Papers

In weakly supervised Whole Slide Image (WSI) classification, feature extractors typically compress each image tile into a single global embedding. Consequently, slide-level aggregators are restricted to this coarse tile scale, concealing fine-grained sub-tile evidence from the attention mechanism. We introduce DI-MIL, a framework that decouples encoding context from instance granularity through decomposed instances. By clustering dense spatial tokens from a frozen foundation model within each tile, DI-MIL converts a single tile into multiple independently weighted instance embeddings. As a training-free post-encoding module, DI-MIL integrates seamlessly into existing pipelines without requiring re-encoding or downstream architectural modifications. We evaluate DI-MIL on cytopathology, a challenging testbed where sparse diagnostic signals are easily diluted within standard tiles. Across four datasets, three frozen foundation models, and two attention-based aggregators, DI-MIL demonstrates consistent efficacy, improving 67 of 72 metric-level comparisons, with the largest mean gains reaching 3.64 points under cytopathology-specific backbones. In a broader comparison against seven representative MIL baselines, DI-MIL paired with ACMIL achieves highest mean performance in 33 of 36 backbone-dataset-metric comparisons. Ablations show that direct smaller tiling inflates the extracted tile count by up to 43.3$\times$ with non-monotonic performance, whereas DI-MIL incurs zero additional image-extraction overhead while achieving the strongest overall results. These results establish instance construction as an orthogonal design dimension in MIL, supporting DI-MIL as a cost-efficient solution under sparse diagnostic evidence.

Many existing wireless digital twins (DTs) rely heavily on ray-tracing (RT)-based channel simulators to achieve scalability in large-scale environments. However, the geometric-optics (GO) approximations underlying RT become inaccurate in propagation regimes dominated by diffraction and refraction, which are prevalent at sub-6 GHz carrier frequencies. This paper presents a hybrid RT and physics-embedded physics-informed neural network (PE-PINN) framework that enhances site-specific wireless DTs with physics-consistent full-wave accuracy. Building on prior PE-PINN work, we introduce targeted architectural extensions, including a finite-length edge diffraction kernel and a lossy dielectric formulation based on complex wavenumbers, to accurately model electromagnetic wave interactions with realistic objects and materials. To balance accuracy and efficiency, we further propose a localized tunnel strategy that deploys PE-PINN models only along dominant propagation paths, selectively replacing or augmenting RT predictions in regions where GO assumptions break down. Comprehensive evaluations against full-wave COMSOL simulations demonstrate that the proposed framework closely matches reference solutions and significantly outperforms RT-only approaches in diffraction- and refraction-dominated scenarios. We further demonstrate seamless integration of the proposed approach into a realistic indoor wireless DT, highlighting its practicality and scalability for next-generation wireless network design.

Open-ended discovery requires learning from repeated attempts while continuing to explore directions whose value is not yet apparent. Search with a frozen large language model (LLM) can reuse previous solutions in context, but cannot update the model from its successes and failures on the test problem. Reinforcement learning (RL) enables such adaptation; however, strongly favoring high-reward trajectories may suppress low-reward yet potentially promising directions too early. We introduce CURIO, a curiosity-driven test-time learning framework that complements task feedback with an Intrinsic Curiosity World Model (ICWM). The ICWM learns transitions in the policy's hidden-state representation and supplies prediction-error bonuses at sampled tokens outside the policy's top-k choices. Epoch normalization and an annealed weight regulate their contribution to the policy update. On six mathematical discovery tasks and single-cell denoising with Qwen3 backbones from 8B to 235B, three-run means improve over a matched task-only RL control on five mathematical objectives, match the best reported performance on Circle Packing, and improve denoising Score and mean squared error (MSE) on both held-out corpora at every tested scale. Relative gains reach 18.3% on Hadamard and 10.8% on denoising Score. Code-diversity measurements show greater structural variation among generated programs, supporting curiosity as a complementary exploration signal for learning in open-ended discovery.

Protein binding prediction is central to target identification, therapeutic binder design, and large scale screening, yet remains challenging because binding depends on sequence, three dimensional geometry, and global structural organization. Recent folding models such as AlphaFold3 and Boltz-2 have substantially improved structure prediction, but their confidence outputs (pLDDT, pTM, ipTM) are not specifically designed for binary binding prediction, and dedicated structure aware predictors often require bound complex structures that are unavailable at screening scale. We introduce PIT-GCL, a dual tower structure aware framework that encodes each protein independently from its amino acid sequence, C{\alpha} point cloud, and a global persistent homology descriptor. Each tower combines residue ESM-2 embeddings with a topological summary computed from the H0 and H1 persistence landscapes of a Vietoris-Rips filtration, and processes the resulting tokens with a structure aware Transformer in which pairwise C{\alpha} distances enter as a learned attention bias. A bidirectional cross attention module then performs latent space soft docking between the two per-protein representations, and the model is trained with a combined binary cross entropy and NT-Xent contrastive objective. On three binary interaction prediction benchmarks, general PPI on PPIRef, TCRpMHC binding on STAG, and whole chain pairs on PPB-Affinity, PIT-GCL outperforms representative sequence based, structure aware, and task specific baselines on general PPI under our evaluation, and is the only method above chance on PPB-Affinity; on TCR-pMHC it leads at a fixed decision threshold but is outranked by a task specific sequence model. Because each protein is encoded independently in the first phase, its representation can be precomputed and reused across candidate pairs, which is convenient for large scale screening.

Let $Q_0:=(0,1)^n$. We define $\mathcal{B}_q(Q_0)$ by replacing the local $L^1$ mean oscillation in the Bourgain–Brezis–Mironescu space $\mathcal{B}(Q_0)$ with its $L^q$ counterpart, which coincides with $\mathrm{BMO}(Q_0)$ when $n=1$. For $n\geq2$, our results reveal different endpoint behaviors for general functions, characteristic functions and the exact perimeter formula. (i) For general functions, $\mathcal{B}_q(Q_0)=\mathcal{B}(Q_0)$ precisely when $q\in(0,\frac{n}{n-1})$. We also establish the corresponding sharp self-improvement and duality results for Hardy-type preduals. (ii) For characteristic functions, the endpoint is attained: the equivalence $\|\mathbf{1}_E\|_{\mathcal{B}_q(Q_0)}\sim\|\mathbf{1}_E\|_{\mathcal{B}(Q_0)}\sim\min\{1,P(E,Q_0)\}$ holds uniformly over measurable $E\subset Q_0$ precisely when $q\in(0,\frac{n}{n-1}]$, where $P(E,Q_0)$ denotes relative perimeter. (iii) The isotropic functional $I_{\varepsilon,q}^{*}(E)$, defined using arbitrarily oriented cubes, converges to $\frac{1}{2}\min\{1,P(E,Q_0)\}$ as $\varepsilon\to0^+$ throughout $q\in(0,\frac{n}{n-1}]$. In dimension two, the formula extends to $q\in(0,q_*]$ for some universal $q_*>\frac{19}{9}$, whereas it fails in every dimension for every $q>q_0$, where $q_0>2$ is defined variationally and numerical computation suggests that $q_0\approx2.15391$. The proofs of the three sharp self-improvements use sparse median domination, atomic block decompositions, and relative isoperimetry, respectively. For the perimeter formula, a uniform De Giorgi blow-up reduces the problem to a geometric cube-section inequality; geometric averaging and an explicit packing yield the planar extension and the obstruction, respectively.

We investigate an information-geometric approach to dense two-color QCD using thermal states defined as normalized Gibbs states in the two-flavor Nambu–Jona-Lasinio model at the mean-field level. The Bures metric and quantum Fisher information are constructed from thermal states associated with effective Bogoliubov–de Gennes Hamiltonians reproducing the mean-field quasiparticle spectrum. On the thermodynamic parameter manifold $(T,\mu)$, where $T$ is temperature and $\mu$ is quark chemical potential, we analyze information-geometric quantities including the trace of the QFI matrix and the metric-volume density. The numerical results show pronounced enhancements of both quantities near the color-superconducting phase boundary, whereas only weaker signatures are observed across the chiral crossover. By contrast, neither observable exhibits a distinct feature associated with the BEC–BCS crossover.

We consider inference for network stochastic differential equations in a small-noise, high-dimensional regime, where the diffusion coefficient vanishes with $\ep\to0$ while the network size and parameter dimension may diverge. We develop a minimum-distance estimation framework based on a deterministic measurement model that may omit nuisance terms in the drift, and derive a non-asymptotic error bound decomposing the estimation error into stochastic fluctuation, nuisance discrepancy, and identifiability terms. For a linearly parametrized interaction model under repeated measurements, we obtain explicit non-asymptotic bounds on the nuisance discrepancy and the identifiability gap in terms of graph connectivity and noise level. Under suitable mixing and balance conditions, this yields consistency and convergence rates for the estimator. We further study graph recovery via adaptive Lasso. The penalized estimator is shown to inherit the rate of the preliminary estimator and to recover the true interaction graph consistently. These results provide a theoretical basis for parameter estimation and edge selection in high-dimensional network SDEs with nuisance drift components.

Let $(M^n,g)$ be a compact Riemannian manifold of dimension $n\ge 2$, possibly with nonempty convex $C^2$ boundary. We study the first nonzero eigenvalue $\lambda_1(M)$ of the Laplace–Beltrami operator, subject to the Neumann boundary condition when $\partial M\neq\emptyset$. Given a reference scalar curvature $R_E>0$, set $K_E:=R_E/(n(n-1))$, and define the traceless Ricci tensor $\mathring{\Ric}:=\Ric-\frac{R}{n}g$ and the Einstein deviation \[ \Theta:=|\mathring{\Ric}|+\frac{|R-R_E|}{n},\qquad \kappa_{\mathrm{Ein}}(p):=\left(\frac{1}{\vol(M)}\int_M\Theta^p\,dV\right)^{1/p}, \quad p>n/2. \] We say that $M$ is $\varepsilon$-nearly Einstein if $\kappa_{\mathrm{Ein}}(p)<\varepsilon$. The main result states that for every $\alpha\in(0,1)$ there exists $\varepsilon_0=\varepsilon_0(n,p,\alpha,D,R_E)>0$ such that if $\diam(M)\le D$ and $\kappa_{\mathrm{Ein}}(p)<\varepsilon_0$, then \[ \lambda_1(M)\ge \alpha\,\lambda_1(n,K_E,D), \] where $\lambda_1(n,K,D)$ is the first nonzero eigenvalue of the Bakry–Qian one-dimensional model problem with curvature parameter $K$, with the convention $\lambda_1(n,K,D)=nK$ when $K>0$ and $D\ge\pi/\sqrt{K}$. The proof combines the Bochner formula for the decomposition $\Ric=(n-1)K_Eg+\theta g+\mathring{\Ric}$ with an auxiliary function $J$ satisfying \[ \Delta J-\tau\frac{|\nabla J|^2}{J}-2J\Theta=-\sigma J \] and Neumann boundary conditions, together with Moser iteration and a maximum principle. As $\kappa_{\mathrm{Ein}}(p)\to0$, the estimate recovers the classical Bakry–Qian theorem.

Aligning large language models (LLMs) with human values is important for safe, efficient, and beneficial AI deployment. However, human values are multifaceted: helpfulness, harmlessness and humor trade off against one another, and different users want different trade-offs. Multi-objective alignment (MOA) addresses this by training a policy that can provide any point of the Pareto front, but existing methods either train one model per preference, interpolate a few separately aligned experts post hoc, or train a single conditioned model without considering which preferences it should be trained on. Since the hard regions of the preference simplex depend on the objectives at hand, existing methods leave them under-trained and do not get the most out of a single model. Therefore, we propose MAESTRO (Multi-objective Alignment via End-to-end STeering and Robust Optimization), which formulates MOA as a minimax problem over preference distributions and trains a single prompt-conditioned policy end-to-end with RL against an adversarial preference distribution: a Dirichlet distribution updated by online mirror descent toward the preferences the current policy serves worst, rather than on a fixed one. On HH-RLHF, BeaverTails and a summarization task, with up to three objectives, MAESTRO attains the best Pareto front on most tasks in a single training run, at the lowest training cost among the compared methods. The largest margins appear in the hard regions that a fixed preference distribution leaves under-trained, confirming that a single prompt-conditioned model is capable of covering the objective trade-offs on its own.

Let $\mathcal{H}$ be a complex Hilbert space, and let $T=H+iK\in\mathcal{B}(\mathcal{H})$ be the Cartesian decomposition of $T$, where $H=H^{*}$ and $K=K^{*}$. We introduce the $L^2$-Cartesian numerical radius and study its basic properties. We compare it with the classical numerical radius $\omega(T)$. In particular, we establish the sharp estimate $ \frac{1}{\sqrt{2}}\omega(T)\le \wcart{2}(T)\le \omega(T), $ and establish lower and upper bounds in terms of the Cartesian parts $H,K$. We also give an equality characterization and explicit sharpness examples. As a consequence, we obtain $\frac{1}{4}\left\|T^{*}T+TT^{*}\right\|\le \wcart{2}(T)^2\le \omega(T)^2. $ More generally, we study the $L^p$-Cartesian numerical radius and prove the sharp comparison $ c_p\,\omega(T)\le \wcart{p}(T)\le \omega(T),\qquad 1\le p<\infty. $ Finally, we present a block-operator analogue of the classical refinement of the triangle inequality.

We generalize the Furusawa–Kaneko model, a simple model of intracellular catalytic reaction networks, to multicatalyst reactions and analyze the generalized model using dynamical mean-field theory. In the thermodynamic and dense-network limit, we derive exact effective equations and analyze their fixed points for arbitrary degree distributions. Under nutrient-poor conditions, network heterogeneity suppresses the metabolic–starvation transition irrespective of the number of catalysts per reaction. In contrast, under nutrient-rich conditions, the bifurcation structure changes with the number of catalysts. With one catalyst per reaction, only continuous transitions occur, whereas two or more catalysts give rise to bistable phases and discontinuous transitions. The bifurcation structure also differs between two and three catalysts per reaction, with three catalysts allowing bistability between metabolic states with different cell growth rates. Our results provide a possible mechanism for bistability and abrupt switching in metabolic dynamics.

We prove several conjectures from the On-Line Encyclopedia of Integer Sequences about the lower and upper Wythoff sequences and the Fibonacci word. Among them are two of Kimberling's three conjectures on the number of ways to write $n=\lfloor h\varphi\rfloor+\lfloor k\varphi^2\rfloor$ with $h,k\ge1$ (A259598): exactly one way if and only if $n+1=2F$ for a Fibonacci number $F\ge2$, and exactly two ways if and only if $n+1\ge7$ is a Lucas number. The third conjecture, that no way exists if and only if $n+1$ is a Fibonacci number, was proved earlier by Kawsumarng et al. We also observe that Kimberling's conjecture on the gaps of the sums of two distinct terms of A003622 and of their complement (A333308, A333309) follows, after a shift by $2$, from earlier Walnut results of Shallit and of Bosma et al. on A260317, and we re-verify it. Next, we prove Kimberling's five 2025 conjectures on the gaps between positions where the Fibonacci word and the "Lucas word" take prescribed values (A383423-A383427). Finally, we prove a conjecture of Mathar on A285383, and we point out that a conjecture of Schmidt on A003250 follows from theorems of Carlitz, Scoville and Vaughan (1973); we also confirm it with Walnut. Most proofs are decision procedures run in the free prover Walnut, and we supply the complete command file.

We show that a collisionless point-vortex gas behaves as a genuine Vlasov system. Starting from the non-canonical Hamiltonian structure of point-vortex dynamics, we derive a reduced Klimontovich equation and the corresponding Vlasov description directly on the physical plane, without introducing auxiliary momentum variables. The theory predicts a rich spectrum of collective phenomena, including vortex Rossby-like waves, global oscillations, resonant critical layers, and a dielectric response operator analogous to that of plasmas and self-gravitating systems. For smooth vortex distributions, differential rotation gives rise to a vortex analogue of Landau damping, whereby collective modes transfer energy and angular momentum to resonant vortex annuli in the absence of collisions or dissipation. Remarkably, differential rotation acts as a stringent mode-selection mechanism: for a Gaussian vortex cloud, only a single quadrupolar quasi-mode survives, while all higher multipoles are destroyed by phase mixing. We further predict a vortex counterpart of the beam–plasma instability, in which a thin vortex ring orbiting an Onsager patch selectively excites Kelvin modes with an azimuthal symmetry controlled by the ring population. These results establish kinetic theory as a natural framework for collective vortex dynamics and suggest new mechanisms for vortex transport, vortex avalanches, and rotational glitches in neutron-star superfluids.

We establish global well-posedness of classical solutions to the two-dimensional primitive equations with fractional horizontal dissipation for arbitrarily large initial data in the full subcritical range $1<\alpha\leq2$. Together with the known ill-posedness results for $0\leq\alpha<1$, this establishes the sharp dissipation threshold for large-data global well-posedness in the corresponding solution framework. The key ingredient is a hydrostatic energy estimate obtained by splitting the nonlinear energy into symmetric and antisymmetric parts and exploiting the commutator structure of the latter. Using anisotropy and incompressibility, we bound the nonlinear energy by the $L^\infty$ norm of the hydrostatic vorticity times a quadratic velocity norm with only one-half additional horizontal derivative. The vorticity maximum principle then yields enhanced velocity bounds, which close the vorticity estimates and verify the continuation criterion throughout the subcritical regime.

Predicting stem-cell lineage fate is central to elucidating biomaterial-stem cell interactions and optimizing strategies for tissue regeneration. While existing approaches demonstrate the feasibility of lineage prediction, they remain limited in modelling compositional heterogeneity and time-dependent differentiation dynamics. To mitigate this gap, we propose PuriGen, a purity-aware deep generative framework for biomaterial-induced lineage prediction from bulk transcriptomic data. PuriGen consists of two key modules, PuritySCVI and PuritySCANVI, which extend scVI and scANVI by incorporating a pretrained GBMPurity head to provide a sample-level purity-like compositional signal. In addition, purity-aware regularisation and temporal constraints are introduced to encourage informative purity prediction and biologically consistent latent representations. Experiments on bulk mesenchymal stem-cell datasets collected across multiple biomaterial conditions and induction stages show that the proposed framework achieves better performance than the existing methods.

As coding agents take on long-horizon software evolution tasks spanning multiple files and stages, longer execution trajectories introduce two coupled challenges: (1) accumulated histories strain context budgets, and (2) repository changes can invalidate earlier execution evidence. Existing approaches address these challenges through techniques like larger context windows, compression, retrieval, or repository representations, but often fail to reconstruct a consistent task state after a context refresh or verify whether recalled evidence remains valid. Thus, we introduce MemTrace, a provenance-aware memory system that preserves execution history and aligns its reuse with the evolving task (e.g., iterative cross-file repair) and repository state. MemTrace stores history as immutable Memory Traces anchored to key information (e.g., files, symbols, tests), and organizes their execution order and dependencies in a Memory Trace Graph. When context is constrained, working memory retains only compact Memory Anchors, from which the agent can reconstruct the latest execution state and locate evidence relevant to its next action. Before restoring historical evidence, MemTrace checks its validity against the current repository state and retrieves only what the next action requires. Across three complementary long-horizon coding benchmarks, MemTrace consistently outperforms all fully evaluated baselines under the same backbone and harness, improving DeepSWE pass@1 by 21.2 points, SWE-EVO Resolved Rate by 4.4 points, and SWE-Milestone Score by 17.8 points under Codex CLI.

Retrieval-augmented generation (RAG) dominates repository-level code completion: it retrieves cross-file context (R), then decodes one greedy completion (G). Existing work mainly focuses on retrieval and stops there. We argue both stages can be improved together, with generation in particular gaining from test-time scaling. We present CARET, a training-free method. For R, CARET routes among retrieval contexts using the agreement among its own samples, cascading to an alternative context when the samples scatter. For G, it samples candidates over a cached prompt prefix, so the long retrieved context is encoded once rather than once per sample. It then selects the final completion by reverse-context likelihood: a correct completion makes the code after the cursor more probable, so the same model grades its own candidates by reading ahead. Across CrossCodeEval, RepoEval-Line, and RepoEval-API with six code models (1.1B to 7B, four families), CARET improves exact match in all 18 combinations by 10.8 points on average over greedy decoding and 5.3 over self-consistency@10. Token-level compute stays near 1.45 times one generation (measured wall-clock 1.3-2.9 times, growing with generator size). Improving retrieval and generation together yields more accurate code than improving retrieval alone, at a budget that stays close to a single pass.

Remote sensing agents rely on perception, measurement, and raster analysis tools to solve Earth observation tasks. We refer to their judgments and quantitative results about ground objects as tool observations. However, these observations are subject to uncertainty and may be incorrect even when tools execute successfully. When agents accept incorrect observations, the errors can propagate through subsequent reasoning and cause task failure. We analyze 1,229 execution trajectories across three remote sensing agent benchmarks. On each benchmark, at least 88.1 percent of tasks depend on tool observations. Among these tasks, at least 22.7 percent contain incorrect observations despite successful tool execution. These errors propagate to the final answer in at least 82.0 percent of affected tasks on each benchmark. To address this problem, we propose RSure-Agent, a framework for verifying tool observations and limiting error propagation. We introduce a verifiable observation protocol that requires tools to return process evidence for the agent to verify their observations. We construct a task-tool reliability prior from offline task feedback. The prior summarizes each tool configuration's past performance across task types and provides a task-specific reference for verification. Using process evidence and this prior, RSure-Agent decides whether to accept an observation, request additional evidence, or reject it. We evaluate RSure-Agent on EarthBench, ThinkGeo, TerraLogic, and CHOICE-420. Across three agent benchmarks, RSure-Agent reduces the error propagation rate by 21.3 to 25.9 percentage points relative to the base configuration with verification and the prior disabled. On CHOICE-420, it improves overall accuracy over direct answering by 5.71 percentage points on average across 11 backbone models. On EarthBench, it reduces the tool-call ratio by 25.9 percent relative to Earth-Agent.

We classify nontrivial simple super-Virasoro modules finitely generated over \(\C[L_0]\) using simple Laurent Weyl algebra modules finite free over \(\C[D]\). The classified modules are finite Cartan-free with equal parity ranks. We also prove finite length without simplicity and construct explicit nonsplit self-extensions.

We introduce a quantum coding framework for discrete small-shift noise, in which errors on qudits are modeled as low-weight $X$- and $Z$-type Pauli shifts, analogous to small phase-space displacements in continuous-variable systems. This structure is approximately respected by nuclear-spin noise and captured by the Lee metric, motivating a quantum extension of classical Lee-metric coding theory. We develop such a formalism for stabilizer codes over $\mathbb{Z}_q$ for arbitrary $q$, using joint and separate Lee metrics for the $X$- and $Z$-components of errors. For qubits, the joint metric counts $Y$ errors twice and can yield codes that detect and correct $X$ and $Z$ errors with fewer physical qubits than codes designed for the conventional Hamming metric. We discuss Lee-weight spreading under Clifford gates and qubitize codes over $\mathbb{Z}_4$ via the Gray map, finding codes with two-fold transversal non-qubit-Clifford gates. For quantum CSS Lee-LDPC codes on $n$ qudits, we prove that the Lee distance cannot exceed $O(n)$, uniformly in $q$, demonstrating an unexpected obstruction to using the large internal Hilbert space of a large-$q$ qudit to make high-Lee-distance codes. Under local Metropolis dynamics, certain classical $q$-ary “helical repetition codes” have exponentially long memory times at fixed temperature for sufficiently large $q$ (that grows with system length), which can be understood as spontaneous symmetry breaking at finite temperature, even in local one-dimensional models. Hypergraph products of these helical repetition codes provide local two-dimensional quantum codes that inherit self-correction for $Z$ errors, but self-correction for $X$ errors remains an open question.

This is the second paper in our series of works to develop the min-max theory for free boundary minimal hypersurfaces in Riemannian manifolds with boundary via the Allen-Cahn equation. Building on our previous work for general critical points, we study the boundary behaviour of limit-interface integral varifolds arising from stable (or finite Morse index) solutions to the Allen-Cahn equation with Neumann boundary condition. More precisely, we prove that the limit-interface is a curvature varifold with boundary in the sense of Mantegazza satisfying a generalized stability inequality. Furthermore, we rule out classical tangent cones at the boundary and show that the first variation of the limit-interface varifold is singular with respect to its weight measure. In particular, our result confirms a folklore conjecture that the boundary concentration examples of Malchiodi, Ni and Wei have unbounded Morse index. As will be evident in our forthcoming work, the results obtained in this paper are crucial ingredients towards the optimal boundary regularity in the Allen-Cahn free boundary min-max theory.

Agent Skills, the SKILL.md files that tell an LLM coding agent how a project works, are revised like code, yet what a revision does to the agent is unknown. From 2,608 first/last revision pairs of 3,159 Skills, we characterize how Skills evolve and how they change together with the configuration of the agent's harness. We then focus on rule changes, revisions that add or remove a rule we can check automatically, such as "run allium check". We measure their effect on 21 models in single answers and on four agents in a sandbox, and their cost on 20 of these models and the four agents. Most revisions (55%) change a rule or procedure, and commits that revise a Skill change harness files such as CLAUDE.md more often than other commits of the same size. Across 16 open-weight models, an added rule raises compliance in a single answer by +0.41 on average. Across the four agents, the rate at which the agent takes the required action rises by +0.23 on average (+0.16 to +0.36), and for the three agents that blind judges assessed, final correctness rises by +0.10 on average (+0.06 to +0.14). The gain comes mainly from rules that name a command or path the old Skill did not mention. Real tools load a Skill's body only when the agent decides it needs it. In that setting the four agents keep about half of the action gain on average (51%), and the three open models about 38%. A revision adds 18-19% input tokens to a single answer and no detectable cost to an agent episode, while loading a Skill's body raises the tokens of an episode by 50% on average.

We develop entanglement-of-formation potentials for feedback-assisted classical communication and one-way randomness distillation. For a finite-dimensional quantum channel without initial shared entanglement, an exact amortization theorem bounds the increase of message information plus entanglement remaining across the communicating laboratories. This proves a classical-feedback capacity bound using a mixed-convex-roof expression previously studied by Winter and Yang in the context of potential capacities. We determine the capacity of flagged mixtures of noiseless and entanglement-breaking channels, improve a published depolarizing-channel converse, and evaluate the new bound exactly for the amplitude damping channel. A state analogue gives a finite-blocklength upper bound on the net shared randomness obtainable with one-way classical communication. Amplitude-damping Choi states provide exact benchmarks, while a full-rank generalized amplitude-damping Choi state demonstrates a useful improvement where we do not evaluate the operational rate exactly. We also distinguish one-way from two-way randomness distillation: a two-round weak-measurement protocol strictly exceeds the exact one-way rate of every nontrivial qubit isotropic state. The protocol preserves quantum side information during its first decoding and extracts additional randomness in the reverse direction. This shows why the one-way state potential is not a general two-way converse. Together, these results establish a common entanglement-based approach to sharper communication and randomness bounds, while revealing how retained quantum correlations enable two-way distillation to surpass one-way limits.

Self-supervised fine-tuning refines the embedding space of a pretrained language encoder without labels. However, the commonly used approaches are computationally expensive. Specifically, contrastive learning-based methods need multiview data and in-batch negative examples, while negative-free approaches require auxiliary graphs/networks. An interesting question arises: can self-supervised fine-tuning be done without relying on either additional negatives or graph data? To answer this question, we introduce SilK (Silhouette-guided K-means), which trains on a Cluster Validation Index, an internal measure of cluster quality without using labels. SilK clusters the corpus and then regresses a simplified silhouette toward a target value. Each document is compared only against the k cluster centroids, never against other documents, so the method needs no augmentation, no negative pairs and one view per document. On BERT-base, SilK trains 1.46x faster per epoch than the fastest baseline we evaluate and uses 45.4% less peak GPU memory than the leanest one. Under frozen-encoder linear probing, SilK stays competitive with the best baselines on three downstream tasks.

When an agentic prover works on an open problem, there is no proof assistant to fall back on: its verifier and lemma library are ultimately language models judging model outputs. We instrumented such a system end to end and analyzed $51{,}754$ traced observations across three full runs ($186$ hours, \$$5{,}694$). We find three connected failure modes. First, the three-model verifier requires unanimity and treats parse or API failure as non-approval; in $10$ of $12$ verification events, one member returned no parseable output or an API error, making acceptance arithmetically impossible without surfacing an error. Second, when the ensemble did function, one verifier approved $3$ attempts that GPT rejected, each claiming to resolve the open problem; a single-verifier design would therefore have announced a solution three times. Third, because nothing could be approved, every review was a refutation, yet the lemma extractor mines reviews as well as proofs: $24$ of $93$ lemmas ($26%$) were extracted from rejected arguments with their refutational context removed. Taken together, these findings show that without external verification, supervision is itself a critical trust boundary: systems must distinguish abstention from rejection, preserve useful disagreement, and preserve the provenance and polarity of information before it becomes future context.

This paper proposes a label-free physics-informed neural network (PINN) for non-associated Mohr-Coulomb plasticity with incremental strength reduction for the reliability of spatially variable $c$-$\phi$ slopes. The PINN is trained with a virtual-work loss on the finite-element mesh and solves many random fields at once on a graphics processing unit. With a solver budget fixed on the homogeneous slopes, it reproduces the Abaqus factor of safety within 2 to 3% root-mean-square on 52 random fields and locates the failure mechanism in the same weak zones, with the plastic strain in the band under-resolved. A neural operator trained only on the PINN solutions predicts the factor of safety, displacement path and failure mode of a million fields in seconds. No finite-element solution enters the pipeline: Monte Carlo fields, importance samples and operator training data come from the PINN, and Abaqus serves only to verify the result. Monte Carlo simulation, the first-order reliability method, importance sampling and the operator give consistent failure probabilities down to $10^{-3}$ for the slope studied, but a 3% scatter in the factor of safety inflates a probability of $10^{-3}$ by up to a factor of two, and the absolute values refer to one mesh. A heterogeneous Bishop analysis gives failure probabilities 2.6 and 8.3 times lower although its critical circles follow the PINN mechanism, because a small difference in the factor of safety is amplified in the tail. The operator also yields the failure mechanism and displacement response conditional on failure.

Time-series foundation models (TSFMs) enable zero-shot forecasting through large-scale cross-domain pretraining, while retrieval augmentation further improves their performance by leveraging historical information. However, existing methods typically correct TSFM forecasts using the ground-truth futures of similar historical windows, which contain both predictive components already captured by the foundation model and sample-specific random fluctuation that is difficult to transfer. In contrast, recurring systematic model bias within prediction errors more directly characterizes the failure modes of a frozen TSFM and therefore provides more valuable correction signals. Effectively exploiting such model bias, however, poses two challenges: prediction errors at different numerical levels are difficult to compare due to scale differences, and the recurring bias must be extracted from prediction errors contaminated by random fluctuation. To address these challenges, we propose GRAM, a general retrieval-augmented framework for frozen TSFMs. GRAM first introduces an Amplitude Memory Module (AMM) that scales prediction errors by amplitude and aggregates them into retrievable prototypes. It then employs a Prototype Graph Module (PGM) to model relations among prototypes to aggregate consistent bias information while suppressing random fluctuation. During online forecasting, GRAM retrieves and expands prototypes relevant to the current query and generates per-horizon corrections to refine the original TSFM forecast. Experiments across multiple datasets and foundation models demonstrate consistent forecasting improvements.

Empathetic spoken dialogue is a sophisticated cognitive process that requires not only recognizing emotions but also inferring a user's latent mental states to provide appropriate support. However, current SpeechLLMs often treat empathy as a direct input-to-response mapping, leading to "superficially warm" but emotionally hollow interactions. In addition, since empathy relies on a multi-stage process with strong inter-step dependency, errors at any intermediate step can cascade through subsequent steps and lead to inappropriate responses, while existing training paradigms lack mechanisms to precisely localize and improve such errors. In this work, we propose EchoChat, a unified framework that reformulates empathetic spoken dialogue as a structured cognitive reasoning process integrating perception, mental-state reasoning, and response generation. To support this paradigm, we first construct EchoDialogue-400K, an acoustically rich dataset for multi-stage empathetic supervision. During the SFT stage, we strengthen acoustic grounding through proposed Acoustic-Anchored Attention (AAA). During the RL stage, we further introduce a novel stage-aware optimization objective with Step-Decomposed Credit Assignment (SDCA) to localize reasoning errors and mitigate cascaded error propagation. In addition, we introduce EchoEval, an expert-annotated benchmark for multi-dimensional empathy evaluation. Extensive experiments demonstrate that EchoChat achieves state-of-the-art performance in perception, reasoning, and response alignment. Project page: https://github.com/dingdongwang/EchoChat

Fluent guidance is not the same as useful intervention. LLM tutors are typically trained to generate the next teacher utterance, implicitly assuming that every student turn warrants a response. However, our experiments indicate that this conflates tutoring capability (what to say) with intervention necessity (whether to say it). We introduce DICE, a framework that decouples intervention decisions from response generation by first selecting an explicit pedagogical action. To calibrate this action selection policy, we define Intervention Value (IV), a rollout-grounded counterfactual metric that compares each action against non-intervention. IV shows that many prescribed interventions provide little or no marginal benefit. We further introduce DICE-Bench, a multi-variant math tutoring benchmark with skill-preserving problem variants for session-level evaluation. Using IV-weighted and KL-regularized policy optimization, DICE learns to intervene selectively while preserving tutoring effectiveness. In simulated tutoring sessions, DICE reduces the over-intervention rate to near zero while guiding students to correct solutions in approximately 3-4 fewer turns on average than existing Socratic tutoring baselines.

AI agents based on foundation models (FMs) have demonstrated strong capabilities to perform complex open-ended tasks. However, they face some common challenges in practice: (a) agent behavior can deviate drastically even for semantically similar tasks, leading to catastrophically propagated errors; (b) high cost and latency due to FM calls, repeated in full whenever a task recurs with different inputs; (c) FMs' limited context and instruction following capability confine how well agents manage the ever-growing execution context and follow complex plans. We introduce $\textbf{A}$gent $\textbf{B}$ehavior as $\textbf{C}$ode $\textbf{Agent}$ (ABCAgent), which uses a symbolic program (e.g., Python code with potential neural functions) to fully specify the agent's behavior at runtime, with a powerful FM agent editing that program for flexibility. Behavior is thus specified without premature variable binding, and its execution is deterministic. We evaluate ABCAgent on six agent benchmarks, two of which we construct to test how well a derived program generalizes to variants of the task it was written for. ABCAgent matches a model-matched neural agent on GAIA and augmented GAIA, and surpasses it where robustness and long control flows matter: 98.3% against 97.3% on GSM-Symbolic ($p = 0.001$), 71.9% against 47.4% $\mathrm{Pass}^4$ on the telecom domain of $\tau^2$-bench ($p = 0.0001$), and more records written correctly at every loop length on our control-flow-augmented WorkArena benchmark. For more parametric task families, ABCAgent is also significantly superior in efficiency. Without authoring a new program, ABCAgent solves 92.6% of GSM-Symbolic instances and 20.1% of augmented GAIA variants, which yields $5.2\times$ lower latency and $7.0\times$ lower cost on GSM-Symbolic, 19% lower cost on augmented GAIA, and $9.5\times$ lower agent latency on $\tau^2$-telecom.