Papers

In this paper we prove in full detail the isomorphism between the solvable group $\mathcal{S}_{2,2+p}$, metric equivalent to the Calabi Vesentini symmetric space $\mathrm{SO(2,2+p)/SO(2)\times SO(2+p)}$, and the solvable group $\mathcal{S}_{\mathrm{L}(-1,p)}$ supporting the Kähler metric of the homogeneous non symmetric special manifold L$(-1,p)$. From an Alekseevskyan point of view the two spaces simply correspond to two different quadratic forms on the same solvable Lie algebra that we present and compare in detail. Furthermore considering the full group of isometries $\mathrm{Iso}_{\mathrm{L}(-1,p)}$ of L$(-1,p)$ we show that $\mathrm{Iso_{L(-1,p)}}\subset \mathrm{SO}(2,2+p)$ is a non-semisimple subgroup of the simple isometry group of Calabi-Vesentini manifolds. Altogether the Special Kähler manifold L$(-1,p)$ can be seen as a coset manifold $\mathrm{Iso_{L(-1,p)}}/\mathrm{H}$ where $\mathrm{H}=\mathrm{U(1)}_L\times \mathrm{SO(p)}$, the generator of $\mathrm{U(1)}_L$ being in $\so(2,2+p)$, yet not in the canonical $\so(2)\oplus\so(2+p)$ subalgebra. The action of $\mathrm{Iso}_{\mathrm{L}(-1,p)}$ on the solvable coordinates of the CV manifold can be constructed directly. This identification provides a valuable tool for Cartan Neural Networks, introducing additional non linear transformations in every map from one layer to the next one of an $r=2$ Neural Network based on the CV Tits Satake universality class; in perspective, this new tool increases expressivity.

We say that a graph is resistance nonnegative or RN if it admits a positive edge-weight that yields nonnegative resistance curvature in the sense of Devriendt and Lambiotte. Analogously, a graph may be resistance positive or RP; we say a graph is strictly RN if it is RN but not RP. In this paper, we show that every $2$-connected strictly RN graph is bipartite with parts whose sizes differ by one, demonstrating that there are no $1$-tough strictly RN graphs. As a consequence, we prove that every $1$-tough RN graph is also RP. Lastly, we quantify the exact toughness values an RN graph can attain below $1$.

Open-vocabulary object retrieval in videos requires answering free-form object queries under bounded query-time cost. Existing index-based systems typically store independent frame-level regions and retrieve them with vision-language similarity, which is effective for appearance queries but mismatched with predicates whose evidence is temporal or relational, such as stopped state, scene-region occupancy, persistence, and object interactions. We identify this gap as an evidence-unit mismatch: the query is expressed over tracklets or object tuples, while the index stores isolated boxes. To address it, we propose STEG-OVR, a structured spatio-temporal evidence graph for open-vocabulary object retrieval. STEG-OVR represents persistent objects as tracklet nodes and temporally compatible object pairs as relation edges, storing appearance, motion, scene occupancy, relative geometry, velocity compatibility, and symbolic relation evidence. A query is decomposed into entity, state, scene, temporal, and relation slots, which activate only the corresponding retrieval channels before soft score fusion and fixed-budget consistency verification. Diagnostic experiments on three object-centric settings show AP improvements from 0.0882 to 0.2073 on Beach, from 0.0834 to 0.1505 on Shibuya, and from 0.701 to 0.743 in a LOVO-style comparison. The gains are strongest for stopped-state and scene-region-occupancy queries, while sustained relations remain sensitive to tracking continuity and predicate calibration.

Underwater human–robot interaction requires gesture commands that are both easy for divers to use and reliable for robots to recognize. We investigate these aspects through a closed-loop diver–robot interaction framework integrating a compact seven-gesture vocabulary, lightweight landmark-based recognition, and command-level interaction logic. We evaluate the framework through a user study and underwater robot experiments in a laboratory tank and a swimming pool. The user study supported the reproducibility of the gestures after brief learning. Recognition analysis further showed that visual similarity was associated with gesture confusion, while intermediate poses during gesture formation introduced temporal ambiguity. Command-level processing mitigated the effects of transient recognition errors on robot execution, reducing unintended triggers and premature task interruptions. These findings show that reliable underwater gesture interaction depends on human usability, gesture recognizability, and execution reliability in underwater interaction.

Electrides, ionic crystals in which excess electrons are delocalized within interstitial voids rather than bound to specific atomic sites, exhibit exotic physicochemical behaviors, yet their potential as electrochemical energy-storage hosts remains largely unexplored. Here, using comprehensive first-principles calculations, we demonstrate that the quasi-one-dimensional subnitride electride Ba$_3$N offers a compelling route to overcome the long-standing performance trade-offs in sodium-ion battery anodes. Spontaneous Na intercalation into the open interchain channels establishes thermodynamically stable phases, generating an exceptionally flat low-potential plateau that avoids the high-potential sloping losses of hard carbon while preserving an essential safety margin against dendrite formation. Crucially, the itinerant interstitial anionic electron sea dynamically flattens the potential landscape by suppressing site-specific orbital interactions, enabling ultrafast Na ion transport with an exceptionally low migration barrier. This work establishes a design paradigm for harnessing electride chemistry to achieve ultrafast battery electrodes.

In this paper, we apply the resonance method to exhibit large values at the central point of the family of quadratic Hecke $L$-functions with prime-related moduli of the Gaussian field under the generalized Riemann hypothesis.

Consider an $N\times N$ random band matrix $H$ with bandwidth $W$ with centered real Gaussian entries. We prove that, under the (almost) sharp assumption $W^2\ll N/\log N$, the bulk local statistics of $H$ are asymptotically a Poisson point process. Combined with the bulk universality results from arXiv:2501.01718 and arXiv:2506.06441, this establishes the Poisson-RMT transition of the local statistics of random band matrices, and complements the results about the localization-delocalization transition of the bulk eigenvectors previously established in arXiv:2501.01718 and arXiv:2506.06441, and arXiv:2508.05802. The key technical inputs are: (1) the fractional moment estimates from arXiv:2508.05802; (2) a novel estimate for the density of states, obtained from the local laws in arXiv:2501.01718 and arXiv:2506.06441.

Periodic resource-block (RB) scanning leaves most of the current wideband channel unobserved and mixes measurements of different ages. We develop an online canonical polyadic tracker with proximal block updates (CP-PBCD) that reconstructs the full channel after each narrow-RB acquisition. Age-weighted finite histories, frequency and temporal regularization, and bounded component management maintain an adaptive low-rank representation. Two warm-started conjugate-gradient iterations and parallel shifted frequency solves provide a fixed per-frame update budget. Training-user spatial projection strengthens noise suppression at low pilot SNR. Experiments cover ten test users, three speeds, four SNRs, and complete 1000-frame trajectories with 1-ms RB acquisition. Direct first-RB CP-PBCD achieves lower mean normalized mean squared error (NMSE) than all six baselines in all twelve conditions. At 3.6 km/h and 20 dB, it improves on periodic physical refitting by 3.91 dB and runs 35.1 times faster, averaging 0.717 ms per online update. Optional dispersed startup pilots improve early acquisition, while a controlled initialization study yields a last-100-frame NMSE range of 0.427 dB across pilot budgets. These results demonstrate accurate current-channel reconstruction through incremental updates with submillisecond average computation.

Before a machine learning model can learn a thermodynamic equation of state, it must discover what its measurements represent: which channels scale with system size, which are intensive conjugates, how sectors pair through contact, and which potential governs stability. When sensors expose only an unknown linear mixture of extensive states and intensive responses, passive observations cannot disentangle physical quantities from coordinate artifacts. We formulate the problem of discovering this hidden thermodynamic ontology directly from anonymous controlled experiments. We present an operational identifiability theory and a constructive polynomial-time algorithm that extracts extensive and intensive scaling sectors from replication contrasts, recovers their dual cotangent pairing from thermal contact and reciprocity, verifies a globally admissible concave potential via discrete cyclic concavity, and determines an invariant matroid of reservoir ensembles. We prove that the residual observational equivalence is strictly (x, lambda) ~ (A x, a A^{-T} lambda + beta), establishing the sharp observational limit that no permitted experiment can break. Blind evaluations on van der Waals fluids and Curie-Weiss magnets confirm robust recovery under ill-conditioned mixing, correctly resolving anonymous Maxwell tie-lines while rejecting non-equilibrium continuations. External validation across six real fluids from the NIST WebBook demonstrates that operational ontology discovery transfers across real physical substances without coordinate leakage.

Text-guided 3D building generation holds tremendous application potential, yet existing generative models typically output inseparable single meshes or non-interactive rendered representations. While procedural modeling can generate editable buildings with hierarchical structures, rule authoring is laborious, and even with the aid of large language models (LLMs), it remains challenging to effectively solve procedural rules under geometric constraints. In this paper, we propose ProxyBuild, a novel hybrid framework for structured building generation. We introduce the Mesh-Anchored Procedural Proxy (MAPP) as a novel intermediate representation, which tightly anchors building components onto geometric shells, thereby decoupling the generation task into two phases: proxy prediction and proxy-to-asset instantiation. First, we construct a building dataset with MAPP annotations to train our designed face-edge bigraph encoder. By explicitly modeling the feature interactions of topological elements on heterogeneous mesh graphs, this encoder accurately infers the semantic roles of faces and edges. Subsequently, conditioned on textual styles and attribute parameters parsed by LLMs, we accomplish high-precision asset retrieval and assembly by integrating a spatial placement logic with hard constraints. Extensive experiments show that ProxyBuild not only significantly mitigates common issues in building generation such as over-smoothing, component collisions, and structural corruptions, but also accurately parses semantic-free shells from diverse sources. Outperforming prior baselines across various metrics, our method can robustly generate structurally clear, detail-rich, and post-editable 3D buildings from text, thereby providing a reliable and interactive content foundation for downstream applications such as virtual reality and digital twins.

Data acquisition (DAQ) systems at future particle physics experiments stand to benefit from the extremes of AI/ML development: large-scale foundation models can enhance the performance of feature extraction algorithms, and small-scale on-detector deployments can enable real-time intelligent data handling. This work provides the first fine-tuning of an industrial foundation model for particle physics DAQ. Starting from the backbone of Google Research's TimesFM (Time Series Foundation Model), we demonstrate fine-tuning on real-time regression tasks for drift chamber trackers and dual-readout calorimeters. Furthermore, the fine-tuned TimesFM model is distilled into a student and co-designed with FPGA implementation to enable these models to run in real-time at future colliders. The fine-tuned distillations meet or exceed the performance of previously published AI/ML solutions for each task. Further, the pipeline of distillation and model compression from TimesFM is generic and can be easily adapted to a variety of 1D waveform tasks across domains.

We realize a time-periodic quadrupole higher-order topological lattice and demonstrate its nonreciprocal radiation. A relative phase between two modulated coupling channels acts as a synthetic gauge field that breaks time-reversal symmetry without closing the bulk gap, and a numerical Floquet analysis finds that zero-quasienergy corner modes persist. With the corners coupled to free space, a signal injected at one corner is up-converted to the first Floquet sideband and radiated, and a free-space wave at that sideband is delivered preferentially to a second corner, with more than 21 dB contrast relative to the first, combining frequency conversion with nonreciprocal routing. The same radiated frequency is reached with modulation frequencies differing by more than an order of magnitude.

Bayesian filtering provides a principled framework for online state estimation under uncertainty, yet its application to systems with high-dimensional states and complicated posterior distributions remains challenging. Recent generative models, such as flow matching, have shown potential in Bayesian filtering. However, they still rely on particle-based representations of the posterior, which lose the rich information of the full distribution, or tackle a trajectory-level inverse problem that conflicts with the recursive structure of Bayesian filtering. To address this, we propose a new perspective of directly encoding the evolving distribution into flow matching model weights, namely, the Belief Flow Filter (BFF). It is a generative filtering framework that updates model weights via gradient descent at test time to track the posterior evolution. Thereby, BFF bypasses the scalability issue of particle representations or the flexibility limitation of Gaussian assumptions in conventional filters. We theoretically justify that the BFF design is structurally aligned with Bayesian filtering, and its training objective targets the recursive filtering operator. BFF is empirically verified across 5 different physical systems, including ones with chaotic dynamics and highly sparse, non-linear observations. The results show that BFF attains the best score in 8 of 9 metric-benchmark cells across the three standard 1D and 2D PDE benchmarks, and similarly leads on the extreme single-moving-sensor setting and on a real-world-grounded tokamak plasma estimation task, demonstrating its potential to accurately approximate the Bayesian filtering operator in high-dimensional probability space.

We investigate how the exceptional-point structure of a dissipative cavity optomechanical system is inherited by experimentally accessible dynamical, spectral, and quantum-statistical observables. At optical-mechanical resonance, the effective non-Hermitian first-moment dynamics exhibits a second-order exceptional point, where two eigenvalues and their eigenvectors coalesce and the eigenvalue splitting follows the characteristic square-root dependence on perturbations. We show that the same square-root feature also governs transient photon and phonon populations, first-order coherence, spectral poles, and second-order intensity correlations. Below the exceptional point, the dynamics is non-oscillatory, whereas above it damped oscillations emerge together with frequency splitting of the spectral poles. At the exceptional point, the Jordan-block structure produces polynomial-exponential relaxation and a second-order spectral pole. Using the quantum regression theorem and Gaussian moment factorization, we further show that the stationary fluctuations satisfy the Siegert relation linking first- and second-order correlations. Although the zero-delay autocorrelations retain their thermal value, the finite-delay intensity correlations exhibit clear exceptional point signatures. This finding connects non-Hermitian mode coalescence with measurable dynamical and correlation observables in cavity optomechanics.

Before a machine can discover a physical law, it must discover what its measurements are: which observations live on cells, which are intensive or extensive, which sectors are dual, and which distinctions are merely gauge. We introduce physical representation-language discovery, the problem of recovering this hidden ontology directly from anonymous controlled experiments. We give an identifiability theory and constructive polynomial-time procedure that recovers a carrier and differential sequence, measurement types and orientation twist, noninvertible refinement semantics, primal-dual Maxwell diagrams, and the residual equivalences that no permitted experiment can break. The theory turns material nuisance into a commutant, uses refinement to separate quantities from coordinates, and selects physics only after its representation has been recovered. For a certified finite experiment family, we prove an end-to-end two-stage measurement bound and a matching minimax rate in dimension, accuracy, and confidence. Blind Maxwell experiments recover complete primal/relative-dual ontologies on regular and unstructured carriers under jointly corrupted observations; an independent unstructured RLC system demonstrates that the result is not specific to Maxwell. The framework scales to tens of thousands of cells per carrier, while stress audits demonstrate robustness across severe physical regimes - including non-Markovian memory, nonlinearities, nonlocality, and complex constitutive hysteresis. A public FDTD audit demonstrates the emergence of anonymous curl structure from incomplete field data, while characterizing the informational prerequisites for complete recovery. The goal is to move scientific ML from learning laws in a human-supplied language to discovering the language in which laws become expressible, establishing exact theoretical limits on observational identifiability.

Gaussian Splatting has enabled real-time novel view synthesis, but its tightly coupled geometry and appearance representation often require a large number of primitives to reproduce high-frequency texture details, leading to substantial memory and optimization costs. Recent textured 2D Gaussian methods alleviate this limitation by attaching texture maps to Gaussian primitives. However, bridging the fundamental structural gap between discrete Gaussians and continuous 2D grids requires complex parameterizations that introduce severe computational overhead. This overhead fundamentally compromises the original efficiency of Gaussian Splatting, making the balance between detailed texturing and computational agility an unresolved challenge. To address these challenges, we propose LiteTex-GS, a fast and lightweight texturing framework for Gaussian Splatting. Our method initializes an extremely compact representation, assigning minimal local texture to each Gaussian and progressively allocates higher resolution only to primitives with significant reconstruction errors. To maintain a streamlined geometric scaffold, we introduce a contribution- and area-aware pruning strategy that eliminates low-utility Gaussians. Furthermore, to mitigate the gradient dilution caused by texture upsampling, we design a resolution-aware update rule that preserves rapid and stable convergence. Extensive experiments on standard novel view synthesis benchmarks demonstrate that our method achieves competitive or superior rendering quality while using substantially fewer parameters and less training time than existing textured Gaussian baselines.

We present a non-perturbative Ward-identity prescription for determining the flowed quark field renormalization factor $Z_\chi$, avoiding the computational difficulties of the conventional ringed prescription. The method is based on vector-current normalization and ratios of flowed and unflowed meson two-point functions. We determine the resulting $\mathring{Z}_{\chi}^{V}(t_f,a)$ on five $2+1$-flavor clover ensembles and validate it in the pseudoscalar, scalar, axial-vector, and tensor channels. Renormalized matrix elements obtained through sequential continuum and zero-flow-time extrapolations agree with independent RI/MOM and RI/SMOM determinations. The finite-lattice-spacing bilinear renormalization factors show differences that decrease toward finer lattices, reflecting the different discretization effects of the renormalization methods. The cross-channel agreement demonstrates the viability of the proposed prescription; together, the method and its systematic validation establish a robust foundation for the non-perturbative renormalization of flowed fermionic operators in future lattice calculations.

Recursive differenced forecasting, the standard remedy for non-stationarity, predicts one-step changes and integrates them by cumulative summation. We show that this reconstruction is a discrete integrator with a pole on the unit circle, so the biased increment errors of a learned nonlinear model are summed without bound and the rollout diverges: at 336 steps its normalised MAE reaches 1.6-3.8 for every neural architecture tested, against 0.80 for a stable linear recursion. We then introduce leaky-integrator reconstruction, a training-free fix that moves the pole inside the unit circle with H(z) = 1/(1 - gamma z^-1), gamma < 1, bounding the accumulation of the model's own increment errors. Applied post hoc with a single fixed gamma=0.9 (no retraining, a two-line change to any deployed one-step or foundation-model forecaster), it beats the traditional recursive integrator at every horizon, with the mean gain over seven diverging architectures and twenty datasets growing from ~3% at H=24 to 23% at H=96, 37% at H=192 and 51% at H=336 (43-75% across those architectures; 78% with an oracle pole), bringing all of them to 0.87-0.97. Based on these extensive empirical experiments, adding a leaky integrator thus improves recursive differenced time-series forecasting.

Repository-level software engineering (SWE) comprises heterogeneous task categories, whose progress under pooled agentic reinforcement learning can be uneven: gains in some categories coincide with regressions in others, while aggregate resolution obscures these changes. Motivated by this category see-saw, we develop a category-aware expert-training and policy-integration framework. Executable task construction and SWE Labeler, an evidence-grounded multi-axis labeling system, organize the training pools. Initial category-specific RL improves average training success while leaving uneven instance-level progress, motivating explicit consolidation of successful behavior and policy-adaptive task selection. Same-origin category experts alternate long-horizon Agentic-miniRL with Refresh-Repair-Expand (RRE): the updated policy refreshes instance mastery, reuses its own verified successful trajectories for Repair SFT, and reselects tasks for further RL. Label-routed multi-teacher on-policy distillation (MOPD) consolidates the experts into one deployable student, with ReLU-gated reward extrapolation keeping only each teacher's improving direction over the reference. Expert training and policy integration require no external model to provide solution trajectories or action targets. On a fixed, audit-filtered Pro-618 subset, we connect Pooled RL and Balanced RL, expert development, and single-model integration through overall and per-category resolution and expert-gain recovery. In final-model evaluations, MOPD achieves mean resolution of 86.19% on SWE-bench Pro V2 and 71.78% on SWE-bench Multilingual, exceeding the base model by 4.57 and 3.89 percentage points, respectively. The same three 27B experts also improve a Qwen3.6-35B-A3B student across the evaluated task sets.

Open-vocabulary audio-visual event localization (OV-AVEL) grounds a text-queried event in time from video, audio, and language. The supervision sources available to this task can differ in temporal-boundary reliability: on OV-AVEBench, our configured visual teacher gives more reliable boundary cues than the configured audio teacher, although the latter is a strong pretrained audio model and remains semantically informative. This is a setting-specific diagnostic rather than a universal ranking of vision and audio. We formulate the resulting challenge as supervision placement: which teacher signals may shape the localization decision, and which should remain auxiliary. Based on this view, we propose OV-OrthKD, a reliability-aware asymmetric distillation framework. Visual feature transfer shapes a decision-aligned representation, audio feature transfer enriches a complementary auxiliary subspace, a text prototype anchors seen/unseen category semantics, and an orthogonality loss limits directional overlap between the two teacher-specific projections. The student continues to use both modalities through query-aware fusion at inference, while the default training recipe keeps audio-teacher supervision off the segment-logit path. On OV-AVEBench, OV-OrthKD achieves 0.816 segment AP and improves F1@0.5 over the official fine-tuning baseline by 2.7 points overall and 3.4 points on unseen categories. Path-assignment, role-swap, corruption, and transfer analyses consistently support supervision placement as a task-specific design axis for OV-AVEL.

We measure the galaxy stellar mass function at $z = 0-2$ using 28M galaxies from the KiDS DR4 which spans an effective survey area of 676.9 deg$^2$. Combining nine-band photometry ($u$–$K_s$) and redshifts derived using deep learning photometry, we use five SED fitting configurations, CIGALE/LePhare and CB19/BC03/M05 Stellar Population Synthesis (SPS). We present the impact of the systematics related to the code, SPS modeling and Star formation History (SFH) , which combined can introduce systematics of $\sim 0.6$ dex. The GSMFs outlined in this work agree well with previous studies (within the uncertainties introduced by systematics) that typically are able to cover measurements for the GSMF only up to $\log(M_*/M_\odot)\sim 11.75$, due to their limited volume. The large KiDS area and galaxy counts, allows us to gain some insights on the “extreme" high-mass end, and our GSMFs imply that possibly there are more massive galaxies than we would expect, from a simple exponential cut-off, at $\log(M_*/M_\odot)>11.75$. However, we heed caution that despite advances done both in redshift estimation techniques and SPS, future studies are required to confirm this behavior. We consider the effects of Eddington-bias (EB) to our observations via two different methods and compare our results with the predictions of semi-analytic models and hydrodynamical simulations. We use the Mean Absolute Difference (MAD) of residuals as a diagnostic metric. Due to inconsistencies ($> 0.5$ dex) between observations and Eddington biased simulations found, especially at the high mass end, we suggest that some theoretical models would achieve better performance once parameter tuning takes into account the effects of EB prior to the tuning of the uncertain parameters involved related to stellar physics and feedback.

Reinforcement learning (RL) offers a natural language for healthcare decisions whose conse- quences unfold over time, yet most reported progress remains far from routine intervention. Ex- isting surveys organize the field by algorithm or clinical application. We instead review healthcare RL through an evidence ladder: problem formulation, retrospective identification, policy estima- tion, stress testing, prospective evaluation, and lifecycle monitoring. This view connects clinical treatment, patient engagement, and health-system operations while exposing a recurring gap: evi- dence that a policy scores well in a historical dataset is not evidence that it will improve care. We synthesize the assumptions and failure modes at each rung, identify what evidence can and can- not transfer across settings, and propose reporting practices for cumulative evaluation. Restless bandits are included as one special case, not as the organizing framework. The central lesson is that healthcare RL should be evaluated as an intervention embedded in a changing sociotechnical system, rather than only as an optimizer of a retrospective reward.

We are concerned with the following partial differential equations arising from urban crime modeling: \begin{equation} \label{main} \begin{cases} u_t = \Delta u - \chi \nabla \cdot \left( u \dfrac{\nabla v}{v} \right) - uv + B_1 + ru - \mu u^2, \\[4pt] v_t = \Delta v - v + uv + B_2, \end{cases} \end{equation} under no-flux boundary conditions in a smoothly bounded domain $\Omega \subset \mathbb{R}^n$ with $n \geq 2$, where $\chi$, $r$, and $\mu$ are positive constants. It is shown in this paper that if the nonnegative source terms $B_1$ and $B_2$ are sufficiently regular and \begin{equation*} \mu > \frac{3}{n} + \frac{1}{n}\left( \chi n + \frac{n(\chi(n-1)-2)^2}{4(n-1)} \right)^{\frac{n+1}{n}} \cdot \left( \frac{(2n+\sqrt{n})^2}{2n-1} \right)^{\frac{1}{n}} + n^{12n+3}, \end{equation*} then the system \eqref{main} with suitably regular initial data possesses a global classical solution. Moreover, under the assumption that \begin{equation*} \label{cond.B2} \inf_{t>0} \int_\Omega B_2(\cdot,t) > 0, \end{equation*} the solutions are uniformly bounded in time.

Accurate multi-user localization is challenging in complex urban environments, where wireless measurements can become ambiguous under noise, blockage, and multipath, while visual observations provide complementary spatial context. This paper presents a vision-wireless fusion framework for multi-user localization using pilot-indexed channel state information (CSI). Orthogonal pilot indices preserve the identities of the communicating UEs in the CSI token sequence and localization outputs. The model encodes each pilot-indexed CSI observation as a query token and uses cross-attention to retrieve user-specific information from spatial visual memory. Self-attention among CSI tokens further captures inter-user interactions, while the resulting multimodal representations are used for user-wise localization. Experiments on different datasets show consistent improvements over model-based, CSI-only, and multimodal-fusion baselines. Further experiments evaluate the model under different wireless and visual conditions.

Long-context language models interface with external knowledge through raw natural language. In retrieval-augmented systems, this creates a persistent index-payload schism: dense vectors enable searchable routing, but models must re-ingest lengthy text payloads for reasoning at O(N^2) attention cost. Existing compression methods further produce private states tied to specific architectures. We introduce Machine-Interpretable Information (MII), the first agent-to-agent (A2A) document-to-state protocol. A dual-timescale state-space Writer compiles documents into a canonical, fixed-bandwidth state (56 tokens), and a lightweight Translator maps it into any frozen Reader's embedding space, reducing query-time cost to O(K). The resulting .mii artifact unifies Retrieval (searchable geometry), Reasoning (global memory), and Reconstruction (grounded details) in a single transferable medium. We demonstrate strong cross-model interoperability across heterogeneous LLMs (e.g., Llama, Qwen, Mistral) – despite the Writer using a legacy GPT-2 vocabulary, forcing genuine semantic translation rather than token-level memorization. Mechanistic probes reveal modular latent structure: entity representations can be causally traced and zero-shot transplanted between unrelated document states while remaining decodable. To address lexical reconstruction under fixed bandwidth, we propose Residual-MII, a cache hierarchy combining compiled global memory with sparse local evidence. On HotpotQA (7,405 queries), Residual-MII exceeds full-context Exact Match at approximately 7% of the attention FLOPs, suggesting a paradigm shift toward compiled, transferable neural document formats.

Changing solvent inertia changes the kinetic part of a molecular Hamiltonian and hence its flow in phase space, without requiring a change in the potential energy surface (PES). We study how this affects product probability in a solute-solvent model with two degrees of freedom. Initial conditions are chosen at the same total energy for each solvent mass. For this family, the deterministic outcome changes from reaching products to returning to reactants at a threshold mass. The initial condition at that mass belongs to the stable manifold of the transition-state periodic orbit. Weak Gaussian forcing of the solvent momentum replaces the abrupt change in outcome by a continuous change in product probability over a mass interval proportional to the square root of the noise strength. The deterministic threshold and a linear response calculation predict the position and width of this probability change without fitting the stochastic simulations. Monte Carlo results at three noise strengths agree with the prediction within sampling uncertainty. The calculation connects solvent inertia to product probability through the geometry of the full Hamiltonian flow, rather than through a change in the PES.

Generation-free world action models (WAMs) retain future-video prediction during training but act from internal video features at inference, leaving unclear what these features should preserve for control. Our representation diagnostics show that representations with more predictable future changes need not make linear action decoding easier. Observed future changes provide additional action information beyond the present, and linearly readable action information is spatially concentrated. These findings motivate Action-Relevant Predictive States (ARPS), a compact predictive interface between the video and action experts. ARPS uses a horizon-conditioned state predictor to aggregate intermediate video features into a compact state that supplies all visual context to the action expert. Future-representation supervision trains different parts of this state to predict visual representations at different future times, together with their changes relative to the present. At inference, the supervision branch is removed, and the action expert only uses the learned predictive state computed from current observations. Controlled ablations show that future supervision substantially improves generalization under distribution shift. ARPS achieves 99.2% success on LIBERO and transfers to LIBERO-Plus without adaptation, reaching 87.3% and exceeding Fast-WAM by 39.2 percentage points.

Delsarte (1973) conjectured that there are no nontrivial perfect codes in the Johnson scheme. In this paper, we prove that there are no nontrivial $e$-perfect codes in the Johnson scheme for $e\in\{1,2,4,9,10,12,16\}$. This paper complements "Perfect Codes in the Johnson Scheme Hardly Exist", thus proving Delsarte's conjecture completely.

FORM is a domain-specific symbolic manipulation language widely used in particle physics for processing the very large algebraic expressions arising from multi-loop Feynman diagram calculations. Despite its central role in precision theoretical physics, no artificial-intelligence tooling exists, to our knowledge, for assisting physicists in writing FORM code. We show that contemporary large language models (LLMs), including frontier models with hundreds of billions of parameters, achieve a zero-percent execution pass rate on our instruction-following and tutorial-style FORM tasks without documentation in a single attempt, establishing FORM as a genuine zero-shot language for LLMs at the time of writing. We then present a verification-driven data generation pipeline that uses the FORM binary itself as an execution oracle to produce and validate a corpus of 4,633 training examples spanning deterministic computations, open-ended programs, tutorial code, and knowledge question-answer pairs. Fine-tuning a compact open-weights model (Qwen3-8B) with quantized low-rank adaptation (QLoRA) yields a specialist that, evaluated on four complementary benchmarks (840 tasks, single attempt each), decisively outperforms frontier models with up to 756B parameters in execution rate and in strict, FORM-verified output matching on the larger benchmarks, and remains statistically indistinguishable from them on the smaller, harder ones. General reasoning and coding capabilities are preserved within 2.6 percentage points.

Recurrent models must preserve information that changes future behavior while suppressing hidden-state error. These objectives conflict: contraction improves stability, but contraction along a future-distinguishing direction destroys memory. We formalize this boundary through the predictive quotient of a recurrent state space. Two hidden states are equivalent when they induce the same conditional future; their equivalence classes form predictive fibers. Every exact semantics-preserving corrector acts as the identity on this quotient. At a regular point with hidden dimension d and predictive dimension k, it can eliminate at most d - k independent directions. This establishes a discrete-continuous boundary: finite predictive states admit positive-radius exact correction basins, whereas an uncountable continuum of future-distinguishable states cannot be decoded after arbitrary positive-radius perturbations in finite-dimensional Euclidean space. To operationalize this principle, we develop an auditable finite-future framework. A compact deployment bank W is evaluated against an independent audit bank A (W subseteq A) on a declared correction domain. Under generative probe access and audit-metric coverage, finite stochastic rollouts furnish a high-probability certificate for the separation margin Omega_{W|A}(delta). Preserving learned W-predictions within this certified margin guarantees bounded audit-semantic distortion. For intrinsic audit dimension k, the required probe outcomes scale as O(M * Omega^{-(k+2)}), where M = |A|; a matching minimax lower bound proves this exponent is optimal. Extending guarantees to continuous futures is achieved via an explicit completeness modulus. Controlled experiments validate the certified margins, scaling laws, and automated probe refinement under a safety-first evaluation paradigm.