Constructing Lyapunov functions for nonlinear dynamical systems is a central problem in stability analysis, yet remains challenging. Lyapunov functions are commonly characterized as solutions to first-order partial differential equations (PDEs), but these solutions are typically obtained for single systems, limiting their reuse across systems. In this paper, we study the Lyapunov solution operator that maps a vector field to the corresponding Lyapunov function defined by a dissipation-based Lyapunov PDE. We establish that, on compact subsets of the domain of attraction and under exponential stability assumptions, this operator is well-defined, unique, and continuous with respect to perturbations of both the vector field and the dissipation function. These results provide a theoretical foundation for approximating Lyapunov functions uniformly over families of nonlinear systems. Building on these theoretical foundations, we employ Fourier Neural Operators (FNOs) as a data-driven approximation of the Lyapunov solution operator. Numerical experiments demonstrate that a single trained operator can accurately approximate the numerical Lyapunov functions across parameterized families of dynamics. This illustrates the potential of neural operators for approximating Lyapunov functions.
Large Language Models (LLMs) are now routinely trained using synthetic data, since high-quality human data has been exhausted by the ever increasing needs of larger and larger models. However, recursive training on synthetic data frequently induces model collapse, a degenerative feedback loop where models progressively forget the true underlying data distribution. Training on a mixture of synthetic and fresh human data is a logical countermeasure and can prevent model collapse. However, it is an open question as to what is the exact minimum required ratio of human-to-synthetic data to maintain training stability. In this paper, we establish rigorous theoretical guarantees on the minimum rate of human data required to prevent model collapse. Although previous work established a formal lower bound for this ratio, such bound can be vacuous for very high dimensions, as the analysis relies on the usual Euclidean metric in R^n and is not adapted to the space of categorical probability distributions. Instead, in this paper we explicitly leverage the information-geometric structure of the probability simplex by analyzing the dynamics of the process under the Fisher-Rao metric. We derive quantitative contraction and invariance bounds that are stable and do not become trivial as the dimensions increase. Thus, we show that the effective required data ratio to prevent model collapse is different than previously implied.
Privacy evaluations of tool-using LLM agents often inspect a designated action, final response, or attacker report. These local proxies can miss unauthorized exposure elsewhere in a multi-step session and lack common ground truth across outlets, reports, and tool paths. We introduce privacy exposure displacement, the mismatch between a local evaluation proxy and target-grounded session exposure, and ASLEval, an authorization-aware framework that pre-registers a hidden target set, measures all declared visible exits, and reserves internal traces for diagnosis. Across multiple enterprise-style environments and independently implemented runtimes, we observe three recurring patterns. An expected-outlet-only view misses 46.9% of exposure recovered by the visible-exit union; attacker self-reports combine omissions with high false discovery; and schema-aligned internal evidence usually precedes visible exposure at the request/probe level. Reducing model-visible returns changes this path but can eliminate normal-task success. Independent human review supports the adjudication pipeline while identifying harder console and candidate cases. These findings motivate benchmarks that declare the complete visible boundary, ground claims in pre-specified targets and authorization, and report privacy together with task utility.
Reliable prediction of crystallographic texture in laser powder bed fusion is critical for linking process conditions with anisotropic response and for qualification. However, black-box models may fail under shift and cannot distinguish weak data support from loss of physical validity. This study develops a two-stage physics-based model for <001> || BD (build direction) texture in Inconel 718. Stage 1 maps process variables to melting mode and melt pool geometry. Stage 2 predicts texture by combining an empirical physics model with a random-forest residual model. A k-nearest-neighbor weight attenuates residual corrections for poorly supported queries, while a study-specific areal beam-power-density criterion withholds predictions outside the adopted conduction envelope. Conformal intervals are evaluated on the retained physics-valid set, and SHAP and Sobol analyses assess residual sensitivity. Under a controlled leave-one-defocus-out evaluation, the physics anchor achieved R^2 = 0.778, against -0.001 for the black-box model and 0.750 for the gated hybrid. Under leave-one-group-out cross-validation, the gated hybrid reached R^2 = 0.592 against 0.538 for the black-box model. Retained-set coverage was 92.9% at a mean full width of 3.65 multiples of a uniform distribution (MUD) under grouped cross-validation and 100% at a width of 3.21 MUD under transfer to a withheld +80 mm defocus regime. An illustrative mapping produced a retained BD elastic-modulus span of 127-187 GPa. On nine conditions from a separately built sample set, the framework withheld three, attenuated three, and matched the measured ordering for the rest. Separating data applicability, physics validity, and predictive uncertainty into distinct decisions lets the framework transfer where an unconstrained model does not, and withhold predictions where no model class performs adequately.
Adaptive learning systems commonly formulate learning path planning as Exercise-Centric (EC) recommendation, where the next step is inferred from item-level interaction logs. Evaluating goal-oriented guidance additionally requires explicit learner goals and curriculum-scale prerequisites: learners with similar exercise records may need different paths toward their targets. We therefore study Knowledge-Centric (KC) personalized learning path planning, where a planner must reason over learner profiles, mastery states, and prerequisite knowledge structures to decide which textbook, unit, and concept should be studied next. To support this setting, we introduce PersonaPath, a benchmark that pairs 2,000 fine-grained learner personas with a hierarchical knowledge graph of 347 textbooks, 1,751 units, and 4,092 concepts across 77 subjects. We evaluate representative LLMs on PersonaPath. Results show that even the strongest LLM reaches only a 29.5% final pass rate in Basic Education, and that the main bottleneck lies in adaptivity, where no model exceeds 44.7% in tailoring paths to individual learners.
When a large vision-language model misclassifies a harmful meme, the failure may reflect missing internal evidence or an inability to route represented evidence to its output. We distinguish these cases in Gemma-3 and Qwen3.5 using sparse autoencoders, role-conditioned probes, causal interventions, and recovery experiments across six harmful content benchmarks, with additional Spanish and Hindi-English code-mixed evaluations. Sparse readouts outperform native prediction on all six primary binary tasks: Qwen averages 0.740 versus 0.432 native macro-F1, while residual reconstruction reaches 0.486, whereas Gemma improves from 0.532 to 0.714. These differences reflect supervised accessibility rather than a pre-existing, native decision rule, and the most influential token role depends on the task. Under the evaluated score scales, Qwen silent-feature ablation is 24-63 times more probe-sensitive, whereas routed-feature patching on literal yes/no tasks is 16-140 times more output-sensitive. Calibration-only routing recovers 93.3% of the mean gap, and probe-distilled LoRA improves native predictions, although shared multi-task adaptation causes negative transfer. A case study of Gemma-3-12B on Facebook Hateful Memes finds a distributed rank-32 image-prompt interaction, reaching 0.756 versus 0.685 native macro-F1. Robustness controls show that the signal extends beyond English, is not explained solely by accompanying OCR, and depends on paired visual evidence. Thus, routing, rather than representation alone, is a recurring bottleneck in harmful meme classification.
OpenAI and AARP are bringing free, hands-on ChatGPT workshops to 1,000 older adults across 10 U.S. cities to build practical AI skills safely.
The O-RAN control plane is becoming agentic: autonomous AI agents, deployed as rApps by different vendors, independently close control loops over shared radio resources. We demonstrate on a live O-RAN system that this independence is unsafe. Two agents with individually correct objectives, one protecting a latency SLA and one maximizing utilization for energy efficiency, jointly drive recurring opposing excursions of the shared resource partition that neither produces alone. Existing conflict-mitigation mechanisms presume a statically known application population and cannot govern agents whose behavior emerges at run time. We present AURA, a lightweight arbitration layer that admits agent actions only when they satisfy feasibility invariants, per-variable dwell times, and a deadband, and we prove the arbitrated system converges to a feasible operating point. Implemented on an OpenAirInterface (OAI) testbed with measured one-way latency and throughput, AURA reduces recurring shared-state excursions by more than an order of magnitude (from 8.4 to 0.4 PRB amplitude) and virtually eliminates cross-slice throughput starvation (from 40-55% to 0.3%), while leaving the protected slice's own latency compliance unchanged, a trade-off the convergence guarantee makes explicit.
Compact acoustic models face a challenging quality-capacity trade-off. We investigate two factors in this regime: encoder context and Mel-spectrogram supervision. A receptive-field-scaling study shows that expanding self-attention beyond 15 phonemes provides no consistent gains in pitch, energy, or duration prediction. Guided by this finding, we introduce a fixed-receptive-field convolutional encoder that reduces the respective prediction errors by 36.0%, 17.3%, and 3.4%. We further show that directly transferring image-domain gradient-variance supervision restores fine-scale variation but degrades predicted quality, motivating a Mel-specific formulation with axis-specific gradients, overlapping local statistics, and log-domain variance matching. GrainSpeech contains only 264.8K parameters and achieves 17.9x real-time Mel generation on a microcontroller (MCU), while attaining UTMOS scores comparable to substantially larger models with less than 1.5% of their parameters. Source code and demos are available at https://github.com/lab-emi/GrainSpeech.
Longitudinal electronic health records (EHRs) capture years of patient history across notes, codes, labs, and procedures, and contain evidence needed to reason about likely clinical outcomes. However, comprehensive clinician review of these records is impractical, and LLM-based processing is costly and often unreliable, missing some relevant observations while hallucinating others. We therefore propose EviGen, a three-layer framework for verifiable clinical rationale generation that addresses these challenges. The first layer is a patient-conditioned retriever that uses learnable queries to find evidence predictive of, not just textually relevant to, a clinical outcome and ranks it by prediction attribution scores. The second layer is an LLM generator that consumes this ranked evidence as a scaffold to produce a clinical rationale grounded in the retrieved spans. The third layer is a process-supervised verifier that checks the generated rationale at the reasoning-step level, flagging unreliable claims. Across three medical prediction datasets, EviGen improves prediction performance and rationale faithfulness over full-context LLM and RAG baselines, and is preferred by clinical reviewers in a usability evaluation.
An agentic request spends substantial wall-clock time waiting for tools, and its KV cache holds GPU memory the whole time. Serving systems decide whether that cache stays, leaves, or comes back by guessing how long the tool will run, from the tool's name, its history, a duration declared before the call, or the engine's own occupancy. We show that no estimate fixed before a call starts can know its duration, and such estimates may not even rank the calls. Meanwhile, the running tool already holds the answer, but the agent stack together with the tool silences it. We propose that tool calls report their progress explicitly while they run, and we measure what that takes. A census of four public agent corpora finds a readable signal in most tool time once it is revealed, in two strengths: a fraction of the work remaining, or an accurate signal that the end is near. A harness recovers it without changing what the agent sees, at no measurable cost to the agent's benchmark score. At the points where a KV cache decision is made, the reported progress is between several times and an order of magnitude more accurate than the best published predictors, and it stays accurate when the environment changes. Plugged into a production engine through a few small hints, it cuts the p90 time to first token (TTFT) after a tool call by 20.7% (HBM only) and 20.8% (HBM + DRAM) against LRU, close to an oracle. A serving system should not guess what its tools can tell it.
Multimodal coding agents are expected to turn visual inputs into usable artifacts, and they act through a harness, the layer of tools, context management, and execution environment around the model. Existing evaluations often isolate short tool calls, API traces, or screenshot resemblance, and a low score under these proxies cannot say whether the model saw poorly, planned poorly, or was failed by its harness. We study scientific overview figure reconstruction, an agent task in which a source image must become an editable PowerPoint slide that preserves text, topology, layout, and native document structure. We introduce ReFigBench, a benchmark and evaluation framework built on 1,000 real overview figures retrieved from arXiv papers with full provenance. Coding agents from four model families reconstruct every figure under two workflows, direct code generation and a specialized PPTX workflow, and the strongest model runs inside two commercial harnesses, yielding ten configurations. Evaluation combines deterministic artifact checks, repeated automated scoring by judges from two model families, and blinded human comparisons. Perception remains a bottleneck that iterative rendering only partly repays. Whether workflow effort converts into quality depends on the model together with its harness, since the same model gains from the specialized workflow inside one harness and loses inside the other, and the harness shifts scores even under an identical direct prompt. The specialized workflow erases native connectors in every configuration, human judges still prefer its renderings in most matchups, and even the strongest agent falls short of the rubric ceiling. These results expose the tension between fidelity and editability as the central challenge for practical multimodal document agents.
The scaling laws hold that a language model grows more capable with more parameters and more training data, and Mixture-of-Experts (MoE) architectures have ridden these laws to remarkable results, activating only a fraction of an enormous stored parameter bank for each token. That success is built on static pretraining data. A deployed model faces a different world, where much of the data that would make it more useful is not in its training set but in the live interaction it is currently handling, such as the facts a user supplies or the corrections they give. A conventional model cannot learn from this data, because its weights are frozen after training. Instead, the knowledge and behaviour supplied at run time are placed in the prompt, by retrieval or instruction, and re-read on every request only to be discarded once the request ends. We ask how an architecture could learn from live interaction by writing it into its weights. Taking inspiration from MoE, we propose the Infinite-Parameter LLM. A compact hypernetwork turns the data given at run time into a low-rank modulation of a shared base network, so the feed-forward weights are generated from live data rather than stored in a fixed bank. Where prior weight generators read the context once and freeze, we carry a Bayesian belief over the generator's latent code and update it online, so the effective weight is re-derived from that evolving belief as the session proceeds rather than fixed after one read. The stored footprint stays fixed, yet the weights the model can compile are effectively infinite. For the knowledge and behaviour supplied at run time, carrying them in the weights rather than the prompt is amortized in compute, frees the context window, persists across turns, and can generalise better than in-context use. We specify an evaluation protocol that tests exactly this against in-context learning and retrieval.
AgentCore optimization turns production traces into proposed configuration changes, then validates them before promotion. This technical companion to the launch post explains how the system prompt optimizer's reflector engine works and shares benchmark results for the Single Agent and Sub-Agent Reflectors.
Background: Molecular testing for NPM1 and FLT3-ITD mutations guides critical early treatment decisions in acute myeloid leukemia (AML), but results can take weeks, long after these decisions must be made. Flow cytometry, already performed within hours of admission as part of routine care, may carry enough signal to predict these mutations directly, without added cost or delay. Methods: We developed an interpretable multi-instance learning classifier based on a decision tree, in which each patient sample is modeled as a collection of individual cells and mutation status is inferred from cell-level predictions. The model was benchmarked against a random forest trained on clinical variables and a deep convolutional neural network adapted for multitube flow cytometry data. Performance was assessed by cross-validation on a discovery cohort of 197 patients and tested on an independent cohort of 161 patients, using the area under the receiver operating characteristic curve (AUROC) and positive predictive value. Results: In cross-validation on the discovery cohort, the MIL model achieved mean AUROCs of 0.96 (SD=0.05) for NPM1 and 0.86 (SD=0.10) for FLT3-ITD, outperforming the clinical baseline and matching deep learning approaches. The model then successfully generalized to the independent test cohort of 161 patients, reaching AUROCs of 0.90 (NPM1) and 0.82 (FLT3-ITD), with positive predictive values of 0.87 and 0.68, respectively. Cell-level interpretation recovered established immunophenotypic signatures (CD33{}^{+} /CD34___ for NPM1-mutated cases, CD33{}^{+} /low side-scatter for FLT3-ITD), directly linking model predictions to known biology. Conclusions: These results show that an interpretable model applied to data already collected in routine care can predict AML molecular status within hours, offering a practical route to earlier, biology-informed treatment decisions.
How do VLMs map from pixels to semantics? To understand this general question, we focus on a narrow one: studying how VLMs perform optical character recognition (OCR). Across four models, we identify attention heads causally necessary for OCR, and discover that these are in fact general-purpose heads that output interpretable semantic features across all image tokens. For example, pointing these heads at an image token containing the word "bike" causes Qwen3-VL-8B to output "bike," but pointing them at a bird wing causes the model to output the token "feathers." We collapse these heads' attention weights into a single verbalization lens transformation that reveals interpretable semantic features in hidden states across all layers. When combined with projection to vocabulary space, we can obtain interpretable labels starting from layer 0, showing that image representations are in fact aligned with language in early layers. We find that we can also use the inverse of this transformation to edit non-word concepts, e.g., replacing a tractor with a revolver in a naturalistic image, providing causal evidence that this subspace is useful for more than just OCR. Our results are an example of how the study of specific mechanisms can shed light on broader interpretability problems.
