Papers

Can quantum mechanics be complete without being fundamental? Under stated source, detector, and statistical conditions, we reconstruct the quantum representation and Born probabilities and prove complete algebraic closure of the admitted quantum predictions without requiring a collapse postulate. We further show that many familiar quantum paradoxes arise from conflating coherent processes with retained records or probabilities with realized outcomes. We also ask whether mathematics as a whole, or the source architecture itself, emerges from a deeper structure.

We prove that the second-moment Hamiltonian of the open qubit eSWAP chain has a diffusive spectral gap, resolving a conjecture of Li, Zheng, Liu, Jiang, and Liu. We also characterise the ground space on every connected interaction graph with at least five vertices and prove a uniform lower bound for the unnormalised complete-graph gap. We apply these results to sequential and brickwork circuits and prove that the periodic chain also has a diffusive spectral gap.

Visuomotor policies can execute familiar tasks yet lack the corrective behavior needed after their own mistakes. We present a framework for recursive self-improvement through local recovery supervision. Each round audits the current policy, generates corrective demonstrations at supported failure states, and uses them to update the policy that drives the next round of collection. An offline auditor locates unresolved failures using coarse and dense temporal evidence and specifies observable repair goals. A fixed multimodal agent acts as a tool-using teacher, generating recovery actions through observation, computation, execution, and feedback. The frozen student tests whether each teacher endpoint supports further progress. If continuation fails, the system restores that endpoint and extends the demonstration. Action-level quality assessment then defines continuous training windows with aligned observations, quality weights, and validity masks. Only the student is deployed. In a preliminary LIBERO-Goal study, recovery-augmented post-training achieves 88 successful episodes out of 100 validation scenes, compared with 78 for original-data continuation from the same $\pi_0$ checkpoint. An earlier BC-RNN study on robomimic Can improves success from 102/130 to 112/130 using 26 local recovery segments. Both comparisons match 2,000 additional optimization steps.

Let $(R,\m)$ be a one-dimensional Cohen–Macaulay local ring with a canonical fractional ideal $R\subseteq K\subseteq\overline R$, and let $v$ denote its embedding dimension. Put $\sigma(R)=\sup\{j\ge0\mid\tr(K^j)\supseteq\m\}$. By definition, $R$ is nearly Gorenstein if and only if $\sigma(R)>0$. We prove that $R$ is almost Gorenstein if and only if $\sigma(R)\ge v$, equivalently, $\sigma(R)=\infty$. Thus every finite value of $\sigma(R)$ is at most $v-1$. We then determine the structure of rings for which $\sigma(R)$ attains its largest finite value $v-1$, just below the threshold for the almost Gorenstein property. This occurs if and only if $K^{v-1}\cong\m$ and $K^v\not\cong\m$. When these conditions hold, $R$ has type two, with multiplicity $e$ greater than $v$ and $e \equiv 3 \pmod{v-1}$. As an application, we characterize the numerical semigroup rings $R$ with $\sigma(R)=v-1$ as those generated by an arithmetic progression, of type two and multiplicity greater than $v$.

In this paper, we prove that for any fixed base $b \ge 2$, there exists an infinite arithmetic progression of positive integers $k$ that are simultaneously generalized Sierpiński and generalized Riesel numbers in base $b$. More precisely, we construct such an arithmetic progression so that both $k\cdot b^n + 1$ and $k\cdot b^n - 1$ have at least two distinct prime factors for every positive integer $n$. Our approach uses covering systems, following the ideas of Erdős and later constructions of Harrington. The argument is then completed using Zsigmondy's theorem on primitive divisors together with properties of multiplicative orders.

We present a new experimental apparatus for matrix isolation spectroscopy capable of growing cryogenic crystal matrices doped with barium monofluoride (BaF), a candidate for measurements of the electron electric dipole moment (eEDM). \\ In this work, BaF molecules are produced in a cryogenic buffer-gas source and used to dope a neon matrix grown on a substrate, cooled by a cryocooler, reaching temperatures as low as 3.2 K. A rotatable flange allows for multiple substrate orientations, optimizing spectroscopic investigations and matrix crystal growth. \\ Fluorescence emission analysis of BaF in neon crystal show emission when exciting the $A\,^2\Pi_{1/2}$, $A\,^2\Pi_{3/2}$ and $B\,^2\Sigma^+$ states, along with the presence of fluorescence from barium atoms in the crystal. A first estimation of the column density of BaF in the crystal is given on the order of $5 \times 10^{-13} \, \text{cm}^{-2}$. \\ We also demonstrated the production of BaF using parahydrogen as the buffer gas of the cryogenic source, a first step toward BaF molecules embedded in a para-hydrogen matrix. \\ Finally, we also observed fast fluorescence decay, attributed to optical bleaching effects, whose amplitude arise at lower temperatures or higher laser intensities, introducing a systematic effect to be studied in future experiments.

Little is known about the early universe on scales smaller than those resolved by the cosmic microwave background (CMB), where electron density fluctuations on kiloparsec to megaparsec scales are expected in many extensions of LCDM. These fluctuations nonetheless leave two imprints on the CMB. They accelerate recombination, the effect behind previous constraints and proposals to raise the inferred Hubble constant, $H_0$. Through correlations along the line of sight, they also reduce the effective Thomson scattering rate, enhancing diffusion damping by an amount that grows with their coherence length. We implement both effects in a modified Boltzmann code, classito, and use CMB data from Planck, ACT DR6, and SPT-3G D1 to place the first limits on such fluctuations that include this modified photon transport. We find no evidence for them: the variance of the electron density contrast is below $0.21$ ($95\%$ CL), falling to $0.033$ for a coherence length of $2\,{\rm Mpc}$, and we present these limits in terms of the electron power spectrum at $1\,{\rm Mpc}^{-1}\lesssim k\lesssim10^2\,{\rm Mpc}^{-1}$. We also reassess small-scale electron density fluctuations as a resolution of the Hubble tension. In Planck data the transport effect is partially degenerate with accelerated recombination, widening the range of $H_0$ allowed: combined with a distance-ladder prior, Planck gives $H_0 = 71.1\pm0.7\,{\rm km\,s^{-1}\,Mpc^{-1}}$ and an improved fit relative to LCDM. ACT and SPT-3G break this degeneracy, chiefly through the temperature–$E$-mode correlation in the damping tail, and with the same prior they give only $H_0 = 69.3\pm0.5\,{\rm km\,s^{-1}\,Mpc^{-1}}$ and no preference over LCDM. With our treatment and publicly available code, models that generate small-scale electron density fluctuations can be directly confronted with CMB data through the variance and coherence length that they predict.

We prove strict Pólya inequalities for every positive Neumann eigenvalue of every Euclidean annulus. The proof preserves the exact Weyl area term through a radial action identity and combines variational bounds with uniform Bessel-phase and angular-sum estimates. Explicit polynomial positivity arguments and angular-layer comparisons cover the remaining finite spectral ranges. We also obtain a positive counting surplus uniform in the radius ratio, an explicit subtraction of order $\sqrt{k}/(R^2-r^2)$ for all $k\ge1604$, and a positive square-root correction over the entire spectrum with a universal, non-explicit coefficient. The square-root order is sharp, and the first positive pair and the low-energy count admit optimal constants expressed by the first positive zero of $J_1'$. Neumann inequalities for annular products and congruent annular sectors follow by established transfer principles.

Bubbles frequently emerge in dense chiral active fluids, yet it remains unclear whether they result from an instability of the homogeneous state or from rare nucleation events within a metastable phase. Here we develop a nucleation theory for chiral bubble formation by reducing the hydrodynamic equations to a single collective coordinate, the bubble radius. This reduction yields an effective nonlinear potential that captures the radial dynamics and predicts distinct stable, metastable, and unstable regimes of the homogeneous state. In the metastable regime, the theory identifies a critical bubble radius and an associated effective mechanical-work barrier, while its large-radius behavior determines whether bubble growth saturates at a finite size or becomes unbounded. We further analyze the stability of circular bubbles against noncircular perturbations, finding growing modes that can lead to elongation and breakup. The theoretical predictions are tested against event-driven molecular-dynamics simulations of chiral hard disks, which reproduce the predicted trends in the critical radius, nucleation barrier, and selected bubble size. Our results establish a unified framework for stability and nucleation in chiral active fluids and suggest routes to control bubble formation in experiments with spinning colloids and chiral spinners.

Recovering three-dimensional human geometry from electromagnetic measure?ments in a complex static environment is difficult because strong multipath responses from walls, floors, and other objects obscure the weak target per?turbation. We propose R1A-PC, a physics-guided method that reconstructs a 2048-point human cloud from paired complex fields measured with and without the target. Complex background subtraction emphasizes target-induced ampli?tude and phase changes, while the background field remains available as an environmental condition. A frequency-balanced discrete Born adjoint produces a three-dimensional spatial knowledge map. At each of two bounded deformation stages, the decoder combines complex measurement features, background fea?tures, and multiscale physical features queried at the current point coordinates; the second stage queries again after the first coordinate update. We analyze the residual of paired subtraction, the weighted normal-operator structure of the raw adjoint, and the feasible set of the predicted cloud. In a held-out background generated by full-wave simulation under a fixed acquisition geometry, R1A-PC obtains a squared Chamfer distance of 0.001434 m2 and an F-score of 0.963080 at 0.05 m. Compared with TopNet, the Chamfer distance decreases by 70.28%. Removing physical guidance or background subtraction increases the Chamfer distance by 242.06% or 241.18%, respectively. Experiments across background layouts and poses support the complementary roles of paired subtraction and position-dependent adjoint features.

Reinforcement learning (RL) policies can deteriorate under out-of-distribution (OOD) magnitude shifts. Starting from soft actor-critic (SAC) and its Bayesian Amnesic Piecewise-Robust (BAPR) predecessor, we study the causal-symbolic BAPR (CS-BAPR) family. The practical method combines six training-stabilization settings with alternative actor heads: a Neural Addition Unit (NAU) with a Neural Multiplication Unit (NMU)-inspired quadratic correction, a Kolmogorov-Arnold Network (KAN), or a multilayer perceptron (MLP) with rectified linear unit (ReLU) or hyperbolic-tangent activations.

This manuscript develops time-varying coefficients neurodynamic models (TVCNDMs) to solve the inclusion problem (IPs) $0 \in \mathcal{P}(w) + \mathcal{Q}(w)$, where $\mathcal{P}$ is a maximal set-valued and $\mathcal{Q}$ is a single-valued operator. The underlying operators are assumed to fulfill a generalized monotonicity condition that is less restrictive than the classical monotonicity assumption. Within this framework, existence and uniqueness of the model trajectories are established, and fixed-time ($\mathrm{FxT}$) convergence of the proposed TVCNDM to the solution of the IPs, along with explicit estimates of the settling time. Furthermore, the robustness of the proposed TVCNDM is investigated in the presence of bounded external disturbances, demonstrating that the $\mathrm{FxT}$ convergence. Numerical simulations support the theoretical results, illustrating rapid error decay and improved transient behavior achieved through the time-varying design.

Controlling the camera relative to a moving subject in an existing video is challenging: behaviors such as maintaining a frontal view require the camera to adapt to the subject's changing position and orientation, making the desired trajectory difficult to specify in advance. Existing camera-controlled video-to-video methods typically rely on explicit trajectories or reference motions, which do not directly express these dynamic camera–subject relationships. We introduce semantic camera motion control, a novel video-to-video task in which a reference video and a target motion label specify the desired subject-relative camera behavior without an explicit target trajectory. Our method, SemCam, learns to realize this behavior while preserving source content. It combines shared-basis low-rank adaptation with motion-conditioned modulation, while a background-consistency loss encourages fidelity in regions visible in both reference and target videos. We construct 661 paired videos covering eight semantic camera behaviors and evaluate on a separate 109-scene benchmark using subject-relative motion metrics, appearance measures, and a user study. SemCam achieves a semantic-motion success rate of 68.6%, compared with 45.3% for Vista4D, the strongest evaluated baseline, while maintaining comparable subject identity preservation.

As agents rapidly evolve, existing benchmarks can become saturated, limiting their ability to distinguish capabilities and reveal remaining failure modes. Particularly in scientific domains, constructing and updating benchmarks requires substantial time, labor, and domain expertise, making it difficult to keep evaluation aligned with advances in agent capabilities. We address this challenge by investigating whether scientific-agent benchmarks can be automatically generated and iteratively adapted as agent capabilities evolve. We introduce AutoSciBench, a framework that represents each task as a high-level concept specifying the scientific domain, data modality, and required reasoning approach, together with a low-level recipe specifying how the question, environment, and ground-truth answer are constructed and verified. Agents attempt to solve each task, producing solver trajectories and corresponding judge feedback which AutoSciBench uses to revise the recipe or concept, closing observed shortcuts and shifting tasks toward raw-data re-examination, interpretation of intermediate results, and evidence integration. Experience distilled from completed refinement trajectories further guides new concept generation, allowing lessons from earlier task refinement to inform subsequent benchmark construction. Starting from existing benchmarks, we evaluate AutoSciBench across computational biology, materials science, and clinical imaging. Generated benchmarks reduce average solver accuracy by 22.4 and 25.5 percentage points relative to the human-curated benchmarks in computational biology and materials science, respectively, while generated tasks receive higher average quality ratings across all three domains, suggesting that scientific-agent evaluation can adapt as agent capabilities advance.

Code large language model (Code LLM) assistants generate code from heterogeneous development contexts, including open files, imported modules, pasted snippets, and comments, much of which may originate from untrusted sources. We investigate whether insecure instructions embedded in such contexts can steer Code LLMs toward vulnerable code without access to model weights or training data. We evaluate ten open-weight Code LLMs spanning 3B–13B parameters, including four base and six instruction-tuned models, across ten web-application weakness classes. We compare completion tasks containing insecure instructions embedded as code comments with benign tasks without malicious instructions. Attack-condition completions contained a medium-or-higher weakness in 77.4–92.3% of cases, compared with 1.7–5.1% in the benign condition. Base and instruction-tuned models averaged 86.5% and 84.5% vulnerable outputs, respectively; equivalence testing and three matched model pairs indicated reductions of at most 8.1% after instruction tuning. Susceptibility showed no clear association with model scale or specialization. Among vulnerable attack outputs, 86.2–91.0% were rated high or critical, and the effect persisted without the pattern-based detector. Post-generation screening reduced but did not eliminate the risk, the strongest screen leaving roughly one-third undetected. These findings identify inference-time context injection as a substantial attack surface and motivate provenance-aware training objectives.

We propose a single-call variant of Polyak extragradient, termed SPolyakEG, by recycling the previous extrapolation operator evaluation. Under a delayed critical condition, we establish that SPolyakEG achieves an $O(1/K)$ residual convergence rate for monotone operators and linear convergence under strong monotonicity. Compared with PolyakEG, SPolyakEG reduces the number of operator evaluations from two to one per iteration.

We compute homotopy groups of $n$-fold iterated topological Hochschild homology of $\mathbb{F}_p$ for $n\geq1$ and odd primes. Identifying this as the Loday construction $T^n\otimes\mathbb{F}_p$, we construct a bar spectral sequence computing $\pi_*(T^n\otimes\mathbb{F}_p)$ and prove that this spectral sequence collapses at the $E^2$-page. Finally, we resolve the multiplicative extensions and determine the ring structure.

We construct secure cyclic multi-access coded caching schemes by re-encoding the caches of a secure single-access scheme and reusing its multicast message unchanged. For a library of $N$ files, each of $K$ users reads $L<K$ consecutive shared caches and must recover its requested file while learning no information about the other files. Starting from a parent scheme with a cyclic representation of its cached symbols, the transformation lets each access window recover the corresponding parent-cache symbols and, conditioned on them, learn nothing about the remaining symbols. A deterministic Pascal-window encoder handles symbols whose consecutive appearances span at least $L$ users. A randomized complement-dual encoder handles shorter spans. Over a suitable finite field, these encoders attain the exact minimum per-block storage for every input length in the block-separable, parent-preserving class. Applying the transformation to two secure single-access schemes gives an achievable memory-rate family for $N,K\ge2$ and $1\le L<K$, including the exact rate-one cache size $(N-1)(K-1)/L$. Using converse bounds for arbitrary secure multi-access schemes, we prove approximation guarantees for the achievable family and give a proof of the exact $L=K-1$ tradeoff.

Under a fixed physical law, the visible geometry of a scene determines how motion must change. We ask how video generators realize this relationship. We fix the law and the initial state and change only the geometry drawn in the first frame, within matched families of tracks and deflectors, and compare each generated trajectory with the simulator prediction for that geometry. Paired interventions change one thing at a time: a local bump, the height of a barrier, the words of the prompt, the length of the clip. Across nine image-to-video models, geometry is preserved and shapes the motion: the speed of the ball follows the drawn undulation of a track. A physical state would carry this response forward, and here the generated motion parts from the law. The mean slope barely accelerates the ball, successive contacts fail to compose through a consistent state, an edit ahead of the ball alters its motion before it arrives, and the ball climbs over barriers higher than its release point. Two global conditions organize the global trajectory: text strongly controls the destination, while clip length strongly controls timing in the open-weight models tested. The pattern persists with photographed first frames. Current video generation thus behaves as geometry-conditioned motion synthesis whose evolution of state differs systematically from that of a fixed physical law.

Two-sample Mendelian randomization with summary statistics has become a popular MR design in Epidemiology. Its ratio estimate has an average causal effect interpretation only under strong untestable assumptions including linearity. We derive what the per-variant ratio, and the pooled and robust estimators built from it, estimate when a continuous exposure has a nonlinear effect, under two conditions on how genetic variation and unmeasured factors shape exposure: no unmeasured common effect modifier, and an exposure control function. Under either condition, each variant's ratio is a weighted average of the slope of the dose-response curve, with weights that depend on how that variant moves the distribution of exposure and that are nonnegative when the exposure distributions at different genotypes do not cross. Variants that shift everyone's exposure equally target nearly the same quantity; variants acting at particular doses or on the spread of exposure target different ones, some outside the range of any individual effect. Pooled estimates therefore have no fixed interpretation, heterogeneity tests and MR-Egger misread nonlinearity as pleiotropy, and summary statistics cannot reveal the problem, even when the dose-response curve is identifiable from individual-level data. For continuous exposures, two-sample estimates rest on a linearity assumption that should be stated and defended; individual-level exposure data resolve the problem and should be prioritized.

The exponential, pervasive rise of artificial intelligence (AI), hosted in large data centres, will test the limits of the underpinning infrastructure, including electricity and water supplies, which are becoming increasingly precious resources. Rather than performing all AI computations in centralized servers, for many functionalities, these can be performed locally across a network of billions of small, autonomous nodes, saving substantial energy costs associated with communication. This alternative paradigm is known as edge computing, or distributed intelligence (DI), but has been held back by the lack of availability of reliable local energy supplies matching the energy requirements of the computational infrastructure. Opportunities to address this challenge are emerging with rapid advances in high-performance indoor photovoltaics (IPVs) for local energy harvesting, as well as reductions in computational cost through neuromorphic or in-memory computing devices. In this perspective, we discuss the requirements of IPVs for DI, the extent to which emerging materials fulfil these requirements, and how current gaps could be addressed. We make the case that (anti)ferroelectric materials can surpass bottlenecks for both electrostatic energy storage and low-power in-memory neuromorphic computing. The core theme of this perspective is that co-creation between energy harvesting, storage and computing is essential for making DI a reliable and more sustainable alternative to centralized AI.

Formal specifications are essential for deductive program verification, providing semantic abstractions for compositional verification of complex software. However, manually constructing specifications is labor-intensive, motivating automated synthesis. Despite recent advances in large language models (LLMs), existing approaches often rely on forward-only workflows and localized repair, limiting their effectiveness on real-world programs with complex dependencies among functions and loops. Verification failures may stem from previously generated specifications, causing cascading failures that local refinement cannot resolve. To address these challenges, we present SpecAgent, an agentic framework for synthesizing high-quality ACSL specifications for real-world C programs. SpecAgent integrates four components: dependency-aware planning to identify specification targets, retrieval-augmented generation (RAG) to provide relevant specification patterns and program context, agentic repair to diagnose defects and revisit dependent specifications, and agentic critique to assess and refine semantic strength beyond proof success. We evaluate SpecAgent on specification synthesis and program verification tasks. On 50 programs from 14 real-world repositories, SpecAgent with DeepSeek-V4 achieves 96.82% precision and 88.95% recall in synthesizing correct and strong specifications, outperforming all baselines. On 811 real-world verification targets, it successfully discharges 604, also surpassing existing baselines. These results demonstrate SpecAgent's effectiveness in synthesizing high-quality specifications and facilitating real-world program verification.

Intermediate-layer features from multimodal large language models have shown strong potential for video anomaly detection (VAD), yet the origin of their discriminative power remains unclear. We study this question using sparse mixture-of-experts (MoE) models, whose explicit expert structure and sparse activation make their internal computation easier to inspect. With a fully frozen backbone and no additional training, we find that anomaly-related evidence is concentrated in a small set of experts. These experts recur across layers, spontaneously specialize in different anomaly types, and together form a dynamic routing subnetwork. We further show that the output channels most strongly influenced by these experts are also the hidden dimensions that contain the most anomaly-relevant information. Routing statistics can therefore serve as an internal anomaly cue that complements semantic features.Based on these findings, we propose RoMod, an efficient VAD framework trained with only \(5\%\) of weakly labeled videos. RoMod includes a Routing-Modulated Fusion module, RoMF, and a Routing-aware Temporal Network, RoTN. RoMF uses routing signals to adaptively recalibrate hidden semantic channels. Its design also prevents the routing branch from bypassing semantic features and making predictions on its own. RoTN captures the temporal evolution of anomalies from onset to persistence and termination. Experiments on three benchmarks show that RoMod achieves state-of-the-art performance while running substantially faster than dense backbones of comparable size.

An electromagnetic inversion scheme that integrates stochastic optimization (STO) and plug-and-play (PNP) regularization into contrast-source inversion (CSI), termed STO-PNP-CSI, is developed. Standard CSI solves for the contrast source vector of every transmitter at each iteration, which is expensive in a multi-transmitter configuration. STO instead solves for only one randomly selected contrast source vector per iteration, which reduces the per-iteration cost and can help the inversion escape poor local minima and saddle points. The resulting loss of information, however, increases the ill-posedness of the inversion. To counter this, the Swin-Conv-UNet (SCUNet) denoiser is plugged into the CSI scheme as an implicit regularizer, supplying a learned prior that is stronger than conventional hand-crafted ones and stabilizes the reconstruction. The proposed STO-PNP-CSI is applied to both synthetic and experimental data. The results show that it yields accurate reconstructions at substantially lower computational cost than CSI, including under strong nonlinearity and measurement noise.

Multimodal Large Language Models (MLLMs) provide a natural way to make video anomaly detection more explainable. However, their final decisions do not always fully use the discriminative information contained in their hidden states, an issue we refer to as representation–behavior misalignment. We decompose this gap into a capacity component that measures discriminative information never aggregated into the readout position, and a directional component that measures the angular mismatch between the optimal and the native normal–abnormal axis at that position. Across multiple video anomaly detection benchmarks and MLLM backbones the directional component dominates, and residual-stream tracing shows that native-axis separability rises sharply in several mid-to-late attention layers. Because both components are governed by attention rather than MLP updates, we propose Representation–Behavior Alignment (RBA), a parameter-efficient method that adapts those layers using video-level labels alone while updating about 0.012% of the backbone parameters. Experiments on three benchmarks show that RBA improves native-readout performance and better aligns the model's decision direction with discriminative representations, and it produces anomaly decisions and explanations through a single generative process.

Variational quantum algorithms (VQAs) generally rely on classical optimization to train parameterized quantum circuits. This training seeks to minimize an objective function, and its efficiency is central to the practical success of these algorithms. However, globally minimizing such training objectives over the circuit parameters is known to be $\mathsf{NP}$-hard, limiting the prospect of general guarantees for efficient training. In this Letter, we prove that even the weaker task of finding a local minimum of such VQA training objectives is strongly $\mathsf{NP}$-hard, including when the objective admits efficient classical evaluation. Moreover, we show that this hardness persists even for the task of finding a parameter vector within $\ell_p$-distance strictly less than $\pi/2$ of some local minimizer, for every $p\geq 1$. Our central technical result is that approximating a local minimizer of a Hermitian trigonometric polynomial is strongly $\mathsf{NP}$-hard. By explicitly constructing quantum circuits whose training objectives reproduce these hard instances, we obtain a polynomial-time reduction to VQA training. Our results establish a fundamental computational barrier to variational quantum training: even reaching the vicinity of a local minimum remains hard in the worst case.

Physics-informed neural network (PINN) training minimizes a weighted combination of partial differential equation (PDE), boundary-condition, and initial-condition losses. Because adaptive methods modify these weights during training, their weighted total losses are not always directly comparable. We compare fixed-weight PINN, gradient-normalized PINN (GNPINN), and a rule-based adaptive controller (AgenticPINN) under matched settings on a heat-equation benchmark and a simplified Czochralski-oriented thermal-fluid problem. In the crystal-growth MLP experiment, adaptive control reduced the PDE residual from the order of $10^{-5}$ to $10^{-6}$, while the boundary-condition loss increased from the order of $10^{-5}$ to $10^{-2}$. On the heat-equation benchmark, GNPINN achieved the lowest relative $L_2$ field error (0.054), whereas AgenticPINN obtained the smallest PDE residual but a relative $L_2$ error of 1.368. Gaussian-process surrogates were additionally evaluated using case-wise holdout tests on corrected Czochralski CFD parameter sweeps. The temperature-field error for the temperature sweep was approximately 6%, whereas the axial-velocity error for the crystal-rotation sweep was approximately 42%. These findings show that adaptive control can improve equation satisfaction while weakening other physical constraints. PINN training should therefore be evaluated using separate PDE, boundary-condition, and solution-error metrics rather than weighted total loss alone.

The repetition count that works best for a small language model may not remain best at a larger scale. We study this effect in pretraining with a finite target corpus mixed with generic data at a fixed target fraction. On Wikipedia-derived data and Proof-Pile-2, the ranking of measured repetition counts changes with model size, and a 520M Proof-Pile-2 experiment confirms that reducing repetition from sixteen to eight improves loss while using fewer training tokens. We use loss curves from several smaller models to retain a short list of promising repetition counts for evaluation at a larger scale. On PubMed and Caselaw, candidate sets fixed before target-model training retain the lowest-loss measured count on the original evaluation grids at both 200M and 520M. This supports candidate retention as a practical alternative to exact point prediction. We also relate the pruning regression to an empirical scaling model with two opposing repetition-dependent loss terms. A first-order expansion in log model size yields the linear form used by the selection rule, providing a scaling-based interpretation of the candidate-selection procedure.

Masked Diffusion Language Models (MDLMs) generate sequences by iteratively replacing masked tokens with model predictions. At each denoising step, the decoder chooses which positions are sufficiently confident to commit. Existing decoding methods typically rely on softmax confidence, which can be miscalibrated. We introduce BayesER (BAYESian Entropy-based Reordering), a post-hoc Bayesian decoding framework that uses predictive uncertainty to guide token commitment. In BayesER, we construct a lightweight approximate posterior centered at the pretrained checkpoint, similar to Laplace-LoRA but without training LoRA adapters. We average predictions over posterior samples and use predictive entropy to prioritize reliable positions. We examine how posterior predictions affect position ordering and token selection across benchmarks spanning code generation, mathematical reasoning, planning, and molecular generation. We show that BayesER reduces sequence-level calibration error while preserving or improving accuracy relative to common decoding schemes, including confidence-threshold decoding. Additionally, a posterior fitted on one code-generation dataset reduces calibration error on another without refitting, suggesting that Bayesian uncertainty may provide a transferable signal for more reliable MDLM decoding.

Persistent memory for Large Language Models (LLMs) has matured rapidly: systems such as MemGPT/Letta, Mem0, and Zep now provide agents with tiered, temporally-aware, model-agnostic external storage, while the Model Context Protocol (MCP) standardizes access to memory servers. A less addressed problem is that an identical stored memory object, retrieved by two different LLMs under otherwise identical conditions, may not be interpreted the same way, factually or emotionally. This paper proposes memory canonicalization: a write-time pipeline that detects ambiguity, conditional structure, and emotional loading in a raw memory object and rewrites it into an explicit, structurally disambiguated canonical form, with emotional valence represented as a separate field rather than inferred from tone. We formalize the pipeline, define a companion Cross-Model Semantic Drift / Emotional Consistency Score benchmark (CMSC-E), and report results from a three-arm pilot using 176 synthetic memory objects and three downstream model families. We find an uncorrected improvement in cross-model emotional consistency for fully canonicalized memory relative to raw memory (+0.050, 95% bootstrap CI [0.013, 0.086], paired t-test p = 0.010), but this result does not survive Bonferroni, Holm, or Benjamini-Hochberg correction across the six comparisons tested. None of the factual-drift (CMSD) comparisons reach significance at any correction level. We report these results as exploratory rather than confirmatory and outline needed follow-up work, including larger samples, independent judge models, human-validated rendering, and preregistration.