Papers

Test-time memorization of sequential information is a foundational capability for any intelligent system that needs to rapidly store and retrieve data, as demonstrated by the attention mechanism in large language models. However, Transformers and linear attention variants are trained via backpropagation through time (BPTT), which has drawbacks such as its enormous memory requirements. Predictive coding (PC), an algorithm that optimizes a prediction-error energy function with local updates, offers a compelling solution but still lacks test-time memory for sequential data. We develop a solution to this problem by treating the per-step memory update $\Delta S_t$ as a latent variable, as opposed to a slow weight to be learned. By taking the log probability of a standard PC-based probabilistic model, we derive a PC-native solution for verbatim sequence memory, and relate our update rule to common choices in the linear attention literature (e.g., DeltaNet). We present an extensive set of empirical tests to probe our system's properties, including its scaling capacity, memory footprint, and ability to infer a context from evidence (e.g., bank (river) vs. bank (money)). We show how DeltaNet-PC can be used for storing single sequences of data, multiple sequences of data, and key-value associative memory pairs with perfect recall accuracy.

The rapid proliferation of distributed energy resources (DERs) aggregated by virtual power plants (VPPs) elevates cybersecurity risk by expanding the attack surface. A coordinated cyberattack has the potential to disrupt distribution-system, bulk-system, and market operations. Existing cyberphysical defense strategies largely assume access to grid network models and operating conditions, which may not be available to third-party aggregators. This paper proposes a novel hybrid, perturbation-based cyber-physical defense for VPP-operated DERs that blends game-theoretic planning with model-free reinforcement learning (RL) under a Bayesian belief-update framework. Topology agnosticism is defined from the VPP information and implementation perspective: the VPP does not require access to the feeder topology, line parameters, switching configuration, or full system state. This work advances the state of the art through three contributions: (1) a multi-output Gaussian process with Hamiltonian Monte Carlo for discrete attacker-type inference, probability of detection, and confidence of detection for modeling the belief distribution; (2) moment-matched Gaussian propagation of posterior beliefs across episodes; and (3) an RL policy that adaptively integrates Stackelberg leader (VPP) actions with exploration. Furthermore, we establish equilibrium existence and derive an episode-level closed-loop utility bound connecting attacker-belief uncertainty with GT-RL action alignment. Evaluations on IEEE 13- and 123-Bus feeders with DER portfolios demonstrate effective detection under attacker-model uncertainty and evaluated feeder re-configuration conditions, while requiring no explicit feeder-topology knowledge. Overall, the results indicate that combining bi-level game-theoretic planning, nonparametric Bayesian inference, and adaptive RL is a promising direction for VPP cybersecurity.

As agentic AI systems take on increasingly complex and consequential tasks, securing them against prompt injection becomes critical. Existing defenses often rely on detecting or reasoning about injected malicious instructions and can therefore remain vulnerable to adaptive attacks that optimize the injection itself. Diffusion language models (dLLMs), an emerging framework for language generation, offer a new opportunity for security enforcement: by iteratively refining their sequence wide predictions, they enable broader-scope constraint enforcement throughout generation. This paper introduces Policy-Constrained Diffusion Agents (CoDA), a framework that enforces task dependent security policies directly within the denoising process of diffusion language models. At each denoising step, CoDA projects token distributions onto a policy-compliant set, maintaining constraint satisfaction throughout generation. We evaluate CoDA across state-of-the-art diffusion language model families under both static and adaptive prompt-injection attacks. Results demonstrate substantial reductions in attack success rate with competitive task utility and practical inference overhead.

We investigate whether a physics foundation model (PFM) pretrained for PDE forecasting can be repurposed for closed-loop fluid-flow control. We construct a PFM-based controller by attaching lightweight Gaussian actor and critic heads to frozen pretrained representations and train the policy using proximal policy optimization (PPO). We evaluate the approach on HydroGym's two-dimensional Kolmogorov-flow environment using vorticity observations at \(64\times64\) and \(128\times128\) resolutions and Reynolds numbers \(\mathrm{Re}=100\) and \(200\). Across these settings, we compare the frozen PFM controller against a baseline MLP policy trained with the same PPO framework. The PFM controller achieves consistently higher reward while requiring smaller executed action magnitudes over training, indicating improved control performance with reduced control effort. These results provide initial evidence that representations learned through self-supervised next-frame prediction can be transferred directly to closed-loop fluid flow control. Project page: https://mahindrautela.github.io/morph.

Canonicalization resolves the rotational and permutation ambiguity of 3D point clouds by selecting a unique orbit representative, maintaining their geometric information while allowing standard architectures, such as Transformers, to operate on them. Existing canonicalizations, however, exhibit discontinuity jumps on molecular configurations and non-trivial invariance errors in popular molecular datasets, which lead to ambiguity in their representation. To bridge this gap, we introduce LexiCan, a canonicalization that is provably invariant under either $O(3)$ or $SO(3)$, empirically invariant to rotations to within $\sim 10^{-6}$ angstroms on the QM9 and QM-sym molecular datasets, and mitigates discontinuity jumps on QM-sym, while running orders of magnitude faster than an existing canonicalization. Finally, non-invariant models perform better on QM9 property prediction and ModelNet40 shape classification with LexiCan than with that canonicalization.

A language model's ability to solve a task individually does not ensure that a team can solve it under unequal access to information and communication. SANZARU examines this gap through cooperative bomb-defusal puzzles adapted from BOMBANANA! (Lefto Studio, 2026). Task information and action authority are divided among three agents: one cannot hear, another cannot speak, and the third cannot see. The benchmark contains 120 puzzle instances across seven families, each targeting a distinct coordination ability. Across 1512 episodes, 7 models achieve an overall success rate of 49%, ranging from 20% to 86% under the evaluated configurations. Teams develop or adopt diverse communication protocols, from simple gesture codes to Morse and encodings of entire manuals. Yet trace analysis attributes about 60% of 771 team losses to communication, and agents attempt to use channels unavailable to their teammates despite explicit role instructions. Together, task outcomes and interaction traces enable evaluation of both collaborative performance and perspective taking throughout cooperation. The benchmark is available at https://github.com/markli404/sanzaru-benchmark.

Existing depth-compression methods for large language models (LLMs) score layers individually or group only adjacent or contiguous layers, implicitly assuming that functional redundancy is local. We test this assumption by computing full pairwise Centered Kernel Alignment (CKA) similarity matrices for thirteen LLMs from six architecture families (1.6B-14B parameters). Non-adjacent layers have 3.6-15.9x more high-similarity pairs than adjacent ones, a structure that prior similarity-based layer merging has not systematically exploited. We propose Fusion via Community Mining (FCM), which builds the full L x L similarity graph, uses spectral community detection to find clusters of functionally equivalent layers, keeps the highest-Block-Influence layer in each cluster, and applies LoRA recovery; a pre-specified rule computed only on calibration data chooses between cosine and CKA similarity. At 2x compression, FCM lowers mean perplexity below ShortGPT on twelve of thirteen models, significantly on ten (Welch's t-test with Holm-Bonferroni correction; up to 50% on Qwen3-4B), with Mistral-7B the only loss (+13.4%). Against FlattenGPT, SWM, and DeltaLLM under matched calibration and recovery, FCM gives the best perplexity on ten of thirteen models (mean rank 1.15), and it also outperforms MKA on three anchor models. FCM matches or exceeds ShortGPT on 15 of 20 zero-shot reasoning cells and also improves MMLU, LAMBADA, HumanEval pass@1, and free-form generation quality. The 2x-compressed Qwen2.5-7B has 46% fewer parameters, 42% lower peak VRAM, and 84% higher decode throughput on a single A100. Spectral grouping outperforms Fisher contiguous segmentation by 41% and uniform partitioning by 51%, and FCM's advantage grows beyond a 2x crossover up to 3x and persists at the 14B scale. Code: https://github.com/Usama1002/fcm-layer-fusion

Distribution-system state estimation is a growing necessity for the modern power grid as the addition of local storage and generation add system complexity that an operator or aggregator is not able to directly monitor. Classical methods work well when all system elements are time-synchronized and at least partly observable, but multi-rate monitoring of sparse heterogeneous sensors typically relies on machine learning approaches. It is a common practice in the literature to structure this task as a two-stage pipeline, first fusing data from disparate sensors and then feeding the fused pseudo-measurements to a separately trained state estimator. We propose a heterogeneous latent graph ODE in which measurement functions and sampling processes are typed and localized on specific buses, paired with a graph- transformer state estimator solving DSSE specifically for multi-rate heterogeneous sensor placements, and demonstrate its effectiveness across multiple IEEE standard topologies as observability degrades.

Spiking neural networks target energy-efficient language modeling through sparse, binary activations, but the efficiency-accuracy tradeoff of spiking language models is uncharacterized at scale. We present the first Chinchilla-style IsoFLOP scaling study of a spiking language model, sweeping SpikeGPT-family models (RWKV backbone) from width 384 to 1536 across compute budgets from $3\times10^{17}$ to $10^{19}$ FLOPs on FineWeb-EDU. We report two findings. First, the compute-optimal frontier is $N_{opt} \propto C^{0.56}$, close to the 0.50 that Hoffmann et al. report for dense Transformers, so spiking does not change how parameters and data should be traded off under a compute budget. Second, against non-spiking RWKV and Transformer baselines trained the same way, the loss gap splits into a backbone cost of about 0.16 nats that does not change with compute and a spiking cost that falls from 0.34 to about 0.23 nats and then levels off. These results give the first compute-optimal recipe for spiking language models and quantify the accuracy cost of their sparsity.

Linear-attention and state-space LLMs carry long context in a fixed-size recurrent state, and quantizing that state is the natural way to cut its cost during long decode. Unlike a weight tensor, the state is rewritten at every step, so a quantizer applied at each step sits inside the recurrence and its errors compound. INT4 that leaves synthetic recall perfectly intact at the start destroys it a thousand steps later. The mechanism is a feedback between the quantizer scale and the state it is derived from. Yoking that scale to a full-precision reference removes the resulting norm explosion entirely, yet recovers only 1.8 of the 5.4 nats lost, so numerical instability and functional degradation are separable failures. The remainder is a resolution problem that locating outliers does not solve, since every outlier-aware scheme here loses to plain persistent scaling. Allocating bits across layers does help, but under article-disjoint splits a learned allocation collapses onto the trivial rule of protecting the first few layers. Run out to 32K, group-wise INT4 is worth no more than discarding the state. Contain the scale rather than locate outliers, and report the decode horizon at which a bit-width was certified.

Modern AI systems increasingly combine large language models (LLMs) with human experts, using the LLM to handle routine queries while deferring uncertain cases for expert review. When expert capacity is limited, however, deferral decisions must account not only for the reliability of the LLM but also for congestion in the expert queue. We formulate this as an online sequential decision-making problem in which, for each query, the system observes the confidence signal of the LLM's answer and must decide whether to output the answer or defer the query to a capacity-constrained expert. The reliability of the confidence signal is initially unknown and must be learned from expert feedback, which is both selectively observed (only deferred queries are labeled) and delayed by queuing. We propose KL-PBD, a learning algorithm that uses Kullback–Leibler lower confidence bounds on the unknown reliability parameters to guide deferral decisions. For $K$ confidence levels and horizon $T$, KL-PBD achieves $O(K\log T)$ gap-dependent regret when the accuracy at every confidence level is bounded away from the deferral boundary, and $\widetilde{O}(\sqrt{KT})$ worst-case regret. We establish matching lower bounds, showing that these rates are optimal up to logarithmic factors. Finally, we validate our approach on synthetic instances and real-world question-answering datasets, namely GSM8K, NuminaMath, and MedMCQA, using Qwen LLMs.

Traffic sign recognition plays a crucial role in the development of autonomous cars to reduce the accident rate and promote road safety. It has been a necessity to address traffic signs that are affected significantly by the environment as well as poor real-time performance for deep-learning state-of-the-art algorithms. In this paper, we introduce Real-Time Image Enhanced CNN ({\our}) for Traffic Sign Recognition. {\our} is a real-time, novel approach that tackles multiple, diverse traffic sign datasets, and out-performs the state-of-the-art architectures in terms of recognition rate and execution time. Experiments are conducted using the German Traffic Sign Benchmark (GTSRB), the Belgium Traffic Sign Classification (BTSC), and the Croatian Traffic Sign (rMASTIF) benchmark. Experimental results show that our approach has achieved the highest recognition rate for all Benchmarks, achieving a recognition accuracy of 99.75% for GTSRB, 99.25% for BTSC and 99.55% for rMASTIF. In terms of latency and meeting the real-time constraint, the pre-processing time and inference time together do not exceed 1.3 ms per image. Not only have our proposed approach achieved remarkably high accuracy with real-time performance, but it also demonstrated robustness against traffic sign recognition challenges such as brightness and contrast variations in the environment.

Decentralized learning must balance collaboration with personalization across heterogeneous agents. This paper studies when cooperation can support statistically coherent groups of personalized models. We show that data-topology compatibility enables robust orbit-wise personalization: when local objectives and communication topology have (approximately) compatible automorphisms, agents within an orbit share (approximately) equal limiting distributions, while different orbits remain distinct without explicit personalization. This creates a new intermediate regime between global consensus and independent local learning. Under exact data-topology compatibility, as a reference system, we decompose the stochastic learning dynamics into orbit-level and transverse components, derive a necessary and sufficient stability criterion for distributional synchronization, and characterize the orbit-structured stationary law. Modelling an approximate data-topology compatible system as an $\varepsilon$-perturbed reference system, we prove the introduced errors have uniform-in-time and stationary $O(\varepsilon)$ bounds in 2-Wasserstein distance. We also prove sufficient conditions for lower stationary average excess risk than both independent local training and the best single shared parameter. Experiments on synthetic data, MNIST, and CIFAR-10 are in full agreement with the theory. The code is available at https://github.com/Veronicaaa1/orbit-personalization.

Foundation models need to support diverse inference budgets, yet training a separate model for each budget duplicates pretraining effort. Elastic models train several nested sub-networks inside one weight-shared supernet, but existing recipes face three obstacles: variable per-step workloads that hinder distributed scaling, limited hyperparameter (HP) transfer across model sizes, and no guarantee that all sub-networks are maximally updated at once. We present \Ours, an elastic transformer that organizes hidden dimensions into a dense core and successive shells, so that every hidden matrix is block lower triangular. One full-width forward pass contains every sub-network's exact hidden states as prefixes, so joint training keeps a fixed computation graph and costs about as much per step as training the widest sub-network alone. We further introduce \muE, an extension of maximal update parameterization (\mup) to \Ours and other elastic architectures. Its scaling rules provably keep all sub-networks of a supernet maximally updated simultaneously (\muI), and keep doing so when the supernet is widened or given more shells; sweeps confirm that HPs tuned on a small non-elastic proxy stay near-optimal for elastic families and larger supernets (\mbox{\muT}). A single \Ours run produces sub-networks that outperform MatFormer and fully elastic baselines at matched parameter counts, and approach separately trained models that together take several times the steps.

To evaluate whether a compact bidirectional state-space autoencoder improves joint classification of species, cell type, and disease state from single-nucleus RNA-sequencing profiles in heart failure (HF), while yielding interpretable gene attributions. Building on the dense denoising autoencoder (DAE) and MLP framework of Ruz Jurado et al., we developed scHFBiMamba, combining a bidirectional Mamba autoencoder (BiMambaAE) with an MLP head. BiMambaAE maps 16,545-gene profiles to 350-dimensional latent representations using 13.2M parameters, about 14.6-fold fewer than the dense DAE (192.9M). We compared six encoder-classifier configurations on 38,275 held-out cardiac nuclei using McNemar tests with Benjamini-Hochberg correction, and assessed nine classifiers on frozen representations. Biological relevance was evaluated by comparing SHAP-derived differentially explained genes with differentially expressed genes against curated HF-related Gene Ontology keywords. BiMambaAE+MLP achieved the highest aggregate F1: pooled macro-F1 across 13 outputs was 0.966 versus 0.957 for DAE+MLP, and the mean category macro-F1 was 0.977 versus 0.970. It significantly improved cell-type and disease-state accuracy (adjusted p=7.1e-3 and p=4.8e-6, respectively), with species F1 of 1.000. SHAP-derived differentially explained genes achieved a pathway-enrichment benchmark F1 of 0.105 versus 0.053 for differentially expressed genes. Compact bidirectional state-space autoencoders can outperform substantially larger dense autoencoders for joint cardiac transcriptomic classification while reducing parameters. scHFBiMamba enables accurate multi-task prediction and hypothesis-generating gene-level interpretation. Code: https://github.com/UgoLomoio/scHFBiMamba.

Data and the governing partial differential equations (PDEs) of continuous-time dynamical systems provide rich structure for statistical learning. A central challenge is how to integrate data with PDE constraints in a principled way to improve generalization. In this paper, we characterize the statistical estimation and generalization properties of learning solutions to the heat equation with a noisy source function from finite, randomly sampled data. We first derive a novel variational formulation, which we characterize as the minimizer of loss function for an energy regularized and ellipticity debiased Sobolev regression. By formulating the learning task as a supervised problem over space-time domains under physically meaningful norms, our approach goes beyond the traditional supervised learning framework by effectively leveraging auxiliary data—samples of the source function of the heat equation—to design a physics-informed energy regularization. Our analysis reveals that learning in linear parabolic PDEs exhibits intrinsic anisotropy between spatial and temporal regularity, in sharp contrast to the static elliptic problems, leading to fundamentally different estimation and generalization behaviors. Specifically, we derive non-asymptotically rate-optimal estimation errors, as well as generalization error, which explicitly capture the interplay among temporal sampling, spatial resolution, and solution smoothness. Our numerical experiments demonstrate substantial orders of magnitude of reduction in testing errors against various physics-informed neural network methods on various parabolic and hyperbolic PDEs.

Latent recursion repeatedly processes internal representations through the same neural network. Recent work has shown this approach to be effective on structured reasoning tasks such as Sudoku and maze solving. However, whether latent recursion can support neural routing remains unclear. We introduce RELAGRAM (Recursive Latent Graph Model), a novel approach that brings latent recursion to graph combinatorial optimization. RELAGRAM encodes a capacitated vehicle routing problem (CVRP) instance as edge tokens; a compact transformer recurrently updates the latent representations of these tokens. An output head maps the answer state to an edge heatmap, from which an autoregressive decoder constructs a feasible solution. On CVRP-100 instances, the 0.53M-parameter RELAGRAM achieves gaps to a PyVRP reference of 13.4%, 9.8%, and 8.3% under greedy decoding, eightfold symmetry augmentation, and 256-candidate search, respectively. Trained only on CVRP-100, RELAGRAM generalizes zero-shot to CVRP-500 and CVRP-1000, achieving gaps of 15.6% and 21.7% under 256-candidate search. Together, these results demonstrate that latent recursion is a promising approach to neural routing.

Weighted sums of random kitchen sinks (W-RKS) is a commonly used feature extraction technique for supervised learning tasks. A major drawback of this method is the redundancy and ineffectiveness of many extracted random features. This paper investigates efficient methods for reducing such redundancy in multi-class classification problems. We specifically formulate feature selection as a variant of the sequentially nested model selection problem and introduce the Successive Empirical Excess Risk Difference Maximization (SEED-MAX) algorithm. It recursively computes empirical risks to identify the most parsimonious yet informative set of features. We derive an analytical lower bound for the probability of correct feature selection by the SEED-MAX algorithm. This lower bound on the probability of correct feature selection can be made arbitrarily close to one by increasing the training dataset size. To further enhance the rate of pruning, we evaluate the features retained by SEED-MAX using the Fisher test (F-Test). Empirical evaluations on UCR time-series classification datasets show that the sequential application of SEED-MAX with the Fisher test achieves approximately 92 percent rate of pruning with negligible degradation in classification accuracy. Implementations of the SEED-MAX and SEED-MAX-F-Test methods are available at https://github.com/OmidiAmin/seed-max-ftest.

Diffusion language models (DLMs) offer new opportunities for controllable text generation. However, their controllability, defined as the ability to satisfy task constraints while preserving their original capabilities, remains underexplored. DLMs' bidirectional attention allows control tokens to guide generation from arbitrary positions in the output sequence, but effective guidance depends on the compatibility between their content and placement. To this end, we propose AnchorDLM, a framework in which an anchor generator produces an anchor consisting of a short output fragment and its position for each query. The anchor is placed as control tokens at the specified position to initialize the output sequence of a frozen DLM and guide subsequent denoising. We train the anchor generator with reinforcement learning (RL) to jointly optimize anchor content and placement, using rewards computed from the DLM's generated outputs based on answer correctness and constraint satisfaction. Moreover, through the lens of discrete flow matching (DFM), we interpret anchor placement as helping to reshape the initial velocity field that guides generation. Experiments on code generation and mathematical reasoning across five DLM backbones show that AnchorDLM improves controllability and further yields gains in reasoning performance across diverse benchmarks.

LLM multi-agent systems split work across agents that communicate through text. An agent summarizes its findings, another agent receives the text. This constrains communication to discrete tokens and costs redundant compute, limiting bandwidth and capabilities of multi-agent systems. Recent works demonstrate KV-cache transfer between LLMs but they either require the LLMs to be within the same family or cannot function across context, thus requiring the receiver to prefill text. We present SwaT (Swarm Telepathy), the first cross-family KV-cache transfer method that allows prefill-free communication in multi-family multi-agent systems. In an agent-to-agent communication setting, combining SwaT with recent advances in KV-cache compaction beats text-to-text communication in both accuracy and speed, with a mean of $40\%$ higher accuracy and a mean of $4\times$ faster wall-clock time. Experiments show SwaT achieves high performance on 17 benchmarks across 12 LLMs and 6 families. Additionally, given a sender Vision-Language Model (VLM), SwaT is able to transfer the vision capabilities to a text-only receiver LLM exceeding text-to-text communication despite SwaT being trained on text-only data. SwaT keeps both sender and receiver models frozen without fine-tuning and only requires $<50M$ tokens and $<1$ GPU-day to train.

AI coding agents operate in iterative loops: they modify code, run tools, inspect the results, and decide what to do next. We call the design of this process loop engineering, which includes context management, model selection, compaction, and termination. Existing efficiency work mainly compresses tool observations or routes selected turns to cheaper models, but the practical opportunity for these optimizations remains unclear. We analyze 600 publicly released coding-agent trajectories spanning two agent scaffolds and two language models. Median observations contain only 118-286 tokens, while the large build logs commonly used to motivate compression occur near the ninety-ninth percentile. Moreover, 98.6% of input tokens are served from a prefix cache, so flat input pricing overestimates loop cost by roughly 7x on average under near-ideal caching. We derive and empirically validate a closed-form break-even condition for model delegation. Delegation increases cost in half of the evaluated settings, near the predicted boundary. More broadly, turn count explains 84% of the variance in log trajectory cost, compared with 4% for mean observation size; the most expensive trajectories have the most turns despite having the smallest observations. These associations suggest that observation-focused methods target a secondary cost factor, and identify unnecessary turns as the larger and largely unexamined opportunity, though we do not establish that turns can be removed while holding task success fixed. We release TurnCost, a tool for re-scoring trajectory corpora under alternative caching, pricing, compression, and routing policies.

Machine-learned interatomic potentials (MLIPs) accelerate molecular dynamics (MD) simulations by learning the energies and forces that govern atomic motion. Recent work has shown that relaxing physical inductive biases can improve computational efficiency and predictive accuracy, raising the question of whether energy-and-force matching alone is sufficient to ensure accurate sampling. We show that, for unconstrained hypothesis classes, the relationship between prediction error and sampling accuracy is exponentially ill-conditioned in dimension. In particular, prediction errors that decay exponentially with dimension can coexist with nearly maximal total variation distance between the learned and target distributions. We identify two failure mechanisms. The first is kinetic trapping, where relaxation to an accurate learned equilibrium requires exponentially long times, even when simulations are initialized from training configurations at which energies and forces are matched exactly. The second is equilibrium mismatch, where the learned stationary distribution itself remains far from the target. Under explicit assumptions, we show that equilibrium mismatch can persist even in local, symmetry-preserving models, where small per-atom errors coexist with a distributional discrepancy that approaches its maximum as system size increases. Finally, we establish global energy-control conditions that guarantee equilibrium accuracy and identify additional conditions required for rapid relaxation.

Plasma experiments observe coupled physical states through sparse, heterogeneous, and incomplete diagnostics. We present a proof of concept toward a multimodal foundation model for plasma state reconstruction during magnetic reconnection, motivated by the Facility for Laboratory Reconnection Experiments (FLARE). Using 250 synthetic VPIC simulations at fixed reference electron beta $\beta_{e0}=0.2$, with 225 training runs and 25 disjoint validation runs, we train a 5.5M-parameter residual 3D U-Net to reconstruct three magnetic-field components and electron density from incomplete observations. The model combines spatial-only pooling, which preserves all 24 temporal frames, with global spatiotemporal self-attention and rotary positional encoding. Independently masking magnetic and density modalities across random, grid, block, and temporal patterns enables sparse sensing, cross-modal completion, density super-resolution, and temporal completion with a single set of weights and no task-specific retraining. With density fully hidden, just 0.1% magnetic spatial visibility reduces median density NRMSE from approximately 0.9 to 0.1. Conversely, observed density improves current-density reconstruction when magnetic data are absent or extremely sparse. With no magnetic observations, roughly 1% density visibility approaches the density reconstruction accuracy achieved with fully observed magnetic fields, although current structure remains more dependent on direct magnetic measurements. Full magnetic conditioning also stabilizes completion of missing future density frames. These results demonstrate bidirectional cross-modal predictive coupling within this simulation regime. Generalization across plasma regimes or to experimental measurements remains untested.

Larger sample budgets benefit from higher sampling temperatures in LLMs, but what temperature tuning optimizes and why it works remain poorly understood. We seek to answer these questions: we pose decoding as pass@$k$ maximization subject to two constraints that encode critical decoding failure modes: an entropy floor preventing diversity collapse, and a cross-entropy ceiling preventing implausibility. We prove that this maximization takes the form of a single closed-form conditional sampling rule, the tilted temperature $q^\star \propto \bigl(p e^{\eta V}\bigr)^{1/T}$. Here, the tilt comes from a verifier potential $V$ that quantifies how likely a partial generation is to eventually pass. Ordinary temperature sampling, verifier-greedy decoding, and reward-tilted policies represent special cases. We further show that, under a natural rule for scaling the diversity budget with sample size $k$, the resulting optimal temperature increases with $k$, turning empirical choice into a theorem. The optimum still needs the unknown verifier potential, which we estimate using two design approaches. In the online setting, our J-EOS algorithm jointly tracks the two constraint multipliers and learns the verifier potential from binary pass/ fail feedback alone. In the offline setting, we show that when the model is calibrated, its log-probability tracks correctness up to an affine map. Under this condition, the tilt collapses into the exponent and the optimum reduces to ordinary temperature sampling. Calibrated Temperature Decoding (CTD) then fits one scalar offline and samples with zero additional inference-time overhead relative to temperature sampling. Building on these decision rules, we design a practical decoding algorithm for code generation and evaluate it alongside CTD on benchmarks including HumanEval and MBPP, showing improvements over standard and adaptive decoding baselines.

Beliefs in a Partially Observable Markov Decision Process (POMDP) are posterior distributions over the hidden state given the agent's history of actions and observations. They summarize everything the history says about the state, so planning in a POMDP is planning in a Markov decision process (MDP) over beliefs. Belief MDPs have continuous state spaces even for finite POMDPs, and exact planning in them is intractable in general. Planners must therefore approximate beliefs and estimate values. Monte Carlo planners do both inside a search tree, with an approximate belief at every node and a value estimate at every leaf. Approximations usually consist of sets of sampled states, with leaf values coming from rollouts, hand-designed bounds, or learned networks. Policies and values computed from these approximations are limited by their quality, and prior methods with learned networks rely on hand-chosen summaries of the sampled states. A belief representation should be computable from the parent node's representation through the POMDP's dynamics, let the search sample from it, and be learned so that it provides the information that policies and value functions need. We present Belief Embedding Tree Search (BETS), a Monte Carlo planner that meets these requirements by representing each node's belief with a generative distribution embedding (GDE) while updating it through the POMDP dynamics. BETS trains its belief model alongside its policy and value networks through experience, with the realized hidden state of the POMDP as the belief model's training target. We evaluate BETS on six configurations of RockSample, LightDark, and PocMan against BetaZero and three planners without learned components. BETS is competitive or leading on all six, while every baseline falls far behind on at least one. Where beliefs are highest-dimensional, it outperforms them by a large margin, even without search.

Repetitive, degenerate generation is a persistent failure of LLM decoding, and the standard remedies (temperature, nucleus, and top-$k$ sampling) are static heuristics. By Kac's lemma and the AEP, a stationary source takes time exponential in its entropy to repeat a block. We therefore maximize the entropy of the sampling distributions under one cross-entropy budget that keeps the output plausible under the model. Offline, the solution is temperature sampling, with the inverse temperature as the budget's Lagrange multiplier. Our contribution is the online problem: the conditionals $p_1, p_2, \dots$ are revealed one at a time, and the sampling distribution $q_t$ must be chosen causally from $p_1, \dots, p_t$ while the budget couples the entire horizon. The optimal temperature is thus a global shadow price that must be estimated from a prefix. We propose Entropic Online Sampling (EOS), which re-solves for the temperature on each prefix. We prove it loses $O(R\log n)$ entropy against the offline optimum while overshooting the budget by $O(R\log n)$, with $R$ an instance-dependent drift parameter. A budget-tightened variant is exactly feasible at the same rate. Conversely, every exactly feasible online algorithm must lose $\Omega(R)$, so EOS is optimal up to a $\log n$ factor. When the conditionals are drawn from a finite mixture, $R=\tilde{O}(\sqrt{n})$. Experiments confirm that EOS tracks the offline temperature and beats fixed-temperature sampling in entropy.

Mixture-of-Experts (MoE) models combine specialized experts through an input-dependent routing mechanism, and their sparse variants underpin many modern large-scale systems. Yet the statistical cost of adaptive routing remains only partially understood. We study the estimation error of least-squares MoE estimators when both the experts and the gating network are Lipschitz in their parameters. We represent each MoE as a gate–expert pair in a Gated Hilbert Space, whose norm $\|\cdot\|_\Delta$ separates the contributions of routing and expert discrepancies. Using its empirical representation, we derive an oracle inequality with a fast rate of order $\tilde{\mathcal O}\big((Kd_{\mathrm{pr},e}+d_{\mathrm{pr},g})/n\big)$ for dense MoEs with $K$ experts. For sparse Top-$k$ and Top-$p$ routing, the selection map is discontinuous in the gating parameters. We handle this by partitioning the gating class according to the selection patterns it induces on the sample. The resulting bounds match the dense rate up to an additive routing cost governed by the Natarajan dimension of the selector. We show that such a routing-complexity condition cannot be dropped: Lipschitz continuity in the parameters alone does not suffice. For linear softmax gating, the routing cost is of the same order as the gating term. Finally, for linear experts, we establish a matching minimax lower bound of order $Kd_{\mathrm{pr},e}/n$, showing that the rates are optimal up to logarithmic factors.

Generative search engines such as ChatGPT, Gemini and Perplexity now decide which Web pages users see as sources, and a growing industry of generative engine optimization advises publishers on how to earn these citations. We study what shapes citation in two 90-day collections of answers to commercial questions in contrasting markets: 158,099 answers with 468,037 citations. Comparing pages of the same website, content matters in one way: pages whose title and paragraphs match the questions people ask are cited more, whereas FAQ blocks, structured data, summary boxes and page speed appear effective only across websites. Page properties nevertheless explain little of the variation between pages of a website. Replaying the questions through the engines' APIs shows why. Every page ChatGPT cites is one its own search retrieved, and which pages that search retrieves, for sub-queries the model rewrites on every answer and that rarely coincide with Google's or Bing's results, explains far more of the variation than page properties (32% against 2.8%). Content acts mainly through this step, by matching the engine's queries in meaning. The model's own knowledge shapes it too: ChatGPT writes brands it knows into its searches, prefers websites it knows, and names brands without any supporting page, and controlled experiments show that brand names reorder its rankings of products with identical facts. Pages are thus cited when searched; brands are also named when remembered. The findings replicate in a market of small B2B vendors. We release data and code.

Industrial anomaly detection benchmarks have advanced rapidly, yet they remain largely static and therefore underrepresent deployment settings in which inspection systems must be extended from one industrial component to another over time. In our setting, continual industrial anomaly detection is framed as a task-incremental problem: each component defines a task, while the learning objective remains semi-supervised. The goal extends beyond conventional anomaly detection, since models should preserve their performance on all components as they are sequentially exposed to new components. This framing is especially relevant because many existing industrial pipelines either assume fully supervised defect labels or study only isolated datasets, leaving open the question of how semi-supervised anomaly detectors behave across a sequence of heterogeneous components. We address this gap by organizing the benchmark as a sequence of related component-level tasks and by defining multiple scenarios, including random, easy-to-hard, and hard-to-easy. In addition to single-dataset continual scenarios, we propose challenging scenarios spanning across multiple datasets. We further evaluate continual performance from two complementary perspectives: image-level anomaly detection and pixel-level anomaly localization. By recasting industrial anomaly detection as a continual benchmark rather than a static train/test problem, our work establishes a concrete path toward studying knowledge retention, adaptation, and generalization in evolving industrial environments.

PATTERN, a synthetic node-classification benchmark still used to rank graph networks, plants a random subgraph in a random host graph and asks which nodes belong to it. Its generator draws 100 patterns once and plants the same ones in every split, so each test graph carries a pattern that also appears in 100 training graphs. A matcher that reads these patterns off the training labels and looks them up in each test graph reaches 99.2 class-weighted accuracy with no trained parameters, against 89.8 for the best published model. Inference under the generator without the patterns reaches 86.8. Two published models, CKGConv and GRIT, score lower on patterns they have not seen: on new graphs with fresh patterns both fall below this pattern-blind predictor, and withholding patterns from CKGConv's training lowers its accuracy on the test graphs that carry them. Training CKGConv with a new pattern in every graph raises its accuracy on fresh patterns by about 2 points, to the level of the pattern-blind predictor, at some cost on the reused patterns. The same kind of inference under the generator matches the best published result on CLUSTER and, without any training, scores above every published result we found on Minesweeper's released board. We recommend that synthetic benchmarks report scores on fresh templates beside reused ones, publish baselines built from their generators, and state how their metric is weighted and pooled.