Papers

Traditional models of collective behavior rely on prescribed interaction rules, leaving unresolved the question of how behavior arises from neural representations of space. Here, we develop a first-principles theory in which movement, decision-making, and collective organization emerge by coarse-graining fast neural dynamics on a topological representation of directional space. For a ring manifold encoding heading, this reduction yields a macroscopic theory of behavior: a decision landscape over directions that admits a harmonic decomposition. In this framework, behavior is governed by a spectral organization of directional information rather than ad hoc rules. We demonstrate that target-seeking, avoidance, choice, spatial decision-making, and diverse forms of collective motion arise as distinct organizations of the underlying harmonic landscape. The theory unifies neural representations, behavioral decisions, and collective dynamics in a single mathematical description.

In diffusion-based generation, a neural network can be trained to predict the clean data, the noise, or the velocity from a noisy input. These prediction targets are interconvertible and describe the same generative process, yet plain Diffusion Transformers operating on large pixel patches succeed with clean prediction and fail with noise or velocity prediction. We argue that this asymmetry arises because noisy targets require the residual stream to preserve noise-dependent input variation through depth for the final readout, forcing subsequent layers to compute on noisy representations. A spectrally concentrated clean target imposes a lighter demand, leaving greater freedom to organize hidden representations for subsequent computation. We call this preservation requirement *residual-stream burden* and show how it shapes representation learning in Diffusion Transformers. Controlled experiments indicate that the exploitable structure is spectral concentration in patch space and that the bandwidth of the persistent residual state is a key resource for noisy prediction. We further show that this account is consistent with recent decoupled pixel-space architectures, whose diverse designs all reduce the residual-stream burden on the main pathway. To examine this understanding from a complementary direction, we expand and reorganize the residual-stream bandwidth directly, introducing Spatially Indexed Hyper-Connections (SiHC) that reach FID 1.71 on ImageNet $256^2$. Together, these results identify residual-stream burden as a mechanism through which prediction targets and architecture jointly shape representation learning in Diffusion Transformers.

We present an expository excursus on modulation spaces, from Feichtinger's original construction on locally compact abelian groups to recent symplectic formulations. We trace the same local-global principle through bounded uniform partitions of unity, the short-time Fourier transform, coorbit methods, and Gabor coefficients, while distinguishing equivalent descriptions from the weighted, quasi-Banach, and Gelfand-Shilov extensions of the underlying functional setting. We also discuss Gabor matrices, convolution and embedding estimates, and an application to a nonlinear dispersive equation. The final part is devoted to metaplectic Wigner distributions $W_{\mathcal A}$. In the shift-invertible case these representations are, up to chirps and a linear change of phase-space variables, rescaled short-time Fourier transforms. This structural fact explains both their characterization of modulation and Wiener amalgam spaces and their discretization by metaplectic Gabor frames, and places the recent symplectic theory naturally within Feichtinger's modulation-space framework.

Large audio-language models (LALMs) produce fluent responses about audio but often hallucinate by making plausible yet ungrounded claims. Existing audio hallucination benchmarks mainly measure response correctness, leaving it unclear whether an LALM hallucinates or simply fails to understand the audio. We challenge correctness-based evaluation by defining two hallucination categories: (i) context, where claims are not grounded in the audio; and (ii) knowledge, where claims about audio-related topics lack support from externally verifiable facts. We introduce MISHAP-Bench, a comprehensive benchmark with 12,000 challenging open-ended question-audio pairs and a rigorous evaluation pipeline covering both categories. To evaluate open-ended responses, we propose a groundedness judge that uses reference rubrics and judge prompts guided by human annotations. We extensively evaluate ten state-of-the-art LALMs and show that hallucination remains substantial. Even a frontier model such as Gemini 3.7 Flash reaches a hallucination rate of 36.5%. We further adapt and benchmark four mitigation methods from multiple domains for LALMs. Despite some improvements, effective hallucination mitigation remains an open challenge. Finally, we call on the community to evaluate hallucination and benchmark mitigation methods with MISHAP-Bench.

This paper proposes a residual learning-based control framework for heterogeneous vehicle platoons subject to parametric uncertainty and external disturbances. A nominal controller designed via Linear Matrix Inequalities (LMIs), along with disturbance-observer compensation, is enhanced by a Recurrent Equilibrium Network (REN) trained offline using stored trajectories and nominal-model prediction errors. The REN is constrained to satisfy a prescribed $\ell_2$-gain bound, enabling sufficient small-gain conditions for local closed-loop stability and disturbance string stability. Experiments demonstrate reduced spacing and velocity errors relative to the nominal controller.

Multicalibration requires a predictor's residuals to be unbiased not only globally, but also after conditioning on the predictor's own level sets and reweighting by a rich class of test functions. Standard boosting approaches in the distributional setting achieve this by repeatedly discretizing the predictor's range then auditing and repairing the resulting level sets. One consequence is that in practice, the algorithm's guarantees are sensitive to this parametrization of the rounding parameter. A natural theoretical question, then, is how to do discretization-free boosting which avoids this rounding within the boosting process itself. Here, we analyze an alternative feature-augmentation boosting paradigm inspired by Tax et al. (2026): at each round, a squared-loss oracle is called on hypotheses that receive the previous predictor's output as an additional feature, and only the final predictor is rounded to have a finite set of level sets to provide the multicalibration guarantee with respect to. We give a theoretical analysis of this procedure through the expressivity of the augmented hypothesis class, and show how the expressivity of this class yields a hierarchy of guarantees, including multiaccuracy, multicalibration, and the stronger notion of level-set multicalibration.

We show that the percolation components on a square grid can be $5$-colored as a factor of iid so that neighboring components get different colors. Above the critical probability, we observe that these regions can be 4-colored. Along the way, we extend the classical correspondence between fiid process and measurable labellings of the Bernoulli shift to this quotient setting, prove a general coloring result about hyperfinite pmp planar graphs, and clarify some foundational issues about how to define planarity for Borel graphs.

At each step, decoding one sequence with a large language model rereads the projection weights, whose traffic is fixed, and the key-value (KV) cache, whose traffic grows with context. Activation sparsity trims the first term and KV-cache sparsity the second, yet their reported speedups are hard to compare because each depends on context length and on the dense attention kernel it is measured against. We derive a byte crossover, the context length at which the two savings are equal, together with ideal speedup bounds for each branch and for their composition, from model dimensions and keep ratios alone. We then time both branches and their composition from 2K to 128K tokens on two GPUs after a dense prefill of real text, with dense and sparse modes reading the cache through the same split-K attention kernel. The projection branch leads at short context and the KV branch at long context, with speedups that follow their byte bounds up to fixed kernel costs. Adding these costs, measured in separate sweeps, lets the byte account predict the measured crossings of three keep-ratio pairs, a second model, and a second GPU to within 4.1K tokens. Timing the dense baseline with masked instead of split-K attention inflates the apparent speedup of the same KV policy about fivefold. An attention-scored KV selection answers the same passkey and multi-key placements as dense decoding up to 127K tokens, whereas a KV window misses most of them. Under matched perplexity budgets, activation sparsity composed with this selection decodes 14 to 26% faster than the best single branch on both GPUs. Code is available at https://github.com/js-lee-AI/ByteCross.

Can vanilla policy optimization explore enough to achieve near-optimal regret in stochastic contextual bandits? We show that standard exponential policy updates driven by offline regression do so under realizability, without exploration bonuses or importance weighting. For $A$ actions, $T$ rounds, and a finite prediction class $F$, vanilla PO achieves $\widetilde O(\sqrt{AT\log(|F|)})$ regret with high probability. Our analysis reveals an implicit exploration mechanism of independent interest: gradual policy updates prevent actions from losing probability too quickly, allowing the regression oracle to learn their expected losses. We further develop a batched version using only $O(\log T)$ regression calls and policy switches, and show how private regression oracles yield differentially private contextual bandit algorithms without composition across batches. For a finite class, this gives pure $\varepsilon_{\rm priv}$-DP and regret $\widetilde O\left( \sqrt{AT \log(|F|/\delta)}(1+\varepsilon_{\rm priv}^{-1/2}) \right)$. Finally, experiments across oracle-based contextual bandit algorithms, with and without privacy, demonstrate the practical effectiveness of policy optimization and the value of explicit exploration under stronger privacy constraints.

Block-diffusion language models are served at hand-picked operating points, such as acceptance thresholds, buffer depth, schedule, checkpoint and precision, and each point is chosen by its mean benchmark accuracy. However, a mean does not tell an operator how often a faster configuration fails on prompts that the slower one answers correctly. On the serving engine and its decode traces, the default commit rule already commits every fully resolved block, a static skip rule captures nearly all of the compute that allocation can save, and self-distillation on engine-decoded targets adds speed at unchanged accuracy. Larger speedups come from lower thresholds, which commit tokens that are still uncertain. We therefore present Redline, a finite-sample procedure that selects operating points, hand-picked or learned, from the correctness of their answers on calibration prompts. Redline keeps the reference-relative risk, the joint probability that the reference answers correctly and a candidate configuration does not, within a user-chosen budget with high probability, and deploys the fastest configuration that passes. It speeds up math at a smaller risk budget than code in both model families, and at a budget of ten percent it deploys a LLaDA2 math configuration that commits over a third more tokens in each forward. It also applies without modification to the acceptance rule of speculative decoding and to weight quantization. On the same calibration data, Redline stays within its stated failure probability, whereas each tolerance of a mean-accuracy rule either gains less speed for some model and task or exceeds the risk budget far more often for another. Code is available at https://github.com/js-lee-AI/Redline.

Large language models are trained to always produce an answer, regardless of whether they possess the relevant knowledge, which leads them to fabricate facts. Prior work has shown that LLMs' confidence estimates correspond poorly to their actual performance, and that fine-tuning can substantially improve them. However, what models actually learn during such training remains poorly understood. We investigate how LLMs acquire metacognitive monitoring, the ability to know what one knows, by training 10 open-weight LLMs to predict their own accuracy on factual multiple-choice questions before answering them. We find that trained confidence reflects two distinct signals. While on questions close to the training data, it tracks the model's true accuracy, in other domains, it instead tracks output consistency: the concentration of the model's answer distribution. Output consistency tracking emerges early in training and generalizes across datasets, whereas accuracy tracking develops later and remains local to the training distribution. These results suggest that calibration training may not teach models to generally detect errors they commit confidently, and they raise broader questions about the nature of metacognition in artificial systems.

Large language model (LLM) agentic systems increasingly rely on models communicating with one another, yet existing uncertainty and multi-agent methods rarely estimate how a particular receiver will interpret a message before it is sent. This matters in heterogeneous systems, where capable receivers can reconstruct different tasks from the same message. We model this as a sender-receiver problem with a latent receiver type and define prospective interpretation risk (PIR): the probability that a receiver reconstructs a task other than intended. Rather than model an LLM's full input-output behaviour, we use black-box probes relating messages, intended tasks, and receiver-specific reconstructions, yielding scalable supervision while separating interpretation from downstream capability failure. Offline, heterogeneous frozen receivers provide supervision for receiver-conditioned risk and the effects of predefined mutable message features. At deployment, history induces a posterior over receiver types, guiding message revision and selection. We introduce value of interpretation information (VoII), querying for receiver information only when its expected communication benefit exceeds its cost. Our theory characterises when receiver information has decision value and bounds such queries. Empirically, interpretation-failure rates vary by 4-13x across receivers. Receiver information reduces PIR calibration error by 68% relative to a receiver-agnostic predictor, largely by correcting receiver-specific risk levels. PIR-guided revision reduces interpretation failure by 44% relative to the original message and 40% relative to a generic rewrite, mostly through a repair that helps every receiver. VoII outperforms information-gain and random querying at matched cost on the interpretation objective it optimises, lowering interpretation failure from 3.84% to 3.79% while querying 18.2% of episodes.

Let $X$ be a smooth projective complex surface with numerically trivial canonical class. With the help of GPT-5.6 Sol, we prove Qin's conjecture that the reduced generating series of intersection numbers of Chern characters of tautological bundles against the total Chern class of $X^{[n]}$ is a quasimodular form with the predicted mixed-weight bound. The main ingredient is a Wick's theorem-type formula for computing traces of normally ordered products of Nakajima operators on $\bigoplus_n H^*(X^{[n]})$. Following the argument of Li-Qin-Wang, the computation of the reduced generating series is reduced to computing the constant term of the supertrace of a product of certain operator-valued currents and the Carlsson-Okounkov operator. Our trace formula shows that this supertrace can be expressed in terms of two quasi-elliptic functions $\widehat Z$, $P$ and a quasimodular function $T$, whose constant terms are quasimodular forms by the theorem of Goujard-Moller. Finally, we give an explicit algorithm for computing the general reduced generating series.

Task-oriented dialogue requires maintaining and updating information across turns, yet language models expose no explicit belief-state object. We study how conversational state is represented, updated, and used inside eight instruction-tuned language models from four families on MultiWOZ and SGD. Structure and values separate: which domains, slots, and requests are active is linearly readable just before the model acts, whereas exact values are far more readable where the user stated them. After a user changes a value, both values remain accessible at their mentions, and causal interventions show that both continue to influence the model's action. In natural closed-loop interaction, query failures separate into cases of weak structural support, incorrect value resolution, and failure to deploy otherwise-supported constraints, with targeted interventions producing systematically different repair behavior across these cases. These findings motivate a state-action controller that starts from the base model action and selectively edits it using structural readouts, without requiring a complete predicted belief state as an intermediate representation. On held-out MultiWOZ interaction across five models, it raises the base model exact-query accuracy from .318 to .621 and task success from .272 to .371 at negligible added cost. Overall, reliable interaction requires not only retaining conversational information, but resolving which available constraints currently apply and ensuring that they govern action.

Glove-based motion capture is emerging as a scalable approach to collecting dexterous-hand demonstration data. However, due to the kinematic gap between the human and robot hand, the recorded human motions cannot be executed directly on the robot, especially for contact-rich tool-use tasks involving in-hand reorientation. Prior work bridges this gap in simulation through reinforcement learning (RL) or trajectory optimization, but the human contact pattern is hard to preserve under such formulations, often producing unnatural manipulation and unstable functional grasps. These methods also train a separate policy or solve a separate optimization for each reference trajectory, which is inefficient. To solve these problems, we propose DexTaG, a tactile-guided RL framework for dexterous manipulation. During training, tactile signals captured by the glove guide policy search toward the measured human contact pattern, reducing reliance on precise reference geometry for contact supervision. To improve efficiency, we train a single generalizable retargeter jointly on all training trajectories of the same object. The retargeter is further distilled into a tactile-free student controller conditioned on the target object trajectory for real-world deployment. On marker-pen and hammer manipulation tasks, DexTaG learns natural, contact-rich behaviors that baselines with distance-based contact heuristics fail to learn, generalizes to held-out trajectories of the same object and task, and outperforms single-trajectory baselines on OakInk2.

This paper conducts an empirical mediation analysis to examine how U.S. stock-market sectors responded to the 2025 tariff-policy episode. Using S&P 500 stock data along with hundreds of firm-level financial variables, we study whether sector membership was associated with differences in stock returns and whether these differences were statistically related to firm financial characteristics. For each of five economically distinct tariff-policy windows, we use high-dimensional linear causal mediation models to estimate the direct sector effects. We use a linear regression model to estimate the total sector effects, and then estimate the indrect sector effects by using the difference between the total sector effects and the direct sector effects. To accommodate a large number of candidate mediators, we use a partially penalized least-squares procedure that regularizes financial-variable coefficients while unpenalizes coefficients of all sector indicators. Wald and F-type tests are used to examine whether indirect and direct effects are significant or not, respectively. The results show that tariff news did not produce one uniform market response. Sector effects vary across five economically distinct tariff-policy windows. The clearest findings are in the direct sector effects. Technology was the sector most negatively affected during the initial decline and escalation collapse, but it also rebounded most strongly during the April 9 relief rally. The results indicate that in addition to Technology, Energy and other trade-exposed sectors were particularly affected during the initial decline and escalation phases. The selected mediators provide evidence that growth, investment, liquidity, profitability, and cash-flow characteristics helped characterize firms associated with sector-level return differences.

Convolutional EEG decoders are trained at a fixed width, usually set by their authors on other data. Growing methods add neurons during training where the loss could decrease the most, but whether they improve compared to a reference width is untested on EEG. Here, we grow three convolutional backbones on 12 motor-imagery datasets under three protocols and compare each with its reference model per subject. The growing ShallowFBCSPNet scores 2.9 points above its reference model with only half the parameters (0.57x), SCCNet changes by at most 1.2 points. Deep4Net growing models show decreased accuracy, but they require adaptation that prevent to compare faithfully the results. These differences follow the selection step, which keeps a candidate neuron relying on a dynamic threshold from singular values decomposition. Overall, these results suggest that growth helps when its criterion can rank the candidate neurons, and that the rate of skipped neuron addition tells where a decoder can be grown small from scratch.

Neural surrogates can accelerate large-scale optimization by replacing expensive or intractable model components with efficient learned approximations, but solving the resulting embedded problems can remain prohibitively costly. For instance, standard exact encodings of neural networks with ReLU activations allow the problem to be solved by mixed-integer solvers, but add large numbers of binary variables to accommodate the nonlinearity of the activations, which can render the problem computationally prohibitive. To address this, we propose DCEmbed, a heuristic for optimization problems with embedded neural surrogates that leverages the difference-of-convex (DC) representation of the network and avoids adding activation binaries. Exploiting shared structure within the DC representation of a ReLU network, we derive a reduced-size, exact formulation for its convex components that can be embedded in optimization problems using just two linear inequalities and one continuous auxiliary variable per hidden neuron. Using this, the problem is solved via an iterative penalty convex-concave procedure, where only the concave portions of the neural terms are approximated at each stage. The original objective, constraints, and any discrete decisions are retained, allowing standard convex or mixed-integer optimization solvers to optimize the host and surrogate jointly at each iteration. In experiments on quadratic programs, mixed-integer resource allocation, and neural two-stage stochastic programming, our method demonstrates much faster progress toward high-quality feasible solutions than approaches using exact mixed-integer embeddings. In particular, DCEmbed achieves $4\times$ lower normalized primal integral than the best exact baseline on the resource allocation problem, while in two-stage stochastic programming it reaches the global surrogate optimum $\sim 5\times$ faster than Gurobi ML.

Merchant matching resolves a noisy payment descriptor to a retrieved merchant entity or returns no match. A key challenge in curating training labels is distinguishing teacher abstention from evidence that no acceptable entity exists: false no-match labels contaminate pseudo-labeled data, while conservative labeling reduces coverage. We investigate whether agreement between two local large language model judges improves pseudo-label reliability. A label is retained only when the judges agree, with separate ordered thresholds for selections and abstentions that guarantee disjoint positive and negative label sets. Retrospective replay on 2,000 expert-annotated queries shows that higher selection thresholds can improve positive-label purity, whereas higher abstention thresholds increase false no-match labels. At thresholds (0.86, 0.80), Muse Glimmer 30B and Gemma 4 31B jointly label 1,633 queries (81.7% coverage) at 96.88% purity; positive and negative purities are 99.47% and 93.38%. This exceeds either constituent model at the same thresholds by more than two percentage points, with lower coverage. A split-half check finds only 0.14 percentage points of threshold-selection optimism. A symmetric threshold of 0.86 adds 40 erroneous no-match labels, while 46 false abstentions persist even with no confidence threshold. Across five matched within-model comparisons, higher reasoning effort yields no clear F0.5 gain and increases median latency by 1.8-5.0 times. These results motivate separate thresholding and auditing for positive and negative pseudo-labels. The study establishes label purity, not student utility; fresh-data curation and student fine-tuning remain necessary to demonstrate downstream value.

We present an extension of the Standard Model based upon the gauged $U(1)_{L_\mu - L_\tau}$ symmetry, featuring an ultra-light vector boson that couples to the difference of muon and tau lepton numbers. This anomaly-free construction, historically motivated by the muon's anomalous magnetic moment, is employed here as an independent phenomenological framework for solar neutrino physics. Through kinetic mixing with the photon, the $Z^\prime$ boson generates an effective matter potential within the solar interior, thereby modifying neutrino flavour oscillations via the Mikheyev–Smirnov–Wolfenstein mechanism. Utilising recent solar neutrino measurements from Borexino, SNO, and Super-Kamiokande, together with an up-to-date standard solar model, we constrain the boson mass to be below $5.7\times 10^{-17}\,{\rm eV}$, a potential ultra-light dark matter candidate. The optimal model, with coupling parameter $\eta_o \approx -2$, yields $\chi_\nu^2 = 2.7$, compared with $\chi_\nu^2 = 3.1$ for the standard three-flavour scenario. This best fit corresponds to an effective four-fermion coupling $g_{Z^\prime}^2 \varepsilon / m_{Z^\prime}^2 \approx 6.6 \times 10^{-23}\,{\rm eV}^{-2}$, approximately $5.7$ times the Fermi constant, equivalent for $\varepsilon \approx 1$ and a reference mediator mass of $1\,{\rm eV}$ to a gauge coupling $g_{Z^\prime} \approx 8\times 10^{-12}$. We also present projections for forthcoming experiments: the Jiangmen Underground Neutrino Observatory (JUNO), operating since August 2025 with world-leading precision on oscillation parameters, together with the XLZD consortium, should substantially refine these constraints. Such ultra-light particles may address long-standing discrepancies in galaxy simulations within the cold dark matter paradigm, whilst terrestrial long-baseline neutrino experiments provide complementary probes of this parameter space.

We establish Bourgain–Brezis selection maps for Hodge systems in new ranges of Besov and Triebel–Lizorkin spaces. Our approach combines the trace-free Beurling–Ahlfors transform with a nonlinear duality method. To control concentrations, we use tools developed by Stolyarov in the study of Maz'ya's $\Phi$-inequalities. These methods yield selection maps in Besov spaces $\dot B^{n/p}_{p,q}(\mathbb{R}^n)$ for every $1\leq q\leq p\leq 2$, and in Triebel–Lizorkin spaces $\dot F^{n/p}_{p,q}(\mathbb{R}^n)$ for every $1<p\leq q\leq 2$. The theorems hold for every dimension $n\geq 2$ and every form degree $1\leq l\leq n-1$. Although our results overlap with some earlier work, they considerably extend the known range of solutions to the Bourgain–Brezis problem and underscore the importance of the trace-free Beurling–Ahlfors transform in its resolution.

Outcome-only reinforcement learning gives software engineering (SWE) agents a terminal success signal but little direct guidance about intermediate decisions. We introduce Counterfactual Rollout Replay (CRR), a training-time procedure that uses forkable executable environments to obtain step-level return contrasts. CRR selects a small set of decision points, restores each state, samples an alternative action, and rolls the branch forward under the policy. It retains the realized training trajectory and replaces the advantage at selected steps with the difference between its terminal return and the sampled counterfactual return. The method needs no human process labels or learned process reward model; free refers to those supervision costs, not replay compute. With a 14B policy, CRR improves pass@1 on SWE-bench Verified, SWE-bench Live, and SWE-rebench, and combines with process-reward and trajectory-search methods. On SWE-bench Verified, an equal-wall-clock comparison on the same hardware yields 41.7% versus 36.7% for extended vanilla (outcome-only) GRPO, a 5.0-point gain with fork overhead included. These results apply to environments with affordable, reliable state restoration; stochastic continuations and expensive or imperfect replay remain limitations.

JET uses pretrained language and vision-language models to select among a finite set of answers without additional training. It evaluates candidate likelihoods directly and shares computation across candidates. Experiments on desktop CPUs and consumer GPUs assess decision accuracy and execution cost. Qwen3.6-35B-A3B achieves 87.48% accuracy on the full MMLU test set and 3.69 requests per second on a separately timed MMLU subset. The accuracy-throughput comparison covers model, hardware, and reasoning choices, with Jev as an external reference. Controlled execution experiments show 2.18-2.23-fold speedups from prefix reuse and cache management, and a 30.8% reduction in process time from input preparation optimizations, with unchanged outputs. Optional reasoning has a task-dependent accuracy-throughput trade-off. These results support local decision inference from existing models.

We can associate a compactness principle $\mathcal K_{\mathcal{D}}$ to the Constraint Satisfaction Problem (CSP) with constraint library $\mathcal{D}$. These principles were studied by Katáy, Tóth, and Vidnyánszky and by Rorabaugh, Tardif, and Wehlau. We expand their work comparing the strength of $K_{\mathcal{D}}$ for varying structures $\mathcal{D}$. We characterize the structures whose compactness principles are provable from ZF; these turn out to be the width-1 structures. We compare some important compactness principles, namely those of $2\text{SAT}$, $3\text{LIN}2$, and $K_2$, settling a question of Katáy, Tóth, and Vidnyánszky. And, we find an infinite chain and an infinite anti-chain of compactness principles related to directed cycles and finite choice.

Robotic manipulation policies are advancing rapidly with increasing reliance on vision-language models for end-to-end decision making. However, reliable deployment remains challenging because many policies lack explicit mechanisms for predicting task outcomes and evaluating whether generated actions will achieve desired final states, causing execution errors to accumulate during long-horizon manipulation. We present Robot-GST, a geometry-aware spatio-temporal behaviour representation and evaluation framework that constructs a Gaussian-SAM robotic environment for real-to-sim policy verification and improves the reliability of real-world manipulation deployment. Our approach constructs a high-fidelity robotic environment from RGB-D observations using 3D Gaussian Splatting and SAM3D, enabling “simulation and evaluation before acting”. It integrates visual observations and language instructions with spatio-temporal reasoning for long-horizon task planning using large vision-language models. To bridge high-level planning and real-world execution, we introduce Gaussian-aware final-state estimation through geometric sampling and state-based trajectory planning. Before execution, candidate action sequences are simulated and evaluated in the Gaussian-SAM environment to filter infeasible behaviours. We validate our approach on representative manipulation tasks involving rigid, soft, and deformable objects, including cube placing, toy packing, and duck rearrangement, demonstrating that geometry-aware spatio-temporal reasoning and state-aware execution improve manipulation reliability across different object categories. Our results suggest that combining geometry-aware reconstruction with high-quality rendering and simulation provides a scalable approach for evaluating robotic manipulation behaviours. Website: https://robot-gst.github.io

The collective behaviour of large language model (LLM) societies is not the sum of their individual outputs. It yields statistically distinct, sometimes-unpredictable phenomena, for which the tools we use to study single agents may not scale. Due to recent incidents involving autonomous agentic systems, however, understanding these systems is paramount. For that we introduce a framework for measuring self-organisation in LLM social systems and apply it to three such systems: a Schelling grid, a social network (Moltbook), and a Twitter-like misinformation simulation ('Rogue'). All three exhibit statistically significant self-organisation. Moreover, their relaxation dynamics vary with the environmental information available to the agents, with open-ended systems (Moltbook, Rogue) exhibiting sharp, phase-transition-like dynamics. Further results show that population-level pathologies can emerge even when the LLMs are safety-tuned or monitored, being primarily driven by the coordinated activity of a population subset. We also show when self-organisation does not emerge under two additional scenarios (a commons dilemma, GovSim, and a LLM-as-a-judge deliberation scheme, ChatEval). We argue that measuring signatures of this kind offers a lightweight, agent-agnostic diagnostic layer for detecting coordinated collective behaviour in deployed multi-agent systems without relying on natural language or model versioning.

LLM agents increasingly solve long-horizon tasks by autonomously interacting with their environment. In doing so, their strategies rely on assumptions about that environment: which resources and tools exist, where they are located, and how they behave. When these assumptions no longer hold, reliable agents must detect the change and adapt while pursuing the same goal. We study this adaptation capability through environmental novelty: a change that keeps the task objective fixed while invalidating an assumption underlying an otherwise successful trajectory. We introduce AGNI, an automated pipeline that extracts trajectory-relevant assumptions, injects targeted environmental changes, and validates that the resulting novel tasks remain solvable. Across three terminal benchmarks, AGNI produces diverse novelties spanning resources, interfaces, constraints, and execution semantics. Evaluating multiple LLM agents reveals a substantial adaptation gap between base and novel tasks. Trajectory analysis suggests that agents often encounter evidence of the change but fail to diagnose its cause and revise their strategy. Finally, post-training for environmental novelty improves adaptation to held-out novel tasks while also improving performance on base tasks. Our results highlight a gap between task competence and adaptive capability and motivate environmental variation as a core dimension of agent training and evaluation.

We show that a heavy higgsino $\tilde h$ with mass $m_{\tilde h}\sim0.1~{\rm PeV}$, which can be made consistent with the recent LUX-ZEPLIN event avoiding constraints from direct and indirect detection, can account for the present cold dark matter abundance of the universe, if the reheating temperature is bounded as $T_{\rm rh}\lesssim 595~{\rm GeV}$. These values can be achieved by a possible out-of-equilibrium decay of a modulus $\phi$ with mass $m_{\phi}\gg m_{\tilde h}$ and a non-vanishing branching ratio into $\tilde h$'s which plays a decisive role in reducing $T_{\rm rh}$ below its upper limit via the non-thermal $\tilde h$ production. The modulus $\phi$ can be identified with the scalar component of the goldstino superfield which is involved in the generation of the $\mu$ parameter of MSSM (with $\mu\simeq m_{\tilde h}$) via the Giudice-Masiero mechanism.

Conformal prediction provides marginal coverage guarantees, yet practitioners may wonder if the observed coverage is truly abnormal or consistent with sampling variation. Inference for realized coverage has received comparatively little attention, especially for time series. We study split conformal prediction with adjacent calibration and test sets of temporally dependent data. Using the functional dependence measure, we derive non-asymptotic bounds on marginal coverage error without mixing assumptions, which can be difficult to verify and may fail even for simple short-memory models. We establish a Bahadur representation to derive, to our knowledge, the first central limit theorem for realized coverage of split conformal prediction under temporal dependence. A consistent block-based estimator of the standard error yields an asymptotically justified test. We further study long-memory time series, which remain understudied in conformal prediction. For Gaussian linear processes, we show how very strong temporal dependence can lead to a non-Gaussian limiting law of realized coverage and establish block-sampling inference with an estimated normalization. The resulting theory explains how temporal dependence changes coverage uncertainty.

LLM-based agents can improve themselves across tasks by reusing and revising the skills they orchestrate into executable procedures. Flow-based training fits this loop: it samples procedures in proportion to reward, and the flow through each skill credits it for the next library revision. Three obstacles stand in the way of making this self-improvement reliable: flow training suffers strategy collapse over tree-structured histories; nonnegative flow-based credit rewards frequent use as if it were benefit; and library edits rest on the task reward the policy optimizes. We introduce R$^2$ Flow, a recursive self-improvement framework that alternates policy learning, independent verification, and versioned skill-library updates on a shared-state orchestration graph. The graph merges histories that differ only in the order of independent steps, allowing flow training to pool evidence across equivalent executions. A flow-share readout of the trained flow, invariant to the backward policy, and a separate signed utility rank which skills to change, verifier evidence decides whether an edit is warranted, and a residual-variance plateau sets when to update. Committed edits reshape the graph the next policy learns on, realizing recursive skill evolution. Across question answering, mathematical reasoning, interactive decision making, and code generation, R$^2$ Flow improves task accuracy and library-edit precision over heuristic orchestration, reinforcement learning, and skill-evolution baselines, and transfers across executors. Code is available at https://github.com/beita6969/r2flow.