Papers

The widely used Transolver family of neural operators is based on physics-attention, which softly assigns the points of an unstructured mesh to a small number of slices, applies self-attention among the resulting tokens, and broadcasts the result back to the points. We provide a comprehensive empirical and theoretical analysis to elucidate the mechanisms which are responsible for model performance. To this end, we perform careful ablations on a challenging suite of nine 3D fluid dynamics benchmarks to find that replacing token attention with a constant linear map does not affect the accuracy. Thus, Transolver does not need a Transformer at all. However, removing the global mixing (slicing/deslicing) or doing it only once leads to performance collapse. We leverage the theory of averaging neural operators to explain and corroborate our findings by showing that just slicing/deslicing, in conjunction with pointwise MLPs, already suffices for universal approximation of continuous operators and attention is redundant in this context. Finally, we provide a novel FlashAttention-style efficient implementation of the key slicing/deslicing module of Transolver. This flashslice kernel streams slice and deslice over the points without materializing the heavy slice-weight tensor, while reproducing the best available implementation to floating point error. At the same time, it leads to very significant memory and compute savings, particularly at large slice counts.

Fix a square-free monomial $m = x_{i_1} \cdots x_{i_s}$ in $S = \K[x_1, \dots, x_n]$, where $\K$ is a field. The ideal generated by all square-free monomials that are Borel moves of $m$ is referred to as the square-free principal Borel ideal, denoted by $\mathrm{sfBorel}(m)$. While the Waldschmidt constant of $\mathrm{sfBorel}(m)$ has been partially studied in the literature, we consider the remaining cases and provide bounds for the Waldschmidt constant of $\mathrm{sfBorel}(m)$. In some cases, we explicitly compute its exact value. Furthermore, we study this invariant for square-free Borel and square-free lex-segment ideals, establishing both bounds and exact values for special cases.

Artificial Intelligence as a Service (AIaaS) composition is an emerging research area that enables clients to combine multiple AI services to meet complex requirements. A recent extension of this paradigm is collaborative AIaaS composition, where multiple AI services are combined to create a unified solution. Research in this field requires datasets with service descriptions, composition requests, and corresponding composition solutions. However, no dataset contains all this information specifically for collaborative AIaaS composition. Existing datasets target traditional web services or sequential AI workflows and lack the AI-specific attributes required for realistic collaborative composition. To address these challenges, we present a collaborative AIaaS composition dataset containing 25,900 AIaaS services from multiple providers across 12 AI task families, along with 10,000 collaborative service requests. We further develop a Multi-Armed Bandit (MAB)-based collaborative composition algorithm that determines the composability of candidate service combinations prior to composition. Experimental results demonstrate that the dataset supports realistic collaborative AIaaS composition evaluation and related research in service recommendation, selection and QoS prediction. The dataset and implementation are publicly available at: https://github.com/deepakkanneganti9/CAIaaS

Long-term memory enables agents to accumulate information and reason across sessions, yet existing research primarily focuses on dyadic text or image-text conversations, leaving long-term memory for multi-party spoken conversations underexplored. This setting requires preserving conversational content, identifying participants across sessions, and retaining who speaks to whom. To this end, we propose VoxPolyMem, an interaction-aware multimodal memory framework combining incremental speaker identification with a memory hierarchy comprising interaction memory, fact memory, and participant profiles. We formulate retrieval as sequential decision-making, where an agent rewrites queries and selects retrieval tools and memory layers based on accumulated evidence to address information gaps. We further introduce Evidence-Gain GRPO (EG-GRPO), which uses round-wise credit assignment to encourage complementary evidence acquisition. We also construct VoxPolyBench to evaluate memory evolution, personalized answering, memory retrieval and reasoning, and interaction reasoning and attribution in multi-party spoken conversations. VoxPolyMem achieves an overall score of 85.0 on VoxPolyBench, surpassing the strongest evaluated baseline by 23.6 points. On Mem-Gallery and H2HMem-Multi, it scores 89.6 and 74.4, respectively, exceeding the strongest evaluated public memory baselines by over 8 points each. These results highlight its potential for persistent, personalized assistance in multi-party multimodal interactions. Code and datasets are available at https://voxpolymem.github.io/VoxPolyBench/demo/

Current agents remain largely stateless across tasks, limiting their ability to continually improve from prior interactions and making memory essential for long-horizon agentic behavior. Existing memory methods seek to reuse past experience, but most rely on a single memory representation (e.g., trajectories, reflections, skills, structured knowledge) whose effectiveness varies across task distributions. Rethinking this design space, we evaluate 13 memory methods and find that no single method generalizes across benchmarks, revealing the potential of managing heterogeneous memory providers. We formulate agent memory as a routing problem in which a memory agent decides which memory provider to retrieve from, whether to inject short-term memory, and which providers should store the resulting experience. Based on this perspective, we propose MemAgent, featuring a content-aware routing architecture and a training-data synthesis pipeline. The routing architecture combines content-aware probing before retrieval, short-term memory gating during execution, and selective multi-provider storage, while the training pipeline synthesizes phase-specific supervision for routing decisions. Across GAIA, WebWalkerQA, and xBench-DS, MemAgent improves average accuracy by 10.0% and outperforms every individual memory method across all three benchmarks. These gains come with less than 0.3% routing overhead and a 12% reduction in average task steps.

LLM agents often operate over multi-turn interactions in which user intent changes before execution. We study intent drift: the failure mode in which superseded parts of the user's intent continue to influence the final answer or tool action. We introduce IntentFlux, an executable benchmark that converts verifiable tasks into dialogues with controlled intent changes while preserving their original graders. In a 627-case calibration, mean task score falls from 0.476 to 0.384 as dialogues contain more superseded and withdrawn information. Across eight models, the rate of fully correct solutions is significantly lower when the same final task must be recovered from an evolving dialogue rather than given directly in a single turn. We further introduce StateForge, which explicitly maintains the active requirements before generation. On General-Test, it improves mean task score from 0.367 to 0.467. Providing the ground-truth final state improves performance further but still does not recover single-turn performance, indicating that state-estimation errors explain only part of the gap. These results establish intent drift as a measurable multi-turn failure mode and explicit state maintenance as a partial mitigation.

Model steering can strengthen a target behavior while degrading other useful behaviors. We introduce Supervised Transcoder Replacement (STR) to reduce these side effects for existing steering methods, including those fitted without a protection objective. STR learns a replacement for the multilayer perceptron (MLP) computation at the steering layer through supervision for target control, non-target preservation, and fidelity without steering. Selected steering methods then fit directions on the frozen replacement while retaining their own fitting objectives. We evaluate three steering methods across Gemma and Llama models using Corrigibility preferences and four harmful-request safety datasets. SALAD-Bench supplies protection training data and a separate in-distribution evaluation split; HarmBench, AdvBench, and StrongREJECT are reserved for out-of-distribution testing. STR substantially reduces steering side effects on the in-distribution evaluation and extends this protection to the unseen safety datasets while retaining effective target control. For target-only supervised steering vectors, pooled out-of-distribution attack success rate falls from 42.46% to 14.42% on Gemma-3-4B and from 34.97% to 12.91% on Gemma-3-12B. These results show that replacement training can benefit steering methods fitted without protection objectives.

Distilling bidirectional multi-step video diffusion transformers into few-step causal models has become a common approach for streaming video generation. While these few-step students are significantly faster than the teachers they are distilled from, they remain slow for real-time generation. In this work we present UnStep, a training-free wrapper that accelerates few-step causal video models at inference by running them with fewer diffusion transformer (DiT) steps than during distillation and limiting the temporal window retained in the attention KV cache. We propose two inference-only mechanisms to recover quality lost by step reduction and attention windowing: renoising the generated latent frames to a near-clean level and reusing the existing clean-cache pass to refine them, and applying truncated SVD to the DiT attention value and output projections. We also accelerate inference with a quality-preserving runtime stack for the DiT and VAE decoder, including more efficient attention calls and KV indexing, fused Triton RoPE with cached coefficients, and VAE decoding with optimized memory layout, precision, and convolution kernels. By reducing computation and optimizing the runtime stack, UnStep sets a new throughput regime for causal video diffusion, by running substantially faster than current methods, reaching 50 FPS on a single H100 without quality loss, and 77 FPS on GB200, all without retraining.

The current deep learning training paradigm employs end-to-end backpropagation, regardless of the training stage, i.e. pre-training or fine-tuning. However, backpropagating through the entire model is neither biologically plausible nor memory efficient, since learning inside the brain is highly localized. Therefore, we propose LocalProp, a training procedure that locally updates the weights of a model. Our neuro-localized weight updates follow the "pre-training then fine-tuning" paradigm, where the pre-training is based on I-JEPA. After locally updating the weights, a pruning operation is performed, followed by a short final fine-tuning phase. Pruning helps by sending the learning signal from higher blocks to lower blocks. We perform experiments on several datasets, including large-scale benchmarks such as ImageNet, and empirically show that LocalProp reaches good performance at a fraction of GPU peak memory. By varying the number of jointly optimized blocks, we identify gradient-propagation span as a practical control over the accuracy-memory trade-off.

Security Operations Centers (SOCs) process large volumes of alerts daily. Alert triage prioritizes high-risk threats while reducing manual review of benign alerts. LLM agents can reason over logs and threat intelligence, but struggle to keep aligned with organization-specific, rapidly evolving SOC operational standards. We introduce REFINE, an LLM-agent framework for enterprise alert triage. REFINE encodes analyst expertise as structured skills and continuously adapts using analyst disposition feedback. It enforces recall = 1.0 as a hard constraint during evolution to maximize auto-closure of false positives, and identifies judgment blind spots by combining alert distributions with model error boundaries. Evaluated on four real industrial SOC scenarios across four MITRE ATT&CK phases with temporal split: REFINE achieves recall=1.0 on all evolution sets. On future test windows, it retains recall=1.0 in three scenarios; the degraded case reaches 0.807 recall, still outperforming self-evolution baselines (0.49-0.58).

We prove an exponential strong converse for the unassisted private capacity of every finite-dimensional degradable quantum channel. We use a single error criterion: the infidelity between the actual message-estimate-environment state and an ideal state consisting of uniformly distributed, perfectly correlated messages that are independent of the environment. At every rate strictly above the channel's maximum coherent information, the optimized fidelity to this ideal state decays exponentially in the number of channel uses. The same bound holds when the ideal environment state is fixed to the actual environment marginal. The proof applies to arbitrary mixed-state encoders and arbitrary collective decoders. Its main operator ingredient is an overlap bound for privacy tests: two receiver placements with a common subsystem of dimension $d_C$ have overlap at most $d_C/M$, where $M$ is the key size, independently of both shield dimensions. We combine this bound with the signed averaging construction presented in arXiv:2608.01308 and a single-filter reduction to symmetric states. A Gaussian filter replaces the common receiver subsystem by a system of controlled dimension from which the original correlations can be approximately recovered using quantum side information. The filter preserves exact exchange symmetry, and a uniform smooth-entropy estimate bounds its output dimension for arbitrary correlated channel inputs. We also obtain an exponential strong converse at zero for antidegradable channels under the same joint criterion and, consequently, for the private capacity of the quantum erasure channel throughout its parameter range.

LLM-driven agents are increasingly deployed in complex applications, where long agentic traces make failures difficult to diagnose. Existing trace diagnosis methods often conflate anomalies, errors, and failures, making diagnostic targets ambiguous; they also lack structured modeling of how causally relevant errors propagate and amplify into final task failures, resulting in unreliable failure attribution. To address these problems, we propose CEG-Agent, a tool-augmented agentic framework for causal diagnosis of agentic traces. Specifically, CEG-Agent introduces an explicit taxonomy of anomalies, errors, and failures, and constructs Causal Error Graphs (CEGs), a unified typed representation that links execution events, diagnostic nodes, and failure outcomes through causal relations. To evaluate causal trace diagnosis, we further construct CEG-Bench, a fully agent-annotated benchmark with high-confidence, consensus-derived CEG annotations obtained through an Adversarial Agentic Adjudication Protocol (AAAP). We validate the resulting annotations against an expert-curated human gold set, which shows close agreement with the automatic annotations. Experiments on CEG-Bench demonstrate that CEG-Agent achieves state-of-the-art performance under both semantically relaxed and structurally exact evaluation criteria. Our code is publicly available.

Handwritten mathematical expression recognition (HMER) refers to the task of recognizing and converting handwritten mathematics into a parsable markup language, usually LaTeX. No current state-of-the-art-competitive system adjusts to the way a specific person writes, and the domain gap between training images (usually digital or perfectly binarized) and images physically taken with a camera used in inference has received fairly little attention for this specific problem. We characterize this domain gap through fragmentation and stroke-width analyses of the images as well as introduce a writer-adaptive fine-tuning pipeline to MFH-CoMER in an attempt to address it. We further introduce sample author-specific datasets, consisting of five handwriting category subsets from two authors, and evaluate using a McNemar's test and permutation tests adapted to limited data. Results suggest an increase in expression recognition rate and a decrease in CER for digital handwriting but more varied results for physical handwriting, with the model struggling for handwriting articles that the base model can already evaluate well. Nonetheless, adapted models were found to have improved results for four out of five subsets. Statistical testing results suggest a consistency in improvement for two of the tested author-specific subsets. Our results point towards the potential feasibility of writer adaptation for the HMER task.

Models of vehicle dynamics learned from logged states and commands complement physics-based models, and latent world models, which predict in a learned representation, are used to plan and train controllers in other domains. Vehicle controllers are usually specified in physical terms: costs, limits, and references depend on position, yaw angle, speed, and yaw rate, and the optimizer compares or differentiates predicted outcomes across nearby commands. A latent model placed in such a controller must therefore let these quantities be recovered and must change its predictions with commands as the vehicle does, and prediction error on its own latent targets measures neither. We contribute a measurement protocol for action-conditioned latent predictors with a physical readout that separately tests retention, physical-neighborhood organization, forecasting, and local response to command perturbations, using an untrained-encoder reference and three matched response paths that locate errors in the representation or the predictor. In a case study of a temporal joint-embedding predictive model trained on signals logged in IPG CarMaker, the representations retain the measured planar outputs, though an untrained encoder of the same architecture retains them slightly better; future-command input improves one-second forecasts with retention nearly unchanged; and responses to small command pulses diverge from the simulator already in latent coordinates, raising regret when choosing among nearby commands in all comparisons. Updating the predictor on responses corrects them locally at a cost in forecast accuracy. Measuring retention, forecasting, and local response separately is thus what qualifies a predictive latent as a candidate model for control, and the protocol provides the basis for its closed-loop evaluation.

Large language model (LLM) agents serving different users often solve related tasks, yet separate user histories can leave reusable experience inaccessible to other agents. Pooling memories expands access but risks transferring preferences that conflict with the receiving user's requirements. We introduce ShareMem, a memory architecture that shares reusable experience while grounding its application in the receiving user's own preferences. Shared experiences indicate how to act and which preferences to consult; the receiving user's memory supplies their concrete values. Two-stage consolidation refines experience locally before integrating accepted edits into a shared pool. During execution, scope-first retrieval jointly selects local and shared experiences under a common entry budget, while a user-bound channel supports initial and agent-initiated preference retrieval. We evaluate ShareMem across web navigation (Mind2Web), online personalized interaction (VitaBench~2.0), and multi-session coding (MemoryCode) with four backbone models. It improves step success, average task success, and dialogue-macro coding scores, respectively, over matched user-local memory across all four models. Ablations favor two-stage consolidation for smaller shared pools, lower induction token usage, and better downstream performance, and support complementarity between experience guidance and active preference retrieval. Further analyses show that sharing helps most when relevant local experience is scarce, while source quality and cross-user preference interference limit useful transfer.

Cloud removal methods are typically specialized to individual datasets and input configurations, limiting reuse across sensors, spectral bands, and observation settings. We introduce GeoCR, a generalist model that unifies RGB-only-based CR and multispectral-based CR from single- or multi-temporal cloudy observations, with optional SAR guidance, within a single network. To accommodate different spectral and sensing domains, compact input and output stems extend a pretrained RGB autoencoder while keeping its encoder and decoder trunks frozen. This shared latent interface enables a single flow transformer to jointly model clean RGB and non-RGB latents, conditioned on separate cloudy-observation streams and optional SAR tokens. Through joint pretraining on the training splits of ten datasets comprising 883,331 cloud-free target images, GeoCR learns a shared cloud removal prior across these heterogeneous configurations. The same pretrained checkpoint supports direct inference without dataset-specific fine-tuning and efficient adaptation through low-rank adaptation (LoRA). We evaluate GeoCR against general image restoration and cloud removal methods on test splits of the contributing datasets under full-band and RGB-only settings. GeoCR achieves the best FID and DISTS on full-band SEN12MS-CR and Sen2_MTC_New and RGB-only CUHK-CR2, outperforming existing models and demonstrating the effectiveness of a reusable generative model across diverse settings.

Let $r\geq11$ be a prime. We show that there are infinitely many integers $C$ for which the Fermat-type equation $$ x^r+y^r=Cz^p $$ has no non-trivial primitive solutions for all sufficiently large (in terms of $r$ and~$C$) prime exponents~$p$. The proof uses several Frey curves to force simultaneous Frobenius trace equalities at the primes above~$3$; a new trace separation argument shows that these equalities imply $3\mid x+y$, after which a further Frey curve and level lowering give a contradiction with the Ramanujan bound.

This work considers strong and weak stochastic Galerkin approximations of random domain problems for the elliptic random partial differential equation (PDE). The random domain problems are realized by sufficiently regular random domain mapping, allowing a transformation on deterministic reference domain. A traditional numerical method for solving the resulting high-dimensional coupled stochastic Galerkin systems is replaced by deep learning techniques. We compare a physics-informed neural network approach, based on the strong stochastic Galerkin residual, with a Deep Ritz approach, based on the weak stochastic Galerkin system, reformulated as Ritz energy minimization. The neural networks serve as surrogates for the deterministic spectral coefficients of the respective stochastic Galerkin solution. The stochastic parameters are not used as neural network input parameters and the stochastic domain is not sampled during training. The efficiency of the methods is demonstrated on a randomly stretched interval and a randomly deformed annulus in two spatial dimensions.

In this paper, we show that a knot with a nontrivial Jones polynomial of span at most 11 does not admit purely cosmetic surgery.

We give a complete classification of proper biharmonic Lagrangian $H$-umbilical submanifolds in complex space forms. Such submanifolds exist only in complex projective space and are locally congruent to an explicit model obtained via the Hopf fibration. In particular, their nonexistence in complex Euclidean space provides a partial affirmative answer to Chen's conjecture.

We present a fully GPU-oriented SVD pipeline based on polar decomposition, motivated by iterative methods that rely solely on matrix multiplications, such as the Newton-Schulz iteration. We show that this approach enables up to a $2\times$ speedup compared to standard implementations. Furthermore, we derive a numerically stable backward pass for the polar decomposition and leverage it to obtain a fully differentiable SVD. Our methods are released as open-source implementations in both PyTorch and JAX: https://github.com/fallnlove/cans_svd.

Evaluating emotion preservation in expressive speech generation involves assessing how closely generated speech matches a reference in emotion. Human listening tests assess this similarity, but their cost motivates automatic measures aligned with human judgments. To support the development and evaluation of such measures, we introduce SES-Bench, a speech emotion similarity benchmark built from human comparisons of two candidate utterances against a shared reference. These comparisons record which candidate listeners find emotionally closer to the reference and the strength of their preference. Using these annotations, we train SES-Judge to score emotion similarity between two utterances. SES-Judge significantly outperforms embedding cosine similarity and prompted large audio-language models in preference accuracy and correlation with human ratings that capture both preference direction and strength.

Kolmogorov-Arnold Networks (KANs) are motivated in part by interpretability: their learned edge functions can be inspected, pruned, and reduced to symbolic structure. In a fixed-basis KAN, this makes a small or zero basis coefficient look like a certificate of simplicity, much as a dead rectified linear unit (ReLU) marks unused computation in a multilayer perceptron (MLP). Fisher nullity gives a precise statistical notion: a parameter direction is Fisher-simple exactly when perturbing it is invisible under the task distribution. We study when these architectural and Fisher notions agree. For a dead ReLU unit, they agree: the closed activation region makes the associated score directions vanish. For a fixed-basis KAN, they do not. In the single-layer Gaussian case, the coefficient Fisher matrix is a basis Gram matrix under the input distribution and is independent of the fitted coefficients. In a multilayer KAN, Fisher simplicity is graph-path based: the data must reach a basis atom and its perturbation must propagate through the downstream network. We encode these two conditions in an effective edge measure and, under local dictionary independence and effective-measure nondegeneracy, show that zero effective exposure exactly identifies Fisher-null directions within an edge. Controlled diagnostics confirm that zero coefficients can preserve rank while effective path disconnections remove the predicted directions. Coefficient magnitude alone is therefore not a Fisher-based pruning criterion for KANs.

De novo 3D molecular generation jointly models molecular size, topology, and geometry. Most methods pre-sample molecular size and generate Cartesian coordinates, limiting variable-size conditional tasks such as fragment completion and scaffold decoration while often relying on equivariant architectures. Internal-coordinate methods avoid rigid-body redundancy but typically require a known molecular graph or autoregressive construction, which may accumulate errors. We propose TreeRef, a tree-based molecular representation that assigns molecular topology and topology-dependent local 3D geometry to a naturally variable-size tree. RingRef nodes encode ring closures while preserving the tree structure, while Null nodes allow molecular size to emerge directly from node occupancy. Based on TreeRef, we develop TreeRef-BFN, a Bayesian Flow Network with a standard Transformer backbone that globally couples these locally defined variables and jointly generates discrete molecular variables and continuous local geometry. A single pretrained TreeRef-BFN supports unconditional generation and variable-size structure-conditioned 3D generation through masking alone, without retraining. Empirical studies demonstrate strong chemical validity, molecular stability, and diversity, accurate local geometric distributions, fast sampling, and competitive property-conditioned generation, establishing TreeRef-BFN as an efficient and flexible framework for 3D molecular generation.

We demonstrate that heterogeneous double-wire metamaterials, comprising two dissimilar and nonconnected wire arrays, enable loss-asymmetric hyperbolic dispersion and strongly asymmetric negative refraction. We unveil that, owing to their strongly nonlocal response and distinctive microstructure, such geometry supports two independent hyperbolic propagation channels with unequal losses, which can be selectively excited by free-space propagating waves incident at opposite angles. This angular selectivity gives rise to asymmetric negative refraction at the air-metamaterial interfaces, characterized by strong angular asymmetry in transmission and absorption, while preserving reciprocity. This phenomenon is scalable and can be realized with metallic wire arrays over a broad frequency spectrum extending from microwave to infrared frequencies, showing that nonlocality can emulate shear-like dissipative asymmetry that, in local media, requires lower spatial symmetry. Our findings open new avenues for directional energy transport and angle-selective wave control in photonic platforms.

Many real-world time series data exhibit structural properties at multiple scales, from short, recurring units to complex sequences composed of these units. Unsupervised discovery of both these components and structure enables the design of intelligent systems that help interpret temporal data, thereby limiting the amount of costly human annotations required. Existing modeling approaches typically overlook the hierarchical structure inherent to many time series, treating recurring patterns at different temporal scales as independent structures. Moreover, most assume access to the complete data sequence and treat discovery as a static process, limiting their ability to evolve as new observations arrive. We introduce Rondo, an unsupervised approach for modeling recurring hierarchical structure in continuous temporal streams. By explicitly constructing vocabularies of reusable units and their recurring compositions, Rondo captures structure shared across complex temporal patterns while refining and expanding its discoveries as the stream evolves. Evaluations on temporal sequences spanning diverse domains and data modalities show that Rondo outperforms existing unsupervised recurrence-discovery baselines, with particularly pronounced advantages in limited-data and continual-stream settings. These capabilities provide a stronger foundation for recurring-pattern discovery, scalable behavior understanding, and adaptive intelligent systems operating on long, unlabeled temporal streams.

Continually adapting large language models requires acquiring new knowledge while preserving previously learned capabilities. Although jointly adapting model parameters and task-specific soft prompts is promising, it has two key limitations: previously learned prompts may lose effectiveness as the model evolves, and relationships among prompts that could support cross-task transfer are not explicitly learned. We propose Learning an Anchored Prompt Space (LAPS), which preserves historical prompt effectiveness and learns relationships among task-specific soft prompts to facilitate positive transfer. Historical prompts are first aligned with the updated model through self-distillation. LAPS then constructs an anchored prompt space whose vertices correspond to learned task-specific soft prompts and whose intermediate geometry is shaped by learnable Bézier control prompts. Once this space is learned, LAPS identifies the best-performing prompt for each task on its validation set, allowing the selected prompt to draw on knowledge acquired from related tasks. Experiments on the TRACE benchmark across three Qwen3 model scales show that LAPS consistently outperforms existing distillation-based, prompt-based, and joint prompt-parameter adaptation methods, improving overall task performance while reducing forgetting.

Deployed LLM agents increasingly rely on persistent, versioned system assets such as routing rules, knowledge segments, prompt instructions, and reusable skills. Failure-localization methods can identify where an error manifests in an agent or execution trace, but repair requires a different decision: which editable system asset should be changed, and is that change expected to improve the task outcome? We study this gap through component-attribute failure attribution, where diagnosis targets versioned, addressable items rather than execution locations. We propose the Detection-Aware Attribution Framework (DAAF), which learns the effects of valid attribute replacements and amortizes this intervention evidence into deployment-time diagnosis. DAAF combines sparse and noisy failure signals to decide whether intervention is warranted, learns component-type-conditioned replacement effects from controlled replays evaluated by executable task outcomes, and shares supervision across requests with compatible intervention responses. At diagnosis time, DAAF uses only the observed execution, registered candidates, and available failure signals; it requires neither counterfactual replay nor task reward and returns no_change, a repair target, or an unresolved decision when evidence is insufficient. On held-out tau^2-bench Telecom tasks, DAAF achieves 80.72% attribute Hit@1, recovers 62.65% of failed executions while limiting clean-task regression to 3.23%, and reaches 71.93% overall task success. These results show that intervention-grounded attribute attribution can connect failure localization to executable system repair.

The planar loop equations of a Hermitian one-matrix model leave finitely many low moments undetermined. Hankel positivity constrains these moments but does not reveal how a fixed multicut family is embedded in moment space. We introduce a finite-plane diagnostic using the Cauchy kernels $f_n(x)=(z_n-x)^{-1}$ which we use as spectral probes. Their Gram matrix is the positive-semidefinite Pick matrix $P_{mn}$, whose positivity defines a finite-node bootstrap analogous to the Hankel bootstrap. For a fixed regular multicut topology, the nonbranching double zeros of the spectral discriminant, which we call dressed saddles, impose transverse constraints on the corresponding moment-space locus, while its remaining directions are filling fractions. Writing $z=E+i\eta$, $E$ selects a spectral region and $\eta>0$ sets a continuous resolution scale. We use $P(z,z)$ as a finite-plane spectral response and interpret $\nabla_{\mathbf m}P(z,z)$ as a moment-space susceptibility. Near a regular real dressed saddle, this susceptibility is enhanced as $\eta^{-2}$ and aligns with a conormal to the filling-fraction manifold, whereas the leading enhancement cancels along tangent deformations. Responses near several independent saddles can therefore reconstruct the conormal space and, through their common kernel, its tangent space. Combining Pick positivity with reality and analyticity of the resolvent, we obtain alternative analytic derivations of known planar results in quartic and sextic models. The asymmetric quartic makes the one-dimensional filling-fraction geometry explicit, while sextic models exhibit independent conormal directions. These results clarify how local consistency conditions constrain the low moments before global period matching and the equilibrium variational inequality select the equilibrium measure.

Reliable multi-hop reasoning requires more than locally supported steps: a trace can be sound at every reasoning step yet still fail to answer the question as a whole. We call this failure regime the local-global gap (LGG), in which the trace is locally sound yet globally insufficient. Local soundness requires each step to be supported by the available evidence and preceding steps, whereas global sufficiency requires the reasoning trace to align with the question and establish the submitted answer. In a human-adjudicated diagnostic of 2,598 responses across three multi-hop QA benchmarks and three models, we find that the LGG occurs in every benchmark-model combination and accounts for nearly half of globally insufficient responses overall. However, conventional faithfulness verifiers that check claims against the evidence largely miss these failures: at thresholds retaining at least 95% of reliable traces, recall for LGG cases is substantially lower than that for locally unsound traces. To address these failures, we formalize three dependencies for reliable reasoning: evidence-to-step support, question-to-trace alignment, and trace-to-answer closure. Instead of post-hoc diagnosis, we introduce E-Closure to supervise these dependencies during training, combining generation supervision on supported original and counterfactual responses with bidirectional switching constraints. Averaged over three benchmarks and three backbones, existing fine-tuning baselines improve accuracy and local soundness over the base models, but at the cost of global sufficiency. E-Closure improves both: among all fine-tuned methods, it achieves the highest average accuracy (92.8%) and trace reliability (89.0%) while yielding the lowest LGG rate (6.2%).