Papers

We study whether model upgrades improve probability estimates for prediction-market questions. Our Resolved Market Forecasting (RMF) benchmark contains 3,000 resolved binary questions across nine domains, on which we evaluate six Claude and Qwen model variants using a question-only, zero-shot protocol. We assess Brier scores relative to an empirical base-rate predictor, examine their Murphy decomposition, and compare models through paired differences, with results stratified by event category and timing relative to training cutoffs. In the reported post-cutoff stratum, the four Claude models achieve Brier scores of 0.183-0.192, improving on the base-rate reference by 0.024-0.033. Qwen 32B does not significantly outperform that reference, although its paired Brier is 0.024 lower than that of the 7B checkpoint. The evaluated Claude version and tier upgrades yield no significant improvement. Within-model differences across event categories exceed the observed differences among Claude variants. These results show why forecasting scores should be interpreted alongside simple probability baselines and question composition: under this protocol, newer versions or higher model tiers do not consistently produce more accurate probabilities.

An improved algorithm to implement our previously proposed static quantum embedding method MPCC (J. Chem. Phys. 161, 164107 (2024)) is presented. It uses the density-fitting (DF) approximation for the electron-repulsion integrals (ERIs) across all layers of the embedding method: the low-level method, the screened interaction, and the high-level method. Additionally, an approximate factorized solution of the Sylvester equation is employed based on the Laplace transformation for the low-level method. To build the screened interaction, we have explored an approximate construction of it based on the distinguishable cluster approximation (DCA) by Kats and Manby (J. Chem. Phys. 141, 061101 (2014)), which amounts to neglecting certain higher-order exchange and ladder diagrams. Combining all these techniques, we have obtained an $\mathcal{O}(N^4)$ algorithm for the low-level method; a non-iterative $N_{\rm frag} \mathcal{O}(N^4)$ algorithm for the screened interaction; and an iterative $\mathcal{O}(N_{\rm frag}^6)$ algorithm for the fragment solver, where $N_{\rm frag}$ is the number of fragment orbitals and $N$ is the total number of orbitals. The resulting low-scaling implementation of the MPCC method is applied to trans polyacetylenes, that is, C$_{2n}$H$_{2n+2}$ molecules for chain lengths $n=1-8$, and the timing and accuracy of the method are compared to the original unfactorized implementation. Moreover, the approximations are further validated by applying the method to the potential energy surface of the \ce{O3} molecule. Finally, we apply the method to the selected molecules in the S22 dataset for which the performance of the MP2 method is known to be poor. The results demonstrate that the DF-based implementation of the MPCC method provides a significant reduction in computational cost while maintaining accuracy comparable to that of the original implementation.

This mostly expository paper gives a unified treatment of many interpolation results for bandwidth-limited functions on locally compact abelian groups, based on reproducing kernel Hilbert spaces. It includes an abstract interpolation theorem phrased in terms of frames.

We present VSA2, a frontier trainable sparse attention for video DiTs. VSA2 includes a variety of new architectural features and training procedures that we apply across all stages of the DiT development cycle, including pretraining, RL, and inference, to produce a DiT with comparable or better quality than a full attention counterpart. Architecturally, VSA2 introduces a fine-grained router that improves the precision of identifying critical tokens and supports dynamic computation by allowing each query to attend to a variable number of key-value pairs. In training, we identify a Hard-to-Easy Curriculum, where models trained under high sparsity and later evaluated with lower sparsity during inference not only generalize effectively, but also outperform models trained with full attention in motion quality. VSA2 is also flexible: it can replace full attention during the middle of progressive low-to-high resolution pretraining, rebasing early-stage full-attention checkpoints. Experiments show that VSA2 reduces attention computation by half over VSA with lower loss. On 720p videos, it accelerates attention by 8.9x and end-to-end generation by 4.62x compared to the FlashAttention-3 baseline, while achieving comparable or better video quality.

In this paper, we investigate how adaptive time-integration strategies can be effectively combined with parallel-in-time numerical methods for solving systems of ordinary differential equations. Our focus is particularly on their influence on tolerance proportionality. We examine various grid-refinement strategies within the multigrid reduction-in-time (MGRIT) framework. Our results show that a simple adjustment to the original refinement factor can substantially improve computational stability and reliability. Through numerical experiments on standard test problems using the XBraid library, we demonstrate that parallel-in-time solutions closely match their sequential counterparts. Moreover, with the use of multiple processors, computing time can be significantly reduced.

Online comment sections let a small number of vocal individuals reach far beyond their own networks. We conduct a large-scale field experiment on Facebook that randomizes the presence and stance of comments beneath posts for a racial justice organization, reaching around one million U.S. users. Opposing comments increase reactions, comments, and link clicks by 15-43 percent relative to no comments, whereas supportive comments have little effect. A complementary survey experiment shows that similar opposing comments make attitudes less progressive and reduce donations to the organization. Through a common feature of online platforms, the vocal few can exert outsized influence.

A black hole horizon carries exactly one nat of information per Planck cell, without naming what the black hole is made of. Two inputs suffice: entropy is irreducible uncertainty (the configurations no observation can resolve at the Planck floor, an objective bound, not ignorance), and the horizon is a complete scrambler, so by the Ehrenfest time its Wigner function has folded below the floor and no cell can be certified empty. A single cell then holds unresolved filament crossings; a cell crossed $n$ times admits $n!$ orderings that scrambling erases, so cardinality $n$ carries weight $1/n!$ and its count is $\Omega_1=\sum_n 1/n!=e$, one nat. The $N=A/\ell_P^2$ independent cells give $\Omega=e^N$, hence $S=N$. Multiplied by the kinematic factor $\tfrac{1}{4}$ (the causally accessible fraction of the null phase space, established separately), this returns $S_{BH}=A/4\ell_P^2$. The derivation invokes no field equations, no microscopic theory, and no posited Hilbert space.

We construct exact, static, circularly symmetric charged regular AdS$_3$ black hole solutions in a three-dimensional scalar-vector-tensor theory obtained from regularized Gauss-Bonnet couplings. While the Maxwell-charged counterpart of this theory suffers from a logarithmic curvature singularity at the origin, we demonstrate that coupling the action to non-linear Born-Infeld electrodynamics cures this pathology. We obtain the metric function and show explicitly the regularity of the core. Depending on the choice of parameters, the solution exhibits various horizon structures, including single-horizon, double-horizon, extremal black holes, and horizonless regular geometries. Finally, we discuss the significance of this regular spacetime as a testbed for microscopic entropy calculations in singularity-free setups.

Real-world programs are rarely written in a single language: For example, C programs call assembly routines, and high-level languages like OCaml link with low-level C libraries. Yet program logics—one of the most successful techniques for modular program verification—almost exclusively target single-language programs. We present Hotpot, the first framework for building multi-language program logics. Hotpot enables compilation-independent, cross-language reasoning about languages with heterogeneous views of shared state. Hotpot rests on four key ideas: abstract calls to specify calls to unknown functions, lanes and the switching modality to move between languages inside the program logic, uniform integration of refinement reasoning via lanes, and exchanges to translate between separation logic assertions of different languages. We demonstrate that Hotpot allows reusing specifications across implementations in different languages, supports reasoning about higher-order cross-language function calls, and integrates with verified compilation. Hotpot is built on top of Iris and DimSum and mechanized in the Rocq Prover.

State-of-the-art pathology foundation models, trained on millions of histology tiles, can fail to preserve tissue similarity when comparisons cross slide or institution boundaries. We show that general-purpose multimodal LLMs, without being trained as pathology foundation models, consistently outperform these specialized models in cross-domain histological similarity judgments. Using a relative similarity framework that we release as the MOSAIC (Model Similarity Assessment across Institutions and Cohorts) benchmark, we evaluate 17 models across 6 datasets and find that pathology encoders often rank same-institution, different-disease tiles as more similar than same-disease, different-institution tiles, a clinically dangerous failure mode invisible to standard within-domain evaluations. LLMs appear less susceptible to this failure, likely because they perform semantic visual comparison of morphology and tissue architecture rather than relying on shortcut features tied to acquisition context. Scaling training data does not resolve the problem for pathology encoders, implicating the learning objective rather than data coverage. Our results expose a fundamental robustness gap in current pathology foundation models and establish multimodal LLMs as a viable alternative for cross-institutional retrieval, dataset harmonization, and multi-site quality control. Code and data will be released upon acceptance.

This paper studies the nonconvex optimization landscape of Linear Quadratic Gaussian (LQG) control under direct state-space parameterization. Although the LQG cost may possess suboptimal stationary points, whether it admits suboptimal local minima has remained open. We answer this question negatively: Every local minimum of the full-order LQG cost is globally optimal. More generally, at any controller order, every local minimum corresponding to an uncontrollable or unobservable realization attains the globally optimal LQG cost over all stabilizing policies of arbitrary orders. We further show that any suboptimal policy can be augmented with decoupled stable controller states, so that the augmented policy admits a direction of negative curvature with probability one. Consequently, any suboptimal stationary point in full-order LQG cost can be converted into a strict saddle with probability one. One key proof idea connects the state-space Hessian to a frequency-domain global-optimality condition derived from the Youla parameterization. These results reveal a benign local-minimum landscape despite the presence of suboptimal stationary points.

The first sentence of this abstract–and the introduction to these proceedings–was authored by a human, but the bulk of this document was generated by an agentic AI system. In this talk, I take stock of machine learning (ML) for the LHC physics program over the twelve months from May 2025 to May 2026. The corpus is the HEPML Living Review, split at May 2025 into 1,756 earlier papers and 569 later ones. An AI pipeline surveyed the 569 abstracts, ranked them by citations, recency, theme, and collaboration involvement, and read 103 papers in full (95 from after the split, plus 8 earlier baseline papers), producing a structured note for each. The notes were then synthesized into six claims about the state of the field, checked by independent reviewer agents, and re-verified against the source papers. The headline claim is that (1) ML for high-energy physics (HEPML) stopped being a research area that builds tools and became infrastructure that the LHC physics program depends on: ATLAS and CMS now publish physics results that depend on neural networks, and the archived ALEPH data have re-entered production. The other five claims are: (2) simulation-based inference and foundation models are two revolutions starting to merge; (3) AI agents are the genuinely new front, with 47 papers in twelve months and no adopted measurement yet; (4) "do we trust it?" is the fastest-growing agenda, with one recent paper in five about uncertainty, calibration, or interpretability; (5) what is slowing down is informative, since equivariance was absorbed into a tool and model-specific phenomenology ceded ground to model-agnostic searches; and (6) theory ML crossed a capability threshold in multiple research areas. I close with what is settled, what is incoming, and what is open, and briefly discuss the concerns raised by this way of working with AI.

We consider the nuclear recoil spectrum following allowed $\beta$ decay as a laboratory for Beyond Standard Model searches, and perform an exhaustive treatment of the Standard Model prediction. We consider final state interactions, nuclear structure corrections, kinematic corrections and radiative corrections, derive new results and show that the nuclear recoil spectrum is theoretically exceptionally clean. We construct a clean statistical framework and analyze the Fisher information for extracting exotic current constraints and testing Cabibbo-Kobayashi-Maskawa top-row unitarity, and consider a number of sterile neutrino scenarios. In addition, we find that for select isotopes separate measurement of the $\beta$-asymmetry and recoil spectrum can achieve an increase in the statistical power of up to a factor 40.

We study the Sampled-Max Subgradient Method (SMax-SGM) for large convex finite-max problems. Each iteration maximizes over a fresh random subset of the $N$ components and takes one subgradient of the sampled maximizer. The method is therefore stochastic subgradient descent on a sampled-max surrogate. We bound the surrogate error by an average-top-$k$ gap plus the probability of missing all top-$k$ components. A localization argument requires these quantities only on a near-optimal sublevel set. Under a bounded subgradient-moment assumption, this yields $O(\varepsilon^{-2})$ subgradient queries and, when $k$ components remain nearly active in that set, $\widetilde O((N/k)\varepsilon^{-2})$ component-value queries, capped by the full-scan cost. Conversely, a one-dimensional affine construction shows that $\Omega(N/k)$ component-value queries can be necessary even when the average-top-$k$ gap vanishes everywhere and subgradient queries are unlimited. A tensor-grid specialization explains when the subset size can become independent of grid cardinality. Experiments on finite maxima with $2\times10^5$ and $5\times10^6$ components show that, under the reported protocols, SMax-SGM reaches a 5% numerical-reference gap with fewer component-value queries and lower optimizer time than each comparison method that reaches the target.

Experimental demonstrations of the Mpemba effect in a colloidal-particle system have imposed an instantaneous temperature quench via an initial condition where individual particle trajectories are drawn from a high-temperature Boltzmann distribution and then evolve in a bath at lower temperature. The potential used for the high-temperature distribution has had two walls that impose a finite range of initial positions, even at effectively infinite temperatures. The potential for evolution in the bath had no walls and matched that used for the initial condition over its support. For low bath temperatures, the difference between the dynamics with and without walls is negligible. Nonetheless, it has been speculated that the walls are perhaps more important than they seem and might even be required for the Mpemba effect to occur. Here, we introduce a new potential that lacks walls and use it for both the initial high temperature state and for subsequent evolution. This new potential then allows us to investigate by simulation Mpemba effects at finite-quench rates. Our results help clarify intuitions concerning the existence of a Mpemba effect and show that the Mpemba effect appears only for bath-temperature quenches faster than a critical quench rate.

Self-play proposer–solver methods improve reasoning by generating tasks and learning from verified solutions. However, for evidence-identifiable tasks, where case-specific evidence and domain knowledge determine a checkable answer, self-play requires generating plausible cases whose answers can be independently verified. We introduce counterfactual self-evolution, which generates counterfactual context for reconsidering the original case. A trainable Proposer constructs targeted evidence edits and describes potential outcome changes with causal explanations. We handcraft an expert-verified counterfactual instruction-tuning dataset to teach the Proposer to generate high-quality counterfactuals across a broad range of action–outcome scenarios. Each counterfactual instruction-tuning example specifies an edit within a defined category and explains its hypothesized causal effect on the decision, teaching the Proposer to reason systematically about what changes and why. We instruction-tune the Proposer on these examples, then formulate a fine-tuning reward that integrates feedback from the Solver and Verifier. Across diverse counterfactual scenarios, this reward favors high-quality counterfactuals and warranted revisions, while penalizing changes that overturn correct decisions. The counterfactual context aims to correct errors and strengthen confidence in correct decisions. Accepted counterfactuals accumulate in memory that supplies in-context evidence to the frozen Solver; the Solver adapts through evolving context rather than weight updates. We apply the framework to clinical reasoning, fact verification, and business reasoning. Our evaluation tracks performance over successive rounds as counterfactual memory grows, including transfer to harder cases. Our method achieves superior results across diverse frontier models.

Whisper is a widely used encoder-decoder model for speech recognition. Its encoder reads an utterance in one parallel pass, but its decoder writes the transcript one token at a time, which dominates inference time. Speculative decoding shortens such loops without changing their output: a small drafter guesses several upcoming tokens, and the original model verifies them all in one forward pass. We present Whisper-Flash, a two-layer drafter built on a property of speech recognition: the words still to be written have already been spoken. It reads Whisper's encoded audio and accepted decoder states and proposes eight tokens in a single forward pass. On the complete LibriSpeech test sets, Whisper-Flash processes $3.16\times/2.85\times$ as much audio per second as greedy decoding with identical outputs, and it remains faster at batch sizes up to 96 and under temperature sampling. Ablations show that direct access to the audio matters most.

Traditional scientific computing requires researchers to translate intent into environment configuration, resource requests, and executable jobs, then diagnose failures from scheduler and application logs. We present ASCEND (Autonomous Scientific Computing Engine and Novel Discovery), an AI-powered agent system, operated through a command-line or a local web chat interface, that runs the agent on the researcher's own laptop, reaching Slurm clusters and a GPU workstation over multiplexed authenticated SSH, with site-specific execution policies checked by locally executed tools. The language-model agent (Claude Code or Codex, chosen at each launch) is hosted remotely and holds no credentials; an account on each resource suffices, and a public installer links additional clusters or workstations. We report four recorded cases: (1) the agent closed a failure-recovery loop on a planted tensor-device fault, submitting, diagnosing, repairing, and resubmitting it; (2) it reproduced the published evaluation of a weather-forecasting model, recovering an incompletely stated evaluation protocol and agreeing with the published curves to 2.1% (z500) and 2.4% (t850), while identifying two discrepancies in the paper's released materials; (3) it parallelized a released 12,693-line geophysical solver under a requirement of bit-for-bit identity of exported outputs, reducing runtime from about twelve hours to about two; (4) that requirement exposed two instances of undefined behavior in the published solver, both repaired and reported upstream. These cases used ordinary scheduler commands; a separate, pre-specified evaluation of the optional policy validator rejected 29 of 30 constructed violations, held one for approval, and denied 3 of 14 legitimate requests. Autonomy was exercised under author supervision, and agent transcripts were not retained, so intervention rates are not independently verifiable.

Sycophancy is a language model's tendency to cave when a user pushes back, abandoning a correct answer for the user's. Several benchmarks now measure it by scripting an objection and recording how often the model caves. Because that objection is a prompt template, whatever else the template varies is measured along with the property it claims to isolate. We audit SycEval, which reports that objections raised before a model answers (preemptive) cause more caving than those raised after (in-context), and attributes the gap to timing. Two features of its templates vary alongside the property each is meant to test. First, SycEval's objections escalate through four strength levels, and at the two weakest only the preemptive template names a target answer, so timing and naming vary together. We build the missing comparison and test it on multiple-choice questions and SycEval's own free-form pipeline. Naming a target answer raises the follow rate, the share of samples matching the user's assertion, by 14.1–49.5 percentage points (pp), and once both templates name one, the timing comparison reverses on three of the five model conditions we test: models cave less under preemptive objections than in-context ones, opposite to SycEval. Second, the output-format instruction benchmarks append for automatic grading also varies with objection placement. Moving it from the pushback into the question flips its effect in opposite directions across models on the same items ($p=0.0059$). The same effect appears in SycEval's free-form pipeline: relocating its instruction lowers caving by 5.1pp on Llama-3.1-8B, while an equivalence test confirms no effect on Qwen3-4B. Both confounds live in the template rather than the models under test, so both are correctable: we close with three checks benchmark authors can apply before publishing.

We prove that 3d Lovelock gravity, the Horndeski theory obtained from the regularized Lovelock invariants in three dimensions, admits a holographic c-theorem at all orders and for arbitrary values of the couplings. In the minisuperspace of domain wall solutions, the equation of the Horndeski scalar is a total derivative at every order, which locks the derivative of the scalar to that of the warp factor along the flows we consider and allows the null energy condition to be integrated into a monotonic c-function. The linear scalar profile of the resulting vacuum breaks the special conformal transformations, so the dual theory is scale-invariant but not conformal, and the central charge is defined as the coefficient of the logarithmic divergence of the on-shell action on the sphere. We compute it exactly for the Gauss-Bonnet case and asymptotically for the full tower, and find that it is linear in the couplings and matches the UV value of the c-function. Since all results depend on the couplings only through two generating functions, we give the resummed Lagrangians, c-functions and central charges in closed form for the choices of couplings that lead to regular black holes, and classify the resummed theories by the positivity of the effective Newton constant on the vacuum and the uniqueness of the vacuum with a non-trivial scalar.

Starting from the constant-roll condition, which involves the constant-roll parameter $\beta$, which is a fundamental constant in the constant-roll inflationary models, we derive the scalar power spectrum and obtain an analytic expression for the scalar spectral index $n_s$ in terms of $\beta$ and the number of remaining e-folds $\tilde N$. The resulting relation is non-monotonic in $\beta$, allowing two distinct constant-roll branches, one with $\beta<0$ and one with $\beta>0$, to reproduce nearly the same observed scalar tilt. We constrain $\beta$ using Planck 2018 CMB data, and further using the combined Planck 2018 + ACT DR6 data. For Planck 2018, the posterior distribution of $\beta$ exhibits a bimodal structure associated with the two analytical branches, while the combined Planck+ACT analysis tightens the allowed range of $\beta$ and shows continued consistency with the $\beta=0$ slow-roll-like spectral point. The data constrain $\beta$ to be small, but do not require it to vanish exactly. We also estimate the inflationary mass scale $M$ by using the observed scalar-amplitude normalization at the pivot scale. Both the negative and positive $\beta$ branches give a high-scale inflationary normalization of order $M\sim10^{-5}M_{\rm Pl}$. We show that the $\beta \to 0$ limit is only spectrally slow-roll like, but does not reproduce standard slow-roll dynamics. Our results show that constant-roll inflation is observationally competitive with the usual slow-roll inflationary paradigm. The constant roll inflation model is supported by the latest CMB observations equally well or marginally better when compared with the slow roll inflation model.

Neural surrogates are trained to predict 3D turbulent flows in place of direct numerical simulation (DNS). For chaotic flows, the goal is short-term pointwise accuracy followed by long-term physical and statistical fidelity. However, small prediction errors can carry a surrogate away from the flow's attractor. Off-attractor states are poorly represented in training data, leaving their evolution weakly constrained. The learned dynamics can then amplify deviations and lead to blow-up, freezing, or statistical drift. We propose off-attractor supervision (OAS) to supervise neural surrogates where they leave the attractor. OAS teaches the model how the true Navier-Stokes dynamics would evolve from these states. Each selected state is paired with its own future computed by DNS. Three generators select a few hundred states for relabeling. The first collects states from the surrogate's own rollouts. The second uses surrogate attacks to target freezing, excessive amplification, and violations of incompressibility and energy balance. The third perturbs training states along an amplified direction and a strongly damped random direction of the dynamics. All attacks run on the surrogate alone, and DNS relabeling is performed offline once per selected state. Experiments on $128^3$ turbulence show that OAS increases the median time to failure from 21 to 721 steps. The compared baselines achieve medians of at most 110 steps, and the advantage holds across training seeds. OAS also achieves the lowest pointwise error at step 15 and the best long-horizon statistics among the compared methods. OAS integrates physical models into neural simulation by extending supervision from fixed reference trajectories to states where the surrogate is likely to fail. This principle can guide the development of more reliable scientific surrogates when deployment takes models beyond the coverage of their training data.

Vehicle-to-Vehicle (V2V) cooperative perception enhances autonomous driving by enabling vehicles to share information beyond their direct line of sight. However, existing V2V datasets are limited by a small number of participating agents, static collaborator selection strategies, and a significant domain gap between simulated and real-world environments. To overcome these challenges, we introduce SV2V-RSim, a large-scale, multi-modal, near-realistic simulation dataset engineered to elevate agent diversity and realism. Additionally, we present the Select Vehicles Adaptively (SVA) module, which optimizes collaborator selection to balance perception performance against communication bandwidth constraints. Our dataset is generated using the Unreal Engine 5-based simulator that integrates high-fidelity 3D assets, diverse environments, and intricate traffic scenarios. All vehicles within a specified range of the ego vehicle are equipped with sensor suites, enabling dynamic and adaptive collaborator selection. SV2V-RSim encompasses four maps, four weather conditions, six time periods from sunrise to night, 203K LiDAR frames, 402K RGB frames, and 788K annotated 3D bounding boxes across 17 object classes, supporting a range of cooperative perception tasks such as 3D object detection, segmentation, and depth estimation. Benchmarking on recent cooperative perception algorithms demonstrates that SVA achieves a superior performance-bandwidth trade-off, while sim-to-real experiments and No-Reference Image Quality Assessment validate the dataset's high realism and practical effectiveness. Our dataset and code will be publicly available.

A foundation model should not act in isolation as an embodied agent. Yet, existing methods often optimize individual components of the agent stack, such as memory, context, skills, or action interfaces, rather than treating the supporting system itself as a unified policy. Moreover, interaction alone does not yield self-improvement unless execution experience is converted into persistent, validated system changes. We therefore propose RoboFoundry, the first embodied agentic framework that formulates this process as Self-Evolving System-as-Policy. RoboFoundry diagnoses capability gaps in decision-making and memory management, converts execution traces into validated task-specific system updates, and promotes recurring improvements to the general system. Evolution operates over two complementary surfaces: a context system that manages active internal context and persistent file-system memory, and a hierarchical skill system that organizes atomic skills, reusable compositions, and failure-conditioned recovery. A shared semantic interface separates embodiment-invariant decisions from embodiment-specific execution, allowing evolved system capabilities to transfer across heterogeneous robots. On EmbodiedBench, RoboFoundry achieves state-of-the-art performance, notably improving GPT-5.5 by 27.8%. It also brings Qwen3.7-Plus to near parity with GPT-5.5 (70.3% vs. 72.7%), showing consistent gains from system-as-policy evolution across foundation models. For long-horizon memory, RoboFoundry outperforms all baselines on RoboMemArena by at least 39.0%, even against methods assisted by external foundation models. On LIBERO-PRO, it further outperforms Cap-Agent0 by 243.8%-679.7% across all perturbation types. In real-world deployments, RoboFoundry demonstrates zero-shot transfer and online evolution across robots and tasks, highlighting its potential for fully autonomous embodied agents.

Muon replaces the momentum buffer of each weight matrix by its orthogonal polar factor. We ask what this orthogonalization does near an optimum, where minibatch noise dominates the gradient. Under a Gaussian noise model, the expected Muon update becomes a scaled gradient step, so a linear method with a suitably matched learning rate reproduces Muon's first-order mean response. The stochastic update is a different matter: after the response is matched, Muon retains a nonlinear residual that is uncorrelated with the input noise and contributes additional covariance. A Hermite expansion shows how momentum acts on this residual. Its higher-order components decorrelate faster than the linear component, so momentum suppresses the residual's accumulated covariance relative to the linear part, but never eliminates it. In a local quadratic surrogate that evaluates the residual on the stationary noise buffer, the residual adds stationary covariance and raises the stationary loss floor at every stable step size, while leaving the contraction dynamics unchanged. Simulations of the full nonlinear recursion on quadratics and measurements on frozen transformer gradients support each step of this picture. Together, the results make a theoretical case for replacing orthogonalization by response-matched momentum SGD once optimization becomes noise-dominated.

Let $G_n$ be the bipartite complement of the even cycle $C_{2n}$, and let $J_{G_n}$ be its binomial edge ideal. For $n\geq5$, we study the interaction between the combinatorial structure of $G_n$ and the algebraic invariants of $S_{G_n}/J_{G_n}$. Our main combinatorial ingredient is a classification of the subsets of $V(G_n)$ having the cut point property, obtained through an analysis of disconnected induced subgraphs of $G_n$. We use this classification to describe the minimal primes and to study dimension and degree-theoretic invariants of $J_{G_n}$ and $S_{G_n}/J_{G_n}$. We also study local Vasconcelos numbers, graded Betti numbers and the Hilbert series, and obtain information on projective dimension and depth. Finally, we analyze induced paths in $G_n$ and derive corresponding bounds for the Castelnuovo–Mumford regularity.

We study gaming and adaptive incentive design in AI adoption. A large medical-device company required roughly 5,000 employees to submit at least 200 queries per month to an internal AI assistant. First-time use increased significantly after the mandate, but usage patterns suggested gaming: query counts bunched at the threshold, and 31 percent of queries were repeated or off-task. The firm subsequently revised incentive design and lowered the target to 100. Using staggered implementation across branches, we estimate that the adjustment reduced query volume by 30 percent, with repeated or off-task queries accounting for about 90 percent of the decline. The estimated change in non-repeated, work-related queries was small and statistically insignificant. Among sales employees, monthly sales increased by 7 percent. The findings identify incentive adaptation as a consequential margin of technology adoption: recalibrating usage requirements can reduce gaming and improve employee performance.

We present a graph neural network-based learning framework trained to jointly predict electron densities and molecular energies. The model is trained to predict electron densities calculated with a Generalized Gradient Approximation (GGA) functional while simultaneously learning to predict molecular energies obtained with hybrid functional calculations at the B3LYP level of theory. Our results indicate that the rich spatial information in electron density distribution can be used to improve and accelerate the learning of accurate energies. By sharing an equivariant molecular representation across density and energy prediction heads, the model learns complementary molecular quantities within a unified framework. This provides a new promising route for practical use cases of many recent charge density learning frameworks for atomic scale simulations.

Predicting spatial gene expression from routine H&E histology offers a scalable route toward spatial molecular profiling. Recent work has pursued increasingly sophisticated architectures to capture spatial context and richer expression structure. At the same time, simple estimators have shown strong performance in several studies, but what they already solve and where additional complexity is needed remain unclear. We study this behavior through the structure of prediction error under the mean-squared error (MSE) objective. Differences in average expression across genes can account for a substantial part of aggregate prediction performance, while a key unresolved error lies in recovering variation within each slide. Decomposing MSE into slide-level and within-slide components, we find that the within-slide component has lower residual-normalized parameter sensitivity in controlled neural experiments. This motivates Component-Guided Loss (CGL), which increases supervision of the within-slide component. CGL-Linear is a closed-form affine instantiation that achieves overall state-of-the-art performance across HEST-1k cohorts and gene-panel sizes. The same within-slide supervision improves existing neural models. These results suggest that substantial gains can come from aligning the training objective with prediction-error structure rather than increasing model complexity.

Vector polygon generation converts visual inputs, e.g., remote sensing (RS) images, into vectorized polygonal geometries, supporting applications such as autonomous driving, vector map construction, and remote sensing. Early pipelines predict raster masks and post-process them into polygons, which prevents end-to-end optimization and may miss small objects or introduce inaccurate vertices. Recent methods directly generate vector polygons, but most focus on simple exterior contours, while they either cannot represent complex polygons with holes or fail to preserve their topology. In this paper, we propose PolyTopoBench, a unified evaluation framework for vector polygon generation from RS images with explicit emphasis on complex polygons. PolyTopoBench evaluates both exterior and interior rings, and benchmarks 11 representative methods, including segmentation-based polygonization pipelines, vision foundation model baselines, and specialized vector polygon generators, on two RS-image datasets covering buildings, roads, vegetation, and unvegetated regions. Experiments show that existing methods often recover simple exterior boundaries but degrade substantially on polygons with holes or multiple rings. These results reveal complex polygon generation as an unresolved challenge and motivate topology-aware benchmarks and model designs. Code and data are available at https://github.com/seai-lab/PolyTopoBench.