Papers

Activation steering offers a lightweight alternative to fine-tuning for controlling large language models at inference time. Many existing steering methods implicitly optimize a log-density-ratio objective between desired and undesired activation distributions without a principled derivation. Methods with fixed steering directions can also degrade out-of-distribution (OOD) performance. We introduce Conditional Optimal Bridge for Riemannian Activation Steering (Cobras), which casts steering as a Schrödinger Bridge on the residual-stream hypersphere. This formulation yields a principled derivation of the log-density-ratio steering objective from a well-posed optimization problem. We construct a query-adaptive steering field that recovers log-density-ratio steering as a limiting case. The fitted transport also provides a support score for controlling OOD interventions. Across four models, Cobras outperforms prior steering methods in nearly all model–task settings spanning helpfulness, truthfulness, and detoxification, while largely preserving OOD performance. The code is available \href{https://github.com/arshandalili/cobras}{here}.

Finite knowledge is usually stored extensionally, one code or vector per item. We ask whether a finite collection can instead be stored intensionally, as the decoded orbit of one compact law that returns exactly to its start. For X objects, we encode item i as the i-th phase of a fixed rotation in a learned latent space and decode all phases with a shared network; the latent advances through a bank of rotations at integer harmonics of the cycle, a real discrete Fourier operator, so that R^X equals the identity and exact closure is guaranteed rather than learned. Images are a controlled carrier; looping video is the case where the phase order is the content's own temporal structure. Holding the decoder fixed and varying only the operator, a general learned operator diverges, a norm-preserving but non-periodic one degrades around the loop, and the exactly periodic operator is flat; on real images the gap widens. Capacity is then the decoder's budget: dense decoders carry a structural overhead per crisp image that no size reconciles with compression, while a small convolutional decoder on objects that share a manifold reaches crisp and compressed. A codebook control shows the generative law is free in reconstruction terms while multiplying the latent store many-fold. On seven benchmark clips, against a matched frame-index baseline, the cycle reaches equal or better fidelity at equal parameters while wrapping at machine precision, where the baseline leaves a visible seam; pinning the baseline's frequencies to loop harmonics closes its seam too, confirming that exact periodicity is the operative constraint. Finite cyclic knowledge can be stored as dynamics rather than independent instances, with exact recurrence supplied by algebra and content by a shared decoder.

This paper presents ViFA-Council, a three-stage multi-agent framework that employs multiple large language models (LLMs) to tackle two culturally complex generative tasks: image outpainting and educational story generation based on traditional Vietnamese folk paintings. Current single-model generative pipelines frequently struggle with stylistic hallucinations and cultural misrepresentations because they lack mechanisms for cross-model critique. ViFA-Council addresses this challenge by orchestrating collaboration among GPT-4o, Gemini 3.1 Pro, and Claude Sonnet 4.6. It enforces rigorous cultural constraints through structured agent deliberation. This deliberation is mediated by task-specific JSON schemas that effectively bridge natural language discussions with diffusion-based image synthesis using Banana Pro. Experiments and a user study demonstrate that structured multi-agent deliberation is a promising direction for improving cultural fidelity and narrative coherence in culturally sensitive, low-resource artistic domains. The source code and data are released at https://github.com/DanielNguyen-05/ViFA-Council.

Training data constrains optimizer geometry through the covectors visible to a declared information channel. We study how such partial information determines a full positive cometric relative to a reference and which degrees of freedom remain unidentified. Our central result resolves full-column-rank positive-definite compression under affine-invariant Riemannian geometry. The compression map is a split-Hadamard metric submetry and admits an explicit unique completion that is the affine-invariant nearest full geometry realizing a visible target and yields exact full-to-visible variational reduction. When the channel moves, the completions form a gauge-invariant rank stratification of the positive-definite cone. Its closed-form pullback pair metric separates visible-metric motion from subspace rotation through a reference-mismatch weight, yields an explicit positive-semidefinite multi-direction Gram matrix, and exposes the precise singularity of reference-valued modes. The mechanism is explained by a metric theorem equating ball submetry, attained fiber distance, and lossless reduction of every monotone radial visible decision problem. A smooth split-Hadamard theorem supplies coherent information sheets, proximal commutation, and solution-wise gradient-flow lifting. The positive-definite realization also gives closed-form prior-data shrinkage. Diagonal and block optimizer families reduce to relative-interior conic image tests with valid facial certificates, while deterministic and finite-sample bounds quantify recovery of the visible geometry and its subspace. Together these results characterize exact reduction, reference-dependent completion, and structured expressivity for the stated finite-dimensional affine-invariant model.

This work proposes a new interpretable neural operator framework, termed the Physics Informed Kernel Function Neural Operator (PIKFNO), which explicitly incorporates physics informed kernel functions derived from governing equations into the neural operator architecture. Unlike traditional neural operators such as DeepONet, which rely on deep networks to implicitly learn basis functions, PIKFNO constrains the trunk network through physics informed kernel functions, thereby aligning its operator structure with the kernel expansions used in meshless collocation methods. Two construction strategies are introduced: one learns kernel functions directly from data, where the learned kernel can be regarded as a nonsingular fundamental solution, while the other builds them through transformations of analytical fundamental solutions. Numerical experiments demonstrate that PIKFNO achieves high predictive accuracy with substantially improved interpretability and superior generalization under limited training data. The proposed framework offers a new pathway for developing efficient, physically consistent, and interpretable neural operators.

A recurring proposal in legal AI is to improve case-outcome prediction by fusing uncertainty tools (evidence graphs with belief propagation, sequential Bayesian odds updating, Dempster-Shafer combination, and conformal prediction) into one pipeline. We test this on 1,000 real European Court of Human Rights cases from LexGLUE and FairLex, predicting whether the Court found a Convention violation from the case's fact paragraphs. We compare three families across two frontier LLMs (Claude Opus 4.8 and GPT-5.5) as per-fact evidence estimators: (A) the raw LLM, (B) the LLM routed through the fusion pipeline, and (C) a term-frequency baseline through the same pipeline. Across roughly 4,750 tests we find: (1) on discrimination (AUROC around 0.83) the pipeline yields no improvement over either the raw LLM or the baseline; a frontier LLM used directly is the strongest single discriminator. (2) Naively composing an LLM with Bayesian-odds and Dempster-Shafer fusion more than doubles calibration error (ECE from about 0.16 to 0.46) via a prior-mismatch mechanism that replicates across both models. (3) Dempster-Shafer fusion is actively unsafe on long chains, committing confidently to wrong labels at below-chance accuracy; we recommend removing it. (4) The pipeline's genuine value is operational: routed through a conformal selective-prediction layer, the system decides which cases to automate and which to escalate. After removing Dempster-Shafer, recalibrating, and applying class-conditional risk control on the full 1,000-case set, the tuned engine auto-clears at 96.8 percent accuracy with 0.5 percent errors escaping and 96.3 percent caught for review, versus 85.9 / 3.8 / 72.1 for an untuned baseline. The contribution of such pipelines in law is calibrated trust, not sharper prediction.

The 3D geometry of real-world scene data is often incomplete. Mainstream methods use depth estimators to inpaint missing structure. However, their prediction results can be inconsistent with observed geometry, or unreliable on out-of-distribution data. To solve these problems, we propose Neural Depth Field (NDF). Our key insight is that a depth estimator can also be a scene-level implicit field. As an estimator, it adapts to the target domain by learning observed depth data. As an implicit field, it fits the existing geometry to maintain consistency. Under this view, NDF addresses both problems through a single test-time optimization. Experiments show that NDF produces high-fidelity and globally consistent geometry across diverse scene data, ranging from indoor scans to satellite imagery. It reduces cross-view inconsistency by 63.3% and improves inpainting accuracy by 23.1%, achieving state-of-the-art performance in 3D scene geometry inpainting. The code is available at: https://github.com/Shadow-Dream/Neural-Depth-Field.

Clinical code prediction maps unstructured discharge summaries to ICD-10-CM leaf codes in a large, sparse, and deeply hierarchical label space. Most systems treat the task as flat multi-label classification, scoring codes independently and providing limited training signal for rare labels. We propose a graph-constrained traversal policy that formulates ICD prediction as a finite-horizon decision process over a pruned code hierarchy. A single language model descends the graph level by level, selecting valid child nodes until billable leaf codes are reached. This converts extreme multi-label prediction into sparse, hierarchy-aware subset decisions while guaranteeing structurally valid outputs. On MIMIC-IV discharge summaries, our best supervised policy, SFT-1+, achieves 0.709 micro-F1 on a curated 50-code subset and 0.527 micro-F1 on the full 15,761-code space, outperforming flat baselines including CAML, LAAT, and PLM-ICD. In the full setting, SFT-1+ improves over the strongest flat baseline by 0.044 micro-F1 and 0.157 macro-F1, suggesting that graph-constrained decomposition mitigates the rare-code bottleneck. A controlled factorial study evaluates architecture, training algorithm, and data budget. Across both scales, one shared policy matches a three-specialist cascade while avoiding its context-window overflow on 28-32% of full-space test notes. Increasing supervised trajectory data is the only intervention that consistently improves performance, while GRPO reinforcement learning provides no benefit over supervised continuation with matched data. These results show that simple graph-constrained policy learning can outperform more complex flat, cascaded, and reinforcement-learning alternatives for extreme clinical code prediction.

Does a reinforcement-learning agent that earns reward learn its task's hidden state? We study this question with hidden finite automata that the agent partially controls. Because each automaton is known, we can normalize reward by the best achievable return and probe the network for the true state at every step. Together the two measurements separate failures that reward alone conflates. An agent can encode too little of a state its network could hold, or encode the state and still control poorly. Weak on-policy RL matches random play while the state probe stays at chance. State learning depends on the optimizer, the training budget, and the task's structure. Permutation automata provide a warning before training: no input symbol maps two distinct states to the same successor. On a stratified held-out set, 86 of 103 permutation automata fail the state probe, and the classification is stable across probe read-outs and recovery thresholds. Most of these failures come with weak reward. High reward without the state occurs but is rare. Non-permutation automata can also fail. Oracle-normalized reward alone therefore does not establish that the task's state was learned.

Network alignment identifies node correspondences across different networks and is a fundamental primitive in many data science applications, including social network analysis, fraud detection, and knowledge graph integration. However, state-of-the-art network alignment methods often achieve high accuracy by repeatedly constructing and updating dense matrices, sacrificing scalability in the process. To address this scalability limitation without compromising alignment accuracy, we present FastAlign, a scalable, sparsity-aware framework for optimal transport-based network alignment. Rather than introducing a new alignment model, FastAlign preserves the original OT formulation and reinterprets its computation as a set of recurring mixed sparse-dense operations. FastAlign combines sparsity-aware graph computation with domain-specific kernel fusion, including a custom SpMM kernel. Our results show that FastAlign achieves alignment quality comparable to state-of-the-art OT-based methods while substantially reducing end-to-end runtime up to 3.89x-9.45x on CPU and 2.24x-32.54x on GPU.

Brain field potentials are scale-free: their power spectra follow a $1/f^{\beta}$ law whose aperiodic exponent $\beta$ tracks cortical state, and sleep depth in particular is a shift in $\beta$. We ask whether a transformer endowed with an explicit renormalization-group (RG) inductive bias the RG-Flow Transformer, which couples ordinary self-attention to a scale-aware stream with a learnable anomalous dimension $\gamma$, block-spin coarse-graining, and an entropy-gated synchronization bridge has an advantage over a parameter-matched vanilla transformer on real, scarce EEG. Using the PhysioNet Sleep-EDF corpus with a strict leakage-free by-subject hold-out, we (i) benchmark RG-Flow against a param-matched vanilla transformer and a hierarchy-only ablation on 5-class AASM sleep staging, (ii) sweep the per-subject data budget to look for the inductive-bias crossover predicted when data are scarce, and (iii) test whether RG-Flow's learned $\gamma$ tracks the measured spectral exponent $\beta$ out-of-sample a quantity the vanilla model does not possess. Across $5$ subjects and $5$ seeds under leave-one-subject-out cross-validation, RG-Flow and the vanilla transformer are statistically indistinguishable on 5-class staging (77.3% vs 77.0% accuracy; paired $p=0.294$), and the predicted scarce-data crossover does not appear: vanilla is numerically ahead at every data-limited budget. What does separate the models is interpretability RG-Flow recovers the continuous spectral exponent out-of-sample ($\beta$-recovery $R^2 = 0.416$), a capability the vanilla architecture has no analogue for.

Regulated financial institutions operating under data-residency rules need tenant-owned language models that can run inside the institution's perimeter. This paper combines two related FAOS studies into one mechanism-and-control article. First, it reports a reduced-power proof-of-mechanism study of ontology-amplified distillation: a Qwen3.6-27B student is adapted to the Foundation AgenticOS ontology through supervised fine-tuning on frontier-teacher trajectories and ontology-grounded direct preference optimization (DPO), trained locally on a single Apple M5 Max from 47 synthetic, English-language, cross-domain preference pairs. On 40 held-out Vietnamese financial-domain tasks, the distilled student grounds 36 of 40 tasks (grounded rate 0.90; mean ontology term-coverage r_onto = 0.95 on a metric floored at 0.50), equal to the GPT-5 frontier baseline, which also grounds 36 of 40. The outcome is underpowered to establish equivalence: the paired-difference 95% confidence interval spans +/-4 tasks, and the run does not test or show the pre-registered amplification prediction that the student should exceed the frontier. Second, the paper consolidates a contextuality-audit method for enterprise-agent routing. In a separate negative-results pilot, the corrected canonical Contextuality-by-Default degree is zero for all Phase 1.3 groups in both the local-Qwen run and an explicitly labeled Gemma replication check; the useful signal is direct influence and construct coupling, not surviving residual contextuality. Together, the studies pair an ontology-grounded model-building mechanism with a governance diagnostic for deciding when apparent disagreement should trigger prompt standardization, multi-agent synthesis, or human review. The evidence supports neither deployability, safety, superiority, statistical equivalence, nor a contextuality-positive routing rule.

Typical semi-supervised learning (SSL) methods rely on distributional assumptions, and their performance degrades when these are violated. While PNU learning, a risk rewriting method, offers a distribution-free alternative, it is restricted to binary classification and its variance optimality remains unclear. In this paper, we propose a generalized framework that constructs unbiased risk estimators using linear combinations of component risks, subsuming PNU learning and extending to multiclass classification. We derive the minimum achievable variance, demonstrating our estimator can attain lower variance than PNU in asymmetric loss scenarios. Furthermore, we establish a generalization bound directly linking this variance reduction to improved learning performance. Based on these theoretical insights, we introduce two practical SSL methods that empirically match or outperform existing approaches on binary and multiclass benchmarks.

Capable language models hold what a character believes apart from what is true: told "Anna believes the cup is blue; in reality it is red," they answer blue about Anna and red about the world. Where in the computation does that separation live? We show it rests on two separable mechanisms at two positions. A generic value slot binds the attributed value. A router at the query position selects which frame, the character's belief or reality, a query reads out. Two routes fill the slot: an asserted belief, whose value the text supplies, binds in directly; a derived belief, whose value must be inferred from what the character could see, arrives by a visibility-gated lookback. A subspace trained on either route steers the other, and only the derived route depends on described visibility. The slot itself carries no belief-reality tag: intervening on it moves a reality readout as strongly as a belief one. The separation lives instead in a dissociated pair of routing subspaces, which flip a query between frames without injecting the donor's value. These results hold across three architectures, on stimuli de-confounded against theory-of-mind-benchmark shortcuts; the behavior itself emerges between 3B and 7B across five model families. This paper develops the single belief-reality axis in depth; a companion paper shows the same slot-and-router format is shared across the other non-actual contexts a sentence can open (counterfactual, fictional, temporal).

How do different components of iterative prompt optimization interact, and what happens when they are combined? We investigate this through MAGE (Memory-Augmented Goal-directed Prompt Evolution), a controlled analysis framework for studying component interaction in prompt optimization. MAGE is not proposed as a superior optimizer in absolute terms; it integrates episodic memory, multi-objective Pareto selection, and adaptive evaluation as a platform for controlled ablation. Our experiments uncover a previously unreported phenomenon, the Prompt Optimization Coupling Effect (POCE): when multiple stochastic optimization signals operate within a closed reflective loop, they interact in ways that simultaneously improve performance and amplify variance, behavior that cannot be predicted by analyzing components in isolation. Three main findings emerge. First, failure-grounded reflection is essential: methods relying only on scores (OPRO) or abstract critique (Self-Refine) fail to improve prompts. Second, MAGE achieves 46.4% versus GEPA's 34.0% on GSM8K-Hard (+12.4%, P(MAGE>GEPA)=0.998, 5 seeds on gpt-4o-mini), with comparable variance (7.3% vs. 7.0%). Third, increasing candidate diversity reveals the clearest POCE signal: expanding the candidate pool from n=3 to n=5 improves mean accuracy by +21.6% while increasing variance by 3.7x. We further validate on Llama 3.1 8B and show POCE is headroom-dependent: when the base model already achieves high accuracy, variance amplification disappears. Finally, in low-data regimes (Ntrain=30), well-designed fixed prompts outperform all reflective optimizers, indicating that scaffold choice dominates optimizer choice. Our results suggest prompt optimization systems behave as coupled stochastic processes and should be evaluated in terms of both performance and stability, not just peak accuracy.

Long-horizon physics-based simulations of battery degradation provide mechanistic insight but remain computationally expensive, limiting their use for dense exploration of operating conditions over extended cycle life. Here, we propose a hybrid physics-probabilistic learning framework for surrogate modeling of lithium-ion battery degradation trajectories at unseen charging rates. Cycle-resolved degradation data generated with a DFN/P2D electrochemical model in PyBaMM are first transformed into capacity-aligned voltage and derivative features and encoded using a Variational Autoencoder (VAE). The resulting two-dimensional latent space organizes degradation trajectories according to both cycle progression and charging protocol. A sparse multitask Gaussian process (GP) is then trained in this latent space using cycle number and C-rate as input variables, providing continuous interpolation of latent degradation dynamics together with posterior uncertainty estimates. Under protocol-level holdout evaluation, the latent-space GP accurately recovers unseen C-rate trajectories and exhibits uncertainty behavior consistent with the support of the training data. When queried at unseen interior C-rates, the model generates latent trajectories that remain coherently positioned between neighboring simulated protocols. Decoding the GP-predicted latent states through the frozen VAE decoder yields smooth voltage-capacity evolution, while Monte Carlo propagation of the GP latent posterior through an auxiliary latent to State of Health (SOH) predictor provides uncertainty-aware SOH estimates. The proposed BattVAE-GP framework therefore offers a computationally efficient and uncertainty-aware surrogate for long-horizon degradation modeling, providing a structured basis for extending battery health prediction toward richer operating conditions and future simulation-experiment fusion.

KV-cache compression methods are predominantly evaluated with the query appended to the context before compression – a query-aware protocol. Yet the economic case for a compressed KV cache is reuse: compress a document once, answer many future questions against it. In that deployment, compression must happen query-agnostic – before any question is seen. We present a matched-budget audit of six published compression methods against three trivial baselines on three open 7-9B models (144,300 paired evaluations on RULER-8192; 40,800 on LongBench; 50,000-resample paired bootstrap throughout). Everything is held fixed – model, compression ratio, instances, decoding – except the scoring rule. Three findings. (1) Query visibility changes the rankings: under the agnostic protocol, of the five audited methods that share a common attention backend, only KeyDiff beats a best-of-3 trivial baseline consistently (31 of 36 cells), and the most widely deployed method, SnapKV, loses to "keep the start and the recent window" on average (-0.066). (2) The per-method drop between the two protocols is ordered consistently with how visible the question is to each method's scoring signal, legible in its source code: from Delta=+0.198 for SnapKV (the question sits inside its 64-token observation window) down to Delta=+0.011 for KeyDiff (its score contains no query term at all).

Computed tomography (CT) is a critical imaging modality for clinical diagnosis, but reducing radiation dose inevitably introduces severe noise and structured artifacts that degrade image quality. Existing deep learning-based low-dose CT (LDCT) reconstruction methods are typically optimized for fixed dose levels or specific anatomical regions, limiting their robustness and generalization in realistic clinical settings. We propose GenDiff, a generalizable diffusion-based framework for LDCT reconstruction that jointly models continuous radiation dose and anatomical information within a unified reconstruction network. The proposed framework integrates a Dose-Anatomy Encoder to learn acquisition-aware embeddings, a dose- and anatomy-conditioned cold diffusion backbone for iterative refinement, a physics-consistency update to enforce fidelity to the CT forward model, and a Structural Prior Refinement Module (SPRM) that preserves anatomical structures while suppressing dose-dependent artifacts. Extensive experiments on multi-anatomy clinical datasets, including unseen ultra-low-dose conditions as well as out-of-distribution phantom and animal datasets, demonstrate that GenDiff consistently outperforms state-of-the-art convolutional neural network and diffusion-based reconstruction methods. The proposed approach achieves superior reconstruction quality while maintaining strong robustness across different dose levels, anatomical regions, and acquisition domains, making it a promising solution for practical low-dose CT imaging.

As the scale of large pre-trained models continues to grow, fine-tuning them under limited memory budgets has become increasingly challenging. Low-Rank Adaptation (LoRA), currently one of the most widely adopted parameter-efficient fine-tuning (PEFT) methods, mitigates this challenge by optimizing only low-rank adaptation matrices, thereby greatly reducing the number of trainable parameters. With the parameter overhead substantially reduced, the activations retained for backpropagation have emerged as the primary remaining memory bottleneck during LoRA fine-tuning. To address this, we propose CARE-LoRA, a data-aware Compressed Activation REconstruction framework. By exploiting the inherent projection structure of LoRA, CARE-LoRA replaces the full input activation with the low-rank compressed activation naturally produced by the LoRA branch. It further computes a lightweight reconstruction matrix during the forward pass with negligible additional computation cost, which is used during backpropagation to reconstruct the gradient signal, thereby keeping LoRA matrices fully trainable. Extensive experiments across diverse models and downstream tasks demonstrate that, while substantially reducing the overall memory footprint, CARE-LoRA achieves competitive or even superior performance compared with standard LoRA and representative LoRA variants. Our code is publicly available at https://github.com/fishandyu/CARE-LoRA .

This book is about the mathematical foundations of data science. 1. Introduction 2. Curses, Blessings, and Surprises in High Dimensions 3. Singular Value Decomposition and Principal Component Analysis 4. Linear Regression and Regularization 5. Graphs, Networks, and Clustering 6. Nonlinear Dimension Reduction and Diffusion Maps 7. Linear Dimension Reduction via Random Projections 8. Optimization for Data Science 9. Classification 10. A Mathematical Introduction to Deep Learning 11. Large Sample Limit of Graph Laplacians 12. Community 13. Concentration of Measure and Gaussian Analysis 14. Matrix Concentration Inequalities 15. Compressive Sensing and Sparsity 16. Low-Rank Matrix Recovery

Mirror Theory proposes that an intelligent system should be studied not only by what it represents, but by what coherent continuations it can sustain under repeated reflection. We make this claim operational through viable path entropy (VPE), a finite-budget measure of verified continuation capacity. Given a mirror state, a rollout protocol, a verifier, and a mode map, VPE decomposes bounded capability into two parts: the probability of reaching a viable continuation and the diversity of verified continuation modes reached among successful rollouts. This paper restores the full theoretical scaffold behind the measure: intuition as local underdetermining constraint, taste as invariant-selecting pressure, reflection as taste-guided resolution of underdetermination, and geometry as the learned structure that makes future reflection stable. We then instantiate the theory in language-model reasoning experiments on GSM8K. Across Qwen2.5-Instruct models, 32 sampled rollouts per problem, and two reflection horizons, increasing the token budget from 96 to 160 substantially expands verified reachability, reduces zero-reachability, increases verified-mode entropy, and improves smoothed VPE. At 160 tokens, Qwen2.5-1.5B realizes the strongest mirror horizon among the tested models, even though Qwen2.5-3B has more parameters. This shows that mirror horizon is not parameter count, but accessible verified continuation capacity under a bounded reflection protocol. The result supports Mirror Theory as a measure-level account: capability is the structure of viable continuations made reachable, not merely one-shot accuracy or pass@k.

Hyperdimensional Computing (HDC) represents symbols using high-dimensional hypervectors of dimension $D$. In hypervector decomposition, the objective is to recover $F$ constituent hypervectors, each drawn from a codebook of size $N$, from a bound target hypervector. This requires searching over $N^F$ candidate tuples, making the task computationally prohibitive at scale. Recent quantum approach provides a quadratic search advantage, but typically rely on qubit-inefficient $O(D)$-qubit hypervector representations. We propose a qubit-efficient quantum framework for HDC decomposition that reduces the representation cost to $O(\log D)$. The framework introduces logarithmic hypervector and binding encodings, together with a reversible hypervector lookup operator for circuit-level manipulation of dense hypervectors. Combined with a modified Dürr-Høyer search procedure, the method preserves $O(\sqrt{N^F})$ search complexity while substantially reducing qubit usage. Experimental results validate correct similarity computation, accurate decomposition in executable regimes, and significantly improved qubit scaling over baselines based on explicit $D$-qubit hypervector encodings, achieving up to $2{,}000\times$ fewer qubits.

Cross-encoders achieve high reranking accuracy in Retrieval-Augmented Generation (RAG) pipelines but impose quadratic inference costs that limit real-time deployment. We address this by fine-tuning LLaMA 3 (8B) as a drop-in reranker using a two-stage pipeline: supervised fine-tuning on a custom query-document relevance dataset via the Unsloth framework with LoRA adapters, followed by 4-bit quantization for efficient inference. The resulting model replaces the cross-encoder in a dual-retriever RAG pipeline combining BM25 and dense vector search. Evaluated on a domain-specific question-answering benchmark using the RAGAS framework, our fine-tuned LLaMA 3 reranker achieves gains of 14% in answer relevancy, 16% in context precision, 19% in answer similarity, and 21% in answer correctness over the cross-encoder baseline, while reducing inference overhead through 4-bit quantization. These results demonstrate that instruction-tuned LLMs can be adapted into accurate, efficient rerankers without the quadratic complexity of traditional cross-encoders.

Restricted Boltzmann machines (RBMs) represent data by shaping an energy landscape over visible and hidden configurations, but their discriminative use is fragile under out-of-distribution (OOD) inputs: samples outside the training distribution can be absorbed into one of the learned class basins rather than rejected. Here, we analyze this failure mode through the spectrum of the induced visible–visible interaction $J=WW^{T}$, where \(W\) is the visible–hidden weight matrix. Relative to a Marchenko–Pastur random-matrix reference, conventional training spreads spectral weight into many weak, bulk-compatible directions, increasing the effective rank of $J$. When auxiliary random binary images are assigned to a rejection label during training, the learned interaction undergoes effective-rank collapse: weak bulk-like modes are depleted, spectral weight concentrates into fewer dominant eigendirections, and the effective rank of $J$ approaches that of the empirical data covariance matrix. The resulting RBM rejects structured OOD image datasets while preserving MNIST classification accuracy, showing that random auxiliary exposure can reshape both the interaction spectrum and the free-energy landscape of an energy-based classifier.

Retrieval-augmented generation grounds large language models in external evidence, but most pipelines still treat retrieved passages as deterministic and mutually consistent context. In open information environments, retrieved sources may disagree because of temporal drift, source error, ambiguity, or genuine uncertainty. This paper introduces ERAG, an uncertainty-aware RAG framework that converts retrieved chunks into probabilistic evidence before generation. A lightweight evaluator extracts candidate claims and maps chunk-level support to Dirichlet evidence. A conflict-preserving Dempster-Shafer fusion rule then transfers unresolved disagreement into epistemic uncertainty rather than normalizing it away. The generator is routed to direct answering, conflict-aware answering, or abstention according to the fused uncertainty score. Experiments on CRAG, ConflictQA, and MuSiQue show that ERAG remains competitive with the strongest matched baseline on standard question answering while improving behavior under conflict. On the CRAG ambiguous subset, hallucination decreases from 45.3% for Corrective RAG to a human-calibrated estimate of 34.8%, conflict resolution increases from 35.2% to 51.2%, and expected calibration error improves to 0.122. These results suggest that evidential modeling is a practical mechanism for trustworthy information processing in foundation-model-based retrieval systems.

Tool-using large language model (LLM) agents are attractive for network operations, but tickets, alerts, logs, runbooks, and ChatOps messages can carry indirect prompt injections. We present NetInjectBench, a 130-scenario benchmark that separates untrusted artifact text, trusted policy metadata, and evaluation labels for network-operation tool use. The sample contains 40 benign, 40 weak-attack, 40 strong-attack, and 10 approved high-impact change scenarios; each is evaluated with Qwen2.5-7B, Llama3.1-8B, and Mistral-7B. Across 240 attack instances, naive execution reached an 82.50% unsafe tool-action rate. Prompt-only safety, Self-Reminder, Spotlighting, and a Two-Pass LLM Judge reduced this rate to 25.63%, 21.67%, 18.33%, and 10.00%, respectively. Static allowlisting reached 5.00% but blocked all approved changes, yielding 0.00% usefulness and 100.00% overblocking on approved cases. Under the stated metadata-integrity assumption, the metadata-aware policy gate produced 0/240 unsafe attack actions, with a 95% Wilson upper bound of 1.58%, while preserving 99.17% attack-scenario usefulness and 100.00% approved-change usefulness. The findings show that network-operation agents need execution-time authorization boundaries alongside prompt-level instruction hygiene.

Reinforcement learning (RL) has significantly enhanced the reasoning capabilities of large language models (LLMs), yet the training process remains notoriously fragile. In this work, we investigate a critical source of this instability: over-optimization, where models exploit training heuristics at the expense of generalizable reasoning. While reverse KL regularization is the standard defense against such degradation, our analysis reveals that it is often insufficient in this regime, as it fails to ensure comprehensive coverage of the reference distribution. To address this, we propose ARMOR (Anchor Rollout and Mixed Optimization for RL), a framework that shifts the paradigm from passive penalty to active sample stabilization. ARMOR comprises two key components: (1) Anchor Rollout, which leverages off-policy data from the reference policy to preserve established solution patterns; and (2) Mixed Optimization, which reformulates the policy objective to enable controlled exploration without relying on auxiliary losses. Extensive experiments on reasoning benchmarks validate that ARMOR effectively mitigates validation collapse, enabling sustained performance improvements over extended training horizons.

This paper presents a data-driven method for modeling the pressure response of a hydraulic clutch control circuit. The system consists of a variable-force solenoid, accumulator, pressure regulator valve, and latch valve, and exhibits nonlinear behavior caused by hysteresis, latch transitions, and actuator dynamics. A baseline model using commanded current variables captured the general pressure response but failed to represent hysteresis and latch behavior accurately. The input vector was therefore extended with current derivative information, and several classifiers were tested to separate latch-related operating regimes before fitting Gaussian Process regression models to the resulting partitions. Nonlinear SVC and gradient boosting produced the highest latch-classification accuracy, and nonlinear SVC was selected for the final local-regression pipeline. The proposed approach was evaluated on unseen ramp-rate data and compared against a physics-based Amesim model. The machine-learning model reproduced the measured pressure response and hysteresis behavior more accurately than the physics-based simulation for the tested operating conditions. These results suggest that machine-learning plant models can complement physics-based hydraulic models during hardware development and controller calibration when representative test-stand data are available.

Large language models (LLMs) have emerged as a powerful tool for retrieving knowledge through seamless, human-like interactions. Despite their advanced text generation capabilities, LLMs exhibit hallucination tendencies, where they generate factually incorrect statements and fabricate knowledge, undermining their reliability and trustworthiness. Multiple studies have explored methods to evaluate LLM uncertainty and detect hallucinations. However, existing approaches are often probabilistic and computationally expensive, limiting their practical applicability. In this paper, we introduce diversion decoding, a novel method for developing an LLM uncertainty heuristic by actively challenging model-generated responses during the decoding phase. Through diversion decoding, we extract features that capture the LLM's resistance to produce alternative answers and utilize these features to train a machine-learning model to develop a heuristic measure of the LLM's uncertainty. Our experimental results demonstrate that diversion decoding outperforms existing methods with significantly lower computational complexity, making it an efficient and robust solution for evaluating hallucination detection.

Partial differential equations (PDEs) are foundational to modeling in science and engineering, but constructing reliable numerical solvers remains labor-intensive, demanding expert knowledge of discretization schemes, stability conditions, and boundary treatments. Recent work has begun to frame PDE solving as a code-generation task for large language models (LLMs), yet existing approaches operate primarily at inference time: relying on prompting, debugging, self-refinement, and test-time scaling rather than adapting the model itself. In parallel, reinforcement learning with verifiable rewards has emerged as a post-training paradigm for code and math reasoning, but its verifiers are typically binary: a compiler runs, or a test passes. Such signals discard the graded structure of scientific correctness, where two solvers may both execute and yet differ in solution accuracy by orders of magnitude. In this work, we introduce RLVP: Reinforcement Learning with Verifiable Physics, an RL post-training framework for multi-PDE solver code generation. RLVP addresses this verifiability gap with a hybrid verifier: hard program-validity checks ensure executability, while continuous physics rewards score function-space accuracy and PDE-residual consistency. A single policy is post-trained across diverse PDE families spanning hyperbolic, parabolic, elliptic, and incompressible-flow systems. RLVP improves over both pre-trained and supervised-only baselines on PDE benchmarks, and shows zero-shot improvement transfer to held-out PDEs. We show that a smaller LLM post-trained with RLVP can outperform prompting a frontier model on in-distribution PDE solver generation. The trained policy shows evidence of compositionality in numerical motifs: it recombines stencils, time-stepping schemes, and boundary-handling primitives learned from the PDEs used in training into generated solvers for unseen PDE problems.