Papers

Large-momentum effective theory (LaMET) provides a first-principles framework for computing the $x$ dependence of light-cone parton distributions from lattice QCD. Over the past decade, theoretical and numerical advances have established a mature multi-stage workflow for systematic calculation of parton physics, although its implementation still requires expert judgment and substantial repeated effort. We present lamet-agent, an open-source large language model (LLM) agent framework that organizes this workflow into an executable, reproducible, and inspectable analysis pipeline. The present release supports collinear quark distributions and implements correlator analysis, renormalization, Fourier transformation, perturbative matching, continuum, physical pion mass and infinite-momentum extrapolations, and automated result review. We validate it on four end-to-end analyses: pion parton distribution functions in the gauge-invariant and Coulomb-gauge formulations, and pion and kaon distribution amplitudes, obtaining results consistent with the published calculations. Extensions to transverse-momentum-dependent distributions, generalized transverse-momentum-dependent distributions, and gluonic distribution functions are planned for subsequent releases.

We explore whether Omni-Language Models (OLMs) can be directly applied to zero-shot Semantic Audio-Visual Navigation (SAVN). Recent work demonstrates that even state-of-the-art specialized models still struggle to achieve generalist multimodal navigation, despite extensive task-specific training. In this paper, we introduce RAO-Nav, short for Reasoning All-in-One OLM, a deployment pipeline for zero-shot SAVN. By leveraging the rich implicit audio-visual knowledge encoded in OLMs, the embodied agent is enabled to “hear”, “see”, “reason”, and “act” in the environment. To further elicit the built-in thinking ability of OLMs, we propose a test-time Latent Navigation Reasoning (LNR) module that can be seamlessly integrated into the decoding space. LNR encourages the model to retrieve more target-relevant observations and make effective navigation decisions. Through comprehensive experiments, we show that our framework surpasses existing state-of-the-art baselines on public SAVN benchmarks without using any training data. Moreover, we introduce a new Global Navigation Instruction setting to further evaluate the ability of OLMs to serve as embodied navigation agents. Code: https://github.com/rikeilong/OmniAV\_Nav.

Feedback linearization is a powerful tool in nonlinear control, but finding the linearizing coordinate transform remains challenging. Feedback linearizing transforms are governed by well-established partial differential equations (PDEs) whose well-posedness is based on the Lie-algebraic Frobenius theorem, but solving the PDEs becomes computationally intractable for large system dimensions. To address this challenge, we propose a cascaded physics-informed neural network (PINN) framework to approximately solve these PDEs. By separately parameterizing terms of different Lie derivative orders, we mitigate the compounding errors inherent in fitting high-order Lie derivatives of neural networks. Furthermore, we use the learned transform to design a tracking controller and establish theoretical bounds on its error with respect to inaccuracies in the learned feedback-linearizing representation. We validate our method on a broad class of feedback linearizable systems, including a multi-input, multi-output planar quadrotor and synthetic examples for which analytical approaches are impractical, and demonstrate that our approach can computationally discover effective feedback-linearizing representations of nonlinear systems for control tasks.

Raw 3D point clouds are a core geometric representation. Establishing their ownership is challenging because point sets are irregular, unstructured, and frequently altered by resampling and geometric preprocessing. We present a blind watermarking framework that operates directly on xyz coordinates and supports both object-level shapes and scene-scale scans. At verification time, the embedded message is recovered from the observed point cloud alone, without access to the original point cloud, color, normals, or mesh connectivity. The method jointly learns watermark embedding and extraction through a feed-forward octree-based architecture, enabling efficient multi-scale geometric reasoning on large point sets. During training, a stochastic transformation layer exposes the decoder to common geometric perturbations, while progressive pose alignment improves robustness to pose changes. Experiments on object-level and scene-level benchmarks demonstrate reliable message recovery under common geometric processing while maintaining low geometric distortion. Qualitative comparisons further show that the learned perturbations are less visually conspicuous and less spatially structured than those of handcrafted alternatives.

This letter proposes a novel form of energy function (EF), called neural-analytic EF, for the stability analysis of power systems. The neural-analytic EF is designed as the sum of neural networks (NNs)-based components and an analytic EF, with the structure informed by the existing EFs derived analytically. It thus integrates NN's expressivity with the generalizability and scalability of analytic EFs. The satisfactory neural-analytic EF is further derived by iterative NN training with a tailored loss function. Numerical results finally demonstrate its superiority.

Audiology consultation requires structured history-taking, audiometric interpretation and patient-centred communication, yet real-world case material is scarce. We present a bilingual AI audiologist pairing a general-purpose large language model with rubric-guided closed-loop engineering, multimodal audiogram interpretation and retrieval-augmented grounding, without fine-tuning the language-model backbone. Using a 21-item rubric and an AI patient simulator, we distilled experience-derived guidance into a 19-rule playbook from 73 training cases (43 English, 30 Chinese) and evaluated the system on 58 independent simulated cases (30 Chinese, 28 English) in a pre-specified, source-blinded comparison with 17 practising audiologists. The AI audiologist outperformed human audiologists on every case (58/58; mean paired $\Delta$ = +1.35 on a 5-point composite, Cohen's d = 1.84, $P = 4.5 \times 10^{-20}$), on 20 of 21 rubric items and in both languages. Component ablation identified the playbook as the largest contributor, offering a practical route to specialist consultation agents in low-data medical domains.

This letter proposes a novel method to establish decentralized stability conditions (DSCs) of power systems. This method formulates DSCs with meticulously crafted neural networks, based on the insight into the structure and properties of the existing analytically derived DSCs. A tailored loss function is further devised to iteratively train the neural networks, ensuring validity and reducing conservatism of the DSCs. Numerical results demonstrate that the resultant neural DSCs are less conservative than the conventional analytical DSCs, and become generalizable if a relatively large-scale system is used for training.

The Hamilton-Jacobi [HJ] analysis and the Faddeev-Jackiw [FJ] quantization for the linearized, non-projectable $\lambda R$ model, extended by the lowest-order term of Blas, Pujolàs, and Sibiryakov and the higher-order term involving the square of the Cotton tensor, were carried out. The cases $\lambda \neq \frac{1}{3}$ and $\lambda = \frac{1}{3}$ are analyzed. Within the Hamilton-Jacobi framework, we obtain the complete set of Hamiltonians, generalized brackets, fundamental differential, characteristic equations, and gauge transformations of the theory. In the Faddeev-Jackiw framework, a symplectic tensor is constructed from which the fundamental brackets are identified. The HJ and FJ brackets coincide, and from the symplectic tensor, the measure for the quantum path integral is calculated. The differences between the cases $\lambda \neq \frac{1}{3}$ and $\lambda = \frac{1}{3}$ at the quantum path integral are discussed.

Exploiting discounted spot instances for HPC requires an application to change its resource allocation at runtime, shrinking ahead of an interruption and expanding onto replacement capacity. Existing elasticity mechanisms implement rescaling as a full process teardown followed by a cold restart at the new processor count, and the restart stage accounts for up to 95% of the total overhead, growing with node count and increasing substantially on GPUs due to CUDA context initialization. In this paper, we present a no-restart rescaling mechanism for the Charm++ runtime system in which surviving processes never exit: a rescaling operation consists of a membership negotiation with a lightweight external coordinator, reconciliation of the UCX communication endpoints with the new cluster view, and a return to the top of the runtime initialization path that preserves live application state. This reduces the cost of a rescaling operation, excluding the load balancing step that any rescaling model requires, from multiple seconds to 8–15ms on CPUs and 7–11ms on GPUs, at 4 to 32 instances. Because processes survive, GPU device state persists in place, eliminating the checkpointing daemons previously required for GPU elasticity, and a launcher-independent bootstrap mechanism removes the dependence on supervised process managers, which are incompatible with spot instance interruptions. Integrated with an existing spot instance management framework, the mechanism cuts the end-to-end overhead of eight simultaneous interruptions to 0.2% of runtime on CPUs and 0.6% on GPUs, and raises the rate at which a job can be rescaled below 1% overhead by a factor of seven.

Who we communicate with influences both our interpretation of their utterances and the design of our own. Such adjustment to the conversational partner is studied as speaker modeling in comprehension and as audience design in production, with the two literatures having developed largely separately. We argue that both adjustments express one rational computation and propose the rational interlocutor (RI) model, a computational account unifying comprehension and production. An interlocutor maintains a model of their partner, defined by three parameters: an identity parameter {\Pi} sets the messages and forms expected from the partner; a fidelity parameter {\Phi} sets how reliably messages and utterances map onto each other for them; a knowledge parameter {\Lambda} sets how knowledgeable the partner is believed to be. Comprehension and production are thus mirror-image modes of one computation over the partner model. Comprehension chooses the message the partner most likely intends to convey, weighing how well each candidate fits the utterance against how likely this partner is to mean it. Production chooses the utterance from which the partner will best recover the message, weighed against the effort of saying it. This explains why comprehenders appear to rely less on the forms produced by a linguistically less competent speaker, while producers tend to invest more effort in designing forms for them. We conjecture that perceived linguistic competence decomposes into two of these quantities: fidelity and knowledge. Their contrasting profiles across second-language (L2) adults, children, and artificial partners produce distinct and testable predictions.

Transformers have redefined sequential recommendation by effectively modeling dynamic user behaviors and long-range dependencies. However, they remain inherently inefficient: standard architectures operate at a fixed rate, allocating comparable computation to every item in a user's history regardless of its information content. This leads to prohibitive computational overhead on long sequences and increased sensitivity to behavioral noise. To address this, practitioners often resort to lossy sequence compression, staged modeling, or truncation. This limits the model's ability to leverage the full context of long histories during inference. Inspired by the recent success of Byte Latent Transformer, we propose DP-Rec, a dynamic latent patching architecture for recommendation. DP-Rec shifts from item-level modeling to patch-level modeling by segmenting interaction sequences using contrastive entropy surprise to identify informative behavioral boundaries. A lightweight patch encoder compresses these temporally contextualized segments into a reduced set of dynamic latent behavior vectors, which are then processed by a larger latent transformer and decoded for next-item prediction. Extensive experiments show that, under constrained computational budgets, DP-Rec scales effectively to long sequences and achieves a superior efficiency-accuracy trade-off over both non-compressed and fixed-size compression baselines.

For a reduced crystallographic root system with Weyl group $W$, Weyl alternants are signed sums of exponentials indexed by $W$. They occur in the numerators of the Weyl character formula and the explicit formula for spherical functions on complex semisimple groups. We establish rootwise bounds that quantify cancellation in these oscillatory sums, with each positive root contributing a factor depending on both the spatial variable and the spectral parameter. More generally, we establish rootwise bounds for all mixed directional derivatives of normalized Weyl alternants. Our proof extends to arbitrary rank the descent strategy used by the second author for pointwise character bounds on $\mathrm{SU}(3)$. The key ingredients include the decomposition of the Weyl group into parabolic double cosets and the relative BGG–Demazure identity. For spherical functions on complex semisimple groups, these estimates recover the recent pointwise bound of Brumley, Marshall, Matz, and Peterson, and they refine the derivative bounds of Cowling and Nevo by controlling arbitrary mixed radial derivatives uniformly across spatial and spectral root hyperplanes. Furthermore, by a standard localization argument relative to the affine Weyl arrangement, we establish periodic alternant estimates for regular integral weights and corresponding rootwise bounds for all mixed radial derivatives of irreducible characters of compact connected semisimple groups.

Agent performance depends on both the underlying model and the harness that manages its tool use and execution. Selecting a suitable pair requires accounting for their compatibility, yet training samples may cover only a subset of the growing combination space. We introduce HM-Router, a routing method that jointly selects a model and harness for each query. It learns separate model and harness representations shared across routes, with an interaction term inspired by canonical polyadic (CP) tensor decomposition to capture how their compatibility varies with the query. This sharing allows training samples from observed pairs to inform predictions for unobserved combinations. We curate a benchmark from 12 public agent benchmarks, covering 293 routes, 73 models, and 25 harnesses. HM-Router exceeds the strongest evaluated learned baseline by 7.3 percentage points in mean routing accuracy and leads at all seven evaluated cost budgets on the six-benchmark subset. When 90% of routes have their training outcomes withheld, allowing unobserved combinations improves normalized accuracy by 15.8 points over restricting the same router to observed routes. HM-Router has also demonstrated training sample efficiency for new routes and components and generalization to unseen benchmarks. Our code and data are open-sourced at https://github.com/hmarkc/HM-Router.

The chiral soliton lattice (CSL) is conventionally described as a periodic winding configuration of a compact scalar field. In this paper, we formulate the CSL in a higher-form framework based on a Stückelberg coupling between a two-form gauge field $C_2$ and a three-form gauge field $A_3$, in which strings and walls can be treated directly as extended sources. Higher-form gauge invariance requires the string worldsheet to be the boundary of the wall worldvolume. In the quadratic dual effective theory, exchange of the massive higher-form mode generates a repulsive Yukawa interaction between parallel walls. With its coefficient fixed by duality, the resulting CSL lattice spacing agrees well with the exact Sine–Gordon result without parameter fitting. We then extend the description to a nonlinear, multi-branch higher-form theory. It reproduces the exact dilute wall–wall interaction coefficient, the periodic CSL and its energy-minimization condition, as well as the gapless CSL phonon. The phonon is identified as a collective displacement of the periodic higher-form background, while scalar winding is reinterpreted as branch flow of the nonlinear higher-form theory.

Leaderboards rank models by their average scores on benchmark items, and they are consulted repeatedly while the evaluation is still running. Existing confidence intervals for a model's rank control their error rate only if they are computed once, after a number of items chosen in advance. If they are recomputed as results arrive, and the evaluation stops once they look decisive, their error rate exceeds its nominal level. Anytime-valid methods keep their guarantees at all sample sizes simultaneously and hence under any stopping rule. They exist for the accuracy of one model, for one pair of models and for the set of models that may be best. For pairwise battles they also give ranks. None gives ranks when all models are scored on the same items, which makes their scores dependent. We construct rank confidence sequences: for every model, a set of ranks that contains its true rank, simultaneously for all models and at all times, at a chosen error level $\alpha$, in finite samples. The construction combines betting e-processes, one for each ordered pair of models, with closed testing over the possible orderings of the models. It allows any dependence between the models' scores on an item. The method has two advantages. A leaderboard can be inspected after every item without inflating its error rate. The evaluation of each model can stop as soon as the question asked about it is answered, which saves compute. When results are examined only once, halfway through or later, little power is lost relative to fixed-sample methods. The paper quantifies these advantages in simulations and on public leaderboard data.

We show that every polytope $P\subseteq[0,1]^n$, and more generally every compact convex set, has Chvátal rank at most $12.22n^2+n\log_2 n+2n+4$. This improves the $O(n^2\log n)$ bound of Eisenbrand and Schulz and, together with the $\Omega(n^2)$ lower bound of Rothvoß and Sanità, shows that the maximum Chvátal rank of a polytope in $[0,1]^n$ is $\Theta(n^2)$. More precisely, if $P$ contains an integer point, then for every $c\in\mathbb{Z}^n\setminus\{0\}$ the inequality $cx\le\max\{cy: y\in P\cap\mathbb{Z}^n\}$ is valid for the $k$-th Chvátal closure of $P$ for some $k\le 12.22n^2+2n+2\log_2\|c\|_\infty+4$. Following Eisenbrand and Schulz, we derive this inequality along a chain of coarser and coarser integer vectors, but instead of halving the vector in each step, we round $\tau c$ for a scale $\tau$ chosen freely in each dyadic window $[2^{-t-1},2^{-t}]$. The main new ingredient is a multiscale version of Dirichlet's approximation theorem, proved by an elementary volume argument: for every $c\in\mathbb{R}^n$, the $\ell_1$-distances of $\tau c$ to $\mathbb{Z}^n$, minimized within each dyadic window and summed over all windows, total less than $1.222n^2$, independently of $\|c\|_\infty$.

Time series foundation models must preserve multi-domain breadth, probabilistic output, and multiple temporal scales, but parameter count grows when each scale receives a separate representation. We introduce Fracast-0, a probabilistic forecasting foundation model that exploits temporal self-similarity to reuse one operator across scales. A parameter-free detector extracts significant seasonal structure. The encoder applies a shared local block along a geometric dilation ladder with scale conditioning, while the decoder combines context-gathered states with an explicit seasonal future state and reuses a second block along another ladder before emitting nine quantiles. Pretraining across six corpora preserves multi-domain breadth within 85,001 parameters. On 97 GIFT-Eval configurations without per-dataset fine-tuning, Fracast-0 is the smallest of 28 evaluated checkpoints and remains non-dominated in the aggregate parameter-accuracy plane with MASE 0.808 and WQL 0.564. It uses 42.0% fewer parameters than TinyCast, whose MASE and WQL are 4.2% and 3.3% lower. These results support cross-scale weight reuse as a practical route to further time series foundation model compression.

Automated science needs agents that can work out the rules of an unfamiliar environment by interacting with it. Interactive rule-discovery puzzles offer a controlled setting for studying this ability: an agent infers hidden rules through experimentation and uses what it has inferred to reach a stated goal. We ask what limits current language models on these puzzles and whether reinforcement learning (RL) improves performance on rules held out from training. To study both, we introduce WITNESS, a 2D grid-based puzzle environment with ground-truth ASCII observations and controlled access to rules. An agentic pipeline generates games for WitnessGym, the RL training suite, and WitnessBench, comprising public validation and private test games. The validation set separately tests new compositions of trained rule primitives and primitives absent from training. Under a shared harness, the best of 18 frontier proprietary and open-weight models solves only 24% of private test level slots, with scores sensitive to the observation interface and agent configuration. Providing ground-truth rules raises Opus-5's validation RHAE-L5 (relative human action efficiency over the first five levels) from 59.9 to 97.8, whereas a 27B open-weight model gains only 2.1 points and remains limited even with the rules provided. RL on WitnessGym raises the 27B model's private test RHAE-L5 from 2.1 to 5.4 and yields a mean gain of 4.1 points on four external discovery benchmarks. Together, these results point to rule acquisition as a major difficulty for frontier models like Opus-5 while smaller models further struggle on rule-based execution, and indicate that RL on hidden-rule puzzles transfers to broader rules and real-world tasks beyond training. Benchmark is available at: https://witnessbench.ai

Andrews and Newman introduced the minimal excludant $\mathrm{mex}(\lambda)$ of an integer partition $\lambda$ and studied the summatory function $\sigma\mathrm{mex}(n)$, and Baruah et al. refined this to the odd- and even-restricted functions $\sigma_o\mathrm{mex}(n)$ and $\sigma_e\mathrm{mex}(n)$. In this paper, we introduce and study the overpartition analogue $\overline{\sigma_o\mathrm{mex}}(n)$, defined as the sum of odd minimal excludants over all overpartitions of $n$. We first derive the exact generating function for $\overline{\sigma_o\mathrm{mex}}(n)$, and relate it to the bivariate generating function of Aricheta and Donato for the overpartition minimal excludant. Using elementary $q$-series arguments, together with a weight-one eta-quotient identity for $\varphi(q)^2$ verified via the Gordon–Hughes–Newman–Ligozat criterion, we establish an infinite family of congruences satisfied by $\overline{\sigma_o\mathrm{mex}}(n)$. Consequently, we obtain that $\overline{\sigma_o\mathrm{mex}}(0)=1$ and, for $n\ge1$, $\overline{\sigma_o\mathrm{mex}}(n) \equiv 0 \pmod{4}$ if and only if $n$ is a perfect square. We further obtain congruences for the partial sums and self-convolution of $\overline{\sigma_o\mathrm{mex}}(n)$; in particular, an infinite family of congruences modulo $8$ for the self-convolution, expressed in terms of the divisor functions $d_1(n)$ and $d_3(n)$. We conclude the paper by establishing a Hardy–Ramanujan-type asymptotic formula for $\overline{\sigma_o\mathrm{mex}}(n)$ via the Wright circle method.

We develop a high-order and positivity-preserving kinetic solver for the multi-species Vlasov-Ampère system that is built within a semi-Lagrangian discontinuous Galerkin (SLDG) framework. The method is designed for efficiency and accuracy across a broad range of conditions, including stiff, multi-scale regimes with strong ion-electron scale separation. Phase space is discretized via high-order discontinuous Galerkin finite elements; time stepping is handled via high-order operator splitting and a series of one-dimensional, unconditionally stable, semi-Lagrangian updates. To improve both accuracy and efficiency, each plasma species is represented on a different phase-space mesh. On every element and for each species, local positivity-preserving limiters are applied to prevent spurious undershoots and rigorously ensure positivity of the cell averages at the next time step. The accuracy and robustness of the resulting method are verified on several standard single- and two-species test cases, including manufactured solutions, two-stream instability, weak and strong Landau damping, ion-acoustic wave propagation, ion-acoustic shock formation, and KEEN wave dynamics.

Telecom-band spin defects in silicon offer a compelling platform for integrated quantum networks by combining scalable silicon photonics with spin-based quantum memories and multiqubit registers. The T center and recently demonstrated Al1 center are particularly promising, but their limited coherent zero-phonon emission requires strong cavity enhancement for efficient spin-photon interfaces. Here, we inverse-design silicon nanobeam cavities for both centers using a unified adjoint-optimization framework targeting Purcell enhancement, resonance alignment, and photon extraction. For each emitter, symmetric cavities maximize Purcell enhancement, while asymmetric cavities provide directional coupling to an integrated waveguide. Three-dimensional finite-difference time-domain simulations yield loaded quality factors up to 3.25 x 10^6, Purcell factors up to 1.43 x 10^5, and cooperativities of approximately 280-5000, corresponding to cavity-coupled emission fractions exceeding 99.6%. The asymmetric cavities direct approximately 90% of emitted power into a single on-chip waveguide while maintaining cooperativity above 280. Under nanometer-scale fabrication perturbations, all four designs remain within the high-cooperativity regime, and high cooperativity persists when the cavity quality factor is constrained to a realistic absorption-limited value of 10^5. This unified, fabrication-compatible framework establishes a scalable cavity-design route for silicon telecom spin-photon interfaces and, to our knowledge, the first cavity designs for the Al1 center.

Secure Transformer inference protects sensitive inputs but incurs substantial cryptographic overhead, with nonlinear operations such as Softmax and GeLU becoming major bottlenecks. Existing compression methods reduce nonlinear complexity, sequence-dependent computation, or model structure through separately defined compression variables. Under aggressive compression, however, these independently optimized perturbations can accumulate: at a matched compression level, stacking representative approximation, token-pruning, and model-pruning methods reduces ViT-S accuracy from 80.20% to 76.41%. We introduce DegreeSpar, which formulates secure Transformer compression as structured sparsification over nonlinear polynomial degrees. Polynomial degree directly controls the cost of secure nonlinear evaluation, while computation-aligned zero-degree structures expose token-level and model-dimension computation as removable within the same optimization space. DegreeSpar further incorporates approximation-aware training for low-degree Softmax and GeLU, enabling aggressive degree reduction and creating the optimization headroom required for structured computation removal. Across vision and language Transformers, DegreeSpar consistently improves the accuracy-latency trade-off across model scales, tasks, and sequence lengths, achieving speedups from 2.29x to 6.63x over the corresponding baselines. Under the same network setting, DegreeSpar achieves 92.68% accuracy on BERT/SST-2 in 110.55 s, compared with 92.66% in 167.26 s for CipherPrune, the closest prior hybrid secure-inference approach. These results establish structured polynomial degree as an effective shared optimization space for secure Transformer compression.

Large vision-language models (VLMs) can judge visual similarity, but their judgments are not directly available as compact image embeddings for efficient comparison. We study how to transfer these preferences into CLIP while retaining its image–text capabilities. We introduce ASK, a kernel-based steering method that learns from elicited pairwise judgments without accessing teacher embeddings or collecting new human similarity annotations. ASK constructs positive semidefinite target kernels within small image groups and combines visual kernel matching with an image–text distributional anchor. Low-rank adapters jointly update the visual and text encoders while regularizing predictions toward frozen CLIP. After adaptation, retrieval uses CLIP image embeddings and cosine similarity, with no VLM calls. Experiments across five image domains, four CLIP backbones, and six judges evaluate teacher agreement, retrieval, and recognition retention. For ViT-B/16, mean retrieval mAP on classes excluded from adaptation increases from 53.8 to 75.0, compared with 71.7 for DINOv2 targets with KL anchoring. Mean zero-shot accuracy with jointly adapted encoders increases from 61.8% to 62.4%, averaged over 12 benchmarks and the five adaptation domains. Prompting provides an additional capability: selecting which visual distinctions the student learns. Human-annotated evaluations across four datasets support this criterion-specific control.

We establish a classification of the gravitational production of light particles across sharp transitions connecting different asymptotic forms of the scale factor. A family of smooth scale factors with a transition duration $\Delta\eta$ is characterized by its regularity in the sharp-transition limit $\Delta\eta\to 0$, leading to three qualitatively different universality classes: $C^0$, $C^1$, and $C^2$-or-smoother. We find that the $C^0$ class exhibits a quadratic enhancement in the energy density of produced particles, $\rho\propto\Delta\eta^{-2}$, while the $C^1$ class shows a logarithmic enhancement, $\rho\propto\ln(1/\Delta\eta)$. No sharp-transition enhancement occurs for the $C^2$-or-smoother class. Using a specific $C^\infty$ model of the scale factor, we derive the energy density analytically and confirm both the predicted quadratic scaling and its coefficient by numerically solving the mode equation. These results identify the regularity of the scale factor in the sharp limit as the key property controlling the sharp-transition enhancement.

On-Policy Context Distillation (OPCD) has recently emerged as a powerful technique for transferring context to student models and for self-improvement. In OPCD, the teacher is conditioned on privileged information, and the goal is to minimize the Kullback-Leibler (KL) divergence between the privileged teacher and the student, evaluated on student-generated tokens. Many existing studies show that using instance-specific gold answers or gold demonstrations as the default privilege can hurt training performance, especially out-of-distribution (OOD). In this work, we instead design general instructions that target common student mistakes observed on the training samples, and show that such simple instructions can outperform gold as the OPCD privilege. In autoformalization tasks, using a matched formatting instruction as the privilege could outperform gold in OOD accuracy by a large margin. In 7 out of 8 experiments using ProverQA, ProofWriter, and ProntoQA as datasets, and Qwen3-Thinking and Olmo3-Thinking families as models, matched instruction privileges outperform gold in OOD by 4 to 17 points, while remaining on par with gold in-domain. Each instruction is only a few sentences (and thus contains much less information compared to all instance-specific gold) and is applied uniformly to every training sample. These results indicate that a general instruction, which applies equally to source and target domain examples, can be substantially more transferable than instance-specific gold in OPCD while maintaining in-domain performance.

We study the gravitational collapse of a spherically symmetric, inhomogeneous dust cloud in five-dimensional AdS Chern–Simons gravity. Working in the torsion-free sector and using comoving Lemaître–Tolman–Bondi coordinates, we derive the reduced field equations and obtain an exact collapsing interior solution. The areal radius evolves periodically in time, but the physical collapsing branch extends only up to shell focusing or an earlier loss of regularity, while the initial density determines a radial function whose square is proportional to the conserved quasilocal mass. This separates the roles of the initial velocity and density profiles in controlling shell focusing and trapping. We derive conditions for central regularity and for avoiding shell crossing, analyze the Kretschmann scalar, and show that shell focusing corresponds to a genuine curvature singularity, the weak and strong energy conditions are preserved throughout the regular collapsing phase. The homogeneous limit reduces consistently to a five-dimensional FLRW interior. The collapsing cloud is matched smoothly to the black-hole branch of the static AdS Chern–Simons exterior. The null expansions show that a finite-radius apparent horizon forms only when the quasilocal mass exceeds a critical threshold. Initially untrapped shells above this threshold become trapped before shell focusing, whereas below the total-mass threshold no finite-radius future-trapped symmetry sphere forms in the regular interior.

We investigate how generalization and memorization develop along the learning trajectory of neural language models. Using controlled synthetic grammars, we examine both the geometry of representation space and model behaviour over training. We find that continuous regions of representation space not occupied by observed tokens become systematically structured from the earliest stages of learning, forming category-level geometric organization that supports generalization to unattested combinations. Generalization therefore emerges from the beginning of learning rather than only after extensive memorization. With prolonged training, larger models increasingly distinguish observed from unobserved grammatical combinations. At the same time, the continuous geometric structure supporting category-level generalization is gradually destructed. Together, these results suggest that neural language models initially learn through categorization-based generalization, followed by a gradual transition toward more exemplar-specific memorization.

AI agents increasingly resemble software systems: they call tools, remember facts, follow policies, delegate work, and take actions with real consequences. % Yet the “program” of an agent is scattered across prompts, tools, memories, workflows, and execution traces, making its behavior difficult to inspect through ordinary testing and debugging alone. % This essay argues that a programming-systems perspective offers a natural lens for making agents reliable. % We recast agents as programmable artifacts whose behavior can be specified over traces and state, checked before deployment, monitored during execution, and improved from observed failures. % The goal is not to make probabilistic agents behave like deterministic programs, but to give them enough structure that their behavior can be reasoned about, controlled, and repaired.

Diffusion Transformers have become the dominant architecture for video generation. Their substantial computational cost motivates scaling inference across multi-GPU servers, yet efficient scaling remains challenging on commodity GPUs connected via PCIe, whose bandwidth is limited. Although sparse attention substantially reduces computation, its implications for communication remain underexplored. This paper argues that attention sparsity should be treated as a communication primitive. We present SparSP, an efficient sparse sequence parallel communication system that co-designs token distribution, communication routing, and asynchronous execution for sparse video diffusion models. First, Dependency-Aware Placement distributes sequence blocks according to diffusion models' sparse attention patterns. Second, Demand-Directed KV Routing transfers KV blocks directly to requesting GPUs without intermediate relays. Third, a Decoupled Transfer Runtime separates communication from GPU computation to reduce resource contention and maximize effective bandwidth. Our evaluation shows that SparSP improves attention performance by 1.38- 1.5$\times$, achieves an average 1.17$\times$ (up to 1.69$\times$) end-to-end speedup across three representative servers and three video diffusion models, and reduces communication volume by 12.54-23.05%. Moreover, we achieve an average 1.53-1.76$\times$ bandwidth improvement over NCCL.

Language models now routinely grade other language models. If post-training makes a model's writing more predictable, it may also teach the same model, as a judge, to reward predictable writing. We test this directly. We follow two open 7-billion-parameter model families, OLMo-2 and Zephyr, from their base models through supervised fine-tuning (SFT) and direct preference optimization (DPO), and measure every stage as a writer of short stories and as a judge of story pairs. As writers, the models drift as feared. Each family's trained model finds its stages' stories more familiar in the order base, SFT, DPO, in all ten prompts, and a model from the other family finds the trained stories 7.0 to 9.2 percent (OLMo-2) and 24 to 25 percent (Zephyr) less surprising per token. As judges, they barely move toward predictable writing. Asked which story is better, a question every judge passes a competence check on, no trained judge's preference for the more predictable story grows by as much as one point of pick probability at its estimate. A one-sided 95% upper bound on that growth is about 5 points on the widest pairs. Training instead makes judges more swayed by story length and by display order, and it breaks "more creative" as a question. Trained judges no longer reliably prefer a story to its own words in scrambled order. For these two families, the practical hazard in a small trained judge of creative writing lies in these measurable habits.