arXiv:2605.22986v1 Announce Type: new
Abstract: Learning reward functions from demonstrations assumes that demonstrations provide adequate supervision over all features -- or task-relevant aspects of behavior. In practice, demonstrations are often imperfect: humans may under-emphasize certain features due to cognitive load or physical difficulty, or the training regime may fail to sufficiently cover all relevant situations. In either case, important features may be underspecified, leading to ambiguity in the learned reward function and misaligned behavior at deployment. We propose a framework that detects such underspecified features and actively solicits targeted corrective demonstrations. Our key insight is that demonstrations implicitly reveal which features are well specified: features that are consistently optimized show little variation across demonstrations, while features that are underspecified vary widely. We leverage this statistical signal to infer which features may have been insufficiently demonstrated. The robot then explains which features it is uncertain about in natural language and queries for demonstrations that explicitly address the identified gaps. We evaluate our approach in a simulated tabletop manipulation domain and in a user study with a real Franka robot. Targeted, explanation-guided queries significantly improve reward recovery compared to random querying and passive data collection, reducing ambiguity that would otherwise persist in learning from imperfect demonstrations.
Science Journals
arXiv:2605.22984v1 Announce Type: new
Abstract: Test-Time Training (TTT) is an emerging paradigm that enables models to adapt their parameters during inference, improving performance on tasks such as few-shot learning, retrieval-augmented generation, and complex reasoning. However, this dynamic adaptation introduces new vulnerabilities that adversaries can exploit to jailbreak models. We identify three threat models for TTT and demonstrate how attackers can leverage them to bypass safety filters. Our results show that TTT can significantly increase the Attack Success Rate (ASR) and the ASR over 10 generation trials (ASR@10). For example, under LoRA, the few-shot and generation-phase threat models achieve an average ASR@10 of 95% and 93% respectively, across models from different families and scales. These vulnerabilities transfer to production fine-tuning APIs. We also show that TTT-induced overfitting can produce degenerate outputs that inflate ASR under standard judges, and propose a validity-aware evaluation to correct for this. Our findings suggest that TTT exposes a new attack surface, strengthens attacks, and undermines existing safety guardrails. As a first step toward defense, we propose a lightweight provider-side detector that flags TTT requests via the perplexity shift on a private harmful holdout, but robust deployment will ultimately require dynamic alignment.
arXiv:2605.22982v1 Announce Type: new
Abstract: Taylor--Aris dispersion of Brownian rods in non-circular ducts is governed by a coupling absent from passive-scalar theory. Pressure-driven shear aligns the rods and makes translational diffusion tensorial, while duct geometry determines how this tensor is sampled across the cross-section. We formulate this problem for dilute rods in regular-polygonal ducts of arbitrary side number. At each cross-sectional point, a local shear-aligned Jeffery--Brownian closure gives four transport fields, namely two transverse diffusivities, a direct axial diffusivity and a signed shear--axial cross coefficient. Because the shear frame rotates through a polygon, these fields enter a conservative two-dimensional transverse operator rather than a radial scalar-diffusion problem. Its zero mode is a non-uniform invariant density, which replaces the area measure in the Taylor--Aris reduction and reduces, in the circular-pipe limit, to a weighting proportional to the inverse shear-direction diffusivity.
The resulting cell problem separates the effects of rod alignment on streamline sampling and transverse relaxation. Alignment produces only a small, non-monotone shift in mean speed, but gives a larger enhancement of the Taylor coefficient by reducing transverse mixing. Normalization by the same-geometry spherical coefficient removes most passive shape dependence and exposes the approach to the fully aligned transverse-mixing limit. Finite regular polygons converge smoothly to the circular-pipe branch, whereas low-sided polygons retain distinct shear-sampling signatures. A biorthogonal spectral formulation resolves finite-time releases. Localized, multi-peaked and broad injections excite different non-zero transverse modes and exhibit different pre-asymptotic variance growth, but modal decay selects the common long-time Taylor--Aris coefficient given by the cell problem.
arXiv:2605.22981v1 Announce Type: new
Abstract: Fill-in-the-middle (FIM) is a pretraining objective widely used to equip causal language models with infilling ability, yet its effect on verbatim memorization remains underexplored. We study the memorization dynamics of FIM in a controlled setting by pretraining matched Llama 3.2 models with FIM and standard left-to-right (LTR) objectives on a FineWeb-Gutenberg corpus containing repeated Gutenberg excerpts. With prefix-based probes, FIM more often recovers short or partially matching spans, while LTR more often assigns high confidence to long exact continuations. We observe that verbatim extraction under FIM-training grows approximately linearly with repetitions over the tested range. Evaluating native FIM-format probes reveals that suffix context is not sufficient: verbatim recall under FIM-training remains strongly anchored in prefix context. Our results also show that evaluating only one span length or probing format can miss important nuances in memorization behavior.
arXiv:2605.22976v1 Announce Type: new
Abstract: Large Language Models (LLMs) are increasingly integrated into software systems for diverse purposes, due to their versatility, flexibility, and ability to simulate human reasoning to some extent. However, poor integration of LLM inference in source code can undermine software system quality. Therefore, inadequate LLM integration coding practices must be documented to help developers mitigate such issues. Following our earlier work on LLM code smells, this paper consolidates and refines the concept by presenting a self-contained taxonomy and a catalog of nine LLM code smells. We also create SpecDetect4LLM, a static source code analysis tool for their detection, and conduct extensive empirical evaluations of its detection effectiveness (precision and recall) as well as the prevalence of LLM code smells across 692 open-source software projects (171,194 source files). Our results show that LLM code smells affect 73.5% of the analyzed systems, with a detection precision of 91.3% and a recall of 71.8%.
arXiv:2605.22972v1 Announce Type: new
Abstract: Humans, animals, and modern machine learning models exhibit impressive abilities to learn complex behaviors and generalize these behaviors to unseen situations. This ability requires us to learn rules and regularities that allow for such generalizations. At the same time, in most complex environments, any rule will have its exceptions. How do learning systems balance between learning general regularities and memorizing exceptions? We argue that a lack of task paradigms has hindered the study of this essential ability. To address this gap, we introduce a novel task, transitive inference with exceptions, that tests for relational generalization and memorization of an exception to the relational rule. We then analytically characterize the behavior of a simple, theoretically tractable model of neural network learning (kernel ridge regression) across a broad family of representations and task parameters. We find that these models can balance between relational generalization and memorization, but unlike for transitive inference without an exception, successful generalization is sensitive to the specific representational geometry. We explain why this task is more challenging mechanistically by drawing on our analytical theory. Finally, we validate our theoretical insights in pretrained language models that are finetuned on ordered relations, finding that these models successfully generalize according to the transitive rule, but also make the kinds of systematic mistakes predicted by our theory. Overall, our theory shows how learning systems can balance between relational generalization and memorization, explains how this can go wrong, and emphasizes the need for new task paradigms designed to probe this ability.
arXiv:2605.22940v1 Announce Type: new
Abstract: Deep learning is increasingly viewed as a dynamical process in parameter space, yet many existing theories still treat training as a closed optimization system. This view is limited for real-world AI, where models operate under uncertainty, resource constraints, distribution shift, downstream decision risks, and human feedback. We propose Human-Centered Learning Mechanics (HCLM), a dynamical and information-theoretic framework for open and controlled learning systems. The central idea is that entropy regularization is useful only when the chosen entropy surrogate generates a non-degenerate information force along the optimization trajectory. Otherwise, entropy terms may produce weak, unstable, or misaligned gradients, causing the dynamics to collapse toward ordinary loss minimization. We introduce the notion of effective entropy and study tractable geometric entropy surrogates, including variance-based and log-determinant covariance proxies. The paper makes three contributions. First, it formalizes entropy regularization through effective information force and characterizes degenerate entropy regimes. Second, it derives convergence, entropy-flow, Wasserstein-gradient-flow, and noisy-representation generalization results under explicit assumptions. Third, it offers a conditional dynamical interpretation of scaling-law-like behavior as a balance between information injection, entropy dissipation, and residual risk, without claiming an unconditional derivation of empirical neural scaling laws. Controlled representation-learning experiments support the hypothesis that geometric entropy surrogates, especially log-determinant covariance entropy, induce stronger and more stable information forces than softmax-normalized entropy.
arXiv:2605.22937v1 Announce Type: new
Abstract: Inference-time scaling can reduce errors in structured query generation, but methods to allocate the compute for query code generation remains underexplored. We study Text2Cypher, where language models generate Cypher queries that execute against property graph databases. Non-executable queries constitute a distinct syntactic failure separate from semantic inaccuracy: a syntax error triggers a system-generated error message from the database. These error messages are typically discarded at inference time rather than leveraged through in-context learning (ICL). We compare two inference methods: Independent Scaling (IS), which performs memoryless resampling, and Reflection-Augmented Scaling (RAS), which conditions each new attempt on prior execution feedback via ICL. Across three Neo4j datasets and five code-specialized language models, RAS reduces the Query Execution Error Rate by 41--50% at n{=}5, outperforming IS at 32--38%. Execution errors are not merely failures to discard but actionable feedback, and structuring inference-time compute around them is a more efficient path to executability than scaling independent samples.
arXiv:2605.22923v1 Announce Type: new
Abstract: Large language models can answer questions about textbooks, lecture notes, and programming exercises more reliably when their answers are grounded in an explicit knowledge source. Retrieval-augmented generation (RAG) is a common approach: relevant fragments of a document are retrieved and inserted into the model context before answering. For mathematical and technical material, the original LaTeX source can be a better starting point than a PDF, because it contains structural information, labels, sectioning commands, macros, and authorial intent that are often lost or distorted in PDF extraction. However, LaTeX source is not automatically AI-friendly. Cross-references must be resolved, custom macros must be interpreted, exercises and examples must be identified, and author-supplied semantic metadata may be needed. This article describes a focused preprocessing approach for turning LaTeX source, together with its compiled auxiliary files and optional author annotations, into Markdown and JSONL chunks suitable for indexing in a vector database.
arXiv:2605.22902v1 Announce Type: new
Abstract: Generative Vision-Language Models (VLMs) perform well on multimodal reasoning, but how visual inputs are transformed to text remains poorly understood. Existing interpretability work on VLMs uses Sparse Autoencoders (SAEs), which decompose static residual representations and miss the functional updates that drive cross-modal interaction. We adopt a function-centric framework based on Transcoders, sparse approximations of MLP sublayers that act as a causal proxy for layer-wise computation. Applied to Gemma 3-4B-IT, the framework decomposes the model into interpretable computational pathways linking image patches to directions in token generation. Transcoder attributions produce stronger and more stable effects on visually grounded tokens under patch ablation than SAE attributions, and align better with semantically relevant image regions. A False Visual Grounding counterfactual analysis confirms that the recovered pathways are specific to vision-language interaction.Finally, we perform a structural analysis of hallucinated generations, by extracting graph-based indicators from circuit traces produced by the transcoders. A logistic classifier over these mechanistic graph features predicts hallucinations at AUC $0.68$. These results show that function-centric circuit decomposition yields interpretable and predictive accounts of multimodal computation in VLMs.
arXiv:2605.22883v1 Announce Type: new
Abstract: Current AI energy benchmarks measure consumption at the granularity of a single model invocation or training run. For classical single-turn workloads this unit remains coherent. For agentic systems - where a single user goal may trigger multi-step orchestration, tool calls, retries, and failure-recovery cycles - the invocation count is an implementation artifact rather than a task property, and inference-level normalization misrepresents the energy cost of goal completion. We present A-LEMS (Agentic LLM Energy Measurement System), a cross-layer measurement framework that redefines the unit of AI energy accounting from energy per inference to Energy per Successful Goal (EpG). EpG aggregates total workflow energy across all execution attempts, including failures and retries, normalized by successfully completed goals. A-LEMS formalizes energy attribution through a temporal boundary model, a five-layer observation pipeline mapping RAPL signals to workflow-level energy, and a reproducibility protocol binding every measurement to hardware and runtime configuration. Building on EpG, we define the Orchestration Overhead Index (OOI), isolating the energy cost of orchestration relative to linear execution under identical task criteria.
Across five reasoning and three tool-augmented task families, agentic workflows consume 4.33x higher mean energy per successful goal than linear baselines (888.1 J vs 205.3 J). This overhead is driven by orchestration structure, not inference compute. For tool-augmented tasks, OOI inverts below 1.0x: agentic execution is cheaper than linear, confirming the metric captures orchestration structure rather than a fixed upward bias.
These findings establish that energy-per-inference is insufficient for agentic AI. EpG and OOI provide the measurement foundation for accurate benchmarking, where orchestration structure is the primary determinant of energy cost.
arXiv:2605.22880v1 Announce Type: new
Abstract: As large language model (LLM)-based agents increasingly participate in online discourse, red-teaming their capacity to support political influence campaigns is critical for information integrity. In pursuit of this goal, we focus on locally deployed open-source LLMs, as opposed to frontier API-only models, given their superior alignment with the operational constraints of privacy-conscious malicious actors deployed in social media environments. We introduce an empirical red-teaming framework for measuring LLM Overton Windows (OWs), defined as the range of political opinions a model can reliably express on controversial topics, and for quantifying how simple natural-language jailbreaks expand that range. We evaluate more than 30 LLMs spanning 10 model families and five countries of origin. We find systematic asymmetries in political expressivity: open-source LLMs are typically more willing to generate left-leaning social media content, OWs tend to contract inversely to model size, and regional differences are substantial despite uneven representation in the open-source ecosystem. Jailbreak potency also varies sharply across model families, motivating a workflow for identifying effective combinations of jailbreak techniques. Taken together, our results establish a practical framework for auditing the political steerability of open-source LLMs and for helping future researchers design stronger countermeasures against LLM-enabled influence campaigns.
arXiv:2605.22864v1 Announce Type: new
Abstract: The maximum softmax probability (MSP) represents a default approach when evaluating uncertainty quantification for language model generation with structured output. Although cheap, it is often miscalibrated. Methods that probe the model's internal activations feed raw hidden states into opaque classifiers, reading activations as static snapshots and leaving implicit the layer-wise trajectory by which a representation is formed. Yet, similar endpoints can arise from very different paths, and how evidence accumulates, reinforces, or reverses across depth might reveal uncertainty that final probabilities obscure. We extract eleven scale-invariant geometric features, tracing the cumulative path of per-layer MLP updates, and feed them to a sparse linear probe. The probe outperforms MSP under selective abstention, with gains scaling with baseline miscalibration up to 21 AURC points. Because every feature has a closed-form geometric meaning, the probe's coefficients trace how and where along depth errors take shape -- which layers commit prematurely, which contradict the running state, where trajectories drift away from their endpoint.
arXiv:2605.22847v1 Announce Type: new
Abstract: The space L of linear value maps on a finite-player cooperative game G^N is finite-dimensional, and admits a canonical inner product induced by the Harsanyi-dividend decomposition of G^N. We show that this inner product is intrinsic: the same value arises from any orthonormal basis of G^N with respect to the Harsanyi inner product. Within this geometry, the subspace L^{ESL} of efficient, symmetric, linear value maps admits a clean structure theorem. The induced orthogonal stratification of L by coalition size yields a canonical linear isomorphism L^{ESL} = R^{n-1}, under which every efficient symmetric linear value map decomposes uniquely into n-1 stratified epsilons, one per coalition size. The classical egalitarian Shapley family of Joosten (1996) is precisely the diagonal slice of this R^{n-1}. The orthogonal projection of any Psi in L^{ESL} onto this diagonal yields an optimal parameter eps*(Psi) equal to the weighted mean of the stratified epsilons under an explicit probability distribution {w_a} over coalition sizes, and the goodness-of-fit R^2(Psi) equals one minus the relative weighted variance of those epsilons. The framework is a literal regression-statistics analogue of the coefficient of determination. At n=4 it produces a clean three-way classification of the standard alternatives to the Shapley value: the Banzhaf value is nearly orthogonal to the egalitarian Shapley axis (R^2 ~ 1%); the equal-surplus-division value is moderately aligned (R^2 ~ 38%); the solidarity value is almost entirely aligned (R^2 ~ 99.6%). Asymptotically R^2(ESD) -> 1, R^2(So) -> 1, and R^2(Bz) -> 1/2, the last reflecting a structural identity between the efficiency defect and the egalitarian-Shapley deviation of the Banzhaf value at every coalition size.
arXiv:2605.23065v1 Announce Type: new
Abstract: Vision foundation models are widely used as frozen backbones across many downstream tasks, making them a single point of failure under adversarial attack. We study multi-level Floyd-Steinberg error-diffusion dithering as a lightweight, model-agnostic input transformation that disrupts adversarial perturbations while preserving semantic content. Unlike prior work, which was limited to binary dithering, grayscale CIFAR-10, and a single small model trained from scratch, we evaluate across six tasks (classification, segmentation, depth estimation, retrieval, captioning, visual question answering), two model families (DINOv2, PaliGemma), and three attacks of increasing strength (PGD, MI-FGSM, SIA), as well as an adaptive attacker using a straight-through estimator. Our results show that Floyd-Steinberg dithering at intermediate quantization levels, especially when combined with post-processing blur, exceeds or matches all tested baselines, including diffusion-based denoising, with substantially less degradation on clean inputs.
arXiv:2605.23572v1 Announce Type: new
Abstract: In the competitive landscape of sponsored search, balancing retrieval quality with production latency is a critical challenge. While large retrieval models based on Small Language Models (SLMs) such as Qwen3-Embedding-4B/8B set strong upper bounds on public benchmarks, their deployment in high-throughput, latency-sensitive environments remains impractical. In this paper, we present HARNESS-LM (HLM), a three-phase training framework for transferring the capabilities of large-scale retrievers into compact, cost-efficient models. The approach comprises: (1) training a high-performance reference ("teacher") retriever by fine-tuning a billion-parameter-scale SLM; (2) aligning query representations via an L2 objective to distill knowledge into a sub-600M parameter student encoder; and (3) applying a final contrastive refinement stage to optimize the student for retrieval performance. We also present a comprehensive empirical study of key design choices, including alignment objectives, embedding dimensionality, model scale, architecture, and optimization strategies, to identify configurations that are most effective in production settings. On a real-world Bing Ads evaluation benchmark, HLM recovers over 98% of the reference retriever's precision across multiple settings, while delivering up to 27x lower online query-encoder latency and 20x higher throughput on NVIDIA A100 GPUs. Online A/B testing on Bing Ads further shows a +1% Revenue, +0.6% Impression, and +0.4% Click uplift over the current ensemble of retrievers running in production with the deployed 190M parameter model, clearly highlighting the practical efficacy of the HLM recipe in a real-world sponsored search setting.
arXiv:2605.11215v2 Announce Type: replace
Abstract: Pre-training large language models on massive GPU clusters has made hardware faults routine rather than rare, driving the need for resilient training systems. Yet existing frameworks either focus on specific parallelism schemes or risk drifting away from a failure-free training trajectory. We propose ReCoVer, a resilient LLM pre-training system that upholds a single invariant: each iteration keeps the number of microbatches constant, ensuring per-iteration gradients remain stochastically equivalent to a failure-free run. The framework is organized as three decoupled protocol layers: (1) Fault-tolerant collectives that isolate faults from propagating across replicas; (2) in-step fine-grained recovery that preserves intra-iteration progress and prevents gradient corruption; (3) versatile-workload policy that dynamically redistributes microbatch quotas across the survivors. The design is parallelism-agnostic, integrating directly with both 3D parallelism and Hybrid Sharded Data Parallel (HSDP) as a drop-in substrate. We evaluate our implementation on end-to-end pre-training tasks for up to 512 GPUs, ReCoVer successfully preserves the training trajectory from a failure-free reference despite of 256 GPUs lost spread across the run. For comparison with checkpoint-and-restart baselines, ReCoVer demonstrates $2.23\times$ higher effective throughput after successive failures. This advantage results in ReCoVer processing 74.9% more tokens at 234 GPU-hours, with the gap widening as the training prolongs.
arXiv:2605.11416v2 Announce Type: replace
Abstract: Selective layer-wise updates are essential for low-cost continued pre-training of Large Language Models (LLMs), yet determining which layers to freeze or train remains an empirical black-box problem due to the lack of interpretable guidance. To address this issue, we propose LayerTracer, an architecture-agnostic diagnostic framework that reveals the evolution patterns of layer-wise representations and stability by locating task execution positions and quantifying layer sensitivity. Analysis results reveal that deep layers act as critical regions for task execution and maintain high stability against disruptive updates. Guided by this finding, we conduct three controlled continued pre-training trials to compare diverse freeze-train strategies, demonstrating that training shallow layers while freezing deep layers consistently outperforms full-parameter fine-tuning and the opposite allocation on both C-Eval and CMMLU benchmarks. We further present a hybrid model case study, which validates that placing high-quality pre-trained modules in deep layers effectively preserves inherent knowledge of the model. This work delivers a low-cost and interpretable solution for resource-constrained teams, offering actionable guidance for layer-wise parameter allocation in continued pre-training and hybrid model construction.
arXiv:2605.13930v3 Announce Type: replace
Abstract: EEG foundation models achieve state-of-the-art clinical performance, yet the internal computations driving their predictions remain opaque: a barrier to clinical trust. We apply TopK Sparse Autoencoders (SAEs) across three architecturally distinct EEG transformers: SleepFM, REVE, and LaBraM to extract sparse feature dictionaries from their embeddings. By grounding these features in a clinical taxonomy (abnormality, age, sex, and medication), we benchmark monosemanticity and entanglement across architectures. A single hyperparameter procedure, driven by an intrinsic dictionary health audit, transfers robustly across all three architectures. Via concept steering, we introduce a "target vs. off-target" probe area metric to quantify steering selectivity and reveal three operational regimes: selectively steerable, encoded but entangled, and non-encoded. This framework exposes critical representational failures: "wrecking-ball" interventions that collapse global model performance, and clinical entanglements, such as age-pathology confounding, where it is impossible to suppress one concept without corrupting the other. Finally, a spectral decoder maps these interventions back to the amplitude spectrum, translating latent manipulations into physiologically interpretable frequency signatures, such as pathological slow-wave suppression and $\alpha$-band restoration.
arXiv:2605.07710v2 Announce Type: replace
Abstract: We present an extension of the Angluin-style learning algorithm for tree automata that incorporates deductive inference. The learning algorithm is provided with a term rewriting system that specifies properties of the target tree language (e.g., the order of subtrees under a symbol f is irrelevant). This term rewriting system is used to infer answers to some queries, which reduces the query complexity of the learning algorithm. We present examples of rewrite systems that express natural properties of tree-structured data, which yield a significant reduction in the number of queries.
arXiv:2605.23407v1 Announce Type: new
Abstract: Cyclic peptides are attractive therapeutic modalities because their closed-ring topology can improve stability and target specificity. However, de novo cyclic peptide design remains challenging for diffusion generators, as macrocyclization requires satisfying sparse, non-smooth, and compositional geometric constraints. Existing constraint-conditioned methods largely rely on inference-time guidance, which can steer samples toward desired closures but does not directly change the learned generative distribution. We propose GeoCycler, a reward-weighted diffusion alignment framework for training conditional latent diffusion models toward macrocyclization feasibility. GeoCycler introduces a type-gated stair reward that activates distance-based shaping only when prerequisite residue or linker types are satisfied, providing dense geometric feedback while avoiding misleading signals from chemically incompatible anchors. Together with positive-only reward weighting and replay-based stabilization, GeoCycler aligns a single generator across multiple cyclization topologies. On the LNR benchmark, GeoCycler improves pass@5 closure success over strong guidance-based baselines across stapled, head-to-tail, disulfide, and bicyclic settings. In particular, it improves head-to-tail success by 20.8 percentage points over CP-Composer while maintaining comparable amino-acid and backbone-dihedral statistics. These results suggest that training-time alignment to sparse geometric constraints is a promising alternative to relying solely on post hoc sampling-time correction for cyclic peptide generation.
arXiv:2605.14634v3 Announce Type: replace
Abstract: Migrating legacy C repositories to Rust promises stronger memory safety, but existing translators often work at the level of files or functions and miss architectural intent. We present RustPrint, a documentation-guided agentic framework for repository-level C-to-Rust migration. RustPrint first converts the source repository into architecture-aware documentation and treats it as a migration blueprint capturing module structure, data flow, APIs, and design rationale. Coding agents then use this blueprint to plan crates, implement modules, check compilability, reduce unsafe code, and iteratively refine the translated repository. RustPrint next compares documentation from the Rust output against the source documentation and uses mismatches as repair signals. It also translates and runs source test suites so runtime failures can guide targeted fixes. Experiments on eight real-world C repositories ranging from 11K to 84K LoC show that RustPrint compiles every target under both an open-weight (Kimi-K2-Instruct) and a closed-weight (GPT-5.4) backbone, while prior LLM-based translators (Self-Repair, EvoC2Rust) fail repository-wide. With the open-weight Kimi-K2-Instruct backbone, RustPrint exceeds an agentic Claude Code baseline on feature preservation (93.26% vs. 52.52%) and on cross-evaluation test pass rate (95.17% vs. 79.85%). These results suggest that documentation-guided coordination is a useful direction for scalable codebase migration.
arXiv:2605.15652v5 Announce Type: replace
Abstract: Vector-HaSH and the Tolman-Eichenbaum Machine (TEM) propose the hippocampal-entorhinal circuit factorizes memory via a grid-cell scaffold for compositional replay. Concurrently, human iEEG shows sharp-wave ripples gate recall and multi-hop replay fidelity decays multiplicatively. Yet, these fields lack a shared algebraic foundation. We introduce VaCoAl, an algebro-deterministic hyperdimensional memory architecture built on Galois-field linear-feedback shift registers. Its deterministic Galois-field diffusion offers a substrate-level alternative to Vector-HaSH's random projections, matching quasi-orthogonality while ensuring bit-exact reproducibility. Furthermore, the path-integral Confidence Ratio CR2 provides an algebraically tractable model for the empirically observed multiplicative replay decay. Biologically, VaCoAl's two operating regimes align with the EC-CA3 direct and EC-DG-CA3 trisynaptic pathways, explaining their 520-Myr conservation. Independent cellular evidence supports that the DG-CA3 pathway implements a biophysical homologue of Galois-field arithmetic. We also link this framework to Judea Pearl's Ladder of Causation. Reversible GF(2) binding provides the surgical algebra for the do-operator (Rung 2), and VaCoAl's dual-orthogonalizer architecture supplies the parallel substrate required for counterfactual reasoning (Rung 3). Ultimately, we prove these formal correspondences and derive testable iEEG predictions, uniting computational neuroscience, electrophysiology, and hyperdimensional computing.
arXiv:2605.17025v2 Announce Type: replace-cross
Abstract: We introduce two approaches to modeling the quantum dynamics of optical $\chi^{(3)}$ solitons. Taking an open-system viewpoint, we project the underlying quantum field into system (soliton) and residual reservoir components. The reservoir is treated as either (i) a discrete ``Lanczos supermode'' (LSM) expansion which localizes dynamics to a few-supermode basis, or (ii) a non-local environment which can be traced out by deriving a Markovian master equation (ME). Using these methods, we analyze and identify the quantum structure of both the soliton's stability and its hierarchy of perturbations. Through numerical simulations, we confirm both methods effectively capture quantum-induced soliton phase shifts in a concise few-mode (single-mode for ME) basis, and the LSM approach also captures photon loss which arises from non-Markovian dispersive couplings. As neither method is limited to the linearized regime, our approaches provide powerful computational tools to analyze complex non-Gaussian quantum dynamics of solitons where other commonly-used methods fail, providing insight into such non-perturbative regimes. We also investigate radiation that occurs in the presence of higher-order dispersion with ultrashort pulses, deriving a ME that predicts photon loss consistent with classical theory, but find that both classical and ME theory dramatically underestimate the actual amount of dissipation, which we explain in terms of dispersive coupling-induced soliton broadening.
arXiv:2605.17767v2 Announce Type: replace-cross
Abstract: We study feature learning in two-layer neural networks within the linear-width regime, where the number of hidden neurons, sample size, and input dimension scale proportionally. While recent work has analyzed feature learning via a single step of gradient descent on the first layer weights in this regime, such one-step update schemes are fundamentally limited: the update to the weights is approximately rank-one, captures only a single direction, and requires the target function to have an information exponent of one. In this paper, we go beyond one-step updates to provide a full characterization of the features learned during the \textit{second step} of gradient descent with step-sizes $\eta_1\asymp N^{\alpha_1}$ and $\eta_2 \asymp N^{\alpha_2}$ for $\alpha_1, \alpha_2 \in [0,0.5)$, where $N$ is the number of hidden neurons. We derive a spectral characterization of the updated weights, demonstrating they behave as a spiked random matrix with multiple outliers, each corresponding to a learned direction. We show that the number of the outliers is determined by the parameters $\alpha_1, \alpha_2$ through $\lfloor \frac{\alpha_2}{1/2 - \alpha_1} \rfloor$. Furthermore, by analyzing the alignment between the learned directions and the target function, we identify a gap between training with independent versus reused batches. While independent batches restrict learning to directions with an information exponent of one, batch reuse enables the second update to capture directions even when the information exponent exceeds one, provided that $\alpha_1, \alpha_2$ are chosen properly. This shows that the benefits of batch reuse, previously observed in narrow-width regimes, persist in the linear-width limit as well. By characterizing these early-phase evolutions, our work proposes a tractable framework for studying optimization and feature learning phenomenology in modern overparameterized networks.