Papers

In this paper we give a polynomial-time reduction from the Subset Sum Problem to unconstrained static output feedback stabilization, establishing its NP-hardness. The construction uses two scalar building blocks to impose approximate discrete choices and a weighted-sum constraint. Once the problem is encoded, we relate the stability of the $N+1$ decoupled loops encoding the problem to that of a coupled plant. This is accomplished by leveraging frequency separation via a band-pass transformation, and comparing the root counts of the true characteristic polynomial with that of the different blocks in different regions of the right half-plane. The construction then naturally bounds every stabilizing gain and gives explicit modulus-margin estimates, ensuring that the plant data have polynomial binary encoding length.

We summarise the recent advances on the generation of high-order harmonics in optical metaphotonic structures such as isolated resonators and metasurfaces. In such subwavelength-patterned structures, extreme nonlinear effects are expected from the interaction between ultrafast laser pulses and structured planar surfaces which support various resonances. High-harmonic generation (HHG) is considered as an effective tool for realising extreme ultraviolet light sources and attosecond pulses, and it was observed previously in gases, liquids, and solids. Resonant metaphotonics can offer a novel sub-wavelength platform for the HHG effects, and it can provide new strategies for the design of efficient integrated light sources. We start our discussion from a brief overview of HHG in gases, liquids, and unstructured solids, and then move to summarising the recent experimental observations of HHG in individual resonant nanoparticles and resonant dielectric metasurfaces. We focus on different types of resonances (plasmonic vs. Mie resonances vs. bound states in the continuum), and also present the observation of non-integer power dependencies of the generated harmonics driven by strong resonances. We also mention current unsolved problems and identify new promising research directions involving HHG in metasurfaces.

In graphical two-choice allocation, each arriving ball is assigned to one endpoint of a random edge. We study rules whose decision is a monotone function of the two endpoint loads, allowing edge-dependent thresholds and fresh randomization. Such a rule has an exact unit-discrepancy coupling: adding one ball to the initial state produces one tagged discrepancy at every later time. We represent the tag by conditional-expectation projections on the marked edge space and obtain diffusive displacement bounds. A transport-volume inequality then converts slow propagation of influence into lower bounds for the load gap. On the cycle with $n$ vertices, from every initial distribution and at every physical time $t\ge 1/n$, the expected gap is at least a constant times $\min\{\sqrt n,t^{1/4}\}$, and the gap exceeds this scale with probability at least $1/8$. After exactly $k\ge1$ allocations, the corresponding scale is $\min\{\sqrt n,(k/n)^{1/4}\}$. No stationarity, symmetry, recurrence, or moment assumption is used. A smoothed threshold rule in the same class has expected gap $O(\sqrt n\log n)$ up to any fixed polynomial time horizon, so the saturated cycle bound is sharp within the class up to a logarithmic factor. The general inequality also yields a lower bound of order $\sqrt{L/K}$ on the $L\times K$ rectangular torus $C_L\square C_K$; combined with a strategy-independent logarithmic bound, this gives order $\sqrt{L/K}+\log(LK)$. These results separate endpoint-local rules from global-information strategies that achieve polylogarithmic gaps on cycles. All numbered results are verified in Lean.

We study finite-blocklength lossy transmission of a Gaussian memoryless source over memoryless, possibly nonstationary block erasure channels under an excess mean-squared distortion criterion. We derive computable nonasymptotic achievability and converse bounds and establish matching third-order, channel-uniform normal approximations. Our achievability bound exactly evaluates the ensemble-average excess-distortion probability of a specified random coding scheme and improves corresponding specializations of known general one-shot bounds. Our converse conditions on the erasure pattern and source energy and combines spherical-cap and volume bounds, with the spherical-cap term providing the geometric prefactor needed for the matching third-order term. In our channel-uniform normal approximation, we show that for fixed distortion ratio, target excess-distortion probability, and block size, the sufficient and necessary information-balance conditions have the same dispersion and $\frac{1}{2}\log k$ terms, where $k$ is the source blocklength, and differ only by bounded remainders that are uniform over the channel blocklength and erasure-probability profile. Numerical evaluations compare the nonasymptotic JSCC bounds and their common third-order normal approximation with an optimized symmetrized SSCC achievability benchmark.

We study the ergotropy and the thermodynamic potentials of a qubit battery charged by repeated interactions with clusters of thermal ancillas, qubits or oscillators, through a composite system-bath coupling that generates steady-state coherence in the energy basis. A single parameter encoding the bath quantum statistics yields the coherence and ergotropy in closed form for any cluster size. For large clusters, the ergotropy becomes independent of the bath statistics and, at optimal couplings, reaches a universal fraction of the equilibrium internal energy of the qubit at the bath temperature. Since the charged state has no population inversion, all extractable work comes from coherence. The ergotropy is flat at low temperatures. We trace this plateau to the third law, and show that the ergotropy is proportional to the equilibrium enthalpy of the qubit, whose slope vanishes with the heat capacity. For a battery composed of multiple qubits, the coherence grows exponentially with the number of qubits while the ergotropy grows linearly, both remaining a nearly constant fraction of their respective maxima. The charged state is a non-equilibrium steady state with finite entropy at zero temperature, sustained by the work of switching the collisional interaction on and off. The cost is nonzero whenever the parallel coupling is nonzero, and, unlike the ergotropy, it depends on the bath statistics.

Coding agents have become real users of high-performance computing (HPC) systems, yet today's HPC abstractions, interfaces, and policies remain designed for human-driven workflows. In our measurement, users running coding agents are only 19.5% of the observed population, but account for 55.8% of job submissions, 29.1% of CPU core-hours, and 42.7% of GPU-hours. Agents are not simply faster humans. They issue commands at 20.8x the human rate, decompose work into fine-grained explore-modify-execute loops, and pursue open-ended goals through trial-and-error campaigns that continue through nights and weekends. These behaviors strain abstractions built for human timescales, surfacing as control-plane pressure on the scheduler, metadata-intensive I/O on bandwidth-provisioned filesystems, repeated rediscovery of what earlier sessions already learned, and new prompt-injection and policy-enforcement surfaces. Neither banning agents nor treating them as ordinary users is sustainable. We instead argue for co-design, that facilities should treat agents as first-class principals where agents become facility-aware tenants. We outline the resulting challenges and opportunities in compute, storage, agent memory, and safety.

LLM watermarking has become an effective approach to distinguishing AI-generated text from human-written text by embedding detectable patterns during generation. However, a small post-generation edit may change the meaning of the text without removing its overall watermark signal, creating a risk that the modified content is still attributed to the original model. We propose Anchor-ECC, which incorporates the error-correcting code (ECC) constraints and explicit boundary anchors into the watermark structure and pairs them with a dynamic-programming decoder to detect and localize post-generation edits. Across Qwen3-8B, Mistral-7B-Instruct-v0.3, and OPT-125M, the approximate-hard setting achieves about 99.7% block-level true positive rate (TPR) with at most 7.6% false alarm rate (FAR) for edit detection under mixed insertions, deletions, and substitutions, while preserving the distinction between watermarked outputs and unwatermarked text. Additional quality experiments identify lower-perplexity configurations that retain strong edit-detection performance. Together, these results extend LLM watermarking from source identification to local integrity verification while supporting configurable trade-offs between detection reliability and generation quality.

Modern multimodal models bring generation and understanding into a single unified system, which enables them to provide and learn from their own feedback. Motivated by this unified capacity, we introduce UniEvo-VL, a self-evolving framework for multimodal models to learn from this constructive self-correction feedback during test-time compute. Instead of relying on a separate, often larger, teacher, we leverage their self-critiques as privileged information and ask a single multimodal model to act as both teacher and student with different contexts. The student only sees the vanilla question, while the teacher conditions on the privileged critique. Then training minimizes the per-state divergence between their denoising diffusion distributions over the student's own sampling trajectories. Experiments demonstrate that UniEvo-VL improves the image generation capabilities of multimodal models, while maintaining their sensitivity to additional reflection information. Specifically, we build on top of the open-source Qwen-image-2512 and observe a significant performance gain from 0.747 to 0.808 on GenEval and from 32.97 to 35.53 on GenEval2 Soft-TIFA. Moreover, attempts with more powerful external critics (e.g., GPT5.6-Luna) show that multimodal models with strong judge capabilities can anticipate a higher self-evolving ceiling. Last but not least, mixed text-rendering outcomes show that our self-improvements may not be uniform across different tasks. Our study aims to shed light on the current hot recursive self-improvement research line to enhance the user experience when using multimodal models without external supervision or guidance.

Readout-side residual hybrids concatenate raw inputs with measured quantum features. Under single-example gradient sharing, a biased first linear layer admits standard analytic recovery of its input, so the bypass exposes raw coordinates without requiring inversion of the quantum circuit. We audit this mechanism using two tabular datasets, four architectures, and metrics conditioned on feature visibility. Iterative gradient matching gives median full-record PSNR of 73-96 dB for residual and input-only heads. Quantum-only heads score 8-11 dB on the full record but 54-96 dB on the six input coordinates they actually encode. These are reconstruction results for the tested six-input, six-observable circuits, not a general statement about quantum encodings. A loss-threshold membership attack remains near chance. The contribution is a visibility-conditioned privacy audit: omitted coordinates must not be credited as protection supplied by quantum processing, and near-exact PSNR differences must not be interpreted as meaningful privacy rankings. Our findings concern individual gradients and do not establish leakage under aggregation or multiple local training steps.

Experimental investigation and modeling of flapping-wing aerial vehicles are limited by the scarcity of large-scale records that temporally align wing kinematics, aerodynamic responses, and flight states. Existing datasets are often limited in scale and affected by measurement noise and temporal misalignment between rapidly varying wing motion and the associated dynamic response, particularly during high-frequency flapping. We introduce FlapKAD, an episode-structured simulation dataset comprising 2,000 rigid-wing flight episodes and 720,152 valid time steps, with bilateral wing kinematics, aerodynamic responses, and flight states recorded synchronously within a common clock. FlapKAD supports a unified bidirectional sequence-prediction benchmark constructed from the same temporally aligned episodes. The forward task predicts future vertical force coefficients and body vertical velocity from histories of realized flap and twist angles, whereas the inverse task reconstructs future flap- and twist-angle trajectories from the corresponding response histories. A benchmark of eight representative time-series architectures across multiple prediction horizons reveals direction- and horizon-dependent model behavior, systematically higher reconstruction errors for twist angle than for flap angle, and no consistent advantage from increased architectural complexity. FlapKAD provides a reproducible dataset and benchmark for studying coupled wing-kinematic, aerodynamic, and flight-state dynamics in flapping-wing aerial vehicles.

Steering large language models typically relies on linear, context-independent interventions in activation space, an assumption that recent work has challenged and that can induce an information bottleneck when a fixed representation must encode many behavioral distinctions. We introduce MetaSteer, a method that learns nonlinear interventions with context-dependent effects and applies them to attention projection matrices, producing activation effects that vary with the input context by construction and requiring no linear concept-geometry assumption. Framed as preference-based optimization, MetaSteer is trained once on a pooled preference corpus and transferred zero-shot to unseen concepts and out-of-distribution contexts. We find that, despite using low-rank adapters, MetaSteer induces structured, context-dependent changes in hidden-state trajectories while partially preserving aspects of their local trajectory dynamics, including velocity and curvature. We evaluate MetaSteer on three controlled text-generation benchmarks and three agentic settings across multiple model families and scales. MetaSteer matches or outperforms strong task-specific steering baselines on most aggregate comparisons in the zero-shot regime. Across the evaluated settings, stronger text-generation steering is associated with stronger agentic steering performance. We further discuss geometric trajectory effects, capability retention, and safety considerations raised by transferable steering.

Large Vision-Language Models (LVLMs) commonly perform spatial reasoning through chain-of-thought (CoT), encoding intermediate reasoning as autoregressive sequences of discrete language tokens. Such hard thinking requires committing to a single token at each step, even when the correct spatial interpretation remains uncertain. This early commitment constitutes premature discretization: an incorrect token selection can propagate errors through subsequent reasoning. We propose Soft Spatial Reasoning, a post-training framework that introduces soft thinking for spatial tasks in LVLMs. At each intermediate reasoning step, the LVLM forms a continuous soft state by mixing token embeddings rather than selecting a single token, allowing multiple candidate continuations to influence the next step. The appropriate degree of softness, however, can vary across reasoning steps: retaining multiple candidates may preserve a useful spatial interpretation, but if those candidates imply conflicting spatial relations, mixing them may interfere with subsequent reasoning. At the core of Soft Spatial Reasoning is AdaptSoft, a controller that uses the current hidden state and predictive uncertainty to adapt the degree of softness at each reasoning step. To train AdaptSoft, we introduce a gradient-alignment learning objective that provides a step-specific learning signal for softness control without intermediate reasoning supervision. Across diverse spatial benchmarks, Soft Spatial Reasoning outperforms hard and fixed-soft CoT baselines using the same backbone, as well as a range of existing LVLMs. The source code is available at https://github.com/rafiibnsultan/Soft_Spatial_Reasoning

Large Vision-Language Models (LVLMs) have made remarkable progress across visual perception tasks, yet spatial reasoning remains a persistent weakness, especially for questions that require reasoning over visual space. Recent spatial-reasoning methods incorporate generated grounding, where models predict bounding boxes, masks, or other localization outputs for task-relevant objects as part of their reasoning trace. However, these approaches typically optimize final-answer correctness alone, allowing correct answers to be rewarded even when the model does not reason from confidently localized task-relevant objects. We introduce SpatialCORE (Spatially COnfident REasoning), a post-training framework that turns the model's own confidence in generated grounding into a learning signal for spatial reasoning. Its central idea is to reinforce grounding that is both accurate and confident, encouraging the model to reason from confidently localized task-relevant objects. SpatialCORE realizes this through a self-regulating spatial reward that weights each predicted bounding box's matching quality by its coordinate-token confidence. An answer gate further ties grounding optimization to final-answer correctness. SpatialCORE achieves state-of-the-art results among open-source and specialized spatial reasoning models across diverse benchmarks, and transfers effectively in zero-shot settings to unseen data distributions. The source code is available at https://github.com/rafiibnsultan/SpatialCORE.

This paper proposes a control strategy for path following that is model-free and relies solely on deceleration for skid-steering planetary rovers navigating deformable loose terrain under continuously imposed traction asymmetry. While conventional controllers that are based on kinematics frequently cause slip-sinkage entrapment by accelerating the wheels during path correction, the proposed approach prevents this failure by setting an upper limit on the maximum commanded velocity. Heading correction is achieved solely through the selective deceleration of the outer wheels, which are located on the outside of the turn, driving them into a negative slip regime to act as a mechanical anchor. The system was evaluated using the four-wheel independent-drive rover EX1 under an asymmetric wheel configuration with different left and right grouser heights that induces significant deviations from the path. Experimental results demonstrate that this deceleration-only control successfully suppresses accumulated lateral drift across various velocity regimes up to 0.7 m/s without causing sinkage. Crucially, direct force measurements from onboard multi-axis sensors provide important empirical evidence of the underlying terramechanics, proving that the targeted deceleration establishes dynamic load equalization across the chassis and completely restores the native thrust capability of the opposite driving wheel.

We describe our winning entry to the Waymo Open Dataset 2D Video Panoptic Segmentation Challenge. The task asks for a semantic class at every pixel of every frame and, for countable objects, an identity that holds across 100 frames and across five overlapping cameras. We build on DVIS++, a cascade of a segmenter, a tracker, and a refiner, as our baseline. We propose hard region supervision (HRS) to improve the baseline. In particular, we use the baseline to define the hard region as where it makes mistakes, and design a loss and an auxiliary prediction head for this region. The auxiliary head is used only in training and removed at test time, so at inference the model trained with HRS has the same architecture as the baseline. In addition, we propose three test-time steps that further improve the results: a two-model ensemble, a merge of the segmenter's output into the final panoptic map, and cross-camera identity linking. On the challenge test set, our entry reaches 0.3547 wSTQ, 0.2071 wAQ, and 0.6075 mIoU, ranking first on all three metrics. It is 3.6 wSTQ points ahead of the second entry and 2.4 points ahead of our DVIS++ baseline.

Error mitigation is expected to turn noisy quantum measurements into more useful estimates. We show that it can instead amplify error. Under control-offset miscalibration, the evaluated unconstrained zero-noise extrapolation (ZNE) estimators are worse than no mitigation on 38-63% of simulated instances and produce extreme tail errors. A small IBM Heron study finds worsening on 80-88% of 18 instances across two depths, with mean error 3.0-4.1 times the raw error. In simulation, the median changes little, so median-only monitoring misses the failures. We then compare methods at the same online shot budget per evaluation and report offline training cost separately. After that cost is amortized, a budget-conditioned neural corrector occupies the low-budget end of the simulated accuracy-cost frontier and falls back to the raw estimate when an ensemble disagrees; its hardware transfer remains unsuccessful. Finally, we treat provider-reported calibration as an input that is not bound to the execution-time device state. A white-box projected-gradient stress test on this metadata increases the corrector's error 8.1 times within the feature ranges used for training and evades the disagreement monitor on half of the worsened cases. Together, the results connect budget-aware evaluation, tail risk, and calibration integrity in near-term quantum learning pipelines.

Long-horizon agentic workflows require models to sustain repeated state-dependent actions all while the context grows, sub-task complexity changes, and new data arrives. Each situation represents an independent axis along which an agent may fail. An agent reconciling a long ledger, for example, must repeatedly read its state, update the correct record, and preserve alignment across thousands of outputs. A model may accept the entire ledger yet lose its place or stop applying the operation consistently as generation proceeds. We introduce Long-Transduction, a controlled diagnostic that tests a model's ability to stay on task during long generation while continuously reading, mutating, and outputting input-context dependent operations such as arithmetic, sorting, variable lookups, and table transformations. Long-Transduction evaluation independently varies local task complexity, input data formatting, and context length isolate failures along each axis. We evaluate seven open-weight models, finding a 62.8% decrease when scaling context length from 4-128K, a 36.5% decrease when varying input format, and a 39.9% decrease by increasing local task complexity. Together, these failures represent critical liabilities in long-horizon agentic workflows.

Machine learning (ML) and artificial intelligence (AI) are becoming powerful tools in scientific research across various disciplines. In this review, we summarize recent progress in AI-assisted studies of nuclear structure and reaction observables, heavy-ion collisions and dense nuclear matter properties, many-body wave functions, experimental facilities and data analysis. This review focus on new progress since the last review in 2023, and machine learning in nuclear physics is evolving from purely data inferences to physics informed learning. Future directions on the integration of physical knowledge with modern learning architectures, large foundation models and other emerging methods are also reviewed. These developments suggest that AI is enabling and advancing new approaches towards most challenging nuclear physics problems.

We study the problem of sampling from a continuous density $\pi\propto \exp(-V)$ on $\mathbb R^d$, where $V\in C^2(\mathbb R^d)$ has a $\beta$-Lipschitz gradient and $\pi$ satisfies a logarithmic Sobolev inequality with constant $\alpha^{-1}$, and write $\kappa = \beta/\alpha$. We introduce the Gaussian cloud sampler, which achieves total variation accuracy $\varepsilon$ using $\widetilde O(\kappa d^{1/5}\,\text{polylog}(1/\varepsilon))$ gradient queries in expectation. The algorithm uses first-order rejection sampling (FORS) to correct the law of smoothed Picard HMC trajectories. To do so, we represent the iterates of the ideal Picard iteration via Gaussian clouds, whose centers are never evaluated, and we develop a suite of likelihood correction gadgets which only use samples from this indirect cloud representation.

Humanoids are increasingly capable of tracking complex whole-body motions, but physical interaction introduces a different challenge. When a robot makes contact with a person or the environment, it needs to respond to external forces while preserving the motion needed for the task. This response can vary across directions in the end-effectors and on the body. For example, an end effector may need to accommodate contact force in one direction while maintaining motion accuracy in another, while the robot body may resist an external force or move with it. We present a compliance framework for humanoid loco-manipulation that combines directional and tunable end-effector (EE) compliance with selectable root compliance for external force rejection or force following. A hierarchical reinforcement learning controller modulates a fixed whole-body tracking policy through high-level EE and root commands, while interaction forces are estimated from proprioceptive history. Our simulation and real-world experiments on a humanoid demonstrate directional stiffness control, online stiffness adjustment, distinct root compliance, compliant manipulation, and collaborative carrying.

Tau and amyloid-$\beta$ (A$\beta$) deposits co-occur in Alzheimer's disease, and tau fibrils have recently been shown in vitro to catalyze A$\beta$ primary nucleation in a fold-specific manner. A two-compartment kinetic model is developed here, describing tau aggregation within the neuronal soma and A$\beta$ aggregation in the surrounding interstitium. The adjustable coupling parameter is the fraction f$_{acc}$ of somatic tau fibrillar material accessible to interstitial A$\beta$. Homotypic A$\beta$ secondary nucleation is restricted to the accessible surface of the consolidating plaque rather than scaling with total fibril mass, which preserves the in vitro calibration of the rate constant while preventing the surface term from growing without bound over decades. Three model predictions emerge. First, the model predicts that tau-catalyzed nucleation can increase the soluble A$\beta$ oligomer concentration and the number of A$\beta$ fibrillar species, by factors of 4.6 and 2.0, respectively, at complete accessibility, while leaving total A$\beta$ fibril mass and plaque volume unchanged, since in the absence of clearance these are fixed by the monomer supply; oligomer burden and visible plaque burden are therefore decoupled. Second, the predicted effect requires substantial accessibility: a 50 % increase in accumulated oligomer exposure needs f$_{acc}$ $\approx$ 0.035-0.15, which is difficult to reconcile with tangles enclosed by an intact neuronal membrane and points instead to neuronal lysis and the formation of extracellular ghost tangles. Third, physiologically relevant oligomer dissociation and proteolytic turnover each suppress accumulated exposure, by approximately three orders of magnitude and, at zero tau accessibility, about seventyfold, respectively, and remove the effect on a biological-age measure entirely.

We develop a task-relative framework for certifying residual wrench authority after hover and contact loading in multirotors with bounded actuators. Using convex geometry, we derive signed margins for prescribed convex reserves, including Euclidean balls and weighted ellipsoids. We obtain computable reserve certificates from actuator-interiority bounds to support slack-maximizing allocation. To preserve the required reserve, we propose command projection onto a tightened feasible set. We then connect the available reserve to structured gain synthesis and certify a local tracking region that respects actuator limits. Within this region, we establish nominal exponential convergence and robust ultimate boundedness. For the prescribed task and morphology family, we show that the optimized octarotor attains a larger margin than the optimized hexarotor at equal total thrust. We evaluate the proposed framework in closed-loop simulations of sustained rigid-wall contact using a fixed-geometry octarotor and a variable-tilt quadrotor with matched installed thrust. The quadrotor's local certificate admits a higher normalized push limit for the prescribed task family. In tests beyond the realizability boundaries, we observe the predicted loss of authority through rotor-thrust limits for the octarotor and tilt-servo limits for the quadrotor.

Production LLM serving stacks combine an inference engine's local prefix cache with a shared KV-cache tier for fleet-wide reuse. The local cache distinguishes requests by adapter, weight configuration and sharing domain, but the shared tier may key entries only by token content and coarse model metadata. This boundary erases provenance and lets identical tokens under incompatible computational or sharing contexts collide. We call this composition gap provenance-blind reuse and present its first systematic study. A source audit of three vLLM connectors confirms the structural omission, while runtime experiments reproduce it across vLLM and two SGLang releases, 12 models from 7 families (0.5 B-32 B), and over 160 configurations. Cross-adapter collisions reduce accuracy from 0.94 to 0.64, incompatible KV representations reduce reasoning accuracy to zero, and salt omission enables 93% prompt identification from timing. We formalize the missing guarantee as the KV provenance contract: for a declared dimension registry, shared keys must be injective over computational and sharing provenance, with identities stable across workers. Any dimension with a stable identity can therefore be added without connector-specific key logic. A canonical descriptor binds per-request and per-worker provenance into lookup and store keys, while a differential checker detects dimensions that change KV state without changing the key. Implemented in vLLM and SGLang 0.5.20 across three cache paths, provenance binding eliminates unsafe reuse while preserving legitimate sharing. Hit-path latency changes remain within 0.34 ms and below run-to-run variation; retention grows with provenance diversity.

Foundation models for computational pathology are usually evaluated using AUC and accuracy, while calibration is often left untested. This matters because a model can be accurate on average but still assign overly confident probabilities to cases that are difficult even for pathologists. We study calibration across eight pathology foundation models. Using pathologist agreement as a measure of diagnostic difficulty, we find that calibration error is consistently higher on low-agreement cases than on high-agreement cases. This pattern is not apparent from aggregate expected calibration error (ECE) alone. We then propose synthetic agreement calibration, a method for improving calibration without collecting multi-annotator labels. Given a trained linear probe, we select high-confidence embeddings as class anchors and interpolate between anchors from opposite classes. The interpolation weights encode a continuous notion of diagnostic ambiguity, which we use as a synthetic agreement signal to retrain the probe with agreement-aware label smoothing. On MHIST, which includes annotations from seven pathologists, synthetic agreement calibration recovers most of the calibration improvement obtained by label smoothing based on real pathologist agreement, while substantially reducing low-agreement ECE relative to the uncalibrated baseline. Discrimination metrics are preserved. On PatchCamelyon and BreakHis, public histopathology datasets without multi-annotator labels, the method improves calibration across the evaluated foundation models, whereas annotator-dependent approaches cannot be used without additional expert annotation.

Recent works have demonstrated that quantum oracles have subtle behavior, as access to inverse, conjugate or controlled queries can exponentially change the query complexity of certain tasks. Inspired by these works, we introduce the notion of meta-complexity of quantum relativization. We ask: for any two quantum complexity classes, under which "types" of quantum oracles are they equal or separated? Different pantheons of oracles (or quantum oracle types, e.g. unitary vs state, poly- vs superpoly-dimensional, closed under inverse or not) form a partially ordered set based on their power in separating complexity classes. Moreover, two oracle pantheons A and B are separated if there exists a pair of complexity classes that are separated under an oracle from pantheon A but yet the complexity classes are equivalent under all oracles from pantheon B. We show that this meta-complexity can be nontrivial by giving a complete classification, within the family of oracle pantheons defined in this paper, of which models can separate the complexity classes $\mathsf{PostBQP}$ and $\mathsf{PreciseBQP}$, the exponentially precise variant of $\mathsf{BQP}$. Both classes equal $\mathsf{PP}$ in the unrelativized setting. Within our taxonomy, they remain equal relative to real or polynomial-dimensional unitary oracles and whenever inverse or conjugate access is supplied. In contrast, we give a separation relative to forward-only complex diagonal unitaries of superpolynomial dimension, as well as a separation relative to single-qubit state-preparation oracles. We view this as a test case for the meta-complexity of oracles which underscores the subtlety inherent to the relativization of quantum complexity classes.

A classical 1977 result by Roter states that a Riemannian manifold of dimension at least four with parallel Weyl curvature must be locally symmetric or conformally flat. We establish Roter's theorem in the symplectic category: namely, a Fedosov manifold with parallel symplectic Weyl curvature must be locally symmetric or Weyl-flat.

We introduce the notion of $K_{\mathfrak{q}}$-algebra, a conjectural axiomatization of the fusion algebra of rotation-equivariant BPS line defects in a 4d ${\cal N}=2$ Supersymmetric Quantum Field Theory. We also introduce the notion of RG flow of $K_{\mathfrak{q}}$-algebras, a conjectural axiomatization of the action of Seiberg-Witten type RG flows on line defects. These definitions enrich the theory of cluster algebras, $K$-theoretic Coulomb branch algebras, skein algebras and quantum groups.

We study a Kyle–Back model in which the informed trader has dynamic mean–variance preferences, leading to a time-inconsistent trading problem that is formulated as an intrapersonal game. The model combines two equilibrium requirements: a trading–pricing equilibrium between the informed trader and the market maker, and a time-consistent equilibrium among the trader's successive selves. Following the framework of Cho (2003), we consider both risk-neutral and risk-averse informed traders. In the risk-neutral case, we derive the equilibrium trading strategy and price impact explicitly. In the risk-averse case, we establish existence and characterize the equilibrium through a coupled system of nonlinear ordinary differential equations. Our main technique is to reduce the equilibrium conditions to a forward–backward ODE system and resolve the resulting boundary conditions by a shooting argument. Economically, the mean–variance preference reshapes the intertemporal trade-off between exploiting current private information and preserving future informational advantage, generating a declining term structure of price impact and shifting both information revelation and informed-trading profits toward earlier stages of the trading horizon.

We investigate Jordan structure and dynamical limits in six families of integrable spin-$\frac{1}{2}$ chains obtained from the boost automorphism method. Local operator algebras connect nilpotent evolution on finite periodic chains to central defects in spectral additivity, polynomial unipotent $R$-matrices and constant braid limits. For conservative endpoint erosion, we determine the characteristic and minimal polynomials and show that the Jordan partition can change while both polynomials remain unchanged. We also identify the deletion limits that distinguish the parity obstruction to removing signs by diagonal similarity in Class 5 from the parity nilpotent dependence in Class 6. Matching expansions and fragmentation recursions yield exact amplitudes and survival probabilities for processes with killing. In addition, we establish criteria excluding conservative Markov realizations and determine which conservative completions of specified reaction densities admit regular $R$-matrices of difference form.

A cumulative token cap can fall inside a mathematical derivation, forcing a test-time controller to choose between stopping at the cap (strict) and allowing the current attempt to finish (advisory). We measure this boundary choice with paired offline replays of 19,200 public traces: 120 AIME, BrUMO and HMMT problems and two archive configurations of one model. Candidate order and a 16-attempt cap are fixed, and answer selection is blind to reference answers and correctness labels. Three findings emerge. First, at the 4k cap, most advisory accuracy gains replace abstention with a correct answer; strict stopping pays for an unfinished prefix that the completed-only selector cannot use. Second, comparisons along realized cost differ from same-cap comparisons: advisory 4k in low has higher accuracy than strict 8k at comparable mean completion cost, while in high its observed accuracy is 0.42 points below strict 32k using 59% of its mean tokens. These aggregate comparisons do not establish equal-compute superiority or accuracy equivalence. Third, increased candidate coverage does not guarantee higher answer accuracy: a log-probability selector loses accuracy while coverage rises, including after a source-grade consistency repair. Same-cap majority-accuracy differences shrink below 1.3 percentage points at 32k. Budget curves should jointly state the cap, realized cost, eligible candidates, stopping rule and selector information.