Papers

An agent that moves must recognise a place from a viewpoint it has never seen. We introduce 4MT-VLM, a dataset of procedurally generated landscapes, each rendered across five stimulus modes that remove appearance cues while holding layout fixed: shape and colour, shape only, colour only, bare terrain peaks with no objects, and a valley viewpoint that puts the peaks on the horizon. The last condition is commonly used in clinics to probe hippocampal function in human patients. We test this benchmark across sixteen different open and closed-source models and report 4AFC performance, a measure which is also used to grade human participants. We observe that models identify a place from the studied viewpoint but lose it once the camera moves, dropping below the 25% chance level at 135{\deg} where a human observer scores 85%. Frontier models (Gemini 3.8 Flash, GPT-5.6) answer only 39% and 31% of rotated trials correctly, recovering to 85% and 55% only when distractors are moved more than 30 meters apart. Our benchmark demonstrates that while current VLMs possess rudimentary cognitive maps, their spatial resolution remains fundamentally too coarse to maintain a stable, 3D understanding of the world once the viewpoint changes.

We introduce the Dual-state Sparsifying Recurrent Unit (DuSpaR) as a computationally efficient building block for speech processing models on resource-constrained edge devices. It employs dual-state recurrence to modulate its input vectors in a stateful feedback loop. Its recurrent cells sparsify the input vector operand involved in matrix-vector multiplication using ReLU activation. By skipping the zero entries dynamically, inference-time savings in multiply-accumulate operations and weight memory fetches can be achieved. We evaluate DuSpaR on three speech tasks: keyword spotting (KWS) on the Google Speech Commands dataset, spoken language understanding (SLU) on the Fluent Speech Commands dataset, and speech enhancement (SE) on the Voice Bank + Demand (VBD) dataset. At similar parameter counts, DuSpaR requires 51.0% and 68.4% less computation than Gated Recurrent Unit (GRU) on KWS and SLU, respectively, while achieving higher accuracy, and 50.1% less computation on SE while maintaining similar quality. At comparable computational cost and across a range of model sizes, DuSpaR also achieves higher KWS/SLU accuracy and better SE quality than other sparsity-aware recurrent models. Ablation studies show that compared with the single-state recurrence baseline, dual-state recurrence reduces the effective compute by factors of 3.1 to 11.3 at similar task performance.

We study nonlinear scalarization of Schwarzschild black-holes for a phantom scalar coupled to the Gauss–Bonnet invariant. Three polynomial couplings satisfying $\zeta''(0)=0$ are introduced to investigate its nonlinear coupling dependence. Since the phantom factor $\epsilon$ disappears in the probe scalar equation, its nonlinear evolution is the same as in the canonical scalar theory. We construct nodeless probe solutions and fully backreacted two branches of lower and primary. At equal mass and equal temperature, respectively, the lower branches have higher Wald entropy and lower Helmholtz free energy than primary branch, but their heat capacities are negative. This implies that lower branch favors than primary branch. Finally, we show that there is no nonlinerly stable scalar phase for a phantom kinetic theory.

World models offer a promising way to help robots understand how the physical world evolves and plan complex behaviours through imagination. Yet existing studies mainly demonstrate what these models can accomplish, leaving unclear when their predictions remain useful for planning and where they fail. We study this question using action-conditioned predictors built on five frozen self-supervised visual backbones: V-JEPA 2, V-JEPA 2.1, VideoMAEv2, VideoPrism, and DINOv2. We use frozen backbones to test representations intended to transfer across environments. We evaluate these models on diverse Meta-World manipulation tasks and real-robot interactions from BridgeData V2. We find that a world model guides action selection reliably only when the goal lies within, or slightly beyond, the trajectory it imagines during planning. With five-step rollouts, the length the predictor was trained on, the world model ranks actions reliably only for targets five to ten control steps ahead, whereas task goals lie 16 to 53 steps away. Neither an 81-fold larger predictor nor longer-rollout training extends this range; the encoder affects both range and closed-loop success, with V-JEPA 2.1 performing most consistently. More fundamentally, the limit persists under perfect prediction: using the real simulator, success falls from 92% to 41% as the target moves from five to twenty steps ahead of a five-step rollout. Planning therefore requires either longer imagined trajectories or closer subgoals. For distant goals, pure imagination succeeds in 23% of episodes, planning with feedback (MPC) raises success to 30%, imagining as far as the goal to 47%, and nearby expert subgoals to 76%. Used within its plannable range, a world model can also improve a vision-language-action (VLA) policy: choosing among eight actions the VLA proposes raises its success from 65% to 77% across 16 different tasks.

Position verification, introduced by Chandran et al. (SIAM J. Computing 2014), allows verifiers to test a prover's claimed position by an interactive protocol. Classical position verification is impossible. Even for Quantum Position Verification (QPV), there always exists an LOCC (Local Operations and Classical Communication) attack if the adversary can hold an exponentially large amount of preshared entanglement. Somewhat surprisingly, we show that we can circumvent this barrier in the idealized continuous-time model, where time is represented by a real-valued parameter and challenge messages can be sent at a time sampled uniformly from a real interval. In this model, we give a BB84-based protocol that remains secure against any finite coalition of LOCC adversaries with arbitrary finite (possibly exponential) quantum storage and entanglement. Our construction can also be instantiated in the discrete-time model. Even though the previous impossibility results apply, we are able to obtain an information-theoretic QPV protocol in which the honest parties' total resources (communication and storage) can be significantly smaller than the adversarial resource bound. In fact, we can achieve any desired polynomial gap between honest parties and adversarial resources. To our knowledge, all previous protocols in the literature required resources of the honest parties to be at least as large as the adversarial entanglement. Interestingly, the resource gap between the honest and adversarial party resources in our protocol depends on how precisely time can be measured. As the precision of the best-known clock improves with further research, the resource gap in our protocol keeps increasing. In particular, the adversarial resource bound keeps increasing while the honest parties' resources remain largely the same. We call this the "I sleep, you work" paradigm.

We present multitable and its Rust reference implementation: a stable hash table both materially faster at equal physical memory and more flexible than the SwissTable in its Rust's hashbrown implementation. As an arithmetic mean over 84 configurations it delivers $\mathbf{2.1\times}$ hashbrown's throughput when both hash the same raw bytes and $\mathbf{1.9\times}$ when hashbrown is keyed on native integers, its best case; on negative lookups alone, $3.2\times$ and $2.9\times$. Multitable reaches any physical load factor up to and including one ($0.9999$ demonstrated), exactly for the requested capacity, compared to hashbrown which doubles at $0.777$ for 4-byte keys and values. At $75\%$ saturation of hashbrown (assumed average case of its rigid ladder) and multitable sized to $0.97$ physical load factor, hashbrown takes $66\%$ more space. The lookup probe count has no cliff as the load factor approaches one. Bucket size, physical load factor, and failure budget are parameters, and the multitable can be grown without rehashing. We implement two variants of multitable: plain and filtered. At equal physical memory on an Apple M2 Pro the filtered multitable leads hashbrown in all $84$ insert, hit, and miss configurations. Multitable is more memory-efficient, at equal mixed-lookup throughput on the map of $4$-byte keys and values the filtered multitable needs up to $12\%$ fewer bytes than hashbrown, and the plain multitable is $18\%$ smaller, holding $\mathbf{22\%}$ more keys in the same memory.

EDF relies on continuous monitoring of its power plants to detect anomalies as soon as they occur. Given the absence of a universally optimal streaming method in unsupervised settings, we compare streaming methods with state-of-the-art TSAD models deployed online on a real nuclear power plant dataset. This work also evaluates Automated Anomaly Detection in a streaming context. Results show higher consistency for online TSAD and strong robustness from ensembling strategies.

In mean-field theory, the ground state of a two-component Bose-Einstein condensate (BEC) in a uniform system is either uniformly mixed or totally separated. Beyond-mean-field effects introduce an additional phase, the mixed-bubble state, in which the two components remain mixed within one of the separated domains. Here we show that a mixed-bubble state can emerge in a binary mixture of spin-1 ${}^{7}{\rm{Li}}$ and ${}^{23}{\rm{Na}}$ BECs even within the mean-field framework. We further demonstrate the existence of a metastable uniformly-mixed state, which undergoes a transition to the mixed-bubble state triggered by a local perturbation.

We develop a multi-view linear-programming framework for locally recoverable codes with arbitrary fixed availability $a$. For any retained order $1 \le s \le a$, the selected helper sets, the recovered coordinate, and their complement form an $(s+2)$-part partition. Recording the Hamming distance on all blocks preserves both compatibility among the selected repair alternatives and their coupling with the remaining coordinates. The resulting joint distribution satisfies centered counting identities, product-Krawtchouk positivity, and collision inequalities from the local-distance condition; for fixed $s$, these constraints give a polynomial-size relaxation for arbitrary, possibly nonlinear, codes over any finite field. Retaining one view recovers the three-block model of our companion paper. We develop the first genuinely multi-view case, $s=2$, in detail and specialize the exact computations to availability $a=2$. The resulting four-block LP projects to both the one-view three-block model and a globally conditioned two-view relaxation, making explicit the information lost by each coarsening. Exact rational primal-dual certificates together with checked constructions prove $M_{\max}(2,8,4,2,2,2)=8$, $M_{\max}(3,7,3,2,2,2)=27$, and $M_{\max}(4,7,3,2,2,2)=64$; in all three cases the four-block bound is strictly stronger than both coarsenings.

Automatic evaluation of faithfulness increasingly relies on a large language model acting as a judge, yet the most reliable judges are proprietary frontier models, costly and ill-suited to high-throughput monitoring. We investigate whether a panel of cheap open-weight judges (4–9B) can be aggregated to stand in for a frontier one, what the substitution sacrifices, and when it is worth making. We propose RAIM, an aggregation scheme robust to the members' correlated errors, coupling a cross-fitted stacked logistic regression with an admissibility test that, read from the members' own outputs, identifies when aggregating them improves on their best member and stays within reach of the frontier judge. We instantiate RAIM with ten judges from disjoint families across eight faithfulness benchmarks. Against Claude Sonnet, the panel retains a median 93% of its Cohen's $\kappa$ and gives up only 2.9 points of balanced accuracy on average; read as paired differences, it clearly improves on one benchmark and clearly worsens on three (only two by a non-negligible margin), leaving four unresolved. At a sixty-fourth of the frontier's inference price, the operative expense is a one-time in-domain calibration on 50–100 labelled records. The panel is also competitive with purpose-trained detectors on their home benchmarks (within 1.3 accuracy points of GPT-4o and 1.9 of the LLM-AggreFact leader), and beats the strongest one we reran by 6 points on our grounded sets. Whether aggregation pays depends on the members themselves: where several capable members err on different items, the panel improves on its best judge and approaches the frontier; where one dominates, the stacker recovers the leader, and only there does the frontier remain materially ahead. Both conditions are read off the calibration set at no further cost, so a cheap panel can stand in for a frontier one wherever this audit admits it.

We present FYAN, a human–AI harness for document-level mathematical formalization. Rather than treating theorems in isolation, FYAN coordinates an end-to-end workflow spanning specification, proof planning, logical review, Lean proof construction, knowledge curation, and validation, with support for independent supervision and human guidance. A central component is evidence-grounded semantic auditing, which assesses whether formal statements faithfully preserve their informal specifications. A language model constructs structured evidence over local correspondences, omissions, scope, and logical relations, while a deterministic validator checks this evidence and produces reproducible judgments. When a substantive but admissible deviation is accepted, FYAN requires an explicit proof-transfer obligation connecting the formal statement back to a source-facing interpretation. With the same model (DeepSeek-V4.1-Flash) in every stage, FYAN proves 86 of 143 FormalTCS theorems under a strict Lean check, against 69 for a general agent harness, and raises the natural-language proof score from 0.501 to 0.851. On ConsistencyCheck, its semantic audit catches more inconsistent statements than a direct LLM judge, both on labels verified against the source (recall 0.777 vs. 0.636) and on the original labels (0.873 vs. 0.820), and localizes each mismatch it reports to a specific hypothesis, conclusion, or scope. FYAN also built ODENumLib, a 9,355-line Lean library for the numerical analysis of ordinary differential equation.

Over a century ago, Henri Poincaré argued that a motionless observer cannot acquire the notion of space. Yet, most visual representation learning methods operate on individual images, while those that leverage multiple views rely on RGB reconstruction, entangling geometry with appearance. We propose Poincar3, a self-supervised method that learns representations from multiple views through self-distillation instead of RGB reconstruction. We combine masked patch and image-level distillation with a teacher that observes additional views, enabling training from scratch without explicit 3D supervision. Poincar3 outperforms both previous single and multi-view self-supervised approaches such as DINOv3, MuM, and Muskie on correspondence estimation, camera pose estimation, and 3D reconstruction. Using a lightweight Poincaré adapter, we also find that our learned features encode camera motion more accurately than existing self-supervised representations.

Random circuit sampling is a leading approach to demonstrating quantum computational advantage, but benchmarking noisy implementations through linear cross-entropy requires costly calculations of ideal output probabilities. We propose a metrological benchmark based on the response to controlled perturbations, characterized by quantum Fisher information (QFI). A relation between QFI and out-of-time-order correlators enables protocols with local or global control. For Haar-random circuits, the average QFI approaches its maximal value in the local protocol and grows linearly with the number of qubits under collective control. In contrast, Clifford circuits yield zero QFI despite extensive operator spreading, showing that the response probes dynamical properties beyond spreading alone. A butterfly protocol further uses system size to enhance sensitivity, yielding a mean inverse sensitivity proportional to the number of qubits with single-qubit readout. Its fluctuations distinguish the Haar and Clifford ensembles despite their identical mean responses. For noisy implementations, we derive an exact relation between the noisy and ideal QFI within a global white-noise model, providing a quantitative reference for the degradation of the benchmark. These protocols enable metrological benchmarking of noisy random quantum circuits without computing ideal output probabilities.

Argument structure prediction (ASP) constructs complete argument structures from discourse by identifying argumentative units and their relations. While recent work has explored diverse approaches—including unified neural models, multi-step pipelines, and prompt-based large language models (LLMs)—their relative trade-offs remain under-explored, particularly in dialogical settings. We present a systematic evaluation of ASP under strict schema constraints, comparing supervised fine-tuning and prompt-based LLMs across single- and multi-step task architectures, generating complete argument structures from dialogical input end-to-end. We benchmark them on three diverse dialogical corpora adapted from Inference Anchoring Theory into bipolar argument structures. Under a shared evaluation framework, we assess predictive performance, cross-domain generalization, schema compliance, and computational efficiency. Our results show that ASP remains a challenging task, with identifying argumentative relations emerging as the primary bottleneck, largely due to the implicit and context-dependent nature of dialogical argumentation. To facilitate future research, we release our data processing pipeline and end-to-end modeling framework for computational ASP on dialogical corpora.

The discovery of the binary neutron star merger GW170817 and its electromagnetic counterparts marked the beginning of the era of multimessenger gravitational-wave astronomy. In contrast, binary black hole (BBH) mergers, which constitute the majority of gravitational-wave sources detected to date, are generally expected to be electromagnetically dark. However, if BBH mergers occur within the dense gaseous environments of active galactic nucleus (AGN) accretion disks, interactions between the merging black holes and surrounding gas may produce electromagnetic emission across multiple wavelengths. AGN disks may therefore provide a natural multimessenger laboratory for studying BBH mergers and their astrophysical environments. A key question is whether such a scenario is supported by current observations and whether the associated electromagnetic signatures are sufficiently distinctive and detectable. In this review, we summarize the current theoretical and observational status of BBH mergers in AGN accretion disks, focusing on the evidence for their occurrence, the physical mechanisms and expected signatures of electromagnetic emission, and searches for candidate counterparts. We also discuss the major challenges in identifying and confirming these associations and the prospects for future multimessenger observations with current and forthcoming multiwavelength facilities.

Large language model (LLM) inference is increasingly moving toward lower precision to realize the throughput of hardware accelerators, but aggressive post-training quantization (PTQ) can degrade model quality. We present QATFactory, an open-source framework for deployment-aligned quantization-aware distillation (QAD) and reinforcement learning (QARL). QATFactory simulates deployment-time quantization while performing matrix multiplications in BF16, allowing models to adapt to quantization noise without requiring training hardware that natively supports the target format; for example, it supports NVFP4 training on H100 GPUs, which lack FP4 Tensor Cores. The framework supports NVFP4, MXFP4, and $\text{llama}.\text{cpp}$'s Q4_K format; dense and mixture-of-experts models; and both full-parameter and LoRA-based training. It exports checkpoints directly to vLLM and $\text{llama}.\text{cpp}$ without an additional lossy conversion step or added inference overhead. With QATFactory, we conduct extensive experiments on models ranging from 8B to 230B parameters and evaluate exported checkpoints in production inference engines. Across models and formats, QAD consistently improves deployed-model quality over strong PTQ baselines. On Qwen3.5-9B, QAD achieves average benchmark accuracies of 68.9% under NVFP4 and 66.0% under MXFP4, outperforming the best PTQ results of 65.4% and 56.4%, respectively. Through our experiments, we found that although both FP4 formats quantize weights and activations at deployment, the best training strategy is format-dependent: NVFP4 generally performs better when only weights are quantized during training, whereas MXFP4 benefits from quantizing both weights and activations. At a fixed training token budget, training on fewer 32K sequences improves average accuracy by 1.9 points over training on more 4K sequences.

High-compression tokenizers are essential for scaling latent image generative models. However, aggressive compression creates a fundamental tradeoff between reconstruction fidelity and generation efficiency: high compression image encoder always increases the learning difficulty of diffusion training, resulting in slow model convergence. Recent representation autoencoders speed up the diffusion training by improving the latent feature's expressive capability by replacing VAE encoders with pretrained semantic encoders, yet they are typically limited to moderate compression and lose pixel-level details necessary for faithful reconstruction. To achieve both high compression and fast diffusion training, we propose DC-SAE, a Decoupled Compact Semantic Autoencoder designed for high-compression image generation with accelerated diffusion model convergence. DC-SAE consists of two key components: (1) a macro-level architecture design that leverages semantic encoders to enable higher compression ratios, and (2) a pixel-level encoder that preserves low-level details, ensuring high-fidelity image reconstruction. We empirically demonstrate that DC-SAE performs strongly on image generation tasks, achieving both compact latent representations and efficient training dynamics. Specifically, on the ImageNet dataset with $512 \times 512$ resolution, DC-SAE achieves $32\times$ spatial compression, with 29.79 PSNR and 3.37 gFID, substantially outperforming the previous state-of-the-art high-compression tokenizer baselines DC-AE by 13.5% and 54.9% on PSNR and gFID, respectively, maintaining comparable throughput and faster diffusion model training convergence. Beyond class-conditional generation, a $1.6$B-parameter DiT using DC-SAE achieves 0.84 on GenEval and 86.007 on DPG-Bench for text-to-image generation at $1024\times1024$ resolution.

Deep learning methods like neural networks have greatly simplified the computation of safety certificates for complex nonlinear systems with unknown dynamics. However, due to the data-driven nature of these certificates and the complex architecture of neural networks, computation time as well as robustness guarantees across unseen data remain a challenge. This work aims to formally verify safety properties of discrete-time unknown systems by synthesizing extreme learning machine (ELM)-based barrier certificates. Compared to neural network counterparts, this approach greatly improves convergence guarantees and computational time due to its architectural simplicity and the convex nature of the underlying optimization problem. By minimizing the Lipschitz constant of the candidate barrier, we present a grid-based sampling technique to formally verify its validity using the minimum number of samples required. We demonstrate through numerical examples the effectiveness of our approach, and compare with traditional deep-learning based certificate synthesis to highlight its benefits.

Process reward models (PRMs) have demonstrated notable effectiveness in test-time scaling and reinforcement learning by providing fine-grained signals for evaluating intermediate reasoning states, but their training relies heavily on costly process annotations. A natural way to alleviate this dependence is to complement limited process supervision with scalable outcome supervision. However, existing PRMs often model reasoning prefixes independently, providing no explicit mechanism for effectively using final outcome to guide the learning of intermediate reasoning states. We introduce Reasoning State Propagation (RSP), which represents each reasoning prefix with a binary validity state and models transitions between successive states across the reasoning trajectory. Specifically, RSP predicts a break probability that a valid state becomes invalid and a repair probability that an invalid state returns to valid. By propagating these transitions, RSP connects intermediate states to the final state, allowing process annotations to supervise intermediate states while outcome labels supervise the final state and can provide learning signals to preceding steps. Across reasoning search, response selection, and reinforcement learning, RSP consistently outperforms representative PRM baselines, with average improvements over Qwen2.5-Math-PRM of 5.6% in beam search and 2.1% in reinforcement learning.

We prove an annealed central limit theorem for the weight of the maximum weight matching on uniformly random simple graphs with prescribed, uniformly bounded degrees and i.i.d. exponential edge weights. In particular, the result applies to random $d$-regular graphs for every fixed $d \ge 2$. The proof separates the fluctuations arising from the edge weights from those arising from the graph. The correlation decay estimate of Lam and Sen (arXiv:2511.18861) yields Gaussian fluctuations for the former. The main difficulty is to analyze the fluctuations of the conditional mean of the optimal weight given the graph. To address this, we prove a stronger perturbative correlation decay estimate that, together with a variance bound, reduces the problem to the central limit theorem of Barbour and Röllin [Ann. Appl. Probab. 29(2) (2019)] for local statistics of the configuration model.

Let $H=\langle a_1,\ldots,a_n\rangle$ be a numerical semigroup. A conjecture on numerical semigroup rings predicts that the defining ideal $I_H$ has a determinantal presentation if and only if the set of pseudo-Frobenius numbers of $H$ has form $\{h+\alpha,h+2\alpha,\ldots,h+(n-1)\alpha\}$ for $h\ge 0, \alpha>0$. We prove this conjecture under the condition that $h$ has a unique factorization in $H$. We also give characterization this unique-factorization condition. As an application, we consider the family of affine-orbit numerical semigroups determined by $m=cA_{n-1}+1$, $1\le c\le a$. We prove that the relevant element $h$ has a unique factorization and the defining ideal is generated by the 2-minors of a $2\times n$-matrix. In particular, the Eagon–Northcott complex of the matrix mentioned above gives the graded minimal free resolution of $k[H]$.

Nikodym constructed a measure-zero Borel set in the plane that contains a punctured line segment passing through each point in the unit square. Fenton and Falconer asked whether a similar construction is possible when “lines through a point” are replaced by “circles or circular arcs with a prescribed center.” This was answered in the negative by Bourgain and Marstrand. We study generalizations of this question, in which “lines through a point” or “circles with prescribed center” are replaced by more general analytic families of plane curves. As a key ingredient, we prove new maximal function and local smoothing estimates for families of curves satisfying a multi-parameter analogue of Sogge's cinematic curvature condition; this allows us to establish the non-existence of Nikodym-type sets in certain specific settings. The result also resolves a local smoothing conjecture by the sixth author. In the other direction, we use a recent nonlinear generalization of Falconer's prescribed projection theorem to construct Nikodym-type sets in other specific settings. Combining these ingredients with tools from tame geometry, we precisely characterize when Nikodym-type sets exist for analytic families of plane curves.

Sound event localization and detection (SELD) aims to jointly recognize sound events and estimate their directions of arrival from multichannel audio. Although recent deep learning approaches have achieved strong performance, their ability to generalize across acoustic environments remains limited, as room reverberation introduces environment-specific characteristics into the learned representations. In this work, we address this challenge by leveraging a physical free-field model as a room-independent reference. Specifically, we propose PG-SELD, a training framework that combines free-field with physics-guided knowledge distillation. Our approach aligns intermediate representations extracted from reverberant signals with those produced by a free-field teacher for matched acoustic scenes. This guidance encourages the model to preserve event- and localization-relevant information while reducing sensitivity to room-specific characteristics. Experimental results on the STARSS23 benchmark show that PG-SELD consistently improves the generalization performance of multiple baseline SELD architectures.

Time series anomaly detection (TSAD) is increasingly deployed in streaming settings, where data arrive sequentially and may exhibit non-stationarity. As a result, several works from the recent literature propose streaming anomaly detection methods that rely on incremental updates to adapt over time. However, most of these approaches originate from the streaming outlier detection literature and largely ignore core characteristics of time series anomalies. Moreover, their empirical evaluation is typically conducted on synthetic or small-scale benchmarks with limited diversity, making it unclear whether streaming methods are truly advantageous in realistic TSAD scenarios. In this work, we carry out the first large-scale experimental study comparing streaming and static TSAD methods under a unified streaming evaluation benchmark. We consider a realistic setting in which an initial batch of data is available for model training, followed by online evaluation of both detection accuracy and computational efficiency. In addition, we propose a distribution-drift dataset of real time series, called TSB- drift, to isolate scenarios where streaming updates are theoretically justified. Our results show that, contrary to common assumptions, static TSAD methods significantly outperform streaming approaches in most streaming settings. Such finding highlights a critical gap between the design of existing streaming methods and the requirements of modern TSAD, and calls for a rethinking of how streaming capabilities should be integrated into TSAD.

The Future Circular Collider (FCC), in its leptonic configuration has been chosen by CERN as main proposition for the next high-energy collider. This project aims to achieve luminosities one to two orders of magnitude higher than ever. Feasibility studies have led to the definition of tolerances on magnet imperfections and correction strategies. This is crucial for ensuring the performance of one of the main elements of the acceleration chain, the High Energy Booster (HEB) ring. The efficiency and overall performance of these strategies greatly influence new magnet specifications and tolerances, affecting main optic functions. Horizontal and vertical orbit corrections use horizontal and vertical kickers, respectively. Skew quadrupoles address vertical dispersion and transverse coupling. Normal quadrupoles correct the horizontal and vertical phase advances. This study simulates the distribution of these four corrector types to minimize the equilibrium emittance at the extraction energy of 45.6 GeV. The calculated strengths of these correctors and the associated misalignments are presented. The study also discusses the limitations and drawbacks of the proposed correction strategy.

This survey presents heat kernel regularization as a method for quantitative stability of Kantorovich potentials for the quadratic transport cost. We give a complete new heat kernel proof on Heisenberg groups equipped with the Carnot–Carathéodory distance. For source densities bounded above and away from zero on bounded John domains, we obtain $L^2$ stability with rate $W_1^{1/2}$ for arbitrary targets in a fixed compact set, including atomic measures. We also establish a new $L^2$ stability estimate on finite-dimensional RCD spaces, with the optimal dimension-independent exponent $1/2$.

We study additive regression under an unknown and potentially non product design distribution, allowing the number of covariates to grow with the sample size. We consider a coupled class that separately controls the smoothness of the marginal densities and of each additive component multiplied by the corresponding marginal density. Under joint-density bounds that hold uniformly in the dimension and suitable dimension-growth conditions, we establish matching minimax bounds for prediction. With known marginal densities, the classical additive rate is attainable. When the marginals are unknown, this rate is preserved if the densities are at least as smooth as the weighted components. Otherwise, marginal-density smoothness determines the minimax rate over the coupled class. Finally, we recover all additive components with total squared error of the same order as the prediction error.

Large Language Model (LLM) agents are increasingly deployed as populations of interacting entities, in which consensus –agreement on a shared answer– emerges as a collective, unengineered behaviour. Prior work on LLM consensus shows that agents can cross-verify their answers and converge towards more factual responses, treating agreement as a proxy for correctness. However, these studies usually fix a single interaction structure, leaving open how consensus depends on how agents interact. We address this gap by introducing RHEON, a physics-inspired framework that recasts a population drawn from a single frozen model as an evolving $O(n)$ spin system on a ladder of interaction geometries of increasing effective dimension –from a 1D ring to a full-coupling mean-field graph– with the sampling temperature $T$ as the tunable source of thermal disorder, evolved through a Glauber-like asynchronous dynamics. Sweeping RHEON across $432$ configurations of prompt, population size, communication topology, and sampling temperature yields Eraclitus-4.7M, a tagged evolutionary corpus of $4.7$ million responses. We find that agents reach their strongest consensus gain within the first few update sweeps and that increasing the number of neighbours per agent accelerates convergence on average. We further show that whether a configuration settles on factually correct or hallucinated consensus is not predictable from its initial state alone, and that the hallucination-minimising temperature depends on how the agents are coupled, so the common near-greedy default is not automatically the safest. Finally, semantic agreement correlates positively with factual convergence, and interaction strengthens the association, yet never enough for unanimity to certify correctness.

In fixed-source Monte Carlo particle-transport problems, obtaining an acceptable variance on the sought response is of paramount importance. Currently, the only rigorous tool to analyze the variance of such games is the framework of the moment equations, which is unfortunately unwieldy to use in practice. In this paper, we establish a formula that enables expressing the variance of a Monte Carlo simulation as a sum of 'variance contributions' collected throughout the underlying particletransport process. This formula applies to both direct and adjoint games, and provides a new tool to pinpoint the variance-inducing mechanisms in Monte Carlo simulations, understand common variance-reduction techniques, and even conceive new ones. We showcase the use of the variance-decomposition formula on several applications. In particular, we revisit zero-variance schemes and analyze existing variance-reduction techniques, underlining their strengths and weaknesses. A few relevant numerical examples substantiate our theoretical findings.

Pulling a fixed set of fields out of documents that arrive in many formats and under drifting schemas is usually done with hand-written byte patterns, which break whenever a key is renamed, a value is reformatted, or a lookalike value appears first. We argue the cause is structural: one pattern must both describe the value and locate it among its surroundings. O-Funnel separates the two. It transcribes any XML, JSON, CSV, HTML or key-value text document into one typed tree over five constructors, gated by an oracle that rejects any capture that does not reconstruct its source. Each needed field is declared in the tree's own terms and located by fusing independent evidence (key, path, value shape, synonym, key spelling, record neighborhood, value profile), so the best-supported node wins and a missing field is reported with a reason. Data no requirement claims becomes residue that a funnel traces back to the requirements to learn new key aliases. On 34,989 real PubMed records, O-Funnel matches a hand-written parser (F1 1.00). After a five-element schema rename, the parser's regular expressions fall to 0.20 while O-Funnel stays at 1.00, with every capture verified complete. On constructed suites that isolate regex failure modes it raises F1 from 0.43 to 1.00, and from 0.80 to 0.94 after self-improvement; on held-out schema-matching instances it is competitive with classical matchers without training. O-Funnel is a dependency-free Python library (pip install ofunnel).