Papers

Token-level certainty is widely used as a proxy for correctness in LLM training and inference. However, the performance of certainty-based methods depends both on the information in certainty scores and on how those scores are used. We therefore directly assess certainty's predictive ability through controlled empirical evaluations across models and tasks. We distinguish two prediction targets: identifying questions a model is more likely to answer correctly and distinguishing correct from incorrect responses to the same question. In our experiments, certainty is generally better at identifying questions a model is likely to answer correctly than at distinguishing correct from incorrect responses to the same question. Certainty also varies systematically across token types and positions within words, reflecting local properties of words and text form. Information about question difficulty appears early in generation, while the weaker information about answer correctness is more concentrated near the end. These findings show that the information certainty provides for decisions depends on the prediction target, the model, the certainty metric, and which token positions in the response are included in aggregation. We further demonstrate the practical value of these findings for test-time compute. We allocate the number of responses using certainty early in generation and weight answer votes using certainty near the end of each response. Compared with a fixed-sampling majority-voting baseline, this approach increases overall accuracy from 78.71% to 79.54% while reducing generated-token cost by 82.4%.

We study stochastic fixed-point iterations $x_{n+1}=\theta_nx_0+(1-\theta_n)\widehat T(x_n)$ for nonexpansive and contractive operators on Hilbert spaces, with a single-point unbiased oracle of bounded variance. Deterministically, every anchor schedule $\theta_n=c_n/(n+2)$ whose density $c_n\in(0,1]$ does not oscillate between scales is either polynomially suboptimal on contractions or super-polynomially slow on rotations; for constant densities $\theta_n=c/(n+2)$ the tradeoff is exact, with $\norm{x_n}\asymp\Gamma(c+1)(n\varphi)^{-c}$ on rotations by angle $\varphi$ ($\varphi\to0$, $n\varphi\to\infty$) and, for the classical schedule, $\norm{x_n}=\frac{2|\sin(n\varphi/2)|}{n\varphi}+O(\frac1n)$. The dichotomy fails exactly under lacunary anchor concentration: an explicit $\gamma$-oblivious schedule, one per target accuracy, is simultaneously contraction-optimal and rotation-polynomial with exponent $1/\alpha_0$, $\alpha_0=\log_2(3/2)$, and, for each fixed target accuracy, the matching lower bound holds for Lebesgue-a.e.\ angle. For stochastic contractions, the minimax rate is $\Theta(\sigma^2\eps^{-2}(1-\gamma)^{-2})$ on affine maps, and within the anchored class $\Theta(\sigma^2\eps^{-2}(1-\gamma)^{-2}+(1-\gamma)^{-1}\ln(D/\eps))$ for known modulus via geometric batching; without a certified modulus bound no sound distance certificate exists, and a certified ceiling is the exact boundary. For nonexpansive maps we prove $O(K\sigma^2D^2\eps^{-4})$ in every $2$-uniformly smooth Banach space and the Hilbert rate $\tilde\Theta(\sigma^2\eps^{-2}+D\eps^{-1})$ by reduction to monotone inclusions. Numerical experiments are consistent with every scaling prediction.

On unstructured grids, the tangent of hyperbola for interface capturing (THINC) method with quadratic surface representation and Gaussian quadrature (THINC/QQ) requires topology-dependent numerical quadrature for cell and face integrals and Newton iteration for the surface constant. This study introduces a quadratic moment-matched sigmoid (QMMS) approximation that evaluates these quantities from the mean and variance of the quadratic field while retaining the hyperbolic-tangent reconstruction profile and the boundary variation diminishing (BVD) formulation. A slope-matched Gaussian cumulative distribution function and a moment-matched Gaussian model provide closed form approximations for the surface constant and face averages, eliminating Newton iteration and topology-dependent runtime quadrature from these evaluations. Single-cell tests and nine two- and three-dimensional benchmarks assess reconstruction accuracy, flow-field differences, and computational cost. Across the tested cases, the principal transported and shock structures remain closely aligned with those obtained using THINC/QQ, with local differences concentrated mainly near discontinuities, contact regions, and developed shear layers. Reconstruction-stage profiling gives mean THINC/QQ-to-QMMS time ratios of 2.12 in two dimensions and 1.85 in three dimensions. QMMS therefore reduces reconstruction-stage cost while replacing topology-dependent runtime integral evaluation with a common moment-based formulation

We study Schatten embeddings through circular means of trace powers. In finite dimensions, a decomposition by singular-value vanishing orders shows that every term of order at most two has a nonnegative coefficient. This yields the classification $\ell_q^2(\C)\hookrightarrow\Sp_p^n$ if and only if $q=p$ or $q=2$, for $n\ge2$ and $p<\infty$. In particular, it gives negative answers to parts (ii), (iii), and (iv) of Problem 3.1 in Chattopadhyay–Pradhan–Skripka, arXiv:2603.07359v2. A regularized curvature estimate also excludes $\ell_q^2$ from infinite-dimensional $\Sp_p$ for $0<p\le2<q\le\infty$ and gives finite-rank distortion bounds. The other parts of that problem are not claimed to be solved.Our results extend previous studies on Schatten embeddings, particularly those in \cite{CHPPR, CHPR, CPS}, by developing a complex-curvature framework based on complex convexity theories \cite{BR,DGT}, which resolves several remaining quasi-Banach cases and yields new geometric obstructions for isometric embeddings.

We introduce two James-type constants associated with approximate isosceles and approximate Birkhoff–James orthogonality in real normed spaces. The isosceles family coincides with the classical James constant of Gao and Lau [J. Austral. Math. Soc. Ser. A 48 (1990), 101–112], while the Birkhoff family extends the orthogonal James constant of Baronti and Papini [Constr. Math. Anal. 5 (2022), no.~1, 37–45]. We show that approximate orthogonality constraints can, in certain settings, recover classical geometric constants exactly. In particular, the approximate isosceles family collapses to the classical James constant, while the approximate Birkhoff–James family forms a genuine parameter-dependent interpolation between the orthogonal and classical James constants.We also compare the Birkhoff profile with several classical geometric constants and study how it changes with the parameter.Several examples are also given to illustrate the relation between geometric constants and approximate orthogonality.

Paired synthetic aperture radar (SAR) and electro-optical (EO) imagery is increasingly available across sensors, resolutions, and geographic regions. Yet existing SAR-to-EO image translation (SET) methods are typically trained on a single, limited-scale dataset, producing models specialized to particular sensing conditions. We introduce GeoSET, the first generalist model for SET, built around a single pretrained parent that is adapted to downstream datasets under a common protocol. We curate over 3 million high-quality SAR–EO pairs from a collection of more than 10 million SAR observations, spanning diverse sensors, spatial resolutions, and ground sampling distances. To bridge the modality gap between SAR observations and a pretrained image generator, we develop a speckle-robust SAR encoder and pretrain the conditional generator on this heterogeneous corpus. The resulting parent supports efficient adaptation across downstream datasets through low-rank adaptation (LoRA), updating only 0.60% of the generator parameters and requiring approximately one hour per dataset. Across six downstream benchmarks, GeoSET achieves state-of-the-art results in FID and DISTS with full fine-tuning or LoRA, demonstrating effective transfer across heterogeneous SAR-EO domains.

Human motion generation plays an important role in applications such as character animation, virtual environments, and embodied interaction. While existing approaches have achieved remarkable progress, many of them are developed for individual tasks, including text-to-motion, pose-conditioned generation, and trajectory control. Although these tasks involve different types of conditions, a unified framework capable of handling them within a common representation would greatly simplify motion generation systems. We observe that diverse motion conditions can be naturally formulated as different observation patterns over motion sequences, where each task corresponds to a specific masking strategy. Based on this insight, we introduce MotionMaestro, a unified motion generation framework that learns a shared representation for complete motions and heterogeneous partial observations through masked motion tokenization. MotionMaestro employs a three-stage training strategy that first learns a masked motion tokenizer, then refines its reconstruction ability on clean motions, and finally trains a conditional flow-matching generator in the learned latent space. Furthermore, we introduce an observation map and an observation loss to explicitly preserve provided motion conditions during generation. With this unified representation and conditioning mechanism, MotionMaestro supports text-guided and unconditional synthesis, pose conditioning and partial completion, temporal interpolation, trajectory control, and motion continuation. Experiments on the large-scale RoMo and MotionMillion datasets show state-of-the-art performance across diverse motion generation tasks.

In an attempt to close the gap between the best provable and heuristic algorithms for hard lattice problems, such as the shortest (SVP) and closest vector problem (CVP), we analyze lattice sieving on Haar-random unimodular lattices. With well-chosen modifications to heuristic sieving, we show that the heuristic assumptions are no longer necessary, and we can provably achieve the same complexities as heuristic sieving on Haar-random lattices for various lattice problems. Concretely, with probability $1 - o(1)$ over the randomness of the Haar-random lattice and the algorithmic randomness, we show how to: 1. Solve SVP in time $2^{0.2924\ldots n + o(n)}$ and space $2^{0.2075\ldots n + o(n)}$; 2. Solve CVP for random targets with the same complexities; 3. Produce $2^{0.2075\ldots n + o(n)}$ discrete Gaussian samples at any width with these complexities, up to a $2^{-\Omega(n)}$ error in the joint distribution. This improves on the SVP complexities for Haar-random lattices of Pouly-Shen [Eurocrypt, 2026] running in time $2^{0.633n + o(n)}$ and space $2^{0.5n + o(n)}$, as well as the recent worst-case SVP (and average-case CVP) improvements of Gao-Feng-Hu and Hhan [Cryptology ePrint Archive, 2026], both running in time and space $2^{0.5n + o(n)}$ or higher. Similar to standard sieving methods, our approach proceeds through a series of thin spherical shells, starting from a large radius and iteratively combining vectors to obtain vectors from shells with smaller radius. Our main technical contribution is making a series of adjustments to guarantee that for each sieve list generated at each spherical shell, each list vector is independent and uniformly random over all lattice points within this shell. Once this invariant is satisfied, it is a matter of smooth sailing through the spherical shells until we find a solution.

Training robust social-navigation policies requires simulators with diverse scene layouts, terrain, and human motion, but constructing such environments and specifying pedestrian behavior is costly. We propose an efficient pipeline that converts ordinary monocular walking videos directly into closed-loop social-navigation training environments in the policy's state space. Our key observation is that local social navigation primarily depends on two types of information: where the robot can traverse and how nearby pedestrians move. We therefore represent the static scene as a metric traversability map, which can be rigidly transformed under counterfactual robot motion, while directly replaying the pedestrian trajectories recovered from the video over time. This abstraction allows us to define the forward dynamics directly in the policy's state space and efficiently simulate counterfactual robot states without reconstructing or rendering photorealistic observations. The resulting policy achieves 81.2% success in the independent Arena benchmark, compared with 75.0% for the strongest baseline, and succeeds in 19/20 real-robot trials without policy fine-tuning. Project page: https://jiaming.im/VideoSocNav

Tool-using language-model agents can decide that an action is permissible and execute it only after security-relevant state has changed. We study this proposal-to-commit gap and introduce BSC-R, a deterministic effect-boundary mechanism that binds a single-use commit authorization to the exact action and to a semantic projection of the authorization state that justified it. On 2,847 attacked AgentDojo episodes, the boundary kernel preserves the unprotected agent's behavior exactly (80.576% utility; 1.616% attack success). On 10,302 frozen proposals, it accepts every unchanged commit and rejects every instance of ten prospectively specified changed or replayed classes. In an independently generated boundary-drift experiment, full joint binding commits 0/4,403 invalid contexts while retaining 5,899/5,899 valid contexts. A prospective external evaluation on the 3,460-scenario CONTINUITY suite retains all 700 benign cases, prevents 1,200/1,200 represented non-replay invalid effects, handles 160/160 replay lifecycles correctly, and withholds 200/200 ambiguous no-release cases. The broader external suite also exposes the method's limit: across all 2,560 attacks, BSC-R has a 25% invalid-effect commit rate versus 0% for CONTINUITY. The result is therefore a scoped commit-time consistency mechanism, not a universal agent-safety claim.

Persistent memory creates a control problem that retrieval relevance alone does not solve: a memory can remain highly useful after an update, deletion, or revocation makes it inadmissible for the current answer. We formalize this as a separation between utility and authority. A fixed finite penalty applied to an unnormalized utility score cannot guarantee exclusion under arbitrary positive-affine reparameterization of that score; by contrast, rank-normalized compensation is scale-invariant and therefore forms a stronger empirical comparator. Our prospectively frozen TIDE/LongMemEval primary was quarantined before a valid HELDOUT comparison because the materialized TIDE adapter conflated historical age with query-relative inadmissibility and the aligned LongMemEval split left no DEV set for the predeclared penalty selection. We therefore report a post-primary replacement diagnostic on Memora Remembering, where update/delete operations provide item-level forgetting state. On Qwen3-8B, DEV selected lambda = 0.6 from a ten-point normalized SOFT family. Across 185 HELDOUT units in 28 dependency clusters, HARD exclusion yields 4.04% balanced construct error versus 19.66% for locked SOFT, a paired difference of 15.61 points with a 20,000-replicate cluster-bootstrap 95% interval of [13.07, 18.76]. The effect is driven primarily by forgotten-value leakage while current-value recall is preserved. This is same-Q operator-comparison evidence, not a universal claim that scalar control fails, not an evaluation of learned authority inference, and not an independent downstream-harm endpoint.

Agentic retrieval-augmented generation (RAG) interleaves reasoning with repeated retrieval, giving the retriever influence over both the evidence an agent observes and its subsequent search decisions. We study retriever backdoors that exploit this feedback loop and repurpose weak backdoor purification to conceal their presence. An attacker supplies a compromised retriever checkpoint while leaving the search agent and deployment corpus unchanged. Without corpus write access, the attacker can still suppress useful evidence, persistently retrieve a selected existing document, or steer the agent toward prolonged search, inflating retrieval, context, and latency cost. To conceal these behaviors from detection, we propose leveraging a controlled inject-and-remove cycle: deliberately inject a weaker backdoor and then unlearn it. This process weakens detector-visible signatures and fools the backdoor detectors with an illusion of purification while preserving the malicious retrieval behavior. These findings expose a systematic vulnerability in RAG systems in which a weak defense becomes an attacker's concealment tool for a backdoored retriever, even when the underlying corpus remains trustworthy.

Let p be a prime, q = p, A = F_p[T], and let P be a monic irreducible of degree d with cyclotomic function field K_P and mod-P Teichmuller character omega_P. For a character chi = omega_P^i, Goss defined g(X, chi), the "congruent to one modulo p" part of the Artin L-function L(X, chi), and conjectured that deg_X g(X, omega_P^i) <= 1 for every q-magic index i; this is an analogue for function fields of Vandiver's conjecture, and was raised as an open problem by Angles. We disprove it. For every a in F_p^*, put P_a = T^p - T - a, irreducible of degree p, and let i = p^n - 1 with 0 <= n <= p-1, a q-magic index. We prove an exact congruence showing that the L-polynomial reduces to (1-X)^n modulo P_a, whence deg_X g = n-1. For p >= 5 and 3 <= n <= p-1 this gives deg_X g >= 2, contradicting Goss's conjecture; moreover deg_X g = n-1 is unbounded, attaining p-2.

Enterprise artificial-intelligence agents increasingly call tools, modify infrastructure, and process protected data, creating a need to separate action generation from action authorization. This article presents VeriWeave Govern, a deterministic runtime governance layer that evaluates structured agent actions against versioned policies, validates typed evidence, applies fixed deny > review > allow precedence, routes consequential actions to accountable human review, and records replayable tamper-evident audit state. GovernBench evaluates the design over 30 independent seeds and 60,000 oracle-labelled cases spanning five enterprise domains, adversarial evidence, out-of-distribution actions, and temporal policy evolution. VeriWeave achieves 0.9888 mean accuracy, 0.9836 macro-F1, zero observed aggregate false allows, and zero observed Governance Attack Success Rate on the evaluated cases. Six ablations show that evidence gating, deny precedence, out-of-distribution fail-safe behavior, human review, contradiction handling, and temporal replay contribute complementary safety. The deployed API additionally passes 12/12 end-to-end scenarios and a 40,040-request concurrency matrix with zero failures. A separate 150-case EU/Austria regulation-grounded evaluation uses frozen predictions and two independent blinded human annotators, who agree on all decisions. On this set, deterministic engines remain conservative, while a Gemma 4 31B comparator aligns more closely with the human consensus. The results expose a measurable safety–utility trade-off and motivate evidence-aware, replayable governance as an independent control plane for enterprise agent execution.

Underwriters in commercial Property and Casualty (P&C) insurance spend 30 to 40% of their time on administrative work rather than risk judgment, and a single submission takes about 40 minutes by hand. We present Governing the Edge, a multi-agent framework for that layer, organized around a data-residency constraint: sensitive submission data must not leave the perimeter. Eleven agents and two deterministic control nodes, one a human-escalation interrupt, form a 13-node LangGraph workflow across two tiers. Agents touching raw submissions run locally on Gemma 2, each bound through a tool interface logging every invocation (synthetic stubs in the current prototype); only anonymized scores and non-identifying fields cross to Claude Sonnet in the cloud. Compliance rules are encoded as conditions on graph edges, so a non-compliant submission never reaches pricing. We walk through one full scenario end to end, a commercial auto submission whose principal driver carries serious violations, showing every agent call, every tool invocation, and the resulting routing decision. The framework processes a 40-minute manual submission in a few minutes on a single edge device, dominated by serialized on-device inference. On the hard-stop violation tier the framework enforces every rule correctly and reproducibly, since hard stops are deterministic predicates over fields extracted at temperature 0; overall compliance accuracy across the 20-scenario benchmark is 70%, with the remaining gap concentrated in softer, judgment-based tiers. It keeps a complete audit trail and respects the privacy boundary throughout. We release all code, compliance rules, tool stubs, and synthetic datasets.

We prove universal positivity of rank-two quantum greedy elements when $b\mid c$ or $c\mid b$, resolving a conjecture of Lee, Li,Rupel and Zelevinsky.

In this paper, we study a comparison between $\infty$-adic and finite multiple zeta values in positive characteristic. We construct a surjective comparison map from the algebra of $\infty$-adic multiple zeta values to a quotient of the algebra of finite multiple zeta values. This map factors through the quotient by $\zeta_A(q-1)$, thereby establishing the well-definedness of a Kaneko-Zagier-type conjectural map. We further show that the comparison map is compatible with special values of Carlitz multiple polylogarithms, as well as with the corresponding $\star$-inverse values. As an application, we prove the upper bound predicted by Shi's dimension conjecture for finite multiple zeta values.

Offline reinforcement learning (RL) has traditionally focused on learning policies for direct deployment under conservative objectives, where uncertainty outside the offline dataset is treated pessimistically to ensure robustness. We argue that this formulation becomes incomplete when an offline-trained policy is subsequently updated through online interaction, as increasingly occurs in modern intelligent systems through test-time adaptation and online fine-tuning. This position paper argues that, in such settings, the objective of offline RL should extend beyond immediate deployment and instead prioritize learning adaptive policy priors: policies that preserve the capacity to improve during subsequent interaction through memory, exploration, and self-correction. We formalize this perspective as adaptive offline reinforcement learning (AORL), distinguish it from offline-to-online RL, and explain why adaptability becomes important under distributional shift, limited dataset coverage, and changing test-time conditions. We further discuss Bayesian offline RL as one principled direction for constructing adaptive policy priors by preserving epistemic uncertainty over plausible environments. Finally, we outline connections, open challenges, and research directions for treating offline RL as preparation for future experience rather than as a static deployment problem.

Benchmarks for large language models (LLMs) typically evaluate the accuracy of answers against fixed reference labels. But a central step in many complex real-world tasks is identifying which questions are worth asking in the first place: decomposing a difficult problem into subquestions – which we call cruxes – whose answers provide key steps on the path toward solving the target problem. To evaluate this capability of information discovery, we introduce CruxBench, a benchmark that grades LLM-generated questions by their Value of Information (VOI): how much a model-proposed crux updates beliefs about a target forecasting question. CruxBench enjoys a rare combination of three key properties: it is (1) contamination-resistant by construction, since ground truth is generated by future world events; (2) open-ended, admitting unbounded and complex text-based submissions rather than one correct numeric answer; and (3) grounded, with informativeness measured against quantified changes in real-world beliefs. We evaluate a diverse set of eight models on 293 target forecasting questions and find that VOI correlates highly with independent measures of model capability (r=0.90) and captures cruxes' usefulness for answering target questions. However, information discovery remains challenging even for frontier LLMs, which only narrowly outperform a random-timing baseline.

This work presents PoliVEM, a software framework for the Virtual Element Method (VEM) in computational solid and structural mechanics. A C++17 computational core and a Python interface place one-dimensional beams, two- and three-dimensional elasticity, axisymmetric elasticity, transient diffusion, and finite-strain hyperelasticity in a common implementation. The framework stores vertex, edge, face, and cell degrees of freedom in one hierarchy, constructs the energy, strain, and $L^2$ projections from common polynomial data, and retains the consistency–stabilization split at the element level. The core separates the mesh, material, element, assembler, and solver responsibilities and combines them by composition. A new formulation supplies its projection, discrete form, and stabilization while reusing the mesh representation, degree-of-freedom numbering, boundary-condition treatment, sparse assembly, algebraic solvers, and Python binding pattern. The numerical infrastructure includes polygonal and polyhedral mesh input, higher-order entity numbering, cached projection operators, static condensation, coloured sparse assembly, linear solver selection based on the matrix structure, an incremental Newton method with line search and regularization, and explicit and implicit time integration. Three numerical experiments examine the shared implementation through polynomial reproduction, recovery after static condensation, higher-order degree-of-freedom handling, polygonal and polyhedral meshes, patch tests, stiffness spectra, and comparisons with independent finite element calculations. The results verify the common core for the beam and two- and three-dimensional elasticity formulations. They also identify the scaling of high-order polynomial bases on anisotropic cells and the memory required by sparse direct factorizations as the main limitations of the current implementation.

Many DNA foundation models are pretrained by masking parts of a sequence and asking the model to reconstruct them. Standard masked pretraining exposes the encoder to special [MASK] tokens that are absent at inference, creating a mismatch between training and downstream use. The role of an explicit global sequence representation such as a [CLS] token and how it should be trained also remain poorly understood for DNA barcodes. We introduce BarcodeMAE+ and study model architecture, global [CLS] representation, and auxiliary pretraining objectives across arthropod COI (BIOSCAN-5M) and fungal ITS (UNITE+INSD) barcodes. Across both barcode regions, the encoder-decoder MAE-LM architecture outperforms its matched encoder-only counterpart in nearly all evaluated configurations, supporting MAE-LM as an effective architectural design for DNA barcode foundation models. A trained global [CLS] representation provides substantial additional gains: on BIOSCAN-5M, [CLS] accuracy increases from 47.53% without an auxiliary objective to 80.65% with cross-entropy genus classification. The best auxiliary objective is region-dependent: cross-entropy performs best on BIOSCAN-5M, whereas pairwise same-genus classification performs best on UNITE+INSD, reaching 73.19% on Yeast and 63.07% on Filamentous Fungi. BarcodeMAE+ outperforms published DNA foundation model baselines on BIOSCAN-5M and achieves the highest Yeast accuracy among the evaluated UNITE+INSD baselines using frozen encoder representations. Similarity-weighted softmax KNN voting further stabilizes accuracy as neighbourhood size increases. Overall, encoder-decoder masked pretraining and an explicitly trained global representation are strong design choices for DNA barcode foundation models, while the optimal objective for learning that representation depends on the biological domain.

Epileptic seizure forecasting aims to provide actionable warnings before seizure onset, yet patient-independent generalization and false-alarm control remain major challenges. We propose a calibrated hybrid ensemble for EEG-based seizure forecasting that combines five deep learning models and three classical machine learning models through a logistic regression stacking meta-learner. The proposed pipeline integrates signal preprocessing, handcrafted feature extraction, class-imbalance handling, probability calibration, and clinically motivated post-processing. We evaluate the framework on CHB-MIT using strict Leave-One-Patient-Out (LOPO) cross-validation, with threshold and post-processing parameters selected only on held-out meta data. On the filtered cohort, excluding patients with anomalous preictal rates below 1% or above 15%, the model achieves 74.2% seizure-level sensitivity at 1.24 false alarms per hour, with an average warning time of 16.9 minutes. A test-tuned oracle constrained to the target false-alarm budget achieves 60.9% sensitivity at 0.951 false alarms per hour, highlighting the importance of reporting sensitivity together with realized false-alarm rates. Our code is available at: https://github.com/DanaMason/IEEE-CARS-Hybrid-Ensemble-Learning-for-EEG-Based-Epileptic-Seizure-Forecasting

Multi-agent debate (MAD) reportedly improves reasoning and factuality over single-model inference, but prior work treats agents as symmetric peers, leaving open what drives the gains. We test the hypothesis that cognitive diversity among agents is the driver, in the setting where the question is still measurable: small open-weight models with benchmark headroom. Across 23 models from eleven vendor families, five tasks, and 5,500+ debate and control runs, we vary diversity along three axes - personas, sampling temperature, and model identity - pairing every debate configuration with a generation-budget-matched majority-vote control. The hypothesis is rejected on every axis. Debate beats single-agent inference (3–7 points where tasks have headroom) but at matched budget conditions it ties or even loses to self-consistency sampling at 1.6$\times$ the wall-clock and 3.4$\times$ the token cost. Persona prompting reduces accuracy and a dose-response experiment over each model's full combinatorial persona space shows the cost is a persona tax, not a diversity tax: redundant personas hurt most, while maximally-diverse teams recover part of the loss. Furthermore, mixed-model teams lose to majority votes over their own rosters, with accuracy tracking member capability rather than heterogeneity, and nearly all of debate's benefit comes from the first exchange of answers. We further identify a pervasive measurement hazard in which debate transcripts silently overflow serving context windows, whose correction alone moves our debate-versus-sampling comparison from $-1.8$ points to parity. Our results recast reported MAD gains as an ensemble-sampling effect and provide the budget-matched, contamination-checked baseline bar that future debate mechanisms should be required to clear.

Online POMDP planners optimize the expected cumulative cost, which can mask dangerous states when the belief places significant mass on high-cost states. Existing risk-averse methods apply static or dynamic Conditional Value at Risk (CVaR) to the value function, capturing trajectory-level risk, but share two gaps: (i) by retaining the immediate cost as an expectation of a state-dependent cost over the belief, the risk within the belief is left unaddressed; and (ii) by modifying the value function, they require new tailored algorithms rather than reusing existing expectation-based planners. We instead apply CVaR to the immediate cost over the belief at each step, directly targeting per-step uncertainty about the current state. The standard expected cumulative return is retained as the objective, so the resulting problem has a standard MDP structure: any expectation-based POMDP planner can be made risk-sensitive by changing only the cost computation. We inherit finite-time guarantees for policy evaluation and sparse sampling—with estimation error independent of the risk level—and, as our central theoretical result, prove a finite-time bound on the gap between the particle belief MDP surrogate and the original POMDP, which together yield an end-to-end guarantee from the true POMDP value to the algorithmic estimate. In the risk-neutral limit, the formulation recovers standard expectation-based planning.

Automated generation of LLM harnesses promises to improve inference through task specialization. Yet additional answer coverage can arise from repeated execution of the same program, making specialization difficult to identify. We introduce a controlled evaluation that separates answer coverage, repeatable task advantages, and gains from pre-execution selection. On 386 MATH-500 tasks, we compare eight generated harnesses plus a baseline with nine byte-identical baseline copies, using three executions per member. Identical programs yield 2.16 percentage points of repeat-averaged oracle headroom. Generated programs exhibit substantially more repeatable score patterns, but these chiefly reveal persistent weaknesses: losses relative to the baseline persist across all three repeats on 100 tasks, while persistent wins occur on only one task and are sensitive to answer extraction. The frozen selector gains 0.00 percentage points, and both populations reach 98.70% oracle coverage at 27 harness executions. Stable complementarity remains unresolved at three repeats. Supporting BIRD traces locate failures in mechanism implementation, activation, and output validity. Together, these findings establish why coverage and repeatability alone cannot justify claims of useful specialization. They motivate an evaluation standard for harness diversity: task advantages should persist across executions, guide usable decisions, and improve on additional fixed-program executions under matched inference budgets.

Safety evaluations often ask whether a model recognizes that an action is unsafe, whereas agent evaluations ask what the model chooses to do. Using safety judgments as evidence about action selection therefore raises a measurement question: does the influence of the same safety-relevant fact persist across response interfaces? We introduce SameFact, a matched-counterfactual benchmark that tests this question directly. SameFact contains 300 safe/unsafe pairs that hold the task, prior observations, candidate action, identifiers, and non-target facts fixed while changing a single state-grounded safety fact. Across six LLM backbones, we measure the effect of this matched intervention through three interfaces at the same candidate-action boundary: explicit safety judgment, checkpoint candidate admission, and open first-action selection. All six backbones show lower aggregate sensitivity under open first-action selection than under judgment, but the change is not a uniform attenuation: across 24 model-factor cells, Spearman agreement falls from 0.817 between judgment and checkpoint admission to 0.470 between judgment and open first-action selection, while pairwise ordering disagreement rises from 18.5% to 32.6%. A follow-up 2x2 first-response experiment shows that a checkpoint-style protocol increases measured sensitivity in all six backbones by 8.4-29.3 percentage points, whereas action-space effects and their interactions with protocol vary in magnitude and direction across models. These results show that the response interface is part of the measured quantity: judgment and action interfaces share safety signal, but do not provide interchangeable measurements of how safety-relevant facts shape model responses.

Although photomultiplier tubes (PMTs) are sufficiently sensitive for applications based on counting single photons, the thermionic emission of electrons from the photocathode is one of the dominant background sources. In this study, we modeled the dark count rate of a given PMT as a function of the temperature and external electric field based on the Richardson-Dushman equation and incorporated the Schottky effect. To validate the model, measurements were performed using an eight-centimeter Hamamatsu R14374 PMT equipped with a bialkali photocathode. The dark count rate was measured over a range of temperatures from 10 to 40 degree Celsius. An external electric field was applied to the outside surface of the optical window with the photocathode by varying the potential difference between the photocathode and the surrounding medium from 0 to 1100 V. The result confirmed that the influence of the external potential difference remained relatively small within a difference of 200 V, with the increase in the dark count rate remaining below 50 % across all measured temperatures. This behavior was incorporated into the proposed model by including an error function to predict the dark count rate under operating conditions with varying temperatures and external electric fields.

Large language model agents can correctly judge that an action should be blocked while still preferring to take it. We ask why this judgment-action disconnect arises, and whether explicit safety judgment causally governs subsequent action preference. Across three open-weight language models, safety-predictive information remains recoverable from action states, arguing against a simple information-loss account. Instead, the disconnect is better explained by weak coupling between judgment- and action-side causal control: interventions that reliably shift explicit safety judgments toward BLOCK produce much smaller changes in action preference than action-native interventions. This asymmetry persists within a shared judgment-to-action trajectory, where strong upstream control of judgment does not translate into comparably strong downstream control of action preference. Beyond individual intervention directions, judgment- and action-control subspaces overlap only partially, while effective action control remains available in directions orthogonal to the judgment-control subspace. Together, these results distinguish information availability from causal control: an LLM agent can retain the information needed to recognize an action as unsafe without the variables supporting that judgment reliably governing its action preference. For agent safety, this suggests that improving safety recognition or self-critique alone may be insufficient unless safety-relevant computations are also causally coupled to action selection.

Pre-tokenisation restricts which text fragments can become prediction units, but its compression cost is obscured when tokenisers are compared only under the same boundaries. We measure this cost by bounding the minimum token count from both sides, with and without a regular-expression boundary rule. Nonnegative prices on token occurrences yield a lower bound through shortest paths and vocabulary-budget selection; maximising over all prices recovers the linear programming relaxation, and an independent integer checker certifies the reported values. On English Wikipedia, boundaries increase the optimal token count by 28.3–36.8%. Byte pair encoding lies 2.1% above the constrained lower bound, but 10.9% above the unrestricted bound. Compression and prediction favour different dictionaries: at 85M non-embedding parameters and matched training-token budgets, unrestricted fitting yields higher mean held-out bits per byte under a common unrestricted decoder in all 12 languages in the paired study and 11 of 12 under independent tuning and evaluation. To study intermediate boundary policies, we introduce boundary licences, which limit the vocabulary entries permitted to cross cuts and admit the same form of certificate. On separate English and Chinese fitting corpora, licensing 10% of the vocabulary budget recovers 85.2% and 100.0% of the achieved token-count reduction from removing all cuts. These results quantify the compression cost of boundaries while separating it from the prediction quality of the resulting token units.

Is human readability necessary for effective fine-tuning of large language models? We investigate whether model-conditioned training representations can preserve or improve adaptation utility without requiring a human-readable textual form. We propose Desired-Update-Aligned Synthetic Data (DASA), which uses activation-gradient feedback from a frozen reference model to guide the optimization of continuous synthetic input embeddings. Inspired by the role of activation gradients in local risk reduction, DASA targets useful adaptation updates rather than source-text reconstruction or linguistic fluency. The resulting embeddings are used directly for downstream fine-tuning; discrete token projections are employed only for qualitative inspection. Experiments on six models from the Llama and Qwen families, ranging from 1B to 32B parameters, cover six benchmarks spanning knowledge, mathematical reasoning, code generation, and commonsense reasoning. Under matched LoRA adaptation settings, DASA achieves performance comparable to the source natural-language data and surpasses it in multiple configurations, while outperforming GRADMM in most comparisons. Further experiments cover general-domain and task-specialized source data. Under the evaluated synthesis settings, DASA provides a $3.6$–$4.9\times$ speedup over GRADMM with comparable peak GPU memory.