Papers

Skills, reusable procedural guidance added at inference, can substantially improve LLM downstream performance (Li et al., 2026). Prior work retrieves skills from a bank by semantic relevance, then uses them as inference-time patches or for model distillation. The individual utility of each skill, however, is largely neglected. We first show that, in on-policy distillation where skill-conditioned policies serve as teachers, fewer than 25% of retrieved skills provide useful distillation signals. We then propose SGUID, a method for selecting a compact subset of skills for distillation. SGUID retains a skill only if it consistently yields effective learning signals during training. The selected skills are then distilled to produce a better model. Our results show that not all skills are worth distilling. Across four models from the Olmo and Qwen families, distilling 6 selected skills matches or exceeds full-bank distillation in mean avg@12 on three of the four models, and on all four after a second round that distills 3 newly selected skills, while the full banks are up to 11x larger. Importantly, SGUID supports stable model-skill co-evolution: after a distillation round, a new candidate bank is curated from the updated model's rollouts, and SGUID selects which skills to internalize next. In the second round, this loop selects 3 new skills and improves Qwen3-8B from 64.3% to 66.3%. The selection step is essential for stability: on Qwen3-4B, naively updating the model with unfiltered skills degrades performance, including a 0.3 percentage point drop on HMMT25, whereas SGUID improves HMMT25 by 0.5 points after the first round and 1.1 points after the second. These results identify skill selection as the key mechanism for stable model-skill co-evolution.

While models of undirected and directed geometry in random i.i.d. disorder with rapidly decaying tails are expected to behave similarly and exhibit features of the Kardar–Parisi–Zhang universality class, the scenario when the background noise is fractal is expected to be significantly different. A canonical example of the latter is Liouville Quantum Gravity, where the planar Gaussian free field forms the fractal background. A toy model capturing some of the essential features is given by Mandelbrot's fractal percolation, a random Cantor set. In the simplest setting, dyadic cubes of different scales are retained independently with probability $p$ (a parameter of the model), and the intersection of all retained cubes forms the set of open sites. Connectivity properties of such sets have been intensely studied. Across [CCD88, Cha95], a surprising result was proven. Namely, while there is a phase transition for connectivity of the fractal percolation set (like in usual bond percolation), directed percolation never occurs. Results of a similar spirit have been obtained in geometric measure theory as well. As a step towards understanding last passage percolation (LPP) driven by the Gaussian free field (initiated in [GGN24]), we study the problem of quantifying LPP in fractal percolation. Developing a multi-scale framework, we show an almost polynomial gap from linear growth of the passage time. The obstruction to high LPP values is the Lipschitz nature of directed paths. Along these lines, [Cha96] showed that any connected subset of fractal percolation must have Hausdorff dimension strictly larger than one. We show that one can construct directed paths passing through open sites in fractal percolation provided they move exponentially fast in the spatial direction—a model we introduce and term as unrectifiable directed percolation.

We determine the two-way quantum and secret-key capacities of the pure-loss channel under an average input photon-number constraint. For transmissivity $\eta$ and photon budget $N$, both capacities equal $g(N)-g((1-\eta)N)$, where $g$ is the entropy of a thermal state. This coincides with the rate achieved by the known reverse coherent information of a two-mode squeezed vacuum. Our result provides the last missing capacity formula for the celebrated pure-loss channel, completing the picture of bosonic quantum communication under pure loss.

Using in a novel way non-abelian Brill-Noether theory, we show that the moduli space of curves of genus 16 is uniruled. This is the highest genus for which such a result is known.

Intelligent grading and automated scoring technologies constitute critical infrastructure for smart education. However, existing document parsing and handwriting recognition benchmarks are predominantly designed for well-structured printed documents or isolated mathematical expressions, lacking datasets that capture the complex characteristics inherent to student answer sheets, including multi-line derivation processes, heterogeneous mixtures of text and mathematical formulae, and noise artifacts such as strikethroughs. To address this gap, we introduce HANS, the first dataset explicitly constructed for real-world educational scenarios, encompassing mathematical expressions, natural language text, hand-drawn tables, and diverse noise patterns including corrections and deletions, accompanied by fine-grained annotations that establish a reliable foundation for robust recognition research. Building upon HANS, we propose NA-GOT, an end-to-end framework that achieves two-stage noise suppression through a lightweight noise suppression module operating at the feature level, complemented by a noiseaware attention mechanism incorporated into the decoding stage. Experimental results demonstrate that HANS poses substantial challenges to existing methods, while NA-GOT achieves significant improvements in both accuracy and stability for answer process recognition. The dataset will be made publicly available upon publication.

We consider policy optimization for online episodic tabular Markov decision processes (MDPs) with adversarial losses and bandit feedback. Policy optimization updates the policy locally at each state and avoids optimization over the occupancy-measure polytope, but its existing regret bounds are larger by a factor of the horizon $H$ than those of occupancy-measure-based algorithms. We close this gap by using regularized $Q$-functions, which allow us to control the stability of the local updates jointly over all state-action pairs rather than separately at each state. The resulting algorithm attains high-probability regret bounds of $\widetilde O(\sqrt{HS(H+A)T})$ for known transitions and $\widetilde O(HS\sqrt{AT})$ for unknown transitions, where $S$ is the number of states, $A$ the number of actions, and $T$ the number of episodes. Both bounds improve the horizon dependence of existing policy optimization bounds, and the latter matches the best-known bound. We further extend the algorithm to adversarial linear-mixture MDPs and obtain the same improvement in the horizon dependence.

Large language models increasingly justify legal decisions by naming the statute or precedent behind a verdict, treated as evidence that the decision follows from it. We test this directly: holding case facts fixed, we substitute the named legal authority for an unrelated one and decode a model's evolving verdict from its hidden states. Across seven open-weight models (8B-70B) and four benchmarks spanning judicial and contractual reasoning, when explicitly required to justify a verdict by naming the governing authority, models name the correct one in 66.7%-100% of generations, while the verdict changing when the authority changes is far less consistent: 0.0%-21.7% on CaseHOLD, 30.0%-76.7% on ECHR and SCOTUS, and 43.3%-50.0% on ContractNLI. Neither scale nor a purpose-built legal-reasoning model (a best-effort LoRA reproduction; Section 6) closes this gap. A red-teaming evaluation on five core models finds compliance with an adversarial instruction hidden in the case facts (73.3%-96.4%) exceeds verdict-swap sensitivity by a wide margin, holding without exception across model rankings. Naming a legal authority is thus a poor proxy for a verdict's dependence on it, while the same verdict remains separately vulnerable to adversarial manipulation. Both findings replicate across checks ruling out prompt-wording noise and confounded sampling, and bear directly on the use of generated legal explanations as compliance or audit artefacts.

When retrieved evidence contradicts an agent's prior beliefs, does it revise its answer, acknowledge uncertainty, or persist with an incorrect conclusion? Existing evaluations of agentic systems focus primarily on task success, offering limited insight into how agents handle such conflicts. We propose to evaluate agents on epistemic humility (EH): the agent's willingness to recognize, act on, and communicate uncertainty during task execution. We operationalize EH through three trajectory-level behavioral dimensions: Identify, Solve, and Escalate (ISE). Through knowledge conflict, situations where the backbone language model's parametric knowledge contradicts the evidence it encounters, or where two contextual sources disagree, we evaluate two conflict settings: (1) controlled conflict and (2) naturally occurring conflict during multi-step agentic execution, each paired with matched no-conflict controls. Evaluating four agents, we find that higher task accuracy does not necessarily correspond to greater epistemic humility: some high-accuracy configurations recognize conflicts during execution but do not communicate unresolved uncertainty in their incorrect final answers. Trajectory-level analysis further reveals that agents frequently detect conflicts in early steps of execution but fail to maintain or resolve them in later steps. Finally, we show that model-level interventions can improve EH, but often at the cost of task accuracy, suggesting that epistemic humility emerges from the interaction among the backbone model, agent harness, and evaluation environment.

A newborn neutron star (NS) that survives after a binary NS merger can inject its rotational energy into the surrounding ejecta while the ejecta are still optically thick. The injected energy is redistributed by the pair cascade, and the nebula becomes a radiation-dominated plasma composed of photons and e^+- pairs. Compton scattering then governs the energy exchange while the photon number is conserved in scattering. This nebula is evolved with a one-zone model that includes pair creation, annihilation, photon injection, diffusion, and in particular the leakage through the jet-induced polar funnel. For typical parameters, we find that the Compton parameter y is much larger than unity at early times. The nebula therefore remains in saturated Comptonization for 100 s to a few thousand seconds, depending on the magnetic field strength of the post-merger NS. The radiation field takes a Wien spectrum with a Compton equilibrium temperature. The nebula is then a so-called Wien fireball. The Compton temperature decreases from tens of keV to a few keV at early times. As long as the ejecta are optically thick, the funnel leakage is comparable to or exceeds the adiabatic loss. The funnel emission is quasi-thermal, and its isotropic-equivalent luminosity is much higher than the spin-down luminosity. We suggest that the quasi-thermal components observed in the extended emission of short gamma-ray bursts could come from the funnel leakage of the nebula fireball.

We study Gaussian regression under squared population $L_2$ loss in a known $m$-dimensional subspace of degree-at-most-$k$ functions on the $d$-dimensional Boolean cube. Random inputs can undersample regions essential for prediction, delaying the parametric rate even when the model is known. For fixed $q_0<1/2$, $1\le k\le q_0d$, and sufficiently large fixed $A$, the worst-subspace sample threshold for minimax error $A\sigma^2(m+t)/n$ with confidence $1-e^{-t}$, $t\ge\log4$, is \[ N=(m+t)\exp\{E_{d,k}+O(k^{1/3})\}, \quad E_{d,k}=d\Psi(k/d), \] where $\Psi(q)=\log2-\mathsf H(\tfrac12-\sqrt{q(1-q)})$ and $\mathsf H$ is binary entropy with natural logarithms. The upper bound holds for every feasible $m$; the matching lower bound holds when $m\le\binom d{\lfloor k^{1/3}\rfloor}$ or $t\ge m$. We sharpen the Polyanskiy–Samorodnitsky uncertainty principle in two respects. First, for fixed leakage $\rho\in(0,1)$, the smallest set carrying a fraction $1-\rho$ of a nonzero degree-at-most-$k$ polynomial's energy has probability $\exp\{-E_{d,k}+O_{\rho,q_0}(k^{1/3})\}$. An Airy-kernel construction proves that the remainder cannot be $o(k^{1/3})$ in general. Second, we construct a subspace of dimension $\binom d{\lfloor k^{1/3}\rfloor}$ such that every function in the subspace has at least a fraction $1-\rho$ of its energy on the same set, whose probability is at most $\exp\{-E_{d,k}+C_{\rho,q_0}k^{1/3}\}$. For sufficiently large $k$, this set is a Hamming ball. A striking consequence is an exponential cost of noise: the parametric rate can require $(m+t)4^k\exp\{-O(k^{1/3})\}$ samples, whereas $O((m+t)2^k)$ suffice for noiseless identification. As $k\to\infty$ with $k/d\to0$, the noisy threshold is $(m+t)\exp\{2k+o(k)\}$.

We study two problems: Local Leakage Resilience (LLR) for Shamir secret sharing, and worst-case Optimal Polynomial Intersection (OPI). Both problems concern polynomials $Q(X)$ of degree less than $k$, over a prime-order finite field $\mathbb{F}_p$. In LLR for Shamir secret sharing, one asks how much one can learn about $Q(0)$ given a few bits leaked from each of $Q(\alpha_1), \ldots, Q(\alpha_n)$, for distinct non-zero evaluation points $\alpha_i \in \mathbb{F}_p$. In OPI, one is given input list $S_1, \ldots, S_n \subset \mathbb{F}_p$, and wants to find a polynomial $Q(X)$ of degree less than $k$ so that $Q(\alpha_i) \in S_i$ for as many $i$ as possible. Leveraging recent connection between these two problems due to (Sun, Wootters 2026), we improve the state-of-the-art for both problems. For LLR, we show that there is some constant $\delta > 0$ so that, as long as $R := k/n \geq 1/2 - \delta$, Shamir secret-sharing is one-bit locally leakage resilient (meaning that one can learn only a negligible amount about $Q(0)$). This is the first result to break the so-called "one-half barrier" for LLR, and improves over the previous best known result, requiring $R \geq 0.668$ (Kasser, 2025). For OPI, we give a quantum algorithm that finds a polynomial $Q(X)$ that agrees with at least a $\mathsf{SCL}_\rho(R)-\varepsilon$ fraction of the lists in expectation, for every fixed $\varepsilon>0$, where $\mathsf{SCL}_\rho$ is the semicircle law of (Jordan et al., 2025). This improves previous algorithmic (and existential) results of (Jo, 2026) and (Horinaga, Yamakawa, 2026). We also give further improved existential results. We also adapt the hardness result of (Yamakawa, Zhandry, 2024) to apply to OPI (rather than a folded version); over large fields, this gives an unconditional separation between the quantum and classical hardness of OPI relative to a membership oracle.

Year-scale quasi-periodic oscillations (QPOs) in blazar gamma-ray light curves have been proposed as signatures of supermassive binary black holes and precessing jets. Red noise can mimic periodicity, and detection alone does not establish persistence or period stability. We develop and calibrate a morphological framework to characterize year-scale modulation and constrain the incidence of stable modulation in blazars. We analyze 120 Fermi-LAT light curves spanning 18.1 yr. Singular spectrum analysis selects the oscillatory mode and period, while weighted wavelet Z-transform ridge tracking measures persistence, period drift, and cycle-to-cycle volatility. Flux randomization, 10,000 red-noise simulations, and about 20,000 injections calibrate the classification. Of 97 quality-selected sources, two show persistent, coherent modulation consistent with a stationary period (Rank I: PG 1553+113 and B2 1215+30), six show coherent modulation whose stationarity cannot be established (Rank II), and 89 form Rank III. Neither Rank I nor Rank II significantly exceeds red-noise expectations. Stationary 1-3 yr injections reach Rank I in 63-97% of trials at signal-to-noise ratio (SNR) = 1, depending on period, and 100% at SNR = 2; 92% of drifting injections reach Rank II. These results limit stable, approximately sinusoidal 1-3 yr modulation to at most 7% of the sample at SNR >= 1 and 5% at SNR >= 2 (95% confidence). PG 1553+113 has the lowest false-alarm probability, 4.7% after trials. Stable year-scale modulation is uncommon, and no source is established as periodic. The framework distinguishes persistent, stationary modulation from coherent variability whose period may evolve or fluctuate, but not the physical mechanism. PG 1553+113 and B2 1215+30 are candidates for monitoring and continuous gravitational-wave searches, although their stability does not establish a binary origin.

Spatial reasoning remains a persistent weakness of vision-language models (VLMs), because RGB inputs do not directly provide geometric evidence. Existing remedies either inject 3D into the model at inference, paying architecture and latency costs, or train with outcome rewards that supervise only the final answer. Spatial errors originate in perception: a misjudged depth or direction can be corrected only by the scene's true geometry, which the 3D-scanned sources of spatial training corpora already provide. We propose GPD (Geometry-Privileged Distillation), which makes geometric evidence the privilege in on-policy self-distillation (OPSD). For each question, depth, semantic, and bird's-eye-view (BEV) cues are rendered as compact text and routed to the teacher alongside the reference answer; a privileged KL, applied only to incorrect trajectories, augments GRPO, and the deployed model remains RGB-only. On the 4B backbone, GPD achieves 57.1 on VSI-Bench and 37.6 average across MindCube, SPARBench, MMSI-Bench, and ViewSpatial, outperforming both GRPO and answer-privileged OPSD across spatial reasoning benchmarks. Ablations confirm the complementarity of 3D and answer privilege, the advantage of question-conditioned routing over full-context injection, and the benefit of restricting distillation to incorrect trajectories.

We study the long-time behaviour of Brownian motion with drift under a rare-event conditioning of the quadratic additive functional $Z_T=\int_0^T W_s^2ds$, where $(W_t)_{t\geq 0}$ is a Brownian motion with drift $\mu$. More precisely, we consider the conditional law of $W$ given the event $Z_T\le \theta T$, as $T\to\infty$, allowing the drift $\mu$ to depend on $T$. We derive sharp, uniform small-deviation asymptotics for $Z_T$, including the exact prefactor, and use them to show that the conditioned process converges weakly to an Ornstein–Uhlenbeck process. Remarkably, the limiting dynamics are independent of the original drift.

Parameter convergence in recursive identification requires persistent excitation, which is typically enforced with a probing signal that degrades performance if retained indefinitely. Regulating the probing amplitude with the one-step prediction error is insufficient, since a small prediction error does not imply parameter convergence. This paper proposes a self-regulating excitation law that scales the probing amplitude with the associated covariance matrix, so that the excitation vanishes only as fast as the estimator's own measure of remaining parameter uncertainty allows. The key idea is that the excitation amplitude must decay more slowly than the covariance measure, the largest eigenvalue of the covariance matrix in this work, for parameter convergence to be preserved. Under the proposed excitation law, the excitation amplitude and the covariance measure are shown to jointly converge to zero while the parameter estimate converges to the true parameter, with the excitation vanishing more slowly than the covariance measure throughout. A scalar exponent in the law trades the rate of covariance decay against the amount of excitation retained. Numerical results confirm both properties.

We prove that there is no uniform description of $\mathrm{LG}^{(n)}$ in terms of colored Jones polynomials for all knots, even when allowing infinitely many colors and arbitrary operations. We prove the $n=1$ case, using an existing cabling formula and the separation of the Conway and Kinoshita–Terasaka knots by $\mathrm{LG}^{(2)}$. We develop an odd cabling formula and use a Vandermonde argument to show that for each $n\geq 2$ some satellite of each of these knots is distinguished by $\mathrm{LG}^{(n)}$.

Let $M$ be a closed manifold of arbitrary dimension. The length spectrum of a negatively curved metric $g$ on $M$ is the set of lengths of all possible closed geodesics of $g$. We prove that metrics whose length spectrum is exponentially sparse, i.e., the gaps between distinct lengths are bounded below by a quantity decaying exponentially in the length, are prevalent, and hence dense, among $C^k$-smooth negatively curved metrics on $M$ for sufficiently large $k$. Moreover, unlike in all known constructions, the exponent in our bound grows only sublinearly in the regularity $k$. This work is motivated by our recent result on prevalent unmarked length spectral rigidity for expanding circle maps and a very recent result by DeWitt, Durham, Reber, and O'Hare that $C^k$-smooth negatively curved metrics with exponentially sparse spectra are locally rigid.

The Information Matrix (IM) test is a natural specification check for likelihood-based models, yet cross-sectional implementations are often badly sized, confound neglected heterogeneity with distributional misspecification, and require third derivatives. We develop the panel information matrix (PIM) test for models with fixed effects. Explicit fixed effects isolate functional-form misspecification from time-invariant unobserved heterogeneity. Although the profile maximum likelihood estimator inherits incidental-parameter bias of order $O(1/T)$, the leading bias of the profile PIM is of order $\sqrt{n}/T$, so it is asymptotically negligible whenever $n/T^2\to 0$, which includes the rectangular regime $n/T\to\mathrm{const}$, and stabilizes under parabolic asymptotics $n/T^2\to\rho\in(0,\infty)$. This robustness arises because the indicator fluctuates at rate $\sqrt{n}$ rather than $\sqrt{nT}$. The same rate argument makes third-derivative corrections asymptotically unnecessary, so the test uses only first- and second-order likelihood derivatives. Simulations confirm that asymptotic PIM critical values suffice in moderately long panels, even when Wald tests for $\theta$ are badly sized, while a parametric bootstrap largely removes size distortions when $\rho>0$.

Understanding a dynamical world calls for more than a latent state that summarizes its observations: the state should also be organized into the factors that stay shared across related observations and the factors that vary between them. For example, a robot pushing a cube to a goal should take the same action when the camera shifts or the lights dim, since nothing in the scene has moved. Existing approaches to this decomposition commonly obtain it through reconstruction, so the latent variables must first explain the entire observational world before their organization can be trusted. Joint embedding predictive architectures (JEPAs) model the latent state directly and never reconstruct, yet no existing result recovers the invariant and variant parts of the state they learn. How to learn the invariant-variant structure of the latent world without paying for its reconstruction therefore remains open. To close this gap, we introduce SplitJEPA, a JEPA that jointly recovers the latent state and its invariant and variant organization directly in representation space, without any reconstruction. We prove that, under stationary Gaussian predictive dynamics and a full-rank variation condition, SplitJEPA identifies the invariant and variant subspaces up to independent block-wise isometries, without introducing an observation decoder. Since the guarantee needs no decoder, the result extends reconstruction-free latent recovery to invariant-variant block identification. Experiments on synthetic nonlinear systems and robotic manipulation tasks support the theoretical results and show their practical value for both robustness and efficiency.

We develop a framework to construct large decoherence-free subspaces with a nontrivial structure. The construction is based on hybrid quantum systems in which quantum matter is coupled to a dissipative bosonic mode. Dissipation imposes a global constraint on the matter by selecting the matter null states in the long-time limit. The decoherence-free subspaces spanned by matter null states can exhibit exotic quantum properties and emergent symmetries that do not characterize the full Liouvillian dynamics. We show how to construct many-body operators with physically interesting null states by employing representation theory of Lie algebras. This approach allows us to choose models based on their underlying algebraic structure. We consider explicitly the example of coupling a lossy optical cavity to the directed tunneling operator in one-dimension. In this case, the symmetries of the decoherence-free subspace originate in an $\mathfrak{sl}(2,\mathbb{C})$ algebra, leading to an exponentially large number of steady states. We characterize the null states for both fermionic and bosonic particles, employing analytical and numerical methods. The states exhibit several properties that underline their complex quantum nature: long-range kinetic correlations and volume-law entanglement. The nonreciprocal nature of the directed tunneling dynamics leads to the emergence in the many-body regime of a symmetry-constrained Liouvillian skin effect. The open light-matter system exhibits a strong symmetry stemming from spinless $\eta$-pairing algebras. We show how the nontrivial properties emerge in the dissipative dynamics from generic initial states, by performing the quantum evolution of the hybrid open system with time-dependent matrix product state. Our framework opens avenues for dissipatively engineering complex quantum correlations and harnessing nonreciprocity in a controlled manner.

The curve graph of a surface is the graph whose vertices are isotopy classes of essential, closed curves on the surface. Edges join vertices with disjoint representatives. The curve graph plays a central role in the theory of mapping class groups of surfaces. Gaster, Greene, and Vlamis have shown that the subgraph of the curve graph induced by curves in a single primitive homology class is uniquely and finitely colorable. In the analogy between the theory of mapping class groups of surfaces and outer automorphisms of free groups, the sphere graph of $M_r$, a connect sum of $r$ copies of $S_1 \times S_2$ plays an analogous role in the theory. Motivated by Gaster, Green, and Vlamis' result, we investigate $\mathcal{S}_v(M_r)$, the subgraph of the sphere graph of $M_r$ induced by spheres representing a single primitive homology class $[v] \in H_2(M_r;\mathbb{Z})$. We show that this graph is uniquely $r-1$ colorable. As a corollary, with $r\ge 3$ we obtain a nontrivial homomorphism from the Torelli subgroup $IO_r \le \operatorname{Out}(F_r)$ to the symmetric group on $r-1$ symbols; this parallels Gaster, Greene, and Vlamis' connection between their coloring and the Chillingworth homomorphism. In the course of our proof we find new smaller generating sets for mapping class groups of $M_r$ with spheres deleted.

We study a family of randomized alternating projection methods that alternate among subspaces spanned by subsets of \(n\) vectors from a prescribed set. We derive an explicit characterization of performance bounds when these subspaces are sampled with probabilities proportional to the volumes subtended by the vectors in their corresponding subsets. For each \(n\), the bound is obtained through an explicit nonlinear transformation of the spectrum of an associated matrix. Our analysis reveals an explicit spectral equalization mechanism that drives the spectrum toward improved conditioning as $n$ increases, establishing an unexpected connection between volume sampling and the Cayley-Hamilton theorem. Furthermore, we introduce a computationally efficient uniform sampling scheme that achieves comparable theoretical guarantees through a specific relaxation strategy. Empirical results show that this relaxation method achieves convergence rates comparable to, and often better than, volume sampling, while avoiding the infeasibility of volume sampling at large scale. Besides the randomized Kaczmarz, these results also directly apply to randomized Gauss-Seidel and coordinate descent methods.

Supervised fine-tuning (SFT) adapts pretrained large language models (LLMs) to downstream tasks, but the required concepts can receive substantially different levels of pretrained support. Frequent concepts are more likely to be well learned, whereas rare concepts may remain weakly represented. We introduce a novel notion named prior barrier to quantify how strongly the pretrained model supports competing concepts over the target concept. We observe that prior barriers follow a long-tail distribution, placing head and tail concepts at different starting points for SFT: head concepts face lower prior barriers, whereas tail concepts require additional instructions to overcome their higher prior barriers. Our theoretical analysis further derives a predictive risk bound for SFT under long-tail prior barriers, explicitly characterizing how the prior barrier and accumulated SFT evidence jointly determine predictive performance. Motivated by this prior barrier-dependent demand, we propose PASS, an adaptive SFT instruction selection method that constructs reference-derived concepts and estimates the distinguishing evidence provided by each instruction, and adaptively allocates the selection budget toward concepts that remain insufficiently covered under the current selection. In this way, PASS jointly considers which instructions can provide useful evidence and where additional supervision is needed under a limited budget. Experiments show that our method consistently outperforms seven state-of-the-art instruction selection methods on four backbone-budget settings. An ablation study further shows that PASS's adaptive allocation consistently improves over uniform allocation.

We investigate how much arithmetic information about a variety can be detected by sections of the geometrically abelian fundamental groups of sufficiently small open subvarieties. Over a \(p\)-adic field, such a section determines a rational point on the Albanese torsor, and, under a conjectural assumption, this point is represented by a \(0\)-cycle of degree \(1\) on the original variety if the variety has index \(1\). For curves, the latter statement holds unconditionally. Over finitely generated fields, such sections still force the relative Brauer group to vanish away from the characteristic. The key input is an identification of the Chern class obstruction attached to a section with the obstruction arising from local Tate duality. As a byproduct, we give a new proof of an open-subvariety strengthening of a theorem of Esnault and Wittenberg.

Large Multi-modality Models (LMMs) have made significant progress in visual understanding and generation, but still face challenges in visual editing, particularly in following complex instructions, preserving appearance consistency, and supporting flexible input formats. To study this gap, we introduce RISEBench, the first benchmark for evaluating Reasoning-Informed viSual Editing (RISE), and extend it to RISEBench++, a more comprehensive and fine-grained benchmark for this emerging task. RISEBench++ extends the taxonomy into a hierarchical scheme spanning six reasoning dimensions: Temporal, Causal, Spatial, Logical, and Counterfactual Reasoning, together with Hybrid Reasoning integrating multiple reasoning types across multi-turn edits. These dimensions are further decomposed into 12 subcategories and 65 fine-grained task types. We expand input formats to include multi-image conditioning and scale the benchmark to 1000 human-annotated test cases, released in English and Chinese. We also improve our evaluation framework, assessing Instruction Reasoning, Appearance Consistency, and Visual Plausibility with human judges and an LMM-as-a-judge approach for more reliable and calibrated judgements. Beyond benchmarking, we introduce RISE-Agent, a training-free agentic framework integrating reasoning-driven planning, tool-augmented execution, and verifier-guided refinement, outperforming most strong existing approaches across diverse RISE tasks. We evaluate 58 visual editing approaches, including 34 open-source models, 19 closed-source models, and 5 agentic methods. The results reveal substantial challenges in reasoning-based visual editing, with even the strongest evaluated approach, GPT-Image-2.5 Sunburst, achieving only 56.6% accuracy. RISEBench++ highlights the limitations of contemporary editing models, provides insights, and indicates future directions for reasoning-aware visual editing.

This paper integrates reference governance with Dynamic Mode Adaptive Control (DMAC) to enforce constraints without a prior plant model. DMAC identifies and updates a discrete-time model online from measured state and input data, and the reference governor (RG) uses this identified model, rather than the true plant dynamics, to predict constrained closed-loop behavior. Because the prediction model changes as DMAC adapts, a governed reference that was previously feasible may become infeasible, and the classical interpolation-based RG may be unable to move the reference in the direction required to recover predicted constraint satisfaction. The proposed DMAC-RG framework instead searches directly over the governed reference rather than over an interpolation factor. When feasible references exist, the governed reference is selected to track the desired command, with an optional penalty on deviation from the previously applied reference. When the finite-horizon feasible set is empty, the reference is selected to minimize predicted constraint violation while retaining the same tracking preference. This work is a numerical investigation and does not provide theoretical guarantees of recursive feasibility, constraint satisfaction, or closed- loop stability. Numerical examples on a linear system, a nonlinear Van der Pol oscillator, and a high-dimensional Burgers equation under partial-state measurement demonstrate that the proposed RG enforces constraints using only the model identified online by DMAC, without access to the true plant dynamics or the complete system state.

Adversarial games have driven advances from heuristic search to reinforcement learning, yet learning and adapting strategies from limited samples remain challenging. AI agents offer an alternative by turning game experience into revisions of executable policies. Building on heuristic learning (HL), we formalize Adversarial Heuristic Learning (AHL), a paradigm that uses AI agents as learning engines to refine game policies and supporting software while keeping model weights fixed. We introduce AAArena, a benchmark comprising 12 authentic adversarial games and 1,920 archived human programs, with an evaluation protocol modeled on real-world game competitions. Agents interpret rules, choose opponents, analyze replays, and revise game agents to achieve their highest ranking within fixed match and evaluation budgets. We evaluate \val{completedmodels} model and harness configurations: Opus5.5 with Claude Code earns 6 gold medals, while no evaluated configuration tops the remaining 6 human ladders. Performance is generally weaker in games with more complex rule specifications. Further experiments show that opponent selection and dense feedback support policy improvement, and that agents learn from both on-policy replays of their own matches and off-policy replays of other players' matches. These results highlight HL's potential in adversarial games and identify persistent challenges in game understanding, strategy implementation, and long-horizon policy development.

We introduce RefineMix, a framework for training discrete diffusion models under severe data scarcity, a common constraint in scientific applications. RefineMix uses out-of-distribution data at selected diffusion times to improve generalization without biasing the sampling distribution. Although this strategy has been explored in continuous diffusion, discrete diffusion presents a distinct challenge: unlike Gaussian noise, masking preserves domain information in surviving tokens, limiting the use of related data at high noise levels. At low noise levels, however, the domains effectively disjoint supports become an advantage, allowing the model to learn from both in-domain and out-of-distribution data without biasing the sampler. We formalize these intuitions and provide a theoretical analysis for the proposed method. Experimentally, across five domain-shift settings, RefineMix matches or outperforms in-domain finetuning and data mixing. For protein sequence generation, finetuning with just 197 in-domain examples nearly doubles the fraction of generated proteins that are simultaneously novel, foldable, and in-family compared to standard finetuning.

Exact diagrammatic quantum Monte Carlo (DiagMC) results for the nearest-neighbor Hubbard model motivate a closer study of the pseudogap. Using the improved two-particle self-consistent approach (TPSC+), we analyze Energy (EDC) and Momentum Distribution Curves (MDC) simultaneously. We show that Fermi-liquid terminology breaks down in the pseudogap regime, requiring a distinction between true and false Fermi surfaces and zero-energy quasiparticle (ZEQ) lines. A false Fermi surface has a momentum-space spectral maximum but a frequency-space depression at zero energy, while a false ZEQ line violates the standard quasiparticle condition $\partial \Sigma'(\mathbf{k},\omega)/\partial \omega|_{\omega=0}<0$.The pseudogap is driven by critical thermal spin fluctuations, which occur in two dimensions because of the Mermin-Wagner theorem. Commensurate fluctuations first open an antinodal pseudogap, leaving true Fermi arcs. With decreasing temperature, the Fermi surface evolves into hole- and electron-like false Fermi surfaces. Incommensurate fluctuations generate hot spots near the diagonal, where the pseudogap persists to the quantum critical point (QCP), whereas at $\mathbf{k}_{AN}$ it disappears before the QCP doping. There, the spectrum has two precursor antiferromagnetic (AFM) bands, both in the unoccupied ($\omega>0$) region. We benchmark TPSC+ against DiagMC results for the Matsubara spectral proxy $-\mathrm{Im}[\mathcal{G}(\mathbf{k},i\pi T)]/\pi$. TPSC+ underestimates pseudogap suppression in the strong-interaction regime, reproducing DiagMC behavior at lower temperatures or doping. This proxy is equivalent to the spectral function with thermal broadening $\eta=\pi T$, which obscures features when $\pi T$ is not the smallest energy scale. Using $A(\mathbf{k},0)$, we find that hole-like Fermi surfaces emerge at any interaction strength at low temperature, even at weak coupling.

While caching key-value (KV) states accelerates Large Language Model (LLM) decoding, this cache can dominate memory usage at long context lengths. One solution is to compress this memory by exploiting inter-layer cache similarities. However, most existing techniques necessitate architectural changes to LLMs and incur substantial overhead. In this work, we propose a symmetry-aware value cache merging strategy that reduces cache memory while avoiding both harmful performance degradation and architectural overhead during decoding. Furthermore, we show that this approach can be exploited alongside existing cache compression techniques, composing with high-ratio quantization or key cache pruning to reach compression ratios that neither method reaches alone, with minimal additional cost. Ultimately, our findings reveal a major source of underutilized capacity in the value cache, offering a simple yet highly effective direction for scaling context windows under memory constraints.