Papers

Large neighborhood search improves an incumbent by releasing selected variables and repairing the resulting subproblem under a time limit. FOVEA casts variable selection as dense semantic segmentation on a fixed $128\times128$ canvas. A small U-Net reads twelve semantic channels and predicts cell scores, which are decoded into a variable set subject to a fixed variable budget. Family-specific layouts connect the search state to the canvas, while one set of network weights serves four problem families. The FP32 network input occupies $786$\,kB across instance sizes. Our analysis bounds constraint coupling for spatially coherent regions, gives a rank certificate for rounds with zero possible improvement, and bounds the coupling advantage attainable on an expander family. On the tested families and hardware, FOVEA trails the strongest graph encoder at $10^{4}$ variables and overtakes it near $1.5\times10^{4}$; the cost model provides an approximate crossover estimate. At larger sizes, where the graph-encoder baselines exceed device memory, FOVEA reduces the primal integral by $12$ to $16\%$ relative to the best runnable baselines. On the expander family, FOVEA performs comparably to random selection, with a coupling advantage close to one.

Transient pressure diffusion in heterogeneous porous media becomes difficult to resolve efficiently when permeability is discontinuous and spans several orders of magnitude. In this paper, we develop a domain-decomposed random-feature evolutional deep neural network (DD RF-EDNN) that separates spatial approximation from temporal evolution. Permeability-informed random features are compressed into an orthonormal pressure space, and a conservative finite-volume operator is projected onto this space so that only the reduced coordinates are advanced in time. This formulation retains the dissipative structure of the discrete flow problem without repeated neural-network optimization. The analysis quantifies dictionary and singular-value truncation errors, proves contractivity under an energy-consistent dissipativity correction, and derives a conditional grid-level estimate for homogeneous dynamics and time-independent data admitting a steady lifting. Numerical experiments on low-permeability inclusions, high-conductivity blocks and channels, and three-dimensional grids assess the accuracy of the method across distinct coefficient configurations. The method reaches a final-time relative $L^2$ error of $9.54\times10^{-4}$ in the principal benchmark and maintains errors on the order of $10^{-2}$ at a permeability contrast of $10^3$. Numerical diagnostics further show that the observed error balance and temporal convergence are consistent with the analysis. These results support DD RF-EDNN as a structure-preserving and interpretable reduced formulation for transient simulations on prescribed heterogeneous media.

Fractional operator algebras provide a natural setting for linking algebraic normal forms to causal inversion, but arbitrary smooth multipliers and Volterra kernels destroy finite fractional rewriting. We construct an algebra generated by polynomial multipliers, fractional powers indexed by an additive subgroup $\Gamma\subset\mathbb{R}$ containing $\mathbb{Z}$, and flat causal convolution operators. Its finite polynomially weighted diagonal-flat convolution operators form the smallest two-sided ideal containing the flat generators, polynomial multipliers are intrinsic, and distributional separation yields a unique finite normal form with an additive order filtration. For monic normal forms, the leading power selects a canonical causal right factor that extends from the flat core to the natural range $J^\alpha C[0,T]$. Completing the negative-order convolution sector in $L^1$ admits integrable Sonine and Prabhakar kernels, while an independently prescribed continuous bivariate Volterra term remains external. Under injectivity and power-type kernel bounds, variable lower-order terms and this bivariate perturbation reduce to one weakly singular second-kind equation, whose classical resolvent exists on every finite interval without smallness assumptions. A finite boundary-jet block incorporates prescribed initial data without changing the reduced kernel. Sonine, distributed-order, and regularized-Prabhakar realizations follow. In the noninteger Prabhakar regime, an exact range criterion characterizes the classical $AC^m$ subdomain, and an explicit Riemann–Liouville example proves that it is strictly smaller than the continuous natural range.

We propose a Verification Reward Model (VRM) framework for training language models to create and repair chip verification artifacts. The central object is a versioned verification contract that binds requirements, permissible stimulus, observation boundaries, reference behavior, evaluation budgets, and acceptance criteria. Compiler, simulator, formal, mutation, coverage, and expert-review evidence are converted into auditable records. Deterministic acceptance checks remain outside the learned model. A learned outcome model predicts expensive future evidence from the specification, the generated artifact, and explicitly masked partial evidence; a semantic critic identifies evidence-supported weaknesses; a deterministic reward composer translates the resulting quality vector into task-conditioned training rewards. Extensions include paired clean/fault interventions, marginal fault-discovery rewards, uncertainty-aware evaluation scheduling, and a quarantined cross-domain learning loop. Evaluation emphasizes independently validated fault detection, false alarms, generalization across design families, and total cost to reach a specified quality level. We describe a first experiment on a small, open-tool-compatible benchmark with lightweight models, with full UVM capability admitted through feature-specific qualification. This is a position paper: we specify the framework and the experiments that would test it, and we report no training, EDA, or silicon results.

We study root-of-unity sections of quotients formed from dilated Euler products. At the boundary point \(q=1\), odd sections tend to nonzero cyclotomic constants, whereas even sections have infinitely many simple real poles. We determine the locations, spacing, and residues of all sufficiently late poles. In the cubic case we find the leading oscillatory error in an elementary approximation and prove that its exponential scale is sharp. At the origin we determine exact contact, including a gap-dependent parity law, and integral divisibility with the first nonzero coefficient determined for every modulus \(|k-1|\ge2\). For Euler powers \(k\ge2\), a moving formal pole controls the section error at small fixed nomes; a real zero-free interval gives a further convergence regime. For the twenty-fourth power we prove explicit CM approximation bounds and a signed asymptotic as the dilation increases.

Let $$ M_{r,p}^{(d)}(g)=\int_{\mathbb R^d}|x|^r|g(x)|^p\,dx, \qquad 1<p<\infty. $$ Write $p'=p/(p-1)$ and $\omega_d=|B(0,1)|$. A direct step in the Wigderson–Wigderson moment method asks for a single-function estimate $$ \lVert g\rVert_1\le K\lVert g\rVert_q^{\,1-p\eta} \bigl(M_{r,p}^{(d)}(g)\bigr)^\eta, \qquad \eta=\frac{d(1-1/q)}{r+d-dp/q}. $$ We give a self-contained proof that, in its scale-invariant regime, this estimate holds exactly when $r>d(p-1)$. We then quantify the transition: the best constant blows up like $[r-d(p-1)]^{-1/p'}$ at the critical line, while on the annulus $1\le |x|\le R$ the endpoint loss is exactly $(d\omega_d\log R)^{1/p'}$. The critical line nevertheless has two sharp Lorentz endpoints. The strong moment controls $L^{1,p}$, $$ \lVert g\rVert_{L^{1,p}}\le \omega_d^{1/p'}M_{d(p-1),p}^{(d)}(g)^{1/p}, $$ and strengthening the weighted norm from $L^p$ to $L^{p,1}$ restores the strong target, $$ \lVert g\rVert_1\le \omega_d^{1/p'} \lVert |x|^{d/p'}g\rVert_{L^{p,1}}. $$ More generally, every power moment has a sharp target Lorentz space, and its secondary index is optimal. These results identify the endpoint lost by the direct same-$q$ reduction. They do not obstruct auxiliary-norm versions of the Wigderson framework, which reach the Cowling–Price range by a different route.

We explore the use of hybrid quantum-classical generative adversarial networks for synthesising CAD-ready vector geometries. Unlike prior work that operates in rasterised or single-Bézier domains, we introduce HMB-GAN (Hybrid Multi-Bézier GAN), an end-to-end differentiable generative framework that constructs closed shapes through stitched multi-segment Bézier representations with geometric continuity enforced by construction. We compare a quantum-enhanced generator with a classical generator within this architecture and evaluate them across point cloud distribution metrics and geometric shape statistics. Results show that despite faster convergence, a reduction in model parameter count, and slightly improved performance on point cloud metrics, the quantum generator suffers from excessive simulator overhead and thus classically-simulated evaluation suffers from hardware constraints. These results demonstrate the feasibility of modelling structured geometries through hybrid quantum architectures whilst highlighting contemporary hardware limitations.

Large Language Model (LLM) agents are increasingly being explored for chip design, but most existing approaches operate directly at RTL. We ask whether agents can design better chips by leveraging higher-level abstractions. We compare Direct RTL Design, Agent-based HLS Design, Post-Compiler HLS Refinement, and Post-HLS RTL Refinement, and combine Agent-based HLS Design with Post-HLS RTL Refinement as Agent-based HLS with RTL Refinement (AHRR). We use FPGAs as a practical, easy-to-deploy platform for end-to-end evaluation, but note that the design-flow tradeoffs we study are largely independent of the target technology. Across a diverse 11-tasks benchmark suite, AHRR achieves a 2.6$\times$ geometric-mean speedup over Direct RTL Design across our benchmark suite. Case studies show that HLS distills design knowledge into abstractions that agents can leverage, while RTL refinement recovers lower-level optimization opportunities. Together, these results make AHRR a promising workflow for agentic chip design. The code and evaluation artifacts are available at https://github.com/ZijD/AHRR.

We prove some residually reducible $p$-adic Galois representations of number fields arise from modular forms. We study the universal deformation ring arising from deformations satisfying the Fontaine-Laffaille condition at primes over $p$. Under certain conditions, we establish the reduced universal deformation ring is a discrete valuation ring. The method uses pseudocharacters and certain bounds on Selmer groups, where the ideal of reducibility as defined by Bellaïche and Chenevier is shown to be maximal and principal. A self-dual assumption is not needed in our argument. The main result on deformations applies to $n$-dimensional representations. In applications, a congruence between Hermitian modular forms due to Klosin is used with our results to prove modularity of some 4-dimensional $p$-adic representations of the imaginary quadratic field $\mathbf{Q}(i)$.

A repair favored under an isolated input fault can be inferior when deployed modules share the faulty information. We introduce an information-interface audit for world models, distinguishing fidelity gaps, where exact inputs become estimates, from availability gaps, where inputs are missing. Fixed-weight interventions measure prediction error, input dependence, and paired closed-loop benefit, including dependencies introduced by reconstruction. In simulated quadrotor model predictive control, coupled, opposite-sign 10% mass/thrust calibration errors reduce a physics-anchored model's success from 69% to 8%; uncertainty training restores 65%. Wind reconstruction recovers control benefit but inherits calibration dependence. For a positive calibration offset, reconstruction-only corruption favors uncertainty-trained reconstruction, whereas shared corruption favors the baseline. Acceleration diagnostics reveal compensation between reconstruction bias and nominal-model error, also observed with a disturbance observer. Repair selection therefore depends on the information paths used in deployment.

Good tutoring adapts to the individual: it tracks what a learner knows, notices why they go wrong, and asks the next question that will help most. Most deployed tutoring tools instead serve fixed item banks and treat a wrong answer as a single bit of signal. We present CoLearn, an interactive, agentic tutor that supports an iterative tutoring loop: the learner practises, and the system builds an evidence-grounded memory of the learner's mastery and misconceptions. This memory is updated as evidence accumulates and is used to generate the next personalised question. CoLearn has three components: (i) a persistent learner-state memory that updates per-topic mastery with a soft-evidence variant of Bayesian Knowledge Tracing, where a large language model acts as a continuous observation function; (ii) adaptive question generation that targets the learner's weakest topic and recurring misconceptions; and (iii) an evidence view that makes personalisation visible and testable through live progress visualisation and blind A/B comparison. In blind A/B evaluation, questions conditioned on this memory are preferred over non-personalised ones 68-69% of the time, and in persona simulations with hidden ground-truth mastery the agent's belief converges toward the learner's true mastery.

The linear advection operator is an ubiquitous building block in fluid and plasma problems. We develop a quantum algorithm for enacting the operator. When the advection velocity is constant in space, our algorithm is exponentially more efficient per time step than classical and avoids spurious oscillations near steep gradients. The algorithm is most cleanly illustrated using the one-dimensional advection equation on a uniform spatial grid with periodic boundary conditions, which can be extended to higher dimensions. The algorithm uses a first-order upwind scheme, which captures discontinuities in the wave envelope but is not unitary. We embed the non-unitary upwind scheme using Linear Combinations of Unitaries (LCUs), and develop an efficient quantum gate decomposition of the upwind unitary, which performs one step of advection using $O(n^2)$ two-qubit gates, where $N=2^n$ is the number of spatial grid points, as opposed to a classical computer which costs $O(N)$. Although LCUs introduces a small bounded probability of failure per time step, we show that the accumulation of failures does not lead to exponential-in-time complexity as one would naively expect. Moreover, when LCUs fails, we develop a probabilistic scheme to recover from the failure state, which avoids a full restart of the simulation. The failure recovery scheme uses quantum Fourier transform (QFT) and effectively achieves quantum indefinite integration of an unknown quantum state. The recovery, which can itself fail, is more efficient than a full restart if the wave envelop is well-resolved to include only low Fourier modes. We emulate our scheme classically and demonstrate small problems on Quantinuum's trapped-ion qubits. Our quantum algorithm provides a subroutine for physics simulations that involve linear advection.

In quantum networks, nodes are connected via sharing of Einstein-Podolsky-Rosen (EPR) pairs, ideally with high fidelity and high rate. However, the fidelity of EPR pairs degrades due to imperfect generation and decoherence errors. Entanglement Distillation is a method that increases the fidelity but operates probabilistically and may destroy all involved EPR pairs upon failure. This failure reduces available EPR pairs for application use, thereby decreasing the service rate. Quantum Error Correction (QEC) is another mechanism to protect EPR pairs against error by forming what we term as Coding-Enhanced Memory (CEM). While effective, CEM requires extra time and resources to form the code, which also reduces the service rate. Existing methods often use static combinations of distillation and CEM, ignoring demand variations. This results in a low service rate without significant fidelity gain. Limited resources together with this rate-fidelity tradeoff make it essential to schedule when to run distillation, form CEM, or serve requests. We propose ReFINE, a demand-aware preemptive scheduler that based on application requirements either serves an available EPR pair immediately or preserves it in CEM. This selective use of CEM, only when needed, enables a better balance for rate-fidelity tradeoff than always using CEM. Between request arrivals, ReFINE either schedules distilling EPR pairs or forming CEM to protect distilled pairs, following one of the three priority policies: ReFINE-D (Distillation-First) first generates EPR pairs for distillation and then forms the CEM, prioritizing service rate. ReFINE-M (Memory-First) first forms the CEM, then generates the EPR pairs for distillation, prioritizing fidelity. ReFINE-C (Concurrent) performs both distillation and CEM formation concurrently, balancing between fidelity and service rate.

Molecular solubility directly affects key aspects of molecular development such as reaction feasibility, formulation performance, separation efficiency, and solvent selection. However, experimental measurement across solutes, solvents, and temperatures remains costly and sparsely sampled. Existing computational models often rely on fixed-solvent assumptions, deterministic formulations, or simplified representations of solute-solvent interactions, limiting their ability to capture complex molecular interactions, continuous temperature effects, and experimental uncertainty. Here, we introduce EnSol, an environment-aware probabilistic framework for molecular solubility prediction. EnSol represents the solute and solvent as molecular graphs and learns separate representations for each before bringing them together through cross-attention to capture solute-solvent interactions. Temperature is incorporated directly into the solvent environment through feature-wise modulation, and a mixture density network predicts full solubility distributions to capture both temperature-dependent behavior and experimental uncertainty. On the independent SolProp and Leeds benchmark datasets, EnSol achieved Spearman correlations of 0.876 and 0.601, respectively, outperforming state-of-the-art solubility prediction models across both benchmarks. Beyond computational benchmarking, experimental validation across chemically diverse solute-solvent pairs showed that EnSol maintained strong predictive performance and supported reliable solvent ranking, achieving a Spearman correlation of 0.715. These results show that EnSol can support reliable solubility prediction and solvent selection across diverse chemical systems while accounting for predictive uncertainty.

We present the first results from the Compact Objects and the Physics of Accretion Survey (COPAS), a high-cadence photometric survey focused on the detection of accreting white dwarf binaries mainly through their outbursts using TESS. From an initial sample of 2,054 cataclysmic variable (CV) candidates observed during TESS Cycle 6 and 7, we identify 11 systems with periods below 83 minutes. This includes 7 AM CVns and 4 CVs. Our Gemini spectroscopic data confirm ZTF18aaxuusk and ASASSN-21eo as AM CVns, while Gaia21akb is confirmed as a CV. We provide the first period measurements for 6 out of the 11 systems. Complementing our TESS data with ground-based observations, we measured superoutburst recurrence times of approximately one year for the AM CVn systems ASASSN-21in and ZTF18aaxuusk, and 1.8-2.0 years for the short-period CVs ASASSN-18rd and ASASSN-15ev. Using TESS, we also estimate the mass-ratio for ASASSN-19ct (q = 0.05 +/- 0.02), which is consistent with a highly evolved low-mass donor star. Though the number of ultracompact systems detected among the total sample is low (0.54%), and likely the result of observational biases and intrinsic population rareness, the reclassification of 5 systems as AM CVns highlights the importance of continuous monitoring to identify more systems through their outbursts and short periods.

Before patients can use AI-assisted psychiatric intake systems, health systems need practical ways to routinely evaluate these tools against their clinical standards for quality assurance. Because clinicians may use different intake styles, evaluation for this task must (1) support comparison across interviewing approaches, (2) minimize clinician burden, and (3) measure clinically relevant performance for health systems deploying these technologies. We present a clinician-grounded evaluation platform built around a memory-augmented patient simulator for open-ended AI interviewing, InterviewPlayground. We created interactive patients using InterviewPlayground with our expert-authored vignettes, constructed a simulated intake platform for the interviews, and designed evaluation modalities relevant to intake. In a pilot of 6 clinicians in a 25-minute assessment compared to a GPT-based LLM intake interviewer, the LLM recovered more of the clinically relevant items embedded in the patient vignettes (88.0% vs. 38.9%), but made more clinical inferences not based on the interview (56.8% vs. 27.8%), and characterized identified safety concerns less often (33.3% vs. 66.7%), setting the stage for deployed quality assurance for this task.

This letter addresses budgeted stealthy false-data-injection (FDI) scheduling against remote state estimation, where a resource-constrained adversary may corrupt at most a fraction $\bar{\Gamma}$ of transmissions. Existing event-triggered schedulers invert a Gaussian innovation tail to set the firing threshold and certify stealth by covariance matching; both are exact only under Gaussianity, which real cyber-physical residuals routinely violate. We propose a distribution-free scheduler pairing the worst-case FDI action with a split-conformal calibrated trigger, requiring neither the plant matrices nor any distributional model. We establish exact pathwise stealth against every magnitude-measurable detector, for any firing rule and innovation law; a finite-sample distribution-free bound on the mean firing rate, with almost-sure budget attainment under stationarity and ergodicity; and a steady-state degradation identity linear in a single scalar energy capture $\psi$, maximized by the same order statistic that delivers the budget guarantee. A conditional sign-symmetry condition delimits when the certificate extends to sign-sensitive detectors, the residual exposure being governed by a fourth cumulant that vanishes under Gaussian noise. Monte-Carlo studies and a heavy-duty truck CAN record confirm the bounds and quantify what the Gaussian assumption costs outside its regime.

Security Operations Centers (SOCs) often rely upon on-the-job training focusing on the specific tools and procedures a SOC utilizes. The complexity in tooling can overshadow the underlying reasoning process, hindering an analyst's ability to learn investigative skills. We formulate the concept of "non-perishable knowledge" which corresponds to investigative thinking skills independent of tools. We developed a scenario-driven training method to understand whether such non-perishable knowledge can be imparted through specially designed incident scenarios, where trainees are presented with and solve investigative challenges in a tool-agnostic manner. We designed two such scenarios based on real-world incidents. Human subjects were recruited from a university's student body for ethnographic study to understand how this training method is received by the subjects and how they perform on such tasks. We collected data from 20 hours of documented training with 25 trainees spread across five sessions. Using grounded-theory, we analyzed the data and uncovered factors that inhibit or promote learning of the investigative thinking skills. Our research combines scenario-based training, ethnographic research, and technical analysis to examine how to best train students in the reasoning skills that industry deems vital to SOCs.

This paper studies a two-server split–merge queue with positively dependent subtask service times modeled through a latent-factor bivariate Erlang construction. An exact characterization of the split–merge completion time is obtained, including explicit formulas for its first two moments and the resulting mean waiting time. Under fixed marginal service-time distributions, independence is shown to stochastically increase the completion time and hence overestimate mean waiting time. Numerical illustrations show that this benchmark gap can be substantial.

The Viterbi algorithm has been previously used to perform forced alignment of audio to text to mine training data from online resources. However, many existing implementations have quadratic time and space complexity, scaling poorly to long input sequences. We propose two optimizations to address this issue. First, we apply the Hirschberg algorithm to perform the alignment in place using linear memory. Second, we model the alignment between speech and text as a constrained random walk, allowing us to prune the search space with arbitrary confidence while accounting for transcription errors. The Hirschberg optimization reduces memory usage from 140 GB to 5 MB for three-hour inputs while producing identical alignments in one-third the time of torchaudio when both run on a CPU. We achieve an additional 2x speedup with pruning on inputs longer than 20 minutes while preserving alignment accuracy in more than 98% of tested cases.

Let $q_m=2m/(m+1)$ and put \[ \beta_0=\frac{3}{2}+\frac{1}{\log 2}=2.9426950408\ldots, \] where $\log$ is the natural logarithm. We give a proof scheme showing that, for every $\varepsilon>0$, there is $C_\varepsilon<\infty$ such that every complex-valued function $f:\{-1,1\}^n\to\C$ of Fourier degree at most $m$ satisfies \[ \left(\sum_{A\subseteq[n]}\abs{\wh f(A)}^{q_m}\right)^{1/q_m} \le C_\varepsilon m^{\beta_0+\varepsilon}\norm{f}_\infty. \] The improvement over the $m^9$ estimate of the earlier draft has two ingredients. The first three Fourier levels are estimated at the scales $m$, $m^{3/2}$, and $m^{5/3}$. These losses are encoded in the weight $M^{\mu_r/r}r^B\min\{r,L_M\}^8$, $L_M\asymp_B \log (M+1)$, with $\mu_r=\lceil3r/2\rceil$ for $r\ge2$. A parity-compatible central window handles $r<L_M$, while a shrinking balanced window handles $r\ge L_M\asymp_B\log(M+1)$, no parity is used in this regime. The leading high-degree loss–gain factor is $\ee\,2^{-B}$; careful uniform bounds close the bootstrap for every $B>1/\log2$. The formula for $\mu_r$ is explained below.

As digital commerce ecosystems expand into low-end consumer electronics (CE), hardware constraints-specifically limited CPU duty cycles and volatile heap fragmentation-become significant bottlenecks for complex transactional flows. Traditional on-device middleware requires high "network chattiness" to manage multi-step state machines, leading to increased latency and potential transaction failure on unstable residential networks. This paper proposes a novel Transactional Backend-for-Front-End (T-BFF) Orchestration Framework designed for resource-constrained embedded platforms. By migrating the transactional state machine and microservice orchestration to a cloud-side layer, we achieve a significant reduction in client-side overhead. Our framework introduces a "Double-Handshake" protocol utilizing non-volatile flash memory for state recovery after hardware reboots. Experimental results on an ARM Cortex-A53 platform demonstrate a 35% reduction in maximum heap usage and a 40% improvement in end-to-end transaction latency. This framework provides a scalable, sustainable blueprint for maintaining transactional integrity on legacy hardware in the 2026 IoT landscape.

As language models (LMs) rise in prominence, there is interest in making them more transparent in order to better understand their internal behavior. Recent interpretability work has focused on using sparse autoencoders (SAEs) to break down neuron activations at a given layer in the LM into human-understandable features, where each feature represents a concept that the model has learned. In this paper, we share work on using SAEs to analyze the behavior of text classification LMs. We present techniques for exploring the relationships between the SAE's features and the model's predictions and errors. We integrate these techniques into SAEfarer, a tool for analyzing concepts learned by text classification LMs. We assess SAEfarer in an expert pilot evaluation with five Ph.D. students.

Learning analytics dashboards (LADs) are intended to help students make sense of their learning data to support reflection and decision-making. However, their visualisations can be complex, particularly for students with low visualisation literacy. Narrative techniques, such as annotated charts and data comics, have been used to communicate insights directly, but not as supplementary materials to empower students to explore their visualisations themselves. In response, we conducted a qualitative study examining how data comics can complement LADs. We interviewed 18 nursing students and 4 of their teachers about a multimodal LAD containing visualisations with data comics explaining them. Analysis showed that data comics were clear, engaging, and helped make complex visualisations more accessible, though they must be carefully designed to avoid overwhelming students with information. The findings suggest that both students and teachers are receptive to data comics as a means of supporting the interpretability of LADs.

We study $(\mathbf{O}^\top \mathbf{A} \mathbf{O} + \mathbf{B})^{-1}$, where $\mathbf{A}, \mathbf{B} \in \mathbb{R}^{N \times N}$ are symmetric positive definite, with limiting eigenvalue distributions ${\rm F}_{\mathbf{A}}, {\rm F}_{\mathbf{B}}$ and spectra bounded and bounded away from zero, and $\mathbf{O}$ is Haar orthogonal. We analyze the deviation of deterministic-equivalent-type approximation $\boldsymbol{\Delta}\doteq (\mathbf{O}^\top \mathbf{A} \mathbf{O} + \mathbf{B})^{-1}- \mathbf{S}^{-1}$ where $\mathbf{S} = \mathbf{B} - z^\star \mathbf{I}$. First, let $\mathbf{O}$ be independent of $(\mathbf{A}, \mathbf{B}, \mathbf{u})$, $\|\mathbf{u}\| = 1$. There is sequence of a standard Gaussian vectors $\mathbf{g}_N$ independent of $(\mathbf{A}, \mathbf{B}, \mathbf{u})$ with $\| \mathbf{S} \boldsymbol{\Delta} \mathbf{S} \mathbf{u} - \sqrt{\frac \tau N}\, \mathbf{g}_N \| \to 0$ a.s. Here $z^\star = -{\rm R}(-\chi)$ and $\tau = {\rm R}'(-\chi)(1 + \eta {\rm R}'(-\chi))$, where ${\rm R}$ is the R-transform of ${\rm F}_{\mathbf{A}}$ and $(\chi, \eta)$ are the first two inverse moments of the free additive convolution of ${\rm F}_{\mathbf{A}}, {\rm F}_{\mathbf{B}}$. Let $\mathbf{K} = \sum_{i \le \lfloor N^q \rfloor} \lambda_i \mathbf{u}_i \mathbf{v}_i^\top$, $q \in [0, C]$, with unit-norm, not necessarily orthogonal $\mathbf{u}_i, \mathbf{v}_i$ and $\limsup_N \max_i |\lambda_i| < \infty$ a.s. If $\mathbf{O}$ is independent of $(\mathbf{A}, \mathbf{B}, \{\mathbf{u}_i, \mathbf{v}_i\})$, then $N^{-q} {\rm tr}(\mathbf{K} \boldsymbol{\Delta}) \to 0$ a.s. The proofs use a dynamical mean-field approach: the generating functions of the free Appell polynomials give a linear dynamics approximating the quantity of interest in the iterated large-$N$, large-time limit, whose fluctuations we analyze.

Replacing attention in a pretrained language model is a compatibility problem: a plausible substitute may alter representations expected by later layers. TinyCeNN-LM introduces a quality-gated post-training conversion framework using CeNN-inspired cellular-recurrent layers with bounded local processing, compact recurrent memory, routing, fusion, and accept-or-rollback validation. Three implementations are studied: Integrated Memory, MemoryFusion, and PDelta3-GDN2-CLVR+Local32. Strict PDelta3 conversion accepts a layer only when representation and NLL criteria pass fixed thresholds. On SmolLM2-135M, layers 0-2 are accepted with cumulative $\Delta\mathrm{NLL}=+0.01209$, while layer 3 is rejected despite acceptable NLL because representation fidelity fails. On Qwen3.5-0.8B, full-attention layers 3, 7, and 11 are accepted with final $\Delta\mathrm{NLL}=+0.02073$. Integrated Memory keeps perplexity within $-0.07\%$ to $+0.93\%$ while reducing total cache by up to $6.01\%$. A sampled 200-item downstream sanity check gives $28.5\%$–$32.0\%$ overall accuracy for converted Qwen releases. The results support conservative, quality-gated structural conversion rather than universal attention replacement or speedup.

Octopus crawling motivates soft robots that exploit redundancy, yet discovering and organizing diverse coordination modes for adaptation remains challenging. To address this, we introduce a Diffusion-based Uncertainty-aware Optimization (DUO) algorithm that learns demonstration-free crawling controllers for a simulated, muscle-actuated CyberOctopus. This work represents the first application of diffusion-based control to soft multi-arm robots in contact-rich simulations. By embedding a variety of locomotion behaviors within a shared control distribution, this approach enables the simulated octopus to navigate dynamic physical constraints, demonstrating that learned coordination diversity inherently facilitates robust adaptation. The main contributions include: (i) a symmetry-structured policy representation that folds radially equivalent controllers into a canonical directional sector, (ii) an online black-box optimization strategy, the DUO algorithm, that discovers and retains diverse coordination modes, and (iii) a control editing technique that adapts existing controllers to novel actuator constraints without retraining. These results show how learned coordination diversity makes motor abundance a practical resource for adaptation in soft multi-arm robots.

Mixture-of-Experts (MoE) decoding on scratchpad-based tensor accelerators (STA) is dominated by moving expert weights while the compute engines sit idle. This traffic is hard to hide, because the experts are known only after routing, and hard to shrink without losing quality or adding critical-path work. We present CARDAN, which represents each expert-weight matrix as a vector-quantized component plus a shared-basis low-rank component and co-designs this representation with a multi-engine decoding dataflow. The representation separates expert-common from expert-private work, so the dataflow overlaps DMA with computation on several engines. Across five MoE families on AWS Trainium3, CARDAN matches or improves BF16-teacher perplexity across all five models and speeds up batch-one decoding by 1.15-1.31x over AWS dense MoE megakernels, rising to 1.7x at batch size 16.

Radiation pressure and radiative cooling often play an important role in deciding the structure and dynamics of astrophysical objects. In this paper, we present a radiative MHD simulation of a circumbinary disk (CBD) around an equal-mass SMBBH. It employs an approximate thermodynamic model based on local thermodynamic equilibrium and diffusion cooling which captures how the internal energy evolves in an optically thick region. The disk reaches a quasi-steady state within $r=5a$ whose mass distribution differs substantially from the one obtained from simulations without physical thermodynamics: the local maximum in the azimuthally-averaged surface density and the lump are completely erased; the time-averaged inner edge becomes more eccentric; and the vertical density distribution depends strongly on the radius. These changes are attributable to the enhancement of the magnetic fields caused by the cooling-driven vertical compression of the disk. Our result emphasizes that the basic properties of the inner CBD are sensitive to both radiation and magnetic physics.

We study the granular structure that emerges in a Fuzzy Dark Matter (FDM) halo formed through kinetic relaxation. After the system reaches a virialized core-halo structure, we separate the density field into a smooth spherical component and a residual density that contains the interference pattern characteristic of FDM halos. The power spectrum of this residual field shows a well defined dominant scale, different from the characteristic scale of the total density and of the smooth core-halo model. We compare this granular scale with a local de Broglie wave-lenght calculated from the velocity field obtained from the density current of the system. We find that both scales remain of the same order of magnitude, with the granular scale systematically smaller than the de Broglie wavelength. The radial behavior of the de Broglie wavelength also reveals a non-uniform internal structure, it decreases from the core and reaches its minimum near the transition between the solitonic core and the outer halo. These results provide a quantitative connection between density fluctuations, the local velocity field, and the core-halo morphology of FDM halos.