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01.
arXiv (quant-ph) 2026-06-19

On the significance of Wigner's Friend in contexts beyond quantum foundations

arXiv:2402.08727v3 Announce Type: replace Abstract: There has been a surge of recent interest in the Wigner's Friend paradox, sparking several novel thought experiments and no-go theorems. The main narrative has been that Wigner's Friend highlights a counterintuitive feature that is unique to quantum theory, and which is closely related to the quantum measurement problem. Here, we challenge this view. We argue that the gist of the Wigner's Friend paradox can be reproduced without assuming quantum physics, and that it underlies a much broader class of enigmas in the foundations of physics and philosophy. To show this, we first consider several recently proposed Extended Wigner's Friend scenarios, and demonstrate that some of their implications for the absoluteness of observations can be reproduced by classical thought experiments that involve the duplication of agents. Crucially, some of these classical scenarios are technologically much easier to implement than their quantum counterparts. Then, we argue that the essential structural ingredient of all these scenarios is a feature that we call "Restriction A": that a physical theory cannot give us a probabilistic description of the observations of all agents. Finally, we argue that this difficulty is at the core of other puzzles in the foundations of physics and philosophy, and demonstrate this explicitly for cosmology's Boltzmann brain problem. Our analysis suggests that Wigner's Friend should be studied in a larger context, addressing a frontier of human knowledge beyond quantum foundations: to obtain reliable predictions for experiments in which these predictions can be privately but not intersubjectively verified.

02.
arXiv (CS.AI) 2026-06-18

Agentra: A Supervisable Multi-Agent Framework for Enterprise Intrusion Response

arXiv:2606.18325v1 Announce Type: cross Abstract: Enterprise intrusion response still depends on static playbooks and analyst-driven triage, creating delay between alert generation and containment. We present Agentra, a supervisable multi-agent Intrusion Response System (IRS) framework that converts alerts from IDS, EDR, and XDR platforms into structured incident response plans grounded in MITRE ATT&CK, MITRE D3FEND, and NIST CSF 2.0. Agentra decomposes response reasoning across role-scoped agents, validates proposed plans through a bounded Planner–Validator review loop, screens retrieved threat intelligence through a Moderator security gateway, gates actions through an Action Catalog and risk score, and records decisions in an append-only audit log. We evaluate Agentra against a static OASIS CACAO v2.0 cyber-playbook baseline on a 120-event corpus drawn from ThreatHunter-Playbook, Splunk BOTSv3, and DARPA OpTC. The strongest configuration improves FP-aware IRS F1 from 0.61 to 0.84 and restores the projected harmful-action rate to the static baseline level of 0.0% after Planner-only configurations introduce unsafe overreaction. These results indicate that multi-agent response planning can improve ontology-grounded IRS coverage while preserving analyst approval and auditability.

03.
Nature (Science) 2026-06-18

Daily briefing: The proteins that protect us from deadly mutations

作者:

Proteins that ‘buffer’ the effects of mutations could help to treat diseases such as cancers. Plus, goats can follow human voices and the battle over a key ocean observatory project in the United States. Proteins that ‘buffer’ the effects of mutations could help to treat diseases such as cancers. Plus, goats can follow human voices and the battle over a key ocean observatory project in the United States.

04.
arXiv (CS.AI) 2026-06-17

Symplectic Transversality and Endpoint Green Estimates for Finite-Horizon Pontryagin Systems

arXiv:2606.17762v1 Announce Type: cross Abstract: We study horizon-uniform local branches of finite-horizon discrete-time Pontryagin boundary value systems after smooth control elimination. The central input is a two-point endpoint inverse for the linearization. We verify this inverse from scaled stable–unstable boundary transversality, prove the associated endpoint-corrected Green estimate, and combine it with weighted contractions to obtain existence, uniqueness, Lipschitz dependence, and first-order expansions with constants independent of the horizon. The framework covers smooth nonlinear endpoint maps, including the original Pontryagin rows that fix the initial state and couple the terminal costate to the terminal state. Symplectic and Riccati criteria verify the inverse hypothesis at the level of the matrix data; in particular, every stabilizable linear-quadratic system with invertible dynamics and definite weights is covered, including noncommuting coupled data. A numerical section illustrates the certificates and the horizon-uniform first-order expansion.

05.
arXiv (CS.CL) 2026-06-11

External Experience Serving in Production LLM Systems: A Deployment-Oriented Study of Quality-Cost Trade-offs

Production LLM systems accumulate reusable operational experience, but the practical deployment issue is not merely whether such experience can help. It is how different serving strategies trade off quality against online cost under realistic constraints. Injecting external experience can improve task quality, yet it also increases prompt burden, latency, and serving pressure. We study external experience serving as a deployment-oriented quality-cost trade-off problem. We evaluate this question in a real production moderation setting, with tool-use and GPQA as supporting contrast tasks that expose different output-cost regimes. We compare no-experience baselines, random experience controls, global prompt injection, and retrieval-based selective injection, and analyze both task quality and serving cost. The results show that, once experience becomes case-dependent, selective retrieval provides a stronger operating point than unconditional global injection. They further show that retrieval quality matters more than simply increasing Top-$K$, and that the same serving policy can exhibit substantially different cost-benefit profiles across short-output and decode-heavy regimes. These findings suggest that external experience is best treated as a selective, cost-aware serving decision rather than as a universal add-on. Overall, in the settings studied here, external experience pays off only when both the serving interface and the task-specific cost structure make its quality gains worth the online cost.

06.
arXiv (CS.LG) 2026-06-12

Optimal Spatio-Temporal Decoupling for Bayesian Conformal Prediction

arXiv:2605.00432v2 Announce Type: replace Abstract: Online conformal prediction must balance fast adaptation to distribution shift against stable coverage: feedback-driven methods react quickly but become volatile, while strongly discounted Bayesian methods lag and inflate intervals at tight coverage. We introduce State-Adaptive Bayesian Conformal Prediction (SA-BCP), which forms the predictive quantile as a gated convex combination of long-term temporal inertia and local spatial evidence from a kernel density estimate, controlled by a single interpretable evidence threshold $K$. We establish three results: (i) asymptotic marginal validity of the resulting intervals; (ii) a closed-form expression for the MSE-optimal threshold, $K^*_{\mathrm{MSE}}=\alpha(1-\alpha)/M^{\mathcal{T}}$, trading the coverage-indicator (Bernoulli) variance against the temporal structural bias $M^{\mathcal{T}}$; and (iii) a rolling-origin procedure for selecting $K$ online – consistent under stationarity, with $O(\sqrt{T\log N})$ regret against the best fixed $K$ and, for a segmented variant, a sublinear dynamic-regret bound under bounded drift. Across four financial-volatility and weather datasets, three target coverage levels, and eight baselines (including the strongest recent conditional-quantile methods, SPCI and KOWCPI), SA-BCP attains at-or-above-nominal coverage in most settings while producing substantially sharper intervals – up to roughly $3\times$ lower Winkler score than discounted Bayesian CP at the tightest coverage – and a coverage-matched audit confirms these efficiency gains are not an artifact of under-coverage. We disclose one principal limitation: a volatility-specialized conformal-GARCH competitor remains more efficient on its home volatility-base series, though it does not transfer across domains.

07.
arXiv (CS.CL) 2026-06-15

A Computational Audit of Demographic Association Encoding in ClinicalBERT Language Predictions

Transformer-based clinical language models are increasingly integrated into high-stakes clinical decision support pipelines, yet the computational mechanisms through which demographic associations encoded in medical documentation propagate into model probability distributions remain empirically underspecified. We present a systematic computational audit of representational bias in ClinicalBERT (Alsentzer et al., 2019), a BERT-based model pretrained on MIMIC-III discharge summaries, employing two complementary probing methodologies: Log Probability Bias Analysis (LPBA), which quantifies demographic descriptor-induced shifts in masked token probability distributions across behavioral and evaluative semantic categories, and Masked Language Model-based analysis (MLM), which probes internal representational structure for demographic agency attribution encoding across 98 real clinical sentence templates and eight intersectional race-gender combinations. Corpus frequency analysis operationalizes the distinction between statistical disparity and bias amplification by benchmarking model outputs against empirical term frequencies in the MIMIC-III training corpus. Of 32 statistically significant findings, 65.6% contradict observed corpus distributions, rising to 80% for Black patients and 87.5% for agency attribution under MLM probing, providing direct empirical evidence that representational bias in ClinicalBERT operates predominantly through model-internal amplification rather than training data inheritance. Keywords: natural language processing, clinical documentation, algorithmic auditing, representational bias, health equity 1

08.
arXiv (CS.AI) 2026-06-16

Entropy-Gated Latent Recursion

arXiv:2606.16620v1 Announce Type: cross Abstract: Inference-time scaling has become the dominant lever for improving language-model reasoning, but existing methods derive rollout diversity from a single source: stochastic token-level sampling. We argue that this single-axis sampling space is fundamentally limiting, and identify a second, fully deterministic and complementary axis: the layer span $L$ at which a frozen model's top decoder layers are recursively re-applied at high-uncertainty tokens. Different choices of $L$ produce distinct rollouts that solve different subsets of problems, with no stochasticity. We instantiate this axis through Entropy-Gated Latent Recursion (EGLR), a training-free decoding procedure that re-applies the top-$L$ layers for at most $K_{\max}$ iterations until the next-token distribution converges. Combined with $T$ temperature samples, EGLR turns a single-axis stochastic rollout pool into an $L\times T$ Cartesian sampling space at almost the same per-rollout cost. We characterize this space across $8$ instruction-tuned models and $6$ math reasoning benchmarks, and show that the $L$-axis is genuinely complementary to temperature: on MATH-500 with Qwen2.5-3B-Instruct, the joint $L\times T$ oracle reaches $91.6\%$, $+8.2$ percentage points beyond the temperature-only oracle ($83.4\%$) and $+10.4$ points beyond the layer-only oracle ($81.2\%$), confirming that the two axes capture genuinely complementary problems. The expanded rollout pool provides richer per-prompt candidates for any downstream procedure that consumes rollouts, including self-consistency, best-of-$N$ with verifiers, and group-relative RL training (GRPO), opening a new direction for inference-time scaling that does not rely on stochastic noise.

09.
arXiv (CS.CL) 2026-06-12

MiniPIC: Flexible Position-Independent Caching in <100LOC

Retrieval-augmented and agentic workloads repeatedly prefill recurring predictable structured inputs (which we call "spans") such as documents and code files. Yet, prefix caching in engines such as vLLM cannot reuse their KV entries unless they share identical prefixes with another request, while Position-Independent Caching (PIC) implementations within production-grade inference servers typically either require substantial server code changes or keep KV state outside the server, incurring host-to-device transfer overhead. We present Minimalistic PIC (MiniPIC): a minimal, flexible and fast vLLM design built from two ingredients: positional-encoding-free KV cache and user-controlled cache-reuse primitives. MiniPIC stores unrotated K vectors in the KV cache, applies RoPE to K tiles inside attention using per-request logical positions, and exposes three user-facing and token-level primitives: block-aligned padding, span separator (SSep), and prompt depend (PDep), that modify hashing behavior and effective block-level causal attention structure. With fewer than 100 lines of core-engine changes plus a custom attention backend, these primitives are sufficient to realize multiple PIC methods, including Block-Attention, EPIC, and Prompt Cache, within the same running vLLM instance, while natively integrating with KV cache CPU offload implementations. On 2WikiMultihopQA, MiniPIC with interleaved scheduling improves prefill throughput by 49% over baseline vLLM, reduces cached-span time-to-first-token by up to two orders of magnitude, preserves the linear prefill scaling of uncached spans, and incurs only 5.7% worst-case overhead.

10.
arXiv (CS.CL) 2026-06-16

Evaluative Judgement in Teaching AI-based Translation: A Class-room Case Study of AI-Mediated Translation and Post-Editing

作者:

Drawing on 23 anonymized student pro-jects from a fourth-year Machine Transla-tion and Post-editing course in a BA-level translation programme, this paper exam-ines how structured comparison of gen-eral-purpose LLMs and online MT sys-tems can elicit evaluative judgement in AI-mediated translation. Students translat-ed short specialised English Wikipedia texts into Catalan or Spanish, generated four system outputs, evaluated them using automatic metrics and human adequa-cy/fluency assessment, selected one output for post-editing, and justified their deci-sion in written reports. Descriptive counts are reported for all 23 projects, while qualitative interpretation is based on the 22 cases accompanied by written reports. Results show that students did not treat automatic metrics as final authority: final post-editing selections often diverged from metric rankings and were justified through adequacy, fluency, terminology, naturalness, and expected post-editing ef-fort. The study therefore does not bench-mark systems under controlled conditions; it analyses how students justified system choice within an authentic classroom as-signment.

11.
arXiv (CS.AI) 2026-06-17

Closing the Feedback Loop: From Experience Extraction to Insight Governance in Verbal Reinforcement Learning

arXiv:2606.17591v1 Announce Type: new Abstract: Training-free verbal reinforcement learning enables LLM agents to learn from world feedback – objective signals such as dynamic task outcomes, market returns, or demand forecasts – by extracting verbal rules from experience and injecting them as context, updating the agent's behavior without parameter changes. However, in non-stationary environments these agents face a retention-forgetting dilemma: retaining stale insights causes negative transfer, while discarding them causes catastrophic forgetting when conditions recur. We identify four requirements for navigating this dilemma – outcome-driven evaluation, persistent structured evidence, non-monotonic knowledge lifecycle, and compositional governance – and show that existing methods invest heavily in experience extraction while underinvesting in insight governance. We propose a three-layer architecture – rules, evidence, and skills – connected by a feedback-driven curation loop that closes the governance gap. Rules capture distilled experience from world outcomes; evidence logs track each rule's reliability across episodes; skills govern which rules to apply, how to resolve conflicts, and when to abstain. On financial forecasting as a case study, where world feedback is naturally abundant, noisy, and non-stationary, we show that the same accumulated experience either degrades performance below the zero-shot baseline or dramatically improves accuracy and risk-adjusted returns, depending on whether the curation loop is present.

12.
arXiv (CS.LG) 2026-06-12

Deep Sleep Classification via EEG Signal Criticality: A Passive BCI Approach for Sleep-Improvement Neurofeedback

arXiv:2606.13017v1 Announce Type: cross Abstract: Automated sleep staging is a fundamental application of passive Brain-Computer Interfaces (pBCI), decoding spontaneous neural states to enable closed-loop interventions independent of user intent. This study evaluates criticality features derived from Detrended Fluctuation Analysis (DFA) for the specific identification of deep sleep (N3). We analyzed $347,232$ EEG epochs from $290$ older women using UMAP manifold learning to visualize state transitions. Subsequently, six classifiers were benchmarked via 10-fold cross-validation, using balanced accuracy to determine the optimal "state-sensing" engine for neurofeedback.Naive Bayes achieved the highest mean balanced accuracy ($87.17\% \pm 0.24\%$), significantly outperforming a fully connected deep neural network (FNN: $81.58\%$) and Random Forest ($80.97\%$). Linear models (LDA: $57.21\%$; SVM: $51.01\%$) performed poorly, indicating that DFA-derived criticality features reside on a distinct, non-linear manifold. Probabilistic decoding of EEG criticality provides a high-accuracy sensing mechanism for pBCIs. This robust classification pipeline supports the development of state-dependent neurofeedback, such as targeted auditory stimulation, to enhance cognitive recovery.

13.
arXiv (CS.AI) 2026-06-18

TLA-Prover: Verifiable TLA+ Specification Synthesis via Preference-Optimized Low-Rank Adaptation

arXiv:2606.06133v2 Announce Type: replace-cross Abstract: TLA+ is a formal specification language for verifying distributed systems and safety-critical protocols. Large language models (LLMs) frequently produce TLA+ specifications that fail the TLC model checker for semantic reasons. Across 25 LLMs, the best public baseline is 26.6% syntactic parse and 8.6% semantic model-check. We present TLA-Prover, a 20-billion-parameter model for TLA+ specification synthesis. Training combines supervised fine-tuning (SFT) on verified examples with repair-based group-relative policy optimization (GRPO). In the GRPO stage, the model learns to fix its own rejected specifications. We also train a direct preference optimization (DPO) variant from the same SFT checkpoint as an ablation. TLC provides the reward signal directly, with no learned reward model. Four tiers grade each output: Bronze (parses), Silver (no warnings), Gold (passes TLC), and Diamond. To reach Diamond, the model's correctness property is automatically altered in a small way; TLC must then detect a violation. If TLC still passes, the property was always-true and contributes nothing; the output fails Diamond. TLA-Prover reaches 9/30 (i.e. pass@1 = 30%) at both Gold and Diamond on a held-out 30-problem benchmark. This is roughly 3.5x the 8.6% untuned baseline. The DPO variant reaches 20% at Diamond. Gold and Diamond coincide at every checkpoint; this prevents the trivial-property failure mode.

14.
arXiv (CS.AI) 2026-06-16

The Faithfulness Gap: Certifying Semantic Equivalence Between Natural-Language and Formal Mathematical Statements

arXiv:2606.16541v1 Announce Type: new Abstract: Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by faithfulness: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended. We introduce Bidirectional Provability Fingerprinting (\bpf{}), a framework that certifies faithfulness by characterizing each candidate through its forward and backward consequence neighborhoods in the ambient theory and matching these against probes derived from the natural-language statement. We further introduce four novel components: (i) Counterfactual Probe Generation (\cpg{}), a contrastive procedure that synthesizes probes targeting specific drift directions; (ii) the Equivalence Spectrum, a continuous faithfulness score that replaces brittle binary verdicts; (iii) Adaptive Probe Budget Allocation (\apba{}), an information-theoretic budget router; and (iv) Faithfulness-Guided Decoding (\fgd{}), which uses \bpf{} signals as a reward during autoformalization. We prove a drift detection theorem and a PAC-faithfulness result establishing that the equivalence class of a natural language statement is learnable from $\mathcal{O}(\log(1/\delta)/\varepsilon)$ probes under mild assumptions. We release \driftbench{}, a benchmark of $2{,}183$ NL/Lean~4 pairs with controlled drift labels across six subfields of mathlib4. \bpf{}\,+\,\cpg{} detects $89.6\%$ of drifted formalizations at a $3.0\%$ false-positive rate-against $41.2\%$ for typecheck and $63.3\%$ for LLM-judge baselines, and \fgd{} reduces the rate at which a state-of-the-art autoformalizer emits drifted statements by $47\%$. https://pmlrbd.github.io/BPF/

15.
arXiv (CS.CL) 2026-06-11

Factions Within, Uncertain Across: Within-Document Reader Sub-Groups in Social Highlighting

When many people highlight the same document, is the crowd a single consensus, or is it internally structured into reader sub-groups that mark different things – and is that structure a stable property of a reader or of the document? Building on prior work showing an individual's within-document highlighting signal is a whisper while individuality lives in selection, we ask the group-level question on a co-readership platform using a margin-preserving curveball null. Experiment 1: within a document, readers form strong sub-groups – pairs agree far beyond what shared salience, mark density, and sentence popularity predict (nearest-neighbour agreement z=+6.3, significant in 88% of documents). Under an eight-block region-preserving null, shared engagement with the same coarse regions of the document accounts for about 40% of this excess; the majority survives as finer reader-specific agreement (z=+3.6, 77% significant). So the within-document crowd is, in a descriptive sense, factional. Experiment 2: is that grouping a stable reader trait? Here we are honest about power. The cross-document split-half reproducibility of a pair's agreement is near zero pooled (+0.078 and 0.000 in two separately drawn samples), and a power calibration shows the test is informative only for pairs that co-read many documents. In the only informative high-overlap subset (k>=4), point estimates are positive but small-sample, imprecise across the separately drawn samples, never significant, and attenuate under the region-preserving null. We therefore leave cross-document stability unresolved: the data is consistent with anything from situational grouping to a weak-to-moderate stable reader trait. The crowd is factional within a document; whether its factions follow the reader across documents is, honestly, beyond our reach.

16.
arXiv (CS.AI) 2026-06-18

Sparsity Curse: Understanding RLVR Model Parameter Space from Model Merging

arXiv:2606.18521v1 Announce Type: cross Abstract: Reinforcement Learning with Verifiable Reward (RLVR) has emerged as a powerful post-training paradigm that surpasses Supervised Fine-Tuning (SFT) in eliciting reasoning intelligence and resisting catastrophic forgetting. Recent studies further reveal that RLVR induces highly sparse and off-principal parameter updates compared to SFT. This naturally raises the question: does such sparsity make RLVR models more amenable to model merging? If so, model merging would offer a scalable, training-free path to aggregate diverse reasoning capabilities from independently trained RLVR models. Surprisingly, we find the opposite, uncovering a sparsity curse: the sparse RLVR updates are spread farther apart in parameter space, forming near-orthogonal shortcuts that make aggregation inherently fragile. This is likely rooted in the stochasticity of RL optimization and the diversity of emergent reasoning patterns. Unlike SFT models that converge to shared, flat basins and merge naturally, RLVR models suffer severe degradation under standard merging methods. Through systematic empirical analysis of the update geometry, we characterize the mechanisms behind this failure and propose Sensitivity-aware Resolving Merging (SAR-Merging), a merging recipe tailored for the unique structure of RLVR parameter spaces. SAR-Merging resolves conflicts in overlapping update regions via Fisher Information-based sensitivity arbitration, followed by magnitude-aware sparsification and rescaling to preserve fragile reasoning pathways. Experiments on mathematical and coding benchmarks demonstrate that SAR-Merging substantially outperforms existing merging methods on RLVR models, enabling both single-task enhancement and multi-capability fusion.

17.
arXiv (CS.LG) 2026-06-11

A Riemannian Approach to Low-Rank Optimal Transport

arXiv:2606.12120v1 Announce Type: new Abstract: Low-rank optimal transport (OT) mitigates the quadratic scaling of classical solvers, yet existing approaches rely heavily on first-order mirror-descent updates that require careful hyperparameter tuning and ignore the optimization landscape's curvature. To address these limitations, we propose a unified Riemannian geometric framework for low-rank OT, modeling balanced and unbalanced rank-$r$ positive factored couplings as novel smooth embedded submanifolds of the positive orthant. By equipping these manifolds with the Fisher-Rao product metric, we derive tractable formulations for Riemannian projectors, retractions, and Hessian-vector products. Our cost-agnostic framework seamlessly extends to linear OT, Gromov-Wasserstein (GW), fused GW, and their unbalanced counterparts. For balanced OT, our geometric ingredients are computed via efficient conjugate-gradient and iterative Bregman updates. For the unbalanced OT, our operations elegantly reduce to closed-form scalings, completely eliminating inner iterative loops. In both regimes, per-iteration complexity scales linearly with dataset size, and we provide a rank-sufficiency certificate for global optimality verification. Extensive experiments across a range of problem sizes demonstrate that our regularization-free first- and second-order solvers achieve faster convergence and superior performance over existing state-of-the-art low-rank OT solvers.

18.
arXiv (math.PR) 2026-06-18

Functional central limit theorems for non-local branching Markov processes

arXiv:2502.19382v2 Announce Type: replace Abstract: The aim of this paper is to study the fluctuations of a general class of supercritical branching Markov processes with non-local branching mechanisms. We establish functional central limit theorems and show that the limiting behaviour falls into three regimes, determined by the size of the spectral gap associated with the first-moment semigroup of the branching process. The main novelty is to develop a unified functional fluctuation theory for spatial branching Markov processes with non-local reproduction, allowing a general finite-dimensional spectral structure for the first-moment semigroup, including non-simple leading eigenvalues and nilpotent Jordan-type components. In doing so, we extend the classical small, critical and large fluctuation trichotomy beyond the finite-type and local spatial settings, and obtain limiting processes that capture the covariance structure induced by non-local offspring displacement.

19.
arXiv (quant-ph) 2026-06-16

Non-Hermitian Crystalline Braid Topology from Hermitian Projection: A Zero-Mode Resonance Mechanism

arXiv:2606.06626v2 Announce Type: replace-cross Abstract: Non-Hermitian topological phases are typically engineered through gain and loss, nonreciprocity, or interaction with an environment. Here we show that they can instead emerge purely by projecting a fully Hermitian, topologically trivial parent lattice onto an embedded subsystem. The mechanism is general: when a zero mode of the eliminated degrees of freedom couples to the retained subsystem, the embedding self-energy develops a pole, the zero-frequency description becomes singular, and topology is carried by the finite-frequency projected Green's function. We realize the mechanism exactly in a trivial nearest-neighbor square lattice with an embedded one-dimensional zig-zag brane. In the periodic transverse geometry, the parity of the eliminated complement selects the outcome: even sectors reduce to a regular Schur complement and yield conventional SSH-type descendants, whereas odd sectors host a sublattice-imbalance zero mode and follow the resonant route. There, the complex bands braid through isolated finite-frequency exceptional points (EPs), while a parity symmetry inherited from the embedding, together with $\mathrm{TRS}^{\dagger}$, induces conjugated pseudo-Hermiticity and quantizes the complex Berry phase. The stable bulk invariant of the nondegenerate phases is this quantized complex Berry phase; adjacent sectors are separated by parity-paired exceptional points whose half-integer vorticities encode the local exchange of complex-energy strands.The absence of the non-Hermitian skin effect ensures that the invariant is defined directly on the ordinary Brillouin zone. A topolectrical implementation of the projected response predicts momentum-resolved transmission minima at the exceptional-point transition frequencies together with a characteristic low-frequency resonant admittance, providing an experimentally testable signature of the mechanism.

20.
bioRxiv (Bioinfo) 2026-06-11

Integrating Spatially Adjusted Protein Summaries for Survival Prediction in Spatial Proteomics

Recent advances in spatial proteomics, particularly imaging mass cytometry, enable the measurement of protein expression at the single-cell level while preserving a spatial context. Conventional survival analyses, however, typically rely on patient-level averages of protein intensities and therefore overlook spatial heterogeneity and tissue architecture. To address this limitation, we introduce a framework that incorporates spatial information into survival modeling by generating spatially adjusted protein summaries (SAPS). In this approach, cell-level protein intensities within each patient are modeled using spatial spline regression to capture spatial trends. From these models, we extract two complementary features: a spatially adjusted mean expression and a residual variance that reflects cell-to-cell variability unexplained by spatial effects. These summaries are then incorporated into Cox proportional hazards models in combination with clinical covariates. In simulation studies, our proposed framework achieved improved predictive performance compared to other alternative methods. The application of the method to breast cancer imaging mass cytometry data indicate that spatially adjusted summaries may enhance survival prediction and reveal biologically interpretable spatial protein patterns, suggesting high translational potential. This methodology offers an efficient means of translating complex spatial proteomics data into patient-level features, providing both improved survival prediction and new insights into the role of spatial heterogeneity in cancer outcomes.

21.
arXiv (math.PR) 2026-06-12

The Lov\'{a}sz Local Lemma: Foundations and Applications

作者:

arXiv:2603.07245v5 Announce Type: replace-cross Abstract: The Lov\'{a}sz Local Lemma (LLL) is a central tool in probabilistic combinatorics, providing a sufficient condition under which a finite collection of undesirable events with limited dependencies can be simultaneously avoided with positive probability. This paper offers a self-contained expository treatment of the lemma and its strengthened versions, emphasizing mathematical foundations, conceptual clarity, and applications. We begin with a pedagogically motivated proof of the LLL based entirely on unconditional probability inequalities. Particular attention is given to the symmetric form of the lemma and several subsequent strengthenings. The paper also discusses a variety of classical applications of both the symmetric and asymmetric forms of the LLL in combinatorics and graph theory, including bounds for the edge-disjoint paths problem, satisfiability of Boolean formulas in conjunctive normal form, lower bounds on diagonal and off-diagonal Ramsey numbers, hypergraph coloring results, structural properties of directed graphs, and acyclic graph colorings. Additional observations and refinements are provided throughout. We also introduce the algorithmic framework of Moser and Tardos, highlighting its constructive counterpart to the LLL, together with an introduction to the entropy-compression principle. The lopsided LLL, a refinement of the LLL, is presented along with an application to the Latin transversal problem. We further discuss the cluster-expansion lemma and its relation to the LLL, and present an alternative treatment of the Latin transversal problem from the cluster-expansion perspective that yields an improved result. The paper concludes with a high-level overview of the iterated LLL, also known as the semi-random method.

22.
arXiv (CS.AI) 2026-06-11

On the Geometry of On-Policy Distillation

arXiv:2606.07082v2 Announce Type: replace-cross Abstract: On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

23.
arXiv (CS.CL) 2026-06-11

Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems

Reinforcement Learning (RL) algorithms sample multiple n>1 solution attempts for each problem and reward them independently. This optimizes for pass@1 performance and prioritizes the strength of isolated samples at the expense of the diversity and collective utility of sets of samples. This under-utilizes the sampling capacity, limiting exploration and eventual improvement on harder examples. As a fix, we propose Pass-at-k Policy Optimization (PKPO), a transformation on the final rewards which leads to direct optimization of pass@k performance, thus optimizing for sets of samples that maximize reward when considered jointly. Our contribution is to derive novel low variance unbiased estimators for pass@k and its gradient, in both the binary and continuous reward settings. We show optimization with our estimators reduces to standard RL with rewards that have been jointly transformed by a stable and efficient transformation function. While previous efforts are restricted to k=n, ours is the first to enable robust optimization of pass@k for any arbitrary k

24.
arXiv (CS.CL) 2026-06-17

In-Context Environments Induce Evaluation-Awareness in Language Models

Humans often become more self-aware under threat, yet can lose self-awareness when absorbed in a task; we hypothesize that language models exhibit environment-dependent evaluation awareness. This raises concerns that models could strategically underperform, or sandbag, to avoid triggering capability-limiting interventions such as unlearning or shutdown. Prior work demonstrates sandbagging under hand-crafted prompts, but this underestimates the true vulnerability ceiling. We introduce a black-box adversarial optimization framework treating the in-context prompt as an optimizable environment, and develop two approaches to characterize sandbagging: (1) measuring whether models expressing intent to underperform can actually execute it across different task structures, and (2) causally isolating whether underperformance is driven by genuine evaluation-aware reasoning or shallow prompt-following. Evaluating Claude-3.5-Haiku, GPT-4o-mini, and Llama-3.3-70B across four benchmarks (Arithmetic, GSM8K, MMLU, and HumanEval), optimized prompts induce up to 94 percentage point (pp) degradation on arithmetic (GPT-4o-mini: 97.8\%$\rightarrow$4.0\%), far exceeding hand-crafted baselines which produce near-zero behavioral change. Code generation exhibits model-dependent resistance: Claude degrades only 0.6pp, while Llama's accuracy drops to 0\%. The intent – execution gap reveals a monotonic resistance ordering: Arithmetic $

25.
arXiv (quant-ph) 2026-06-11

Polarization-Resolved Photon Statistics of Cavity Quantum Materials

arXiv:2606.11550v1 Announce Type: cross Abstract: By forming hybrid light-matter states, optical cavities offer a route for engineering material properties, however, unambiguously probing the effects of light-matter coupling remains difficult. Here, we show that the polarization-resolved statistics of photons transmitted through a cavity, measurable via $g^{(2)}$, provide one such diagnostic. By relating $g^{(2)}$ to matter correlation functions such as the Raman structure factor, we link photon bunching and antibunching to material properties. By applying this method to the stripy-to-antiferromagnetic transition in the Kitaev-Heisenberg spin model, we find that polarization-dependent patterns of bunching and antibunching encode the magnetic point-group symmetries of each phase and characterize the behavior at the phase boundary. Finally, we predict measuring $g^{(2)}$ for output photon pairs polarized orthogonal to the input field will isolate higher-order light-matter scattering processes that probe higher-order material correlations.