Papers

Robot world models support policy evaluation, planning, and synthetic data generation, but these applications require predictions that distinguish successful actions from failures. Across four released checkpoints from two architecture families, we observe weak sensitivity to action changes and success-like predictions on verified failures. Although recent work incorporates failures into model training, which data can repair released checkpoints without changing their architecture or training objective still remains underexplored. To this end, we introduce CureWM, which constructs alternative actions from successful demonstrations across a severity grid, verifies their outcomes through execution in simulation or on hardware, and fine-tunes released models on the resulting failures and surviving successes alongside nominal demonstrations. This construction provides controlled action contrasts from shared starting contexts. On 484 held-out LIBERO failure counterfactuals, optimism falls from 80% after fine-tuning on the official data to 30–43% across four independently fine-tuned CureWM models (38% mean). In two separate evaluations on a physical robot arm, failure predictions scored as success-like by a latent-distance diagnostic decrease from 90% after fine-tuning on successful demonstrations alone to 33% with CureWM. With failure counts per task, successful replay data, and training budget matched, counterfactual failures yield a success–failure value gap of 0.124, compared with 0.014 for freshly collected on-policy failures. These findings support execution-verified counterfactual replay for post-hoc repair and show why reduced optimism must be evaluated alongside success–failure discrimination. Code is available at https://github.com/jiuyixu25/CureWM.

In one complex variable the Schwarzian derivative characterizes the Möbius transformations, arises from a second-order linear equation, and controls univalence through the theorems of Nehari and of Ahlfors–Weill. This chapter presents what is known about these three properties for locally biholomorphic mappings in $\mathbb{C}^n$. Starting from Oda's definition we construct a bilinear operator whose norm, taken with respect to the Bergman metric, is invariant under the automorphisms of the ball, and we show that this operator measures the extrinsic curvature of the preimages of hyperplanes. We study the linearly invariant family defined by a bound on this norm, we prove that a sufficiently small bound implies univalence, and we describe the extension of Ahlfors–Weill type, which takes values in the space of hyperplanes. The polydisk and convex mappings are also treated, and open problems and exercises are included.

In wide Bayesian neural networks, Gaussian mean-field variational inference is prone to "prior dominance": the Kullback-Leibler (KL) regularization term of the ELBO outweighs the expected log-likelihood, and the variational predictive distribution collapses to the prior predictive as the width $M$ grows. Tempering the likelihood, by raising it to the power $1/T$ for a temperature $T < 1$, is equivalent to scaling the KL term by $T$. We ask in this paper how fast $T$ must decrease with $M$ to counteract this degeneracy and strike a good balance between the two terms. For single-hidden-layer linear networks with isotropic Gaussian priors, we derive the limiting predictive distribution under schedules of the form $T = \tau/M^{c}$, with constants $\tau, c > 0$, as $M \to \infty$ and compare it with the untempered neural network Gaussian process (NNGP) posterior, the infinite-width limit of the exact posterior. Our main result is that the predictive expectation and variance undergo phase transitions at different scales: the limiting expectation leaves its prior value at $c = 1/2$, once $\tau$ falls below an explicit threshold, and equals the least-squares prediction for $c > 1/2$, whereas the limiting variance keeps its prior value for $c < 1$, matches the NNGP's for $c=1$, and vanishes for $c > 1$. With suitable choices of $\tau,c$, one can recover either the NNGP posterior expectation or its variance.

Cosmological parameters can be estimated from dark sirens, gravitational waves events without electromagnetic counterpart, by using inference methods which estimate statistically the source redshift from galaxy catalogs. We study the effects of applying different apparent magnitude cuts to the GLADE+ catalog, analyzing events from the third LIGO-Virgo-KAGRA gravitational wave transient catalog (GWTC-3), consisting of 42 binary black holes, 3 neutron star black hole systems and the event GW190425 associated to a binary neutron star coalescence. We find that the inclusion of fainter galaxies has no significant effects on the joint analysis of almost all the events, while for some single well localized event, the effects can be more important, in particular for the event GW190814. To understand why inclusion of fainter galaxies in general has negligible impact on the estimation of cosmological parameters, we compare the redshift of the events with the redshift distribution of dimmer galaxies, and find that most of them are not located in redshift proximity of the events, explaining the limited impact of their inclusion. The event, GW190814 is an exception, as its distance localization, converted into redshift, overlaps with fainter galaxies, unlike what happens for other events, which are farther away. These results show the importance of event localization and catalog depth in determining the impact of catalog completeness on cosmological parameters estimation. To check quantitatively what is the information gained by adding fainter galaxies we have analyzed its impact on the line of sight prior calculation. Based on the results for GW190814 we expect that fainter galaxies will play a more significant role in the estimation of cosmological parameters also for the joint analysis of multiple events, when deeper catalogs will be available.

Compared with analytical physics, learned dynamics models promise robot simulation that is faster, inherently differentiable, and easily adaptable to real data. Neural Robot Dynamics (NeRD) pursues this by keeping collision detection analytical and replacing a simulator's numerical dynamics for the robot with a learned model. Three limitations remain. NeRD offers little speedup over the simulator it learned from, accepts contact only at predefined points, and has no two-way coupling with objects it manipulates. FlashNeRD removes all three with a parallel streaming architecture that makes each prediction faster and more accurate, an encoder that accepts contacts wherever they occur, and two-way coupling with objects simulated by analytical solvers. Experiments across five robots show faster and more accurate dynamics, faster policy learning, and faster inference-time planning. Across three robots, FlashNeRD's dynamics model is up to $55\times$ faster than an optimized NeRD and more accurate over long rollouts. This speedup extends to policy learning, where PPO trains an ANYmal locomotion policy in 34 seconds, $3.8\times$ faster than the analytical simulator and $2.7\times$ faster than an optimized NeRD. With DIAL-MPC, a sampling-based MPC method, the robot climbs all six test platforms where fixed-contact NeRD manages one, at approximately half the analytical simulator's planning time. Cube-reorientation policies trained with FlashNeRD complete within 2% of the simulator-trained policy's target count.

This article analyzes the idempotence of Giuga numbers and Carmichael numbers. The first sections will lead us to define an arithmetic function through which we will find a new characterization of Giuga numbers. The following sections will lead us to generalize Carmichael numbers, finding numbers that are Fermat pseudoprimes in certain specific cases, and to formulate various statements and open questions regarding their properties. Finally, we will find a new alternative condition, based on idempotence, that a number must satisfy to be a counterexample to the Agoh-Giuga conjecture and which, therefore, presumably, no number will ever satisfy. We will almost always work under the premise that n is square-free, since both numbers always have that property, but in certain situations we will extend some of the results to the general case.

Near-ultraviolet (NUV) observations can uniquely probe low-density, high-altitude gas in ultra-hot Jupiters (UHJs) via strong resonance lines of metals. WASP-76b is a well-studied UHJ with prior detections of refractory metals and complex day-night chemistry, making it a prime target for atmospheric escape diagnostics in the NUV. We present HST/STIS E230M (2274 - 3119 $\mathring{\mathrm{A}}$) transmission spectroscopy of WASP-76b. While broad- (~ 200 $\mathring{\mathrm{A}}$) and narrow-band (4 $\mathring{\mathrm{A}}$) transmission spectra do not show spectral features, a velocity-resolved single line analysis reveals clear excess absorption in both components of the Mg II doublet (2796 $\mathring{\mathrm{A}}$ and 2803 $\mathring{\mathrm{A}}$, $k$ and $h$ lines). The Mg II signal is localized to the blue wing (Doppler velocities [-50, -10] km s$^{-1}$) and is recovered with narrower 0.5 $\mathring{\mathrm{A}}$ bins; the inferred absorption exceeds both the optical continuum radius and the Roche-lobe scale, suggesting a highly extended upper atmosphere. We estimate a mass-loss rate of $\dot{M}\sim10^{12.14}\,\mathrm{g\,s^{-1}}$ from ATES. The present NUV data do not improve constraints on lower-atmosphere properties, and a comparison with upper-atmosphere forward models disfavor scenarios with extreme Mg enrichment. Together with the near-solar metallicity inferred from optical+IR spectra, this suggests that the Mg II absorption can arise in an escaping upper atmosphere without requiring extreme Mg enrichment, qualitatively consistent with hydrodynamic escape. Ongoing HST programs expanding the sample of UHJs focused on NUV observations will enable comparative tests of composition and kinematics in escaping atmospheres.

Reconstructing an editable CAD model from a 3D shape remains a challenging engineering task. Existing methods can propose CAD operations, but no single source of proposals works equally well across different part geometries and stages of reconstruction. We introduce CADFather, an autonomous agentic system that coordinates complementary tools to recover parametric CAD programs from 3D meshes. A vision-language assistant inspects renders of the target and intermediate reconstructions, then decides which candidate CAD programs to extend, which tools to invoke, how many proposals to generate, and when to finish. Learned and algorithmic tools propose CAD operations, while numerical optimization refines the parameters of existing programs. Proposed or refined programs are executed and evaluated to provide feedback for subsequent decisions. The agent maintains alternative candidate programs for each target part and preserves the best valid result throughout reconstruction. CADFather uses pretrained generation and assistant models without additional training. We evaluate reconstruction quality and execution validity on the full DeepCAD, Fusion360, and MCB test sets, as well as on CADENA-Bench, CADBench, and BenchCAD. We additionally analyze computational cost and the trade-off between cost and reconstruction quality.

Accurate thermal modeling is essential in metal additive manufacturing (AM) for understanding the process-structure-property chain. Physics-informed neural networks (PINNs) offer effective surrogate thermal modeling by minimizing physics-based residual losses at collocation points. However, prior works typically rely on manually-crafted, static collocation sampling strategies, which are neither principled nor scalable across process conditions, hindering their generalization capability. In this work, we provide theoretical analysis through empirical risk minimization, showing that process condition-aware adaptive sampling is strictly more favorable than conventional static sampling for generalization. Building on this insight, we propose an adaptive sampling strategy within a two-stage framework: (1) a conditional Flow Matching model that learns approximate high-residual distributions across different process conditions, and (2) a mixed sampling strategy combining this distribution with a domain-informed base distribution to generate adaptive collocation points for refining the PINN predictor. Experiments on metal AM numerical benchmarks demonstrate that our method consistently outperforms state-of-the-art PINN baselines, achieving an average 62.1% reduction in relative $L_2$ error under an identical collocation budget, by capturing process-dependent heat dissipation regions often overlooked in the literature. To the authors' knowledge, this is the first adaptive sampling strategy for PINNs in metal AM, contributing to the enhanced generalization and broader applicability.

Reference-based object compositing inserts or replaces an object using a background image, a reference image, and a 2D compositing mask. These inputs guide appearance and placement but leave the completed scene's geometry implicit, which can distort object structure or alter the surroundings. Our Depth-to-RGB (D2R) framework predicts composite depth for a scene not yet observed in the RGB inputs. It learns reference-conditioned corrections to a frozen depth estimator using encoder features of paired completed scenes as targets. The unchanged decoder maps the corrected representation to the intended scene's depth, which a separately trained renderer holds fixed during RGB synthesis. Under matched architecture and training, encoder-feature supervision reduces OOD Stage-1 AbsRel by 31.4% relative to decoded-depth supervision. We also introduce AnyInsertion++ with paired in-distribution and category-disjoint splits to evaluate generalization beyond compositing training categories. The complete D2R system leads 12 open-source and 3 closed-source baselines in estimator-derived geometry and photometric quality on both paired splits. On category-disjoint data, D2R reduces AbsRel by 43.7% and improves PSNR by 2.4 dB over the matched RGB baseline. Across three unpaired benchmarks, D2R leads both identity metrics and reduces mean CLIP reference cosine distance by 55% relative to the strongest baseline. Project page: https://shjo-april.github.io/Depth2RGB/

Induction heads provide a mechanistic account of in-context learning in sequential data, but existing theory largely assumes that the context relevant to a prediction forms a contiguous block. In multidimensional data, serialization breaks this assumption by scattering spatial neighbors across distant positions in the token sequence. We study how transformers overcome this routing problem in multidimensional stochastic and deterministic cellular automata, where each trajectory is generated by an unknown local rule and presented as a flattened sequence without an explicit coordinate-based spatial inductive bias. We introduce spatial induction heads, two-layer gather-and-match circuits in which the first layer reconstructs the relevant spatial neighborhood and the second matches the resulting configuration against earlier occurrences. We give two explicit realizations of the gather and show that the positional dimension required for spatial routing depends only on the local neighborhood and spatial dimension, not on grid volume or trajectory horizon. We further construct a matching layer which implements Bayesian counting. The end-to-end circuit can approximate the Bayesian posterior arbitrarily closely for stochastic rules and can predict exactly for deterministic rules. Empirically, trained two-layer transformers generalize to unseen rules in one and two dimensional settings, achieving near-perfect deterministic rollouts and less than 0.005 nats KL from the Bayes-optimal predictor on stochastic rules. Attention patterns and layerwise probes align with the predicted gather-and-match computation, providing mechanistic evidence for spatial induction in trained transformers.

We study cluster recovery in a two-state Gaussian hidden Markov model in the slowly mixing regime, where the transition probability $\delta$ may vanish with the sample size. Temporal persistence creates long homogeneous segments and fundamentally changes the recovery problem relative to the i.i.d. Gaussian mixture benchmark. Rather than being purely adverse, label dependence provides exploitable structure: the statistical difficulty becomes concentrated near the rare transition points, giving rise to recovery regimes governed explicitly by their frequency $\delta$. We first characterize, up to universal constants, the oracle Bayes risk for offline and online clustering. Both problems exhibit a nonstandard polynomial risk regime, but the sequential constraint induces an additional logarithmic localization cost, yielding a genuine online/offline gap. We also study fixed lag prediction with delayed label feedback and identify the effective memory horizon beyond which past labels no longer improve the optimal rate. When the signal direction is unknown and possibly high dimensional, the problem is governed by the effective signal strength \[ r_n^2 = \frac{\|\theta\|^4/\sigma^4} {\|\theta\|^2/\sigma^2+d/n}. \] We derive minimax lower bounds and construct fully adaptive polynomial time procedures attaining the sharp recovery rates. In particular, almost full recovery is possible precisely when $r_n^2\gg\delta$. If $n\delta\gtrsim\log n$, adaptation to both the signal $\theta$ and the transition probability $\delta$ incurs no first order loss, and the sharp exact recovery threshold (under the Hamming loss) is \[ r_n^2 = 2\log(n\delta)\,(1+o(1)). \] Thus the effective complexity of the problem is governed by the number of latent transitions, rather than by the sample size itself.

Parameter-efficient fine-tuning (PEFT) offers many parameterizations, yet their methodological and functional differences remain unclear. We compare six methods in language and diffusion models to examine how their parameterizations relate to task performance, forgetting, and changes in pretrained weight geometry. Motivated by the spectrum-preserving design of orthogonal fine-tuning (OFT), we first ask whether spectral preservation is itself important for adaptation and retention. We find that the selected LoRA-family methods also approximately preserve pretrained geometry, and that restoring their slightly drifted singular-value spectra largely preserves task performance, questioning the necessity of explicit geometric preservation. Beyond this, we observe that some methods exhibit distinct adaptation–retention trade-offs that vary across settings: LoRA most consistently limits forgetting at competitive performance, DoRA achieves higher mean task scores than LoRA in most comparisons, while PiSSA often incurs greater retention costs. Further intervention experiments suggest that while performance gains from different PEFT methods can be attributed to modifications in different groups of spectral components, we consistently find that restoring dominant rather than intermediate or trailing components produces the largest mean reduction in general-text NLL or base-image drift. Together, these results motivate evaluating geometric constraints through their functional consequences rather than preservation alone. Code is available at https://github.com/Kuaaannn/PEFT_methods.

We study the tropical octahedron recurrence on the lattice tetrahedron $\{(x_1,x_2,x_3,x_4)\in\mathbb Z_{\geq0}^4: x_1+x_2+x_3+x_4=n\}$ with an intrinsic double-hive boundary law. Let $M_1^{(n)},M_2^{(n)},M_3^{(n)}$ be independent standard $n\times n$ GUE matrices and, for fixed $\ell_1,\ell_2,\ell_3>0$, set $ X_r^{(n)}=\ell_r\sqrt n\,M_r^{(n)},\qquad r=1,2,3. $ The boundary law on the two upper panels is the Gibbs density on the cone of double hives whose four exterior sides correspond, in the prescribed orientations, to the spectra of $X_1^{(n)},X_2^{(n)},X_3^{(n)}$, and $X_1^{(n)}+X_2^{(n)}+X_3^{(n)}$. We then perform an octahedron-recurrence sweep to obtain the value at every lattice point of the tetrahedron. After scaling lattice positions by $n^{-1}$ and recurrence values by $n^{-2}$, we prove that the resulting random field converges uniformly in probability to a deterministic Lipschitz function on $\{(x_1,x_2,x_3,x_4)\in\mathbb R_{\geq0}^4: x_1+x_2+x_3+x_4=1\}$. For every strictly interior target lattice point we construct a canonical planar bipartite graph supported on a union of three triangular panels and prove an exact perfect-matching formula for the recurrence value. Its variable weights are explicit interlacing gaps from the minor processes of $X_1^{(n)},X_2^{(n)},X_3^{(n)}$, together with explicit seam and matching-independent terms. The asymptotic analysis of this formula yields a surface-tension variational characterization of the deterministic limit. This matching rule supplies, in the present four-simplex setting, the kind of higher-dimensional combinatorial formula identified as a major cluster-algebra problem by Henriques and Speyer.

Randomized exploration is central to bandit learning, multi-agent reinforcement learning, and zeroth-order policy search, yet its independence and privacy are usually only treated as technical assumptions. We show that these properties are critical for security purposes and demonstrate how an adversarial agent can exploit privileged information on another agent's exploration. We analyze a deceiver-victim pair in the minimal two-player strongly monotone setting, where a deceptive player obtains leaked signals that are merely correlated with the victim's exploration. We show that, by coupling their own exploratory action with this information, the deceptive player injects an externality that steers the learning dynamics to a new steady state, called the deceptive Nash equilibrium (DNE). We prove that the deceptive bandit learning (DBL) dynamics converge to an arbitrarily small neighborhood of the DNE while retaining optimal convergence rates. Interestingly, our analysis attains these optimal rates while relaxing second-order smoothness conditions from standard bandit optimization literature. We characterize conditions under which deception strictly shifts the steady state and its effect on the deceiver's cost, illustrating the results in a resource-allocation game.

Agentic artificial intelligence (AI) systems are becoming the interface to buildings, answering questions and controlling operations, but a building's readiness for them has not been systematically assessed. This study proposes a framework to quantify it. First, a building's knowledge graph sets two ceilings. The answerable-readiness ceiling is the share of operational questions its data could answer, and the actuation-readiness ceiling is the share of control actions it exposes. Second, a reference AI agent's accuracy on a fixed set of these questions shows how much of the ceilings is realized. On a simulated office, the agent realizes 0.62 of a 0.64 answerable ceiling, so missing data, not the AI, limit readiness, except in naming a fault's cause. Across 37 public real-building graphs, the median answerable ceiling is 0.16, and in 15 of 45, unlinked sensors lower it. The framework turns "is this building AI-ready?" into an auditable, ranked retrofit question.

Topology reasoning jointly detects 3D lanes and traffic elements from multi-view images and infers their structural connectivity. Current methods model lanes as discrete polylines, lacking smoothness, analytical tangent directions, and global spatial support for attention, while providing sparse topology supervision. We propose TopoCurve, a geometry-driven architecture for 3D topology reasoning grounded in a structured parametric lane representation. Lanes are modeled as endpoint-fixed cubic Bézier curves, enabling continuous geometry with exact endpoints and analytically defined directionality. We exploit this shared curve geometry across the entire pipeline. Endpoint distance and tangent alignment are encoded with multi-scale Fourier features and injected into the topology head. Sampled curve points serve as geometry-aligned references for deformable cross-attention spanning the full lane. Parallel curve-anchored attention branches provide diverse predictions for one-to-many topology supervision. These components form a tightly coupled cascade where representation enables geometric reasoning, guides feature aggregation, and supports denser supervision. TopoCurve achieves 50.6 OLS on the OpenLane-V2 benchmark without any post-processing, establishing a new state-of-the-art among end-to-end camera-only methods, and outperforms all existing approaches on endpoint detection (56.8 vs. 52.6 on DET_p).

Humanoid robots still struggle to plan contact-rich whole-body manipulation from egocentric RGB and proprioception. Workhorse learns such manipulation from robot-free human demonstrations. A visual planner predicts five-link targets: the poses of the torso, both wrists, and both feet. A reinforcement-learning whole-body tracker follows them on the robot. Both policies train separately on the same recorded human poses, without retargeting. We augment the training data of each policy to imitate the errors that the other makes at deployment. On a real Unitree G1, Workhorse transport boxes with its hands and a kick, catches a thrown box, and topples and climbs a suitcase. During box transport, we show recoveries after a person pushes the robot or takes the box away. In a simulated copy of the demonstration room, the system completes box transport in 77% of episodes, and in 64% under 40 N.s pushes. With both policies retrained from the same demonstrations, a simulated second humanoid completes box transport in 83% of episodes without pushes.

The rapid growth of 3D Gaussian Splatting (3DGS) research demands significant effort to reimplement papers before building on them. We introduce SPLATIFY, a multi-agent framework that converts 3DGS papers into trainable gsplat-based implementations, where generic paper-to-code methods and frontier models fail. SPLATIFY achieves this through five innovations: (1) A context-free grammar for gsplat over a modular method template with extension points for losses, densification, rendering, and optimization, constraining synthesis so generated code satisfies gsplat's architectural invariants by construction. (2) Architectural elements for faithful reproduction: fork-aware citation recovery retrieving component-level code at function-level granularity, Graph-of-Thought synthesis in topological dependency order, RAG-guided in-context example selection from over 20 verified implementations, and visual feedback combining PSNR-guided regeneration, Gaussian-level structural checks, and VLM-driven patching. (3) Knowledge-driven compositional improvement that autonomously finds weaknesses and composes complementary regularizers, losses, and densification strategies to improve upon original results. (4) Interdisciplinary method discovery where agents retrieve physical priors from outside the 3DGS literature and compose them with rendering knowledge to produce methods for previously unaddressed scene types. (5) SPLATIFY-Bench, an evaluation framework across 30 diverse 3DGS papers. On papers without public code, SPLATIFY matches expert implementations while reducing development time from weeks to minutes, and through compositional discovery further improves PSNR by up to 2.4 dB. We additionally demonstrate novel methods for volumetric nebula rendering and other scientific domains, synthesized entirely by SPLATIFY.

Steering an LLM agent means deciding whether to correct it, at which step, and with which mechanism. Uncertainty is often used to decide when to correct an agent, but whether it can guide these decisions remains unclear. We steer agent trajectories separately at every non-terminal step with each of four mechanisms and run each continuation to completion. The resulting stepwise outcome table (SOT) holds about 82,000 counterfactual continuations of 1,864 trajectories from three benchmarks and two agents. It shows that uncertainty can identify failing trajectories, but that no single signal reliably locates the step at which steering helps. We therefore propose VoS (Value of Steering), a trajectory-level monitor, offline or online, that learns from SOT the value of steering at each step and decides where to steer by it. A harm-budgeted trigger decides whether to steer, limiting the fraction of successful trajectories that VoS disturbs. VoS improves on unmodified execution in all 12 settings of benchmark, agent, and offline or online use, by 7.8 points on average, and outperforms the strongest of five existing uncertainty-triggered methods in 11, by 2.9 points on average. Ablations show that training on measured outcomes and a tight harm budget are both essential.

Dasgupta, Stevens and Navlakha (2017) showed that the Drosophila olfactory circuit, modelled as a random sparse projection followed by winner-take-all, is a locality-sensitive hash that beats classical LSH. The projection was random because the wiring was unknown. We test it against four electron-microscopy connectomes (MaleCNS, hemibrain, FlyWire, BANC; four animals, seven hemispheres). First, the 2017 pattern holds in a reimplementation of its protocol on SIFT, MNIST and odour mixtures (GloVe is near chance at short codes for every method): the fly hash beats k Gaussian projections at short hash lengths (3.1x in AP@200 on MNIST at k = 4). Second, against the tested real-valued Gaussian baseline that advantage is per active cell, not per operation: Gaussian projections given the same projection arithmetic retrieve better on every dataset and input dimension tested. Third, across four connectomes the measured pairing of glomeruli gives no consistent retrieval advantage over degree-preserving rewiring: retrieval is slightly lower (median -1.6%), and the small odour deficits depend on how missing odour responses are treated. Separately, equalising glomerular fan-out at fixed connection count improves retrieval in the model in every hemisphere, while equalising inputs per cell lowers it on average. Yet the fan-out profile is similar across the four sampled animals (median between-animal Spearman rho = 0.86), structural synapse counts do not offset it, and its relation to odour tuning is weak. In the model that uneven allocation costs retrieval. For practice: measured wiring gives no consistent retrieval advantage over degree-preserving random wiring, so a fly hash needs no connectome data, and its advantage is per active unit, which may suit hardware where active units rather than arithmetic are the binding cost, a hypothesis we do not test.

We prove that there exists an absolute constant $c>1$ such that for every $n \geq 3$ there exists an $n$-dimensional real normed space $X$ for which every linear projection $P$ onto a hyperplane satisfies $\|P\| \geq c$. More generally, for every integer $k \geq 1$ there exists a constant $c_k>1$ such that for every $n \geq k+2$ there exists an $n$-dimensional real normed space $X$ such that every projection $P$ onto a subspace of codimension at most $k$ satisfies $\|P\| \geq c_k$. The proof is based on an idea of Gleit and Lazar, who established an analogous result for the space of real $n \times n$ matrices equipped with either the trace-class norm or the operator norm

Before tool-using LLM agents are deployed in environmental and geospatial workflows, teams need evidence that an agent reliably selects the right operations against real APIs. We introduce GeoNatureAgent (GNA), a framework for pre-production evaluation of tool-using agents: a fixed sixteen-tool geospatial interface published as a Model Context Protocol (MCP) server, so the agent under test is the only variable, scored against an identical tool layer, task suite, and deterministic scorer. Its flagship instance is a 103-task benchmark (a 93-task main suite across 18 categories plus a ten-task comparison expansion) evaluated against an open, self-hostable geospatial API serving three environmental indicators across Spain and Portugal. We evaluate nine LLMs under three temperature-1.0 seeds, reporting capability and per-case cost as orthogonal axes. (1) Claude Sonnet 4 achieves the highest capability (61.7% +/- 0.7% on all 103 tasks; 60.8% on the main suite), followed closely by DeepSeek V3.2 (57.9%), while no other model exceeds 53%; (2) the cost-accuracy Pareto frontier is mostly open-weight, with DeepSeek V3.2 offering 93% of Claude's capability at 11.3x lower list-price cost; (3) under strict all-checks scoring the best model sits 24-36 points below the 85-97% reported on general-purpose GIS benchmarks, whereas per-check partial credit for the top four models (86-90%) is comparable, so much of that gap reflects scoring strictness rather than task difficulty alone. The MCP server, evaluation harness, benchmark, and API are publicly available; swapping the tool executors and task suite instantiates an equivalent benchmark for any geospatial domain.

Deterministic inference is essential for reliable and trustworthy machine learning. Prior studies of text generation have shown that changing factors such as batch size, batch composition, hardware, or inference engine can alter the generated text, even when the prompt, model parameters, and sampling randomness are fixed. These differences have been attributed in part to floating-point non-associativity, shape-dependent kernel selection, and other implementation-level differences in numerical execution. However, it remains unclear whether, when, and to what extent the same factors affect text classification. We present a systematic study of serving-context non-invariance in text classifiers, which prior work has measured only through generated text. We train 180 models spanning discriminative, pseudo-generative, and fully generative classifier formulations and evaluate each across four categories of serving contexts, holding the checkpoint and the text fixed. Label stability does not imply score stability. Changing only the batch shape changes no labels across fp32 comparisons, yet under bf16 it moves up to 56.7 percentage points of predicted probability mass, with label changes concentrated at small margins. Fully generative classifiers change more labels than their discriminative counterparts under the same serving changes. We derive sufficient conditions for label stability under each serving change and give a separate mitigation for each mechanism. Our results identify and quantify the serving conditions that must be fixed for reproducible text classification.

The near-Earth asteroid (3200) Phaethon exhibits unusually high linear polarisation at large phase angles. Previous observations revealed a significant difference between apparitions: measurements obtained in 2016 showed a polarisation up to $\sim10$ percentage points higher than those obtained in 2017 at comparable phase angles. The distinct surface regions and viewing geometries sampled during the two apparitions have been suggested as possible explanations for this difference. Here, we present new R-band polarimetric observations obtained with the Nordic Optical Telescope, covering phase angles $32^\circ<\alpha<103^\circ$. The 2019 measurements show polarisation intermediate between higher and lower values measured in 2016 and 2017, respectively. Using a recent shape model, we calculate the distribution of reflected flux across the surface during the three individual apparitions and find that the 2019 observations sample the surface more similarly to 2016 than to 2017. We explore several possible explanations for the different polarisation behaviours, including differences in regolith grain size, related surface albedo, and observing geometry. While the available observations do not allow these effects to be uniquely disentangled, our results and analysis suggest that surface heterogeneity is the most plausible underlying cause, with viewing geometry potentially contributing to the observed polarimetric differences.

Many organizations fine-tune publicly available pretrained Automatic Speech Recognition (ASR) models and deploy them in black-box settings, assuming limited access provides protection. We show this assumption is fragile: adversarial perturbations crafted on the public base model transfer effectively to fine-tuned target models, severely degrading performance and posing concerns for safety-critical applications. We propose TransferBreaker, a unified fine-tuning framework that suppresses adversarial transfer by integrating Base Adversarial Fine-Tuning, which restricts adversarial training to base-effective perturbations; Latent Jacobian Regularization, which enforces latent-space invariance by suppressing adversarially sensitive directions; and HybridGrad-AFT, which improves robustness against adaptive attacks by interpolating transferable perturbations from base and target gradients. We theoretically justify all components and evaluate TransferBreaker across three languages and four large ASR models, reducing adversarial WER from 92.6 to 27.8. Our code is publicly available at https://github.com/rohban-lab/TransferBreaker.

Policy learning drives many of the most consequential and heavily-invested applications of reinforcement learning today. Yet the core optimization problem it rests on (maximizing expected return) is notoriously non-convex, even under a direct policy parameterization, and the field has largely responded by avoiding it: optimizing convex surrogate approximations of the return under trust-region constraints (NPG, TRPO, PPO, AWR). We show that this seemingly unstructured problem is not actually structureless. In log-density-ratio coordinates $y := \log[\pi/\pi_n]$, the exact per-iteration objective, computable via per-decision importance sampling (PDIS), is a difference-of-convex-constrained difference-of-convex (DC-constrained DC) program. This structure lets us move beyond surrogate approximations: it recovers CPI, NPG, TRPO, and AWR as special cases along interpretable axes, and it opens a multi-step axis $k$ that couples consecutive decisions. We solve the per-iteration program with sequential convex programming (SCP), the standard solver for difference-of-convex problems, and give convergence guarantees under mild conditions, bridging the difference-of-convex optimization and RL literatures. Empirically, multi-step Convex-Concave RL (CCRL) wins on diagnostic MDPs where credit must propagate across a horizon (its advantage growing with the dependency length), is competitive with a tuned PPO on classic control, and on a realistic, stochastic, mid-horizon healthcare domain converges markedly faster than tuned PPO to the same near-optimal survival, with an 11.3% higher area under the training curve.

Natural-language feedback in interactive learning often explains why an action failed by pointing to violated requirements. Misinterpreting this feedback can lead an agent to rule out valid solutions. We study this setting by modeling user intent as latent constraints over an action space and formulating learning from language feedback as pure exploration over feasible regions. We introduce TRACE, an algorithm that organizes candidate constraints in a tree and tests each proposed refinement by generating actions that satisfy it. TRACE commits to the refinement only if the resulting feedback does not contradict it over repeated tests. We distinguish two ways of using the same feedback: (i) falsification, which detects contradictions to the constraint set currently being tested, and (ii) identification, which may additionally name a violated constraint. We prove high-probability coverage bounds with dependence on the candidate class size $H$ for TRACE-Falsification. With reliable identification, TRACE-Identification can replace this dependence by $K/p_{\mathrm{ext}}$, where $K$ is the number of latent constraints and $p_{\mathrm{ext}}$ lower-bounds the probability of extracting a missing true constraint from informative feedback. We evaluate TRACE across six language-feedback tasks. On RecMovie, TRACE-Identification achieves 73% and 86% final-output success under caps of 20 and 60 evaluated outputs, compared with at most 42% and 48% for the evaluated prompting baselines given the same feedback and output caps. Controlled identity-corruption experiments further show greater robustness than direct accumulation when the falsification detector remains reliable.

Nuclear spin relaxation has been widely used to probe molecular reorientation in solids, yet its interpretation has always required assuming both the relaxation mechanism and the form of the underlying correlation function. In rotator-phase solids more unknowns enter the picture: in ammonium iodide, the proton T$_1$ passes through a maximum and decreases with temperature, a behavior attributed to spin-rotation coupling. Here we model both the dipolar and the spin-rotation contributions to $^1$H relaxation in solid NH$_4$I from first principles, by combining molecular dynamics with machine-learned force fields trained on density functionals and ab initio spin-rotation coupling tensors. The computed rates reproduce the measured values above the order-disorder transition, together with their temperature dependence and frequency independence, and show that fluctuations of the NH$_4^+$ angular momentum dominate relaxation throughout the rotator phase. The orientational and angular-velocity correlation functions obtained directly from the simulations further share an oscillatory component at lattice-phonon frequencies, revealing a coupling between lattice vibrations and cation reorientation that contributes measurably to relaxation. Separating this component yields a reorientational barrier in agreement with neutron scattering. The approach makes nuclear spin relaxation a quantitative benchmark for simulated dynamics in molecular solids and provides direct access to angular-momentum correlations in the solid state.

We establish local asymptotic normality (LAN) for joint inference on scale and roughness in stationary Gaussian random fields observed on increasingly dense regular grids in a fixed domain. Scale and roughness are represented by the coefficient and decay exponent of the leading spectral tail. Under spectral regularity conditions, we identify the joint normalization governing the LAN expansion and prove consistency and asymptotic normality of the maximum likelihood estimators. For \(N\) observations, the estimation errors are of order \(N^{-1/2}\) for roughness and \((\log N)/\sqrt N\) for scale. After componentwise normalization, the errors converge to a perfectly correlated Gaussian pair. Knowing either parameter improves the convergence rate for estimating the other by a logarithmic factor. The analysis uses generalized locally Toeplitz (GLT) theory, for which we develop a truncation principle accommodating nonintegrable limiting symbols and quantitative bounds on the contribution from low frequencies. We verify the assumptions for Matérn and generalized Wendland covariance families, establishing uniform spectral bounds for the latter. We also show that consistency and the limiting distributions persist under covariance misspecification when the true and fitted spectra share the same leading tail and their difference decays sufficiently rapidly. This includes misspecification between Matérn and generalized Wendland models under explicit parameter restrictions.