchmark it helps only modestly and is matched by a simpler output-based baseline. The result is a diagnostic for a hidden process failure, with clear limits rather than a general accuracy lever.

Hidden-state probing -- a linear classifier on a frozen vision-language model's internal activations -- has emerged as an attractive evaluation tool for flagging indirect prompt injection (IPI) in multimodal computer-use agents before the agent emits a corrupted action. We argue, on a single-backbone cautionary case study (Qwen2.5-VL-7B on Mind2Web, teacher-forced replay), that a high probing AUC on a clean-vs-attack split is not, on its own, evidence of malicious-content detection. Two post-hoc diagnostics -- a paired-construction scalar baseline on text-side injections, and same-step nuisance-matched visual controls on the overlay surface -- do not license an unqualified malicious-content interpretation of the headline while leaving room for partly-semantic readings. We package the diagnostics as a candidate control set with reporting heuristics for what a high clean-vs-attack AUC does and does not license. Labels are injection-surface-present, not attack success; generalisation beyond this backbone and benchmark is a conjecture.

We present a formal model of mesh inference: how a population of independent agents, each holding private state and exchanging only admitted, typed observations, derives a conclusion none of them holds alone, with no central coordinator and no agent exposed. No agent shares weights, gradients, or hidden state, and the agents may span different teams, networks, and organizations. Motivated by the observation that asking a model is energy-minimizing inference, we model the mesh as a coupled free energy that each agent relaxes locally. We show that a single admission/emission policy governs three properties. First, mesh inference converges to a unique answer for any admission, symmetric or not, because the coupling is always an M-matrix. Second, it is identification-complete: it derives the centralized optimum exactly when the contributing views are carrier-connected. Third, it is observation-only: no node transmits its internals, and confidentiality is the dual of identification. Content-addressed lineage is the only global side-channel. In the linear-Gaussian regime every derived answer is determined, hence equal to the centralized optimum, at O(diam^2) latency, the measured price of removing the center. One such derivation is one turn of a center-free learning loop, which we formalize as architecture rather than prove. The open problem we state is when asking improves the collective rather than corrupting it: whether the non-linear closure derives an upgraded answer or a confident error. To our knowledge, this is the first formal characterization of when a center-free, observation-only mesh recovers the centralized optimum.

Large language models show strong reasoning ability, but their internal reasoning process can remain unstable in complex multi-step settings, where early hidden-state errors may propagate to incorrect predictions. We propose ReLAR, a reinforcement-guided latent refinement framework that iteratively updates hidden representations before decoding. ReLAR maintains a compact latent reasoning state and uses learned depth and action controllers to adaptively determine both the number and direction of refinement steps. The controllers are trained with a policy gradient objective based on step-wise likelihood improvement, enabling efficient input-dependent reasoning without explicit chain-of-thought generation. Experiments on medical, mathematical, multi-hop reasoning, and open-ended generation benchmarks show that ReLAR improves accuracy, generation quality, and reasoning stability with substantially lower inference overhead than explicit reasoning baselines.

A constitution tells a language model what to value, but little tells us whether it does. Adherence is judged from outputs, and output evidence is most fragile on value conflicts, where what matters is not which value a model mentions but which one it is willing to sacrifice. We provide evidence that this arbitration can be read from activations in a structured margin readout. We introduce Constitutional Value Potentials (CVP). For each value we learn a scalar potential from the hidden state: an internal pressure to preserve that value, supervised not by the prompt but by an independent judge's verdict on which value the model's own response actually preserved. The signed difference of two potentials is a priority margin. A constitutional clause becomes the claim that a margin stays positive, and a single monitor score flags when it does not. The monitor predicts conflict violations with AUROC up to 0.95, beats a strong hidden-state probe, and generalizes to held-out synthetic conflicts across three Qwen2.5 scales. The signal appears as the answer begins, from the prompt tail and first response token. Read this early, the same signal reveals whether an adversarial priority hack has actually pushed the model toward a violation, rather than only whether the prompt looks adversarial. The same directions also support intervention tests: under selected steering settings, moving along a value direction shifts judged trade-offs in the intended direction. Together, these results suggest that some constitution-relevant priorities are accessible as activation-space margins, rather than only as output behavior.

Large language models encode rich information in their hidden states. This work asks whether the correctness of code that Qwen3-4B-Instruct-2507 has not yet generated is already legible in its hidden states, evaluated on a set of 444 tasks from LiveCodeBench. The correctness of the model's first-attempt code is linearly decodable from the hidden state at the final prompt token, captured before any output token is generated, with a leakage-free held-out AUC of 0.881 +/- 0.008 across 50 outer splits. To assess whether this signal is explained by prompt length, each hidden state dimension is residualized with respect to its linear effect. The probe still achieves an AUC of 0.842 +/- 0.010, substantially above a logistic prompt-length baseline of 0.657 +/- 0.014, and none of the nonlinear models tested improves upon it. A companion question about whether self-repair leaves a geometric signature in the model's hidden states could not be answered, because successful repairs following a failed first attempt are too rare in this setting to support the analysis. The contribution is both empirical and methodological, providing evidence that pre-generation hidden states contain a robust signal of eventual code correctness, together with a confound-control diagnostic that quantifies how much of that signal survives adjustment for prompt length.

Looped language models turn hidden states into runtime state: each state is decoded for prediction and fed back into future computation. This creates a basic supervision question: which state variables does cross-entropy actually control? We show that dense per-loop cross-entropy controls the variables exposed by the readout, not every variable active in the recurrent transition. Hidden-state scale gives a concrete failure mode. Scale-invariant readouts such as RMSNorm and LayerNorm hide radial scale from the immediate cross-entropy loss, while pre-norm residual recurrence continues to carry and update that same scale. Thus per-loop loss can make early exits usable without controlling recurrent scale. In 44M and 129M looped transformers without inter-loop normalization, per-loop cross-entropy through RMSNorm readouts still drives final hidden-state norms into the thousands or tens of thousands. Scale-visible readouts and explicit norm penalties keep norms in the tens, and scale-removing recurrence is the complementary architectural fix. The resulting design rule is simple: dense supervision trains exits; recurrent scale control requires either making scale visible to a loss or removing it from the loop. Consistent with this rule, scale-controlled variants achieve lower perplexity at matched inference-depth operating points in our variable-depth benchmarks.

Latent chain-of-thought compresses reasoning by replacing visible reasoning traces with continuous hidden-state recurrence, but existing formulations are difficult to optimize with standard on-policy reinforcement learning (RL) and hard to interpret causally. Our key insight is that a single pair of explicit boundary tokens can address both issues at once: discrete entry and exit anchors make the latent block compatible with standard on-policy RL, and the same anchors offer a natural foothold for mechanistic analysis. Motivated by this, we propose SWITCH, a switchable latent reasoning framework. The model emits <swi> to enter latent mode and </swi> to exit. Because the boundaries are ordinary discrete tokens, the GRPO policy ratio is well-defined at every decision point. The same anchors also expose the latent steps to direct probing and causal intervention. We train the model with a visible-to-latent curriculum and a Switch-GRPO objective that propagates gradients through recurrent latent computation. SWITCH consistently outperforms prior hidden-state-recurrence latent reasoning approaches at similar scale. Mechanistic analysis through the boundary tokens further reveals three findings: (i) <swi> is a sharply localised, learned switching policy rather than a stylistic artefact; (ii) the latent step it opens performs problem-specific, causally important computation rather than acting as an inert placeholder; and (iii) that computation is concentrated at a single hidden-state transition on entry. Together, these results show that hidden-state-recurrence latent reasoning is both RL-trainable and open to direct mechanistic analysis, including of how on-policy RL itself improves the model from the inside.

Deployed large reasoning models (LRMs) often behave unexpectedly. Test-time steering controls LRM outputs by intervening on their hidden representations, but it can degrade output quality. We argue that prior steering work implicitly relies on internal features that detect behavior in already generated text. We show that these detection features are poor predictors of future behavioral outcomes, and thus not the natural intervention target. Instead, we train activation probes to predict future behavior likelihoods from intermediate reasoning steps. These probes predict the most likely behavior with 64%-91% accuracy, revealing a separate type of internal prediction features. Building on these prediction features, we introduce a text-level steering method, Future Probe Controlled Generation. FPCG samples multiple candidate sentences and chooses the best one according to a probe predicting the future behavior likelihood. This enables steering with almost no output quality degradation. FPCG also enables steering in several evaluations where activation steering fails. These results show that distinguishing detection and prediction features enables a more nuanced approach to controlling LRM behaviors.

Criticality has been proposed as a key organizing principle in biological neural systems, yet its origin and relevance in artificial neural networks remain unclear. We analyze hidden-state dynamics in trained long short-term memory (LSTM) networks and show that small networks near their optimal training epochs (steps) exhibit scale-free avalanche statistics and branching parameters close to unity, indicative of near-critical dynamics, while larger models remain subcritical. To explain the coexistence of subcritical branching with robust $1/f^β$ noise, we introduce a mixture branching process framework that links heterogeneous branching dynamics to long-range temporal correlations. These results identify critical-like behavior in LSTMs as an emergent, capacity-dependent dynamical regime.

Recurrent neural networks maintain a hidden state $h_t$, but its probabilistic meaning is often unclear. We study hidden-state stability through \emph{backward coherence}: the extent to which $h_t$ can be reconstructed from $h_{t+1}$ by a learned backward projector $g_φ$. Under contraction and summable backward drift, the hidden-state sequence forms a quasi-reverse-martingale. This yields almost-sure convergence, rates under mixing, an interpretable limiting representation, finite pathwise stopping times, and a theoretical framework for time-uniform confidence sequences. Simulations support the theory. Backward-coherence regularisation reduces the empirical quasi-martingale total $\hat Q$ by $43$--$58$, reaches stability $28$--$44$ earlier than an unregularised RNN, and gives tracking-error recovery consistent with geometric bounds. Additional tests confirm echo-state forgetting rates bounded by $ρ$ and verify the increment-sum tube $R_t$ with $100$ simultaneous coverage, although $R_t$ is conservative; in practice, the defect-tail proxy $\hat Q_t$ is the more useful monitor. The backward-coherence loss is also equivalent to minimising a Kullback--Leibler divergence in a Gaussian backward model, linking the method to variational inference. Extensions cover $φ$-mixing inputs, change-point tracking, and finite-sample concentration. Three real-data studies further validate the approach. On PhysioNet 2012 ICU data, the Reverse Martingale RNN (RMRNN) matches RNN mortality-prediction AUC while reaching stable representations 13 hours earlier. On FRED-MD, it reduces one-month-ahead forecast error by about fourfold under concept drift. On UCI Human Activity Recognition, it maintains lower post-transition tracking error with geometric decay. The guarantees apply under the stated assumptions; universality is not claimed.

We study causal discovery from observational data when some variables are hidden and the data-generating process follows a location-scale noise model (LSNM). Existing methods that handle hidden confounders typically assume additive noise, but in practice, causes often modulate not just the mean but also the variance of their effects. We prove that acyclic directed mixed graphs (ADMGs) satisfying a bow-free condition are identifiable under LSNM with hidden variables, establishing the first identifiability result for causally insufficient models beyond noise additivity. We further provide sufficient conditions for identifying causal direction even when the bow-free assumption is violated. Our two-stage algorithm, LSNM-UV, is sound and complete, and experiments demonstrate improved performance over additive baselines on heteroscedastic data.

On-policy distillation (OPD) supervises the student exclusively in the output space by matching next-token distributions. This paradigm suffers from two limitations: (i) a high-variance gradient estimator whose signal-to-noise ratio collapses as the student approaches the teacher, and (ii) an LM-head information bottleneck that discards the teacher's intermediate hidden states. We propose On-Policy Representation Distillation (OPRD), the first method to lift on-policy distillation into the hidden-state space. OPRD aligns student and teacher representations across selected layers on the same on-policy rollouts, providing dense, deterministic, per-layer supervision while bypassing the LM head entirely. Theoretically, OPRD provides a deterministic per-sample gradient, removing the token-level estimation variance that plagues OPD, and exposes structural information that any output-space objective necessarily discards. Empirically, OPRD closes the student-teacher gap on competition mathematics benchmarks (AIME 2024, AIME 2025, and AIMO), where every output-space baseline plateaus below the teacher, while training 1.44x faster and using up to 54% less memory. We further extend OPRD to the cross-architecture setting via OPRD-Bridge. By exploiting the observation that heterogeneous models share a low-rank representational structure, we construct a frozen projector pair that aligns representations across arbitrary depth and width mismatches, shifting the alignment from the output space (which depends on a shared vocabulary) to the representation space. We validate OPRD-Bridge on both cross-architecture (Qwen3-4B -> Qwen3-1.7B-Base) and cross-tokenizer (Phi-4-mini-reasoning -> Qwen3-1.7B-Base) settings, demonstrating successful knowledge transfer even when the vocabulary-based alignment channel is unavailable. Code: https://github.com/ShenzhiYang2000/OPRD.

Human language comprehension unfolds sequentially: each word is processed in the context of those that came before, and the interpretation builds incrementally over time. Surprisal, the negative log probability of a word given its context, has been the dominant predictor of incremental processing cost. But surprisal reduces rich sequential representations to a single scalar at each word, discarding information about the direction in which the interpretation has been evolving. Dynamical-systems approaches suggest that the trajectory of the evolving interpretive state, not just its position at each moment,should shape processing, and language itself may have local momentum, since speakers plan utterances a few words at a time. We introduce trajectory extrapolation error: at each word, we fit a linear trajectory to the preceding hidden states of a transformer language model and measure deviation from the extrapolated path. On the Natural Stories corpus, this measure is nearly orthogonal to surprisal (r = .044) and independently predicts self-paced reading times. The effect is especially pronounced in garden-path sentences, strengthens with model scale (GPT-2 Small to Large), and replicates across architectures with different positional encoding schemes (GPT-2 vs. Pythia/RoPE). A displacement control shows the effect is not reducible to representational change magnitude: displacement and extrapolation error predict in opposite directions. These findings reveal two dissociable components of processing cost: word-level prediction error (surprisal) and sensitivity to the local momentum of the unfolding interpretation (trajectory extrapolation error).

Large language models hallucinate confidently, making uncertainty quantification (UQ) essential for reliable deployment. Existing methods rely predominantly on token-level signals, leaving the geometric structure of intermediate hidden states underused. In this paper, we take the geometric complexity of hidden-state matrices as a measure of the global uncertainty of LLMs, while treating token-level uncertainty estimation as a local metric. We show that hidden-state geometric entropy (global uncertainty) and token-level entropy (local uncertainty) are statistically near-orthogonal, capturing distinct failure regimes for reliability prediction. In particular, global geometry recovers the confident-but-wrong failure mode that local signals systematically miss. Building on this, we propose Global-Local Uncertainty (GLU), an unsupervised, single-pass score that fuses the two signals via a multiplicative gate. Across three model families and six benchmarks, GLU matches or outperforms all unsupervised baselines while requiring only a single forward pass and remaining length-normalized and architecture-agnostic.

Reasoning models achieve strong performance on challenging tasks by generating explicit intermediate reasoning traces before producing a final answer. Yet the internal structure of representation space when reasoning remains poorly understood: how do a model's hidden representations differ during thinking versus the embeddings of the input prompt, and can this structure be exploited to elicit stronger reasoning at inference time? We show that both input embeddings and thinking embeddings (mean-pooled last-layer hidden states over the prompt and reasoning trace, respectively) exhibit extremely high conicity, with all vectors clustering tightly around a single mean direction. Crucially, these mean input and thinking directions are non-collinear, with thinking embeddings occupying a geometrically distinct region of embedding space across many different models and benchmark tasks. This observation motivates casting the input-to-thinking transition as a rotation problem admitting a closed-form solution via orthogonal Procrustes analysis. We propose Rotate2Think, a training-free method that estimates this rotation from a small set of correctly solved examples and injects the resulting synthetic thinking vector between thinking delimiters at inference time, providing a geometric primer at the onset of the reasoning trace. Evaluated across multiple benchmarks and model families, Rotate2Think improves accuracy in 30 of 32 model-benchmark configurations across mathematics, science, and code tasks, and generalizes zero-shot to multimodal reasoning on MATH-Vision.