Papers

It is well known that the matrix structure affects the convergence of iterative methods, particularly those utilizing Krylov subspaces. The matrix structure, determined by its graph, dictates the propagation order of updates to the vector components that are recursively computed during the conjugate gradient method iterations. Along with the propagation of these component updates, round-off errors also propagate. We present a model for the propagation and accumulation of round-off errors and demonstrate that the larger the values of topological characteristics of the matrix graph, such as its diameter, effective diameter, and pseudodiameter, the slower the round-off error accumulates during the method's iterations, and the longer the propagation of round-off errors remains local when computing the components of the search direction, residual, and approximate solution vectors. Round-off errors arising during the computation of these components affect only those components whose corresponding vertices in the matrix graph are at a distance not exceeding the current iteration number. As the iteration number increases, the propagation of round-off errors between the vertices of the matrix graph becomes global, leading to the loss of orthogonality of residuals and conjugacy of search directions. In the context of mixed-precision computations, this implies that for a matrix with a larger graph diameter (or, more practically, effective diameter), a greater number of method iterations can be performed in a lower-precision mode before the onset of convergence stagnation.

Thermodynamic computing lets stochastic physical dynamics carry out a computation and reads out the result as a time average. Recently, thermodynamic computing has been demonstrated on several hardware platforms, including digital CMOS circuits based on stochastic computing. Superconducting single-flux-quantum (SFQ) logic offers very high clock rates and very low switching energy, but it heavily penalizes state, memory, fan-out, and feedback, i.e., exactly the per-neuron accumulators on which such designs rely. We therefore realize thermodynamic computing in SFQ logic through a co-design of a generative model and its circuit in which the datapath holds no state at all. The model is a class-conditional flow-matching image generator, which transforms Gaussian noise into an image of the requested class along a short, deterministic path of four Euler steps; in hardware, these steps are unrolled into a feed-forward pipeline of stochastic bitstream operators, whose output is read out as a time average, as in thermodynamic computing, without any relaxation phase. Each layer of the model is a butterfly-factorized linear map built exclusively from multiplexers that operate on split-unipolar bitstreams. The ReLU activation, which in stochastic computing requires a per-neuron up/down counter (accounting for 60-70% of the JJs in a counter-based design), is replaced by a stateless AND-NOT gate whose one-clock input skew is provided at no cost by SFQ gate-level pipelining. The models are trained directly on the stream representation of the hardware, with a regularizer that bounds the stream gains. Synthesis with an SFQ design flow shows that stochastic streams tolerate relaxed path balancing, which reduces the Josephson-junction (JJ) count of a hard-wired stage by 40-47%.

Target-conditioned cyclic peptide design requires coordinating interfacial side chains with macrocyclic closure. Existing end-to-end generators concurrently update geometric and chemical variables from noise, assigning residues to disordered coordinates. Meanwhile, predictor-assisted workflows often get stuck in local traps because they lack feedback in the propose-and-filter stage and ignore 3D structural proposals during sequence search. To overcome the drawbacks of these two paradigms, we propose DC-FLOW, a staged generative framework built around Delayed-Coupling Flow Matching. In principle, DC-FLOW postpones sequence and side-chain activation until a target-conditioned backbone takes shape, resolving structural ambiguity before chemical assignment. Then, it feeds delayed activations back into the backbone, achieving co-evolution of backbone geometry and emerging residue identities by coupling their flows. This mechanism enables more reliable macrocyclic closure and favorable interface packing. For predictor-assisted workflows, DC-FLOW supplies 3D proposals with in-trajectory guidance, enabling cascaded test-time scaling to prune redundant backbones and terminate unpromising refinement early. Extensive experiments show that DC-FLOW improves cyclization fidelity, diversity, and interface energetics, substantially increasing the yield of confident cyclic peptide binders under a fixed final-candidate budget. Our code is available at https://github.com/mianqiu00/DCFlow.

Audio Large Language Models (Audio LLMs) are embedded in agents for smart homes, vehicles, wearables, and embodied systems, where acoustic inputs can propagate from perception into persistent state and consequential execution. This setting extends security analysis beyond model behavior to the system conditions that determine how acoustic inputs can influence agent behavior and external actions. Existing surveys examine acoustic security, LLM-based agents, and edge deployment in isolation, leaving their security interactions in deployed Audio LLM-based agents insufficiently characterized. This survey introduces an Acoustic Sensing-to-Action (S2A) system model that traces these security implications along the path from acoustic sensing to external execution, while accounting for edge-cloud runtime and lifecycle transformation. We use the model to synthesize attacks, defenses, and evaluation methods across the acoustic, agent, and edge-system literature. The synthesis shows that security gaps can emerge within components and at the transitions between stages, where protections developed for one stage do not necessarily provide end-to-end assurance in the deployed system. These findings motivate security evaluation that follows acoustic influence from sensing to action across persistent state, system boundaries, and changing deployment conditions in real-world agents.

Video understanding agents rely on a harness to acquire evidence, use tools, and reason, but improving it requires substantial effort. Recent self evolution methods seek to optimize harnesses through execution feedback to reduce human intervention. However, existing methods often rely on annotated video questions and answers or focus on updating model parameters, leaving harness evolution from unlabeled videos underexplored. VideoEvoHarness jointly evolves a Questioner and a Solver harness from unlabeled videos with frozen model parameters. The Questioner constructs questions and computes reference answers directly from video memory records. Question quality assessments and Solver execution trajectories guide question generation policy revisions. The Solver supports evolving skills, strategies, hyperparameters, and tools using execution feedback. Executable strategies define workflows in code, reducing repeated interpretation of natural language instructions. Each round, candidate harnesses are compared on identical validation questions, with validated improvements retained for later use. Experiments on benchmarks and a dedicated benchmark question set, using videos disjoint from evolution videos, show higher overall accuracy than initially and transfer gains across backbones. Overall accuracy on this set also improves progressively across rounds. This supports our foundational framework for harness evolution from unlabeled videos, opening a promising direction for self evolving video agents. Code is available at https://github.com/Wei-Xin-Xu/VideoEvoHarness.

Contrastive representation learning (CRL) is a fundamental paradigm for learning transferable representations. Recent work identifies its population target as the pointwise mutual information (PMI) $\log\frac{p(x,y)}{p_X(x)p_Y(y)}$ between two modalities $X,Y$, where $p$ is the joint density function and $p_X,p_Y$ are the marginals. However, it remains unclear why standard inner-product scores $f(x)^\top g(y)$ can effectively approximate a generally nonseparable population target PMI. In this paper, we address this question from the aspect of approximation for CRL. By linking PMI to a compact operator, we show that $D$-dimensional inner-product models perform rank-$D$ spectral approximation, with error controlled by the spectral tail. We then study neural network realizations: in general settings, we show that deep neural network scoring functions are universally consistent, and the approximation error rates depend on the smoothness of the PMI function; under structured low-rank data models we obtain improved rates attained by moderate-width encoders. Finally, we establish a fast calibration rate from contrastive excess risk to downstream retrieval error under a density-ratio Tsybakov noise condition.

Computing multiple eigenstates of non-Hermitian many-body operators plays an important role in investigating excitation spectra, spectral properties, and relaxation dynamics in interacting and open quantum systems. However, this task is challenging because the eigenvectors are generally nonorthogonal and the Hilbert space dimension grows exponentially with system size. Here, we formulate the generalized preconditioned locally harmonic residual (GPLHR) method in a matrix product state (MPS) framework to efficiently compute multiple targeted right eigenstates whose eigenvalues lie near a specified shift in the complex plane. Successive randomized compression (SRC) is employed to accelerate operator applications. We test the method on transcorrelated and complex Hubbard chains, an interacting non-Hermitian Su-Schrieffer-Heeger (SSH) chain, and a Liouvillian model. The results demonstrate that GPLHR combined with MPS provides an efficient and accurate approach for computing multiple eigenstates of non-Hermitian many-body operators.

This paper characterizes Cohen-Macaulay algebras in the sense of Auslander and Reiten [Progr. Math. 95(1991)] within the following two classes of finite dimensional algebras: (i) truncated path algebras and (ii) Nakayama algebras. For the former, our characterization in terms of ordinary quivers shows that if a Cohen-Macaulay truncated path algebra $\Lambda$ is connected, then $\Lambda$ or $D(\Lambda)$ gives a dualizing module, where $D$ denotes the standard duality. For the latter, we show that every Cohen-Macaulay Nakayama algebra $\Lambda$ is Iwanaga-Gorenstein. In particular, $\Lambda$ always gives a dualizing module. Consequently, there is no non-trivial Cohen-Macaulay algebra among truncated path and Nakayama algebras.

We construct a Hausdorff quasitopological abelian group that is second-countable and semiregular, with a bounded continuous function that does not factor through any regular first-countable semitopological group. Its regular and Tychonoff reflections coincide, have a countable network, and fail even factorizability through arbitrary first-countable semitopological groups. This gives negative answers to \cite[Problems~6.1, 6.2, 6.4, and~6.5]{Tk2026} of Tkachenko. The construction starts with a countable cone group whose common separation reflection is not Fréchet–Urysohn, answering \cite[Problems~6.8 and~6.9]{Tk2026} negatively. In contrast, symmetrization gives affirmative answers to \cite[Problems~6.6 and~6.7]{Tk2026} without separation assumptions. We also show that every countable semitopological group admits simultaneous factorizations of countable families through second-countable Tychonoff semitopological groups.

Compressing the key-value (KV) cache is essential for serving long-context large language models (LLMs) under memory constraints. While current scalar quantization methods achieve significant compression, they typically face a quality-fidelity trade-off, either suffering from performance instability at 2-bit precision or necessitating 3-bit keys to maintain model quality. In this work, we demonstrate that a uniform low-bit k2v2 configuration (2-bit keys and 2-bit values) can preserve near-baseline quality by using vector quantization (VQ) based on the $E_8$ lattice for KV keys. We show that structured VQ exploits correlations across adjacent dimensions to achieve signal-to-quantization-noise ratios (SQNR) higher than those of independent scalar quantization at the same key payload rate. To ensure practical utility, we adapt a table-based asymmetric scoring algorithm that avoids explicit codebook dequantization during attention computation and preserves decode-throughput parity with scalar baselines. Across five LLM families, our $E_8$ k2v2 approach yields \textasciitilde$6\times$ KV compression, roughly 20% smaller than scalar k3v2 (3-bit keys and 2-bit values), while retaining near-baseline long-context perplexity. In our full-suite perplexity evaluation, $E_8$ improves over scalar k3v2 in 80% of model–dataset–context settings. These results indicate that $E_8$ lattice VQ improves quality per byte while keeping throughput at parity, suggesting that structured key quantization is a useful primitive for KV-compression stacks. Overall, our work provides a low-overhead primitive for expanding the quality-memory frontier in long-context LLM inference.

Let $\mathcal{C}_{r}^+$ be the set of all balanced signed graphs with underlying graphs $C_r$. A signed graph is called $\mathcal{C}_{r}^+$-free if it contains no subgraph isomorphic to any member of $\mathcal{C}_{r}^+$. In this paper, we characterize the extremal graphs that achieve the maximum index among all $\mathcal{C}_{2k+1}^+$-free unbalanced signed graphs of order $n$ when $k\ge 2$ and $n\ge 187k$.

Generative engines such as ChatGPT Web retrieve webpages to answer user queries, but only a subset are shown as citations. Understanding this retrieval-to-citation process is important for generative engine optimization (GEO), which aims to improve content visibility in generative-engine responses. However, prior studies mainly analyze final responses, leaving the internal execution process and its variation across model settings less understood. To this end, we conduct an observational study of four ChatGPT Web settings from ChatGPT 5.2 to 5.5, covering Instant and Thinking modes at the URL, hostname, and entity levels. We examine how ChatGPT rewrites queries, retrieves candidate webpages, and selects references. The Instant settings remain mostly single-round, while GPT-5.4 Thinking frequently performs multiple retrieval rounds. Across repeated runs, candidates retrieved more often are also more likely to be cited. We then evaluate Google Search and the OpenAI Responses API as external proxies. Responses API candidates provide broader coverage, while its citations more closely match sources cited by ChatGPT Web. Both proxies match ChatGPT Web better at the hostname and entity levels than at the exact-URL level. Even when combined, they recover only about one quarter of cited URLs. We further test whether these external signals remain predictive when combined. Within the external candidate set, a supervised model combining them reaches AUCs above 0.74 for GPT-5.3 and GPT-5.5 at all three levels. These findings suggest that GEO should distinguish retrieval visibility from citation visibility, account for rewritten queries and run-to-run variation, and consider hostname- and entity-level presence in addition to exact URLs. Differences across settings also suggest that GEO strategies should be re-evaluated when the deployed setting or serving environment changes.

For the first time, we study the effects of mass transfer on alloy droplet impact, solidification, and solute non-homogeneity or MacroSegregation (MS). For this purpose, a multi-physics model, including fully-coupled hydrodynamics of multiphase flow, wetting, conjugate heat transfer, phase change, and mass transfer, is established and validated carefully across several benchmarks. In addition, a concentration-flux-correction algorithm is proposed to conserve the solute mass within the droplet at the numerical discretization level. The validated model is subsequently used to explore the impact and solidification of an alloy droplet. The results show that accounting for mass transfer and solute transport improves the prediction of the dynamics of a solidifying splat, in a consistent manner with experimental observations, while this effect has been neglected in all previous studies. The analysis demonstrates that this improvement results from the flow sensitivity to the mushy region thickness, which is regulated by local solute concentration through the solidus and liquidus temperatures. Furthermore, analyses of the MS map identify several critical segregation regions most susceptible to defect initiation, such as cracking, including a long negatively segregated vein within the lamella, formed by the severe advective flow through the mush in the middle stages of the impact, a positively segregated region near the rim of the splat, appearing as a result of hook formation, and a major positively segregated zone at the top of the rim, which develops following the accumulation of the solute-rich melt sustained by washout from the lamella.

Bridging the structural gap between biological brains and artificial neural networks presents a pathway to altered computational dynamics. This paper introduces a Reservoir Computing framework that replaces random networks with biologically realistic modularity by applying the Weighted Stochastic Block Model (WSBM) to Echo State Networks (ESNs). This topological parameterization constructs reservoirs reflecting latent functional sub-circuits. Furthermore, the integration of Input Dynamical Similarity Analysis (InputDSA) provides a mechanism to isolate and compare how structural priors modulate intrinsic recurrent dynamics versus external inputs. By evaluating these architectures, we establish that structural diversity does not necessarily predicts behavioral diversity across the selected network subset. Furthermore, our demixed analysis confirms Anna Karenina principle of dynamics, demonstrating that environmental constraints enforce dynamical convergence in successful agents, while failing networks degenerate into idiosyncratic trajectories.

Speaker anonymization (SA) aims to conceal speaker identity while preserving linguistic content and emotion, but existing streaming systems often lose emotion information through discrete content bottlenecks or require emotion-specific modeling. We present LiveAnon, a voice-conversion-based streaming SA system that directly conditions an autoregressive codec language model on hidden features from a pretrained streaming ASR encoder, preserving emotion without emotion-specific supervision. To reduce codec-generation latency, we introduce capped RVQ decoding, which preserves dependencies among coarse codebooks while predicting the remaining codebooks in parallel. Under VPC24, LiveAnon improves intelligibility and emotion preservation over fixed-target Stream-Voice-Anon (SVA), a strong prior streaming SA system, matches emotion-prompted SVA in emotion preservation, and achieves the strongest semi-informed privacy among streaming systems. Under VPC26, it ranks second across all metrics among the evaluated anonymization systems, demonstrating a strong privacy-utility balance.

We prove that the optimal constant in the Chang–Marshall inequality is $e$, as conjectured by Andreev and Matheson. More precisely, if $f$ is analytic in the unit disk, vanishes to order $m\geq1$ at the origin, and has normalized Dirichlet integral $d\leq1$, then the boundary mean of $e^{|f|^2}$ is at most $e^{d/m}$. Equality holds precisely for monomials. The proof uses an auxiliary closed planar curve and the isoperimetric inequality to establish monotonicity of the exponential functional along normalized radial dilations.

Strong direct-sum theorems relate the information needed to solve many independent instances of a communication problem to the information needed for one instance. For Gap-Majority composition, an optimal information bound was previously known, but preserving the number of communication rounds incurred an additional logarithmic loss. We prove a round-preserving Gap-Majority lemma with constant additive information loss, independent of both the number of instances and the number of rounds. More generally, we establish a variance direct-sum theorem for additive square-integrable observables over product distributions. For protocols with a bounded number of terminal answer values, the extracted single-coordinate protocols preserve the round budget, and their average information cost is at most the original information cost divided by the number of coordinates, plus a term depending only on the answer alphabet and the allowed variance loss. The proof uses centered counterfactual conditional means and a global variance amortization argument. Rather than encoding absolute conditional means for every possible terminal answer, we encode the information not already determined by the common view. The total squared innovation is controlled by a telescoping variance potential, yielding an information loss independent of the number of coordinates. We also derive same-round mean-square estimation bounds for arbitrary terminal outputs.

Let $\zeta^t(\boldsymbol{k})=\sum_{d=1}^{r}S_d(\boldsymbol{k})t^{r-d}$ be the interpolated multiple zeta value of an admissible index $\boldsymbol{k}$ of depth $r$. We show the monotonicity property of coefficients $S_1(\boldsymbol{k})\ge\cdots\ge S_r(\boldsymbol{k})>0$. In the proof, we represent the coefficients as integrals over a common measure space and compares the integrands pointwise. As consequences, we determine the sign and vanishing of $\zeta^{-1}(\boldsymbol{k})$ and locate the zeros of $\zeta^t(\boldsymbol{k})$ in the closed unit disk.

Zero-Shot Object Navigation (ZSON) requires an agent to locate target objects in unfamiliar environments without additional training for the test categories or environments. Recent approaches leverage large language models and vision-language models to construct spatial representations and guide exploration. However, whether the available evidence sufficiently supports a navigation choice, and how new evidence changes the search value of previously visited locations, remain insufficiently addressed. We propose RefBeliefMap, an uncertainty-guided mapping framework that distinguishes target-location belief from spatial and semantic evidence uncertainty. By jointly modeling intra-observation uncertainty and inter-observation disagreement over a sliding memory window, RefBeliefMap assesses the reliability of both evidence channels. When competing frontiers remain insufficiently resolved, these uncertainty estimates guide active observation and semantic reasoning to refine the evidence supporting target-location beliefs before navigation commitment. Building on the refined map, we introduce RefBeliefNav, which jointly evaluates unexplored frontiers and historical waypoints according to their target-finding potential, expected information gain, and navigation cost. This unified objective allows historical locations to be reconsidered as new evidence changes their search value, coordinating exploration and revisitation. Experiments on HM3D and MP3D demonstrate state-of-the-art performance among the evaluated zero-shot baselines, with ablation studies examining the contributions of modules. Real-world experiments on a Unitree Go2 quadruped robot further demonstrate the sim-to-real transferability of our method.

Recent experiments highlighted the essential role of the orbital degrees of freedom underlying current-induced magnetic dynamics. However, a microscopic picture of how orbital angular momenta are transferred between itinerant and localized electrons, and the way it feeds back into transport, remains elusive. Here we develop a theoretical framework for the orbital exchange interactions by generalizing the Anderson-Kondo model to incorporate the orbitals of conduction bands. Illustrating with the $p$-orbitals, we determine the way electrons acquire orbital polarization and its influence on the transport properties, uncovering the orbital counterparts of phenomena analogous to spin filtering and tunnel magnetoresistance. Reciprocally, we demonstrate that orbital-polarized currents can exert torques on localized magnetic moments without having to convert into spin currents, which enables electrical switching of magnetization even when spin polarization becomes inactive. These striking discoveries lay a microscopic foundation for orbitronics and reveal critical mechanisms for orbital manipulations of magnetic order.

We adapted Nemotron-3-Nano-30B-A3B for eight Indian languages without changing its backbone architecture. We expanded the vocabulary in place from 131,072 to 163,072 entries using continued byte-pair encoding and AdaptMix rebalancing, reducing tokens per word by 38.6%. We initialized new input and output rows by averaging their original constituent rows, then trained them on 90% Indic and 10% English text before updating the backbone. Continual pretraining then progressed through broad training, high-quality annealing, and long-context training over approximately 1.27 trillion tokens. The annealed checkpoint gained 12.9 points on the Indic MILU benchmark but lost 3.4 on English MMLU. We also report practical negative results. Direct token addition underperformed continued byte-pair encoding. AdamW weight decay changed rows intended to stay fixed. Perplexity on an Indic-heavy holdout did not select the learning rate that best preserved English performance.

Large language models are generally more capable than smaller ones, but their memory requirements can make local deployment difficult. We ask whether part of this capability gap can instead be recovered by running a smaller or more compressed model multiple times and selecting among its outputs using public or model-generated tests. Single-user local inference can leave hardware underutilized, allowing parallel candidate generation to trade additional test-time computation for accuracy at modest latency cost. Across four code-generation benchmarks, verified retry recovers substantial accuracy lost to model size or compression. A 7B Qwen model with eight parallel attempts essentially matches a 32B model on MBPP+ and exceeds it on the other three benchmarks, while using about $4\times$ less model memory, running up to $6\times$ faster, and using less energy, as measured on Nvidia GPU. We observe similar tradeoff across model sizes, compression levels and hardware choices, although exact benefit depends on the hardware profile and problem setting. These results show that model capacity can be traded for verified test-time computation when correct solutions remain reachable within a modest retry budget.

Gnani-Evon-v3.3-30B-A3B is a long-context hybrid Mamba-Transformer mixture-of-experts model for reasoning, instruction following, and tool use in English and eight Indian languages. Starting from NVIDIA's Nemotron-3-Nano-30B-A3B checkpoint, it retains the 52-layer backbone and changes the vocabulary, training data, and post-training objectives. An in-place expansion from 131,072 to 163,072 tokens reduces mean Indian-language fertility by 38.6%. The new embedding rows are initialized from their upstream decompositions and warmed before the backbone is updated. Continual pretraining then adds broad English-Indic data, high-quality annealing, and direct training at a 131,072-token sequence length. The central result appears after post-training. Reinforcement learning across four verifiable task environments improves mathematics, graduate-level science, and instruction following, but degrades Indic extractive question answering because the rewards do not require an answer in the requested language. The share of Indic extraction items answered in English rises from 8.7% to 91.7%. Accuracy conditional on answering in the target script roughly doubles, which is consistent with preserved reading ability but is measured on a self-selected subset. Two unreleased studies test repairs. A scoped Indic reward restores the language convention. A 26B-A4B generative judge outperforms a 235B-parameter model on RM-Bench, and distillation restores 81% of the capabilities displaced by optimizing against it. Relative to the architecture-identical starting checkpoint, the released model gains 5.2 points on an Indic aggregate while giving up 1.7 points of English retention. The unreleased Indic-aware branch trades further, gaining 14.6 Indic points at a cost of 5.4 in English. A planned FP8 release reduces the artifact to 32GB with near-zero mean change across 32 paired benchmarks.

We exhibit a fixed $4\times 4$ binary matrix with no polynomial induced ordered removal bound. At depth $h\geq 1$, let $m=2^h$. Our explicit host has order $(14h+2)m$, exactly $2m^6+\frac{1}{2}(m-2)m^5$ induced copies, and exact editing distance $m^2$ cells. Its normalized editing distance is $\Theta(h^{-2})$, while its induced-copy density is $\Theta(4^{-h}h^{-8})$. The lower bound holds against arbitrary cell edits through an injective family of $m^2$ protected selections. An exhaustive arithmetic classification identifies every induced copy and proves that a matching canonical repair creates none. The original-copy transversal number is exactly $m$, yielding an unbounded gap between hitting existing copies and eliminating all copies. The identities and the obstruction at every depth are formalized in Lean, with verification sources included as ancillary files.

Gaussian mixtures can have more modes than components. For three Gaussian components with a common covariance, four modes are attainable, whereas the best general upper bound was eight. We prove that four is the exact maximum in every dimension $d \ge 2$, for arbitrary means and positive weights. We further show that the sharp bound drops to three when the whitened means are collinear or form a right or obtuse triangle. The result covers degenerate modes without genericity or separate finiteness assumptions. Our proof maps modes to local minima of a separable free-energy functional on the probability simplex, reduces the problem to counting scalar inverse-function branches, and controls competing branches through curvature and stationary-height comparisons.

Rapid advances in large language models have made software engineering agents capable of tackling complex coding tasks. Within a containerized environment, a coding agent receives tool responses or execution results, and determines its later actions by those earlier results. However, most existing coding agents never look ahead: their policies do not anticipate the consequences of actions, and the terminal reward barely attributes a failure to certain earlier steps, so an ill-judged edit can corrupt the repository state irreversibly before any signal arrives. Recent code world models aim to address these challenges, but they are either trained and then frozen before reinforcement learning (RL), or reduced to an auxiliary next-token loss on the environment's outputs. We present ANTE (Anticipate, Then Execute), an agentic RL framework that verifies the policy's pre-action predictions by real execution and turns them into per-step credit for its actions and trust-or-abstain decisions. With an internal belief stated before each action, Belief-Anchored Policy Optimization (BAPO) turns the settled predictions into per-step advantages by anchoring credit on the policy's own forecasts. To turn the trained forecasts into better actions at inference, thereby facilitating effective test-time scaling, ANTE-TTO (test-time optimization) selects among candidate actions without an external scorer. ANTE raises Qwen3-32B from 25.0% to 57.2% pass@1 on SWE-bench Verified, 6.2% above a matched GRPO baseline trained without the belief state; its world model's accuracy climbs from 44% to 69% during RL, and the learned foresight capability transfers across harnesses and out-of-distribution domains. In summary, we aim to build a code world model that knows what has happened, what holds now, and what the next action will achieve.

In this paper, we consider the following reaction-diffusion system \begin{equation*} \begin{cases} u_t=\Delta u+F\bigl(x,t,u,v,V(t)\bigr), & (x,t)\in\Om\times(0,T), v_t=\Delta v+G\bigl(x,t,u,v,U(t)\bigr), & (x,t)\in\Om\times(0,T), \mathcal B u=\mathcal B v=0, & (x,t)\in\partial\Om\times(0,T), u(x,0)=u_0(x),\quad v(x,0)=v_0(x), & x\in\Om, \end{cases} \end{equation*} where \begin{equation*} U(t)=\int_{\Om}u(x,t)\dd x,\qquad V(t)=\int_{\Om}v(x,t)\dd x, \end{equation*} and the boundary operator $\mathcal B$ is either \[ \mathcal B_D w=w \qquad\text{or}\qquad \mathcal B_N w=\partial_\nu w, \] $\Om\subset\R^N$ be a bounded domain with sufficiently smooth boundary, $N\ge 1$, and $\nu$ is the outward unit normal on $\partial\Om$. Under certain conditions, we obtain the upper and lower bounds for the blowup time of the solution to the system.

Design-space exploration of LLM inference clusters requires predicting how hardware and serving policies interact with hierarchical key-value (KV) caching. Isolated operation profiles alone do not determine cluster latency: reuse changes computational demand, while KV location, capacity, and contention govern execution order. We present a compositional discrete-event simulator based on separating local service costs from shared resource and KV availability. Compute and transfer models calibrated on one-prefill/one-decode (1P-1D) deployments are reused across compatible workers, enabling policy and topology comparisons without per-configuration latency fitting. Validation against SGLang covers Qwen3-8B and Qwen3-32B on 1P-1D and 3P-1D clusters. Mean request end-to-end latency error is 1.34% for question answering and 6.36% for captured coding sessions, measured as mean absolute percentage error. CPU simulation reduces replay turnaround by 15.33 times on average; real replay includes prescribed arrival gaps. Measured session-affinity and simulated retention studies demonstrate how the framework guides policy selection by predicting the joint effects on computation, latency, and KV occupancy.

Large language models (LLMs) can produce harmful content while generating a response. A useful safeguard should not only detect this risk during generation but also intervene while leaving safe responses largely unchanged and provide an auditable record of the internal patterns supporting its decisions. We propose TRACE (Temporal Risk Assessment and Concept Editing), a framework that tracks harmful-response risk during generation, selectively edits token activations, and leaves an auditable trace of its detection and steering decisions. TRACE learns a codebook of recurring activation patterns, with each codebook vector representing a latent concept. At inference time, it assigns each token activation to the nearest codebook vector to obtain the corresponding concept. A gated recurrent unit (GRU) processes the activations and their assigned concept features to predict completed-response harmfulness and a monotone cumulative streaming risk. During steering, activations assigned to harmful concepts are steered along directions defined by nearby benign targets. An external LLM labels the learned concepts post hoc, making detection sequences and harmful-to-benign edit records interpretable. Experiments across three generators and the WildGuard and S-Eval benchmarks show that TRACE improves streaming F1 over Kelp in five of six comparisons while remaining competitive on completed-response detection. TRACE's selective steering reduces Harmbench attack success with little change in refusal on originally safe responses. The post-hoc audit reveals recurring semantic structure in the learned concepts and distinct traces associated with harmful detection, safe generation, and activation edits.

We show that criticality concentrates extensive sensing information into a local trajectory. In the rapid-readout limit of an all-to-all dissipative feedback network, a single binary trajectory has a Fisher-information rate linear in $N$ for a common weak field, as does the full record. Critical slowing does not remove this gain because the local weight of the slow mode decreases with $N$. An analytic bound guarantees that the local record retains more than half of the full information across the entire channel-parameter range. We also identify how parameter drives and observation dynamics determine local access to collective information beyond permutation symmetry. Furthermore, our sparse-readout theorem establishes a $k^{-1}$ decay of fractional information loss: only $\Theta(\varepsilon^{-1})$ trajectories are needed to retain a fraction $1-\varepsilon$ of the full information rate. Any growing readout set, even of vanishing density, asymptotically recovers the full common-field Fisher-information rate.