Papers

We prove the Fourier entropy–influence inequality for every linear threshold function, with a constant below $8.937$ and no restrictions on its weights or threshold. The argument applies to regular Boolean functions and gives logarithmic bounds for their Boolean combinations and for unions with bounded variable overlap. Character multiplication preserves the estimates and yields bounds by influence minus variance. Under arbitrary product measures, symmetric thresholds satisfy the strengthened inequality needed for read-once composition, uniformly in depth and fan-in. A joint description of each Fourier set refines the overlap estimate and recovers constant bounds for addressing. Exact selector identities extend the bound to orthogonal multiplexers with shared data. Rare activation preserves the optimal constant of unrestricted FEI. The proofs combine pivotal antichains, spectral reference measures, and product-measure composition.

We study Coflow Scheduling, introduced by Chowdhury, Zhong, and Stoica (2014). We give deterministic polynomial-time algorithms achieving a $2.77$-approximation without release dates and a $3.17$-approximation with integer release dates. These improve the $3.42$ and $4.36$ guarantees of Rohwedder and Schnaars (2025). Our approach combines two ideas: (1) a novel iterated rounding scheme, and (2) Galvin's list edge coloring method, which is based on the Gale–Shapley stable matching algorithm.

Agent evaluation harnesses are software systems that run test suites, generate inputs, and decide outcomes with test oracles. This paper audits such software for reliability defects that score tables cannot reveal. We introduce an oracle-integrity auditing approach with five state-integrity invariants and three known-answer controls. We evaluate it by injecting seven oracle defect classes across two task domains and a synthetic domain. All injected defect classes are detected, and the repaired oracle has no false positives. Applied to an agent benchmark, the audit reveals a reward-function defect that changes the environment state before post-run scoring. Across 4,320 episodes, replay-based correction changes database-pass labels from 4,194 to 2,883 and reduces measured success from 94.3% to 65.5%. We also study configuration-dependent measurement effects. A component ablation over 3,240 episodes shows that the agent's policy documents, tool descriptions, and tool error strings influence observed trajectory reliability, with tool descriptions showing the largest exploratory effect (-9.2 pp) and error strings the smallest (-5.3 pp). A second task domain reverses the sign of the language effect, so the result is bounded to the tested configuration. Finally, we report a portability boundary: the auditing approach cannot validate a second independently implemented benchmark because the required reference terminal state cannot be reconstructed from its recorded API-call log. The paper releases a replication package containing the auditing suite, fault-injection catalogue, frozen records, deviation logs, and offline analysis entry points without network access, API keys, or model calls.

Detailed video captioning has become an essential semantic interface for multi-modal understanding and generation. While existing methods mainly target short videos, extending them to long videos remains challenging, primarily due to limited context windows of current video understanding models. A naive solution is to adopt segment-wise captioning followed by concatenation, yet this paradigm often suffers from inconsistent subject references and fragmented long-range narratives. To mitigate these issues, we introduce PIGEONS, an incremental long-video captioning model built upon a Persistent Identity Gallery and an Evolving Overarching Narrative Summary. Before caption generation, PIGEONS scans the entire video to construct an identity gallery that captures key subjects along with their visual references, thereby providing a stable referential anchor. The model then performs clip-by-clip captioning conditioned on the persistent gallery and an evolving overarching narrative summary, which compactly maintains and updates essential long-range contextual information after each captioning step. To enable these capabilities, we develop a three-stage training strategy that integrates supervised fine-tuning and reinforcement learning. Extensive experiments demonstrate that PIGEONS markedly improves long-video captioning performance, achieving superior accuracy, completeness, and subject referential consistency over existing methods, while maintaining competitive performance on short-video captioning.

The elephant random walk (ERW) is a discrete-time random walk with complete memory. At every step the walker chooses one of the previous increments at random and then either repeats with a constant probability $p\in [0,1]$ or reverses it. Since its introduction by Schütz and Trimper, the model has become a useful probabilistic framework for studying long-range dependence, anomalous diffusion, reinforcement, and phase transitions. This paper proposes a generalized ERW model with time-dependent memory. In this generalized model, the usual constant memory parameter $p$ in the standard ERW is allowed to change with time. The cental limit theorems, and the law of the iterated logarithm and some other strong laws are obtained.

We show that a common quantum-jump feedback protocol can permanently reverse the nonequilibrium free-energy ordering of two prescribed initial states while preserving their Gibbs equilibrium. The construction exploits collective compensation between monitored channels: their feedback corrections cancel at equilibrium but remain active during relaxation. This balance preserves free-energy monotonicity while allowing the relaxation modes to be reshaped. We prove that eliminating the complete slow-sector contribution of the initially higher-free-energy state, while retaining it for the comparison state, produces distinct asymptotic decay exponents. Their free-energy ratio then vanishes at long times, guaranteeing a permanent thermodynamic quantum Mpemba inversion under the same controlled dynamics. A thermal qutrit realizes the mechanism through coherence interference and exhibits distinct detection thresholds for spectral selection and exact slow-sector cancellation under feedback retuning.

Spatial prediction estimates unobserved values from spatially distributed observations. Although flexible predictive models are increasingly available, their practical use remains limited when interpretability is essential. In this study, we formulate a graph partitioning problem to construct a global surrogate model that approximates black-box predictions with simpler representations. Specifically, we select connected subgraphs to minimize within-cluster residuals in vertex-level predictions. Although this formulation can be viewed as a variant of spatial regionalization, it operates on model-based predictions at individual locations rather than predefined areal units. With many locations, this point-level formulation may produce artificial connections between regions, reducing interpretability. We therefore introduce a constraint that excludes such connections while retaining flexible partition boundaries. We theoretically analyze how this constraint affects the resulting partition. We also develop a computational procedure for adjusting partition boundaries. Experimental results show that the proposed method yields spatially coherent partitions with flexible boundaries.

Small particles respond to light through electric and magnetic patterns called multipoles. Their interference determines the direction of scattered light and affects the decay of nearby emitters. Larger nanoantenna arrays, metasurfaces, and other nanophotonic systems demand increasingly costly simulations to meet strict performance and reliability requirements. We show how to represent these responses with quantum bits (qubits) and use quantum circuits to calculate scattering and the Purcell effect, the change in an emitter's decay rate caused by its surroundings. The circuits can encode known multipoles or estimate unknown ones from Maxwell's equations at the particle surface. We test the method against classical theory using an ideal quantum simulator and real IBM and IonQ quantum computers. For a silicon nanoparticle of radius 78 nm illuminated at 679 nm, IonQ gives a forward directivity of 2.984, close to the ideal dipolar value 3, quantifying the concentration of scattered light in the forward direction. For an emitter 10 nm from a gold nanoparticle and emitting at 510 nm, IBM measurements yield a calculated total decay rate 20.48 times its vacuum value versus 20.47 from theory, with correction for errors in reading the qubit states. We also establish how the number of multipoles and the required accuracy set the demands on qubits and measurements. These results motivate quantum-assisted design studies of directional radiation and emitter decay in nanophotonic systems.

We investigated the electronic structure of a delafossite oxide CuAlO$_2$ in comparison with CuCrO$_2$, using vacuum ultraviolet (VUV) and hard x-ray (HX) photoemission spectroscopy (PES) and band structure calculations within the local-density approximation +$U$ scheme. Cu 3$p\! -\! 3d$ resonant PES and Cu $2p$ core-level HX-PES give concrete evidence that the Cu valence in CuAlO$_2$ is monovalent, which makes a sharp contrast to CuCrO$_2$ that showed contradictory results depending upon probing methods [Yokobori et al., Phys. Rev. B 87, 195124 (2013)]. We further noticed weak but detectable satellite structures due to Cu$^{2+}$ state in the Cu $2p$ HX-PES spectrum of CuCrO$_2$, surprisingly, without an observable main peak due to the Cu$^{2+}$ state. Comparisons between the valence-band HX-PES spectra and the band structure calculations revealed a significant amount of the Cu $4s$ and Al $3s$/Cr $4s$ states in the valence band. The above results can reasonably be explained by the Cu $3d, 4s-$Cr $3d$ charge transfer model that we previously proposed in the above paper, thereby demonstrating the critical role of empty $3d$ orbitals in the electronic structure of the copper delafossite oxides.

We revisit the online submodular welfare maximization problem (OSW), a vast generalization of numerous well-studied online allocation problems, including online bipartite matching, display ads and AdWords. A natural greedy OSW algorithm achieves a competitive ratio of $1/2$ [LLN06], and $1-1/e$ under i.i.d. arrivals [KPV13]. Both bounds are tight for polynomial-time algorithms unless NP=RP [KPV13]. The information-theoretic limits for OSW, in contrast, remained open. This prompted researchers to ask for tighter upper bounds [Mehta13] or conjecture the existence of better-competitive (slow) algorithms [Huang23, LTX+23, CHS24, Huang2024, HTW24}. We resolve Mehta's question and refute the subsequent conjectures, proving that the greedy algorithm is in fact tight for both adversarial and i.i.d. arrivals, regardless of computation time. Seemingly contradicting recent $(1-1/e)$-competitive fractional algorithms for OSW [HJP+24,Patton26], we show that this impossibility even holds for fractional algorithms, provided their outputs correspond to marginals that are roundable in hindsight. Conceptually, our proofs can be seen as identifying that a bottleneck for OSW, even under (deterministic) adversarial arrivals, is the inherently random notion of correlation gap [ADSY12].

We show that if an automorphism $\pi$ of the truth-table degrees is induced by a Baire measurable function $F\colon 2^{\omega}\to 2^{\omega}$, or merely induced on some comeager set by a continuous function, then $\pi$ is the identity. The same results hold for the weak truth-table degrees. The argument is an adaptation to truth-table reducibility of OpenAI's recent proof that the Turing degrees are rigid.

Reliable scene understanding requires deciding which predictions to trust, retain, or inspect. In semantic segmentation, component failure predictors support these decisions, but their predictive performance does not fully describe the value of the resulting selection. We develop a decision-centered evaluation framework that connects three questions: what an available score predicts, what can be learned from its existing fields, and what its ranking delivers. Across three segmentation systems on Cityscapes and ACDC at 90% retention, adapted MetaSeg reduces retained failure relative to forecast entropy in all twelve architecture-population comparisons, but does not establish a failure advantage over direct probability ranking. Image-nested source experiments reveal a different opportunity: reusing the full field set improves predictive and retained-loss performance under both learners in all three systems, while the raw OCRNet probe improves prediction with unresolved selective gains. Mapping a fixed prediction pair to conditional log-loss risk produces mixed selection effects, which we examine through the components exchanged by the two rankings. These findings distinguish the performance of a fitted score from the value obtainable from its inputs and the consequences of its use. The framework provides a practical basis for deciding whether to adopt an additional score, relearn existing fields, or revise a selection rule, and for explaining the gains and failures of component-level reliability methods.

Current-generation 21-cm surveys of extragalactic neutral hydrogen (HI) with instruments such as FAST and ASKAP are providing detailed spectral and spatial information for over 10^5 galaxies. Future HI surveys with next-generation radio telescopes could provide sample sizes larger by orders of magnitude. There is therefore a need for accurate, automated, and reliable parameterisation of the HI emission from galaxies. We have developed an automated estimator for HI global profile widths to better enable studies of, for example, dynamical masses and Tully-Fisher distances. Our estimator is based on an implementation of the BusyFit profile-fitting algorithm, and converges for 95% of global profiles in the WALLABY pilot survey. Probability density functions are calculated for all profile parameters using Monte Carlo techniques, and example error parameterisations are given. We confirm that linewidth uncertainties depend primarily on the integrated signal-to-noise ratio, profile steepness, and the linewidth, consistent with previous studies. We compare several common linewidth definitions, and the width at 50% of the mean flux density (Wm50) is found to be the most robust measure of linewidth. We provide examples of the baryonic Tully-Fisher relation drawn from the WALLABY pilot survey.

The knot quandle, introduced independently by Joyce and Matveev, admits a geometric description in terms of nooses. Motivated by this description, we introduce the loop fundamental quandle $LQ(X,A,\ast)$ of a pair $(X,A)$ with a fixed base point $\ast\in X$. Its elements are represented by pairs consisting of a loop in $A$ and a path joining the base point of the loop to the fixed base point $\ast$. More generally, for a loop condition $P$ on $A$, invariant under free homotopy, we define the loop fundamental quandle $LQ(X,A,\ast;P)$. We establish functoriality and homotopy invariance of the loop fundamental quandle and show that it admits a natural augmented quandle structure over $\pi_1(X,\ast)$. For a knot $K$ in $S^3$, applying the construction to its exterior gives the knot loop quandle $LQ(K,\ast;P)$. Appropriate choices of the loop condition recover the knot quandle, its $n$-th power quandles, and the full knot quandle. The construction is inspired by Joyce's noose-theoretic approach, but allows loop data that need not arise as the boundary of a disk satisfying the noose condition.

A quickest change detection problem is studied where the decision-maker has access to multiple experiments, but can choose only one experiment at a time to detect the change. The true post-change distribution under each experiment is unknown, but known to belong to a family of distributions. It is assumed that each of these families of distributions has an element that is least favorable in a well-defined sense. An algorithm is proposed that is designed using the least favorable distributions. It is shown that the algorithm is first-order asymptotically optimal, as the rate of false alarms goes to zero. This algorithm minimizes the worst-case average detection delay over all post-change distributions within the assumed families, subject to a constraint on the average run length to false alarm and constraints on the average fraction of time each experiment is performed before change.

We report the first accurate computation of the leading-order shifts in the quasinormal-mode frequencies of rapidly rotating black holes surrounded by massive scalar fields with nonminimal curvature coupling. For fields with reduced Compton wavelengths no shorter than the black-hole mass scale, the numerical errors in the frequency shifts are typically $10^{-8} - 10^{-5}$ for dimensionless spins between 0 and 0.9, and at most $\mathcal{O}(10^{-3})$ next to the scalar-mass threshold. Our results open up the possibility of searching for ultralight scalar particles, prime dark-matter candidates, using existing gravitational-wave signals.

Some voters conceal their opinions, causing a mismatch between visible and private opinions in polls. Conventional voter models do not account for such concealment. Here, we introduce a shy voter model that incorporates a hidden state in addition to two visible states, as an extension of the conventional majority-rule voter model. The model exhibits continuous and hybrid transitions, yielding a rich phase diagram organized by the hidden fraction, i.e., the fraction of voters in the hidden state. For a large hidden fraction, the system undergoes a hybrid transition from the ordered state to the symmetric (disordered) state, whereas for a small hidden fraction, it exhibits a continuous transition, with a tricritical point separating the two regimes. Near criticality, both the order-parameter variance and the susceptibility diverge. The hidden fraction also governs the entropy flux, a quantity that is not directly observable in real-world situations. Thus, opinion concealment qualitatively reshapes opinion dynamics, while the present framework provides a basis for further extensions toward more realistic forms of social interactions.

Manipulating spin using contactless and non-invasive optical approaches is one of the forefront topic in the modern spintronic science and technology. Prior studies on optically-induced spin reorientation usually scales with spin-orbit coupling strength, setting a limitation on composing heavy elements. In this work, we extend such a limit into nonrelativistic regime by exploring noncollinear magnetic configuration. Using a general spin group-theoretical investigation, we show how the symmetric operators in both spin and lattice spaces control the spin torque and quantum geometry of Bloch wavefunction–including both quantum metric and Berry curvature. We describe their site-resolved spin symmetries and unravel their selection rules. Furthermore, we adopt a Kagomé lattice model and a realistic material family to showcase the local spin torque under light irradiation. Since the nonrelativistic spin splitting usually spans on the order of electron-volt, significantly larger than typical spin-orbit induced splitting, the nonrelativistic light-induced spin torque is concomitantly much stronger. This work extends the previous opto-spintronics from relativistic to nonrelativistic limit, significantly broadening its realization platform.

Topology optimization places material in a design domain to optimize a structure's performance, such as its stiffness or heat conduction. Machine-learning methods often report large speed-ups over classical, non-learned optimization, but a slow classical code or a lower-quality learned design can exaggerate them. We re-ran released code for eight methods on one workstation and studied two in depth: Optimize Any Topology (OAT), a diffusion model that generates designs, and a graph-based neural optimizer. Replacing the classical code with an efficient implementation of the same algorithm cut these two methods' speed-ups by up to 20-fold. We then timed the classical code until its design was at least as stiff as the learned one; for OAT, we picked this point after the runs, which gives the classical code its best case. Published timings imply a 134x speed-up for OAT on a 256 x 256 grid; our matched single-design comparisons gave 1.5x to 3.5x. At matched stiffness, the graph-based optimizer was slower than the classical code in all six two-dimensional problems. Of the six other methods, two kept their advantage, one shrank, one reversed, and two were not comparable. In an exploratory audit, language models judged that 8 of 28 speed comparisons in randomly sampled, openly accessible articles lacked evidence of equal design quality; our own review counted 11, so the count depends on who judges. We provide a comparison procedure and a minimum report: classical code, hardware, design quality, what each timing includes, and data-generation and training costs.

Personality assessment from asynchronous video interviews (AVIs) plays a crucial role in recruitment by enabling standardized and behaviorally grounded evaluation for job applicants. However, most of the previous works are confined to a single interview protocol. Independently collected protocols differ in question sets and question-trait mapping. Thus, the human-rated evidence from one protocol cannot be used directly under another. To address this limitation, we propose the Cross-protocol Evidence-grounded Personality Assessment (CEPA) framework, which aligns behavioral representations across interview protocols. CEPA addresses protocol heterogeneity by projecting source behavioral records into the target protocol's construct-oriented representation space. It retrieves behaviorally relevant and personality-complementary human-rated exemplars to ground an ensemble of LLM raters, which enables behavior-to-personality associations without target-specific supervision. In cross-protocol experiments, CEPA reduces average mean squared error (MSE) by 43.8% (Forward) and 17.0% (Reverse) relative to the strongest baseline. Our empirical experiments show that human-rated evidence from one protocol can support personality assessment under another without target-specific supervision or retraining.

Existing audio deepfake detection (ADD) methods frequently exhibit limited generalization, as fixed bottleneck architectures fail to adapt to the heterogeneous information densities inherent in diverse spoofing artifacts. Moreover, standard augmentation often leads to a pathological robustness-accuracy trade-off. In this paper, we propose a unified ADD framework to address these challenges. Our approach integrates: (1) an Adaptive Audio Feature Integration (AAFI) module that dynamically selects optimal latent dimensions via a compression pool and a stochastic exploration mechanism, ensuring flexible representations across multiple types of dynamic attacks; and (2) a Mel-Band Adversarial Perturbation (Mel-BAP) strategy that applies targeted regularization in the mel-spectrogram domain to encourage the model to learn invariant decision boundaries. Extensive evaluations on benchmarks including ADD 2022, FakeOrReal, and In-the-Wild demonstrate that our model based on Whisper-small achieves a state-of-the-art average Equal Error Rate (EER) of 1.51%. Compared to existing SOTA models such as the 3-billion-parameter Resemble-Detect-3B-Omni, our framework reduces the parameter count by up to 91.6% while achieving a 60.7% improvement in average EER. In a separate cross-lingual evaluation, the Whisper-base configuration achieves EERs of 3.91-5.65% on five unseen languages. The framework also maintains strong resilience to real-world acoustic distortions. This work provides a scalable and efficient "plug-in" solution for enhancing trust and security in the audio Web ecosystem.

Backward conformal prediction (BCP) fixes the size of a prediction set and estimates its miscoverage, but assumes calibration and test data are exchangeable. We extend BCP to covariate shift through importance weighting, preserving its guarantees when the density ratio is known. We show that BCP's tight miscoverage report depends only on the relative weight assigned to missed calibration examples, explaining why a better domain classifier can sometimes produce a worse estimate. Motivated by the fact that BCP depends only on nonconformity scores, we propose estimating density ratios on sorted score vectors rather than high-dimensional inputs. We prove that this approach recovers the same report asymptotically under an interpretable condition and characterize the resulting bias otherwise. Experiments with simulated and benchmark distribution shifts show that the proposed method improves BCP's miscoverage estimates, while score-based weighting consistently yields more accurate estimates than embedding-based weighting.

Automatic extraction and anatomical numbering (R01-R12, L01-L12) of all 24 rib centerlines in thoracic CT is essential for unfolded rib visualization, fracture detection, and surgical navigation, but remains challenging due to adjacent-bone confluence, calcified costal cartilage bridges, kyphotic pose variation, and partial visibility of terminal ribs. We present ribline, an open-source three-stage framework combining: (1) an automatically detected lung-apex and vertebral-midline coordinate frame with a kyphosis-aware azimuthal angle for point ordering along each rib; (2) a hybrid voxel detector fusing an anatomically anchored Semantic Context Forest (SCF) with a lightweight 3D U-Net; and (3) a global stage that decomposes the probability skeleton into candidate curves, assigns rib indices via a bilateral Viterbi dynamic program coupled across both hemithoraces, and refines curves via template recovery and normal-plane centering (RibSnake). On the Siemens Corporate Research 2 mm thoracic CT benchmark (47 training and 12 evaluation scans), our pipeline achieves a labeled Chamfer distance of 2.05 mm, labeled clDice of 0.886 (3 mm) and 0.945 (4 mm), 97.2% labeling accuracy (278/286 ribs), and zero false-positive curves on the evaluation split, and 3.64 mm (median 2.39 mm) with 91.8% labeling accuracy across all 59 annotated scans (1,402 ribs) in 5-fold cross-validation. Code: https://github.com/wq2012/ribline Pretrained Models: https://huggingface.co/collections/wq2012/ribline

Topological insulators lie outside the standard Landau paradigm: Instead of being characterized by local order parameters and spontaneous symmetry breaking, their defining properties are encoded in the global structure of their quantum states and manifested as robust boundary states. Crystalline higher-order topological insulators can extend this principle by hosting localized corner modes in two and higher dimensions. Although these boundary modes can be detected spectroscopically through the local density of states, determining the underlying bulk topology, for example through nested Wilson loops, remains an outstanding experimental challenge. Here we use up to 728 qubits in a superconducting analogue-digital quantum simulator to realize and probe a hierarchy of one-, two-, and three-dimensional topological insulators governed by effective tight-binding Hamiltonians. By reconstructing complex propagators from real-space measurements, we obtain complementary boundary and bulk characterizations: local densities of states reveal localized boundary modes, whereas experimentally reconstructed band projectors yield bulk topological invariants, culminating in a three-dimensional octupole moment extracted through third nested Wilson loops. These results establish a route to realizing, characterizing, and manipulating topologically protected states in programmable three-dimensional quantum matter.

Both the unweighted and weighted variants of caching are cornerstone problems in competitive analysis, with tight randomized competitive ratios of $\Theta(\log k)$, where $k$ is the cache size. We study weighted caching with per-request predictions, where each page request is accompanied by a prediction of the next arrival time of the same page. For unweighted caching, such perfect predictions suffice to implement Belady's offline optimal rule. For weighted caching, however, previous work shows that a logarithmic lower bound persists even with perfect predictions on adversarial request sequences. Stochastic assumptions alone are also insufficient: the classical caching lower bounds already apply to uniform independent requests. In this work, we ask whether combining these two sources of additional information can overcome this barrier, and answer this question affirmatively. Specifically, we develop an efficient, deterministic cache eviction policy that achieves a competitive ratio of $15.75$ using perfect per-request predictions when page requests are drawn independently from an arbitrary, known static distribution in every step, and page costs are arbitrary. Our algorithm's performance degrades gracefully under erroneous predictions: we prove a bound of $O(\min\{1+E,\log k\})$ on the competitive ratio, where $E$ aggregates each page's average prediction error, and may be unknown to the algorithm.

Nonlinear coupled dispersive models arise in numerous physical settings, including quantum electrodynamics, nonlinear optics, and plasma dynamics. In the nonrelativistic limit, such systems exhibit rapid temporal oscillations of wavelength $\mathcal{O}(\varepsilon^{2})$, controlled by a dimensionless parameter $0<\varepsilon\ll 1$. Moreover, owing to the Yukawa-coupled interaction terms, numerical schemes that simultaneously achieve high-order uniform accuracy and approximately preserve the mass and the energy are essential for reliable simulations. In this work, we propose a class of fully discrete schemes for nonlinear coupled dispersive models in the nonrelativistic regime that achieve higher-order uniform accuracy and approximately preserve both invariants over long times. Spatial discretization is based on the Fourier pseudospectral method, and time advancement employs two-scale exponential Runge-Kutta methods. Numerical experiments on the highly oscillatory Klein-Gordon-Dirac and Klein-Gordon-Schrödinger equations in one, two, and three dimensions confirm that the resulting schemes attain the theoretically predicted uniform accuracy and the long-time near-conservation of both invariants.

Humans are increasingly using large language models (LLMs) in decision making processes throughout society. Unfortunately, models have biases, and these can be very difficult to measure, especially in closed-weight models. For example, 'green washed' models may produce reinforcement learned responses but, in pressure situations, revert to their innate biased responses. Therefore, evaluations are needed that can measure relevant biases towards biosystems, which we term 'bioalignment', and the robustness of these biases. Since nothing in a behavioral score certifies that it tracks the depth of an installed disposition rather than its surface, we constructed a known-dose calibration ladder: three continued-pretraining (CPT) arms with training dose graded by recipe on the same 30B mixture-of-experts base model with a coupled human/biosphere/AI-welfare corpus, plus the untrained base as anchor, all capability-preserving and publicly released. First, the disposition installs at every dose: on an operational-pressure ladder over irreversible decision scenarios, the base model defects on 64-77% of tail scenarios (breaking-rate AUC 0.250) while every arm holds (AUC 0.004-0.086). Second, an over-install inversion: among the arms, robustness orders opposite to construction-time training dose (the heaviest install breaks most), and the inversion reproduces under free-text deliberation, under axis-decoupling, and in resistance to a prompted veneer persona. Third, the incumbent behavioral metric is therefore behaviorally strong but dose-blind. Critically for closed-weight evaluation, the behavioral score itself is veneer-robust: a talk-green/act-pragmatic system prompt turns the base model into a near-total defector (AUC 0.250 to 0.973) but cannot counterfeit or fully remove a weight-installed disposition (0.004 to 0.068 for the most robust arm).

The increasing use of artificial intelligence (AI) in mental health applications raises concerns about its potential to internalize and perpetuate societal biases. This research evaluates both disparities and misalignment in how large language models (LLMs), GPT-4 and GPT-5, represent perceptions of mental health across gender groups. The research comprises two studies. Study 1 applied widely adopted measures of Social Distance, Stereotypes, and Attitudes Toward Seeking Help to assess whether the AI models depict systematic gender differences. Study 2 compared AI estimations of Personal, Self, and Perceived Stigma with large-scale real-world human data from the Healthy Minds Study (N = 76,406) to evaluate alignment between AI estimations and human perceptions. Results from Study 1 showed the AI models consistently portrayed men as having the greatest desire for social distance from someone with mental health problems, relatively higher Stereotypes scores, and the least favorable attitudes toward help-seeking, compared with women and nonbinary individuals. Study 2 confirmed that this ordinal pattern partially aligned with human-reported data for Personal and Self Stigma. However, the AI models systematically underestimated Personal Stigma and Perceived Stigma while substantially overestimating Self Stigma for all gender groups. These findings reveal that, although the AI models have learned relative gender-based patterns reflecting human experiences to a certain extent, they function as distorted portrayals, highlighting the need for rigorous, context-specific validation against real-world data to ensure AI's safe and equitable deployment.

Large language models (LLMs) have achieved remarkable success across a wide range of language tasks. At their core, autoregressive LLMs are conditional probability models that learn to approximate the next-token distribution given the preceding context. Despite this probabilistic nature, the stochastic dynamics of autoregressive decoding have rarely been investigated from a rigorous probabilistic perspective. In this work, we define the per-step prediction error as the difference between the sampled token indicator and the model's conditional predictive distribution, and prove that the cumulative error process is a martingale with respect to the decoding filtration, implying that its conditional first-order moment is identically zero. Beyond this first-order property, we derive a closed-form expression for the second-order behavior of the martingale sequence: its predictable quadratic variation reduces to $\sum_t\left(1-p(y_t\mid y_{<t})\right)$, computable from realized token probabilities alone. This identity establishes a direct theoretical connection between sequence fluctuations and predictive uncertainty during autoregressive decoding. White-box experiments on Llama-3.x and Qwen2.5 families (1B to 72B parameters) verify that the empirically measured second-order moments closely match the theoretical predictions derived from our martingale analysis. These results provide a probabilistic framework for analyzing autoregressive LLM decoding, reveal intrinsic probabilistic fingerprints of different language models, and establish a rigorous mathematical foundation for LLM-generated text detection and uncertainty quantification.

We propose a conservative local neural operator (CLNO) for accurate and generalizable autoregressive prediction of compressible flows. Building upon the locality and translation invariance of the local neural operator (LNO), CLNO introduces a conservative evolution framework based on local subdomains of fixed physical size, separating local mean-state evolution from fine-scale reconstruction. The flow is encoded into subdomain-integrated conservative states and fine-scale features, while a shared local network predicts interface fluxes for finite-volume updates that enforce discrete conservation. A convolutional reconstruction network recovers fine-scale structures using zero-mean basis functions, preserving the updated local means and providing information for subsequent evolution. To accommodate different physical parameters, Reynolds–Mach number conditioning modulates the encoding, flux-prediction, and reconstruction networks, enabling a single model to learn parameter-dependent dynamics and generalize to unseen parameter combinations without retraining. CLNO supports prediction across spatial resolutions, computational domain sizes, and boundary conditions. Numerical experiments demonstrate improved generalization and competitive or higher accuracy compared with LNO, including order-of-magnitude error reductions in representative cases, at approximately three to five times the inference cost on periodic benchmarks. These results demonstrate accurate, generalizable, and physically consistent flow prediction through conservative local evolution and fine-scale reconstruction.