Physics-informed neural networks and finite element methods provide two different paradigms for the numerical approximation of partial differential equations: the former are commonly trained by minimizing pointwise strong residuals, whereas the latter are naturally built from weak variational formulations and the finite-dimensional systems obtained after discretization. In this work, we introduce a common framework based on the discretization of functional Gauss--Newton problems by finite families of linear measurements. We show that, through an appropriate duality pairing, the linear measurements can be represented by test functions. The resulting Gauss--Newton system is then precisely a Petrov--Galerkin discretization of the linearized functional problem. This perspective recovers pointwise collocation and natural-gradient constructions as particular cases, while making the choice of test functions an explicit algorithmic design choice. We specialize this framework to elliptic problems, where it naturally leads to weak residual formulations and to a hybrid finite element--neural construction acting on complementary approximation spaces. Numerical experiments support the proposed framework and demonstrate the effectiveness of weak Gauss--Newton formulations and hybrid finite element--neural approximations.
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Allen's interval algebra is a qualitative calculus for temporal relations, but its thirteen base relations are crisp predicates over exact interval boundaries. This is inadequate for temporal information from language, perception, databases, or uncertain histories, where times, durations, and boundaries are uncertain and expressions such as "just before" or "roughly during" have graded meaning. We develop the probabilistic Allen algebra (PAA): a generative and complete extension in which relation probabilities are derived from distributions over interval boundaries rather than assigned as scores. Time points are Gaussian; intervals have Gaussian midpoints and truncated-Gaussian durations. Every relation is a boundary-ordering predicate in one common probability space: point-point relations reduce to error functions, and point-interval and interval-interval relations to multivariate Gaussian orthant probabilities induced by linear inequalities. Contact relations (meets, starts, finishes, equals) receive positive measure through a tolerance band, and under a single tolerance the thirteen relations form a true partition that recovers crisp Allen as the tolerance vanishes. The construction derives Allen's taxonomy rather than positing it: coarse predicates such as precedence, overlap, and containment are unions of leaves whose probabilities are leaf sums, and this hierarchy is preserved as intervals collapse to points and thirteen relations reduce to five and then three. Each relation further decomposes into correlation-aware temporal primitives in the spirit of CIDOC CRM. The algebra is scale-invariant and separates graded expressions such as "shortly before" from contact relations. All results are Monte-Carlo validated and shipped as an open, tested Python package.
Search advertising connects user intent with commercial content and plays a critical role in platform monetization. Recent systems typically align pretrained generative models with a single business reward, such as eCPM, or use naive reward fusion for preliminary multi-objective alignment. However, an ideal search advertising system must jointly account for heterogeneous objectives, including relevance, click propensity, and commercial value, to balance user experience and business value while mitigating globally suboptimal performance caused by gradient competition. We propose UniPolicy, an objective-aware multi-policy alignment framework. UniPolicy combines objective-specific prefix tokens, sparse MoE-LoRA routing, and objective-specific residual FFNs to hierarchically decouple parameters within a shared backbone, providing differentiated parameter and policy-expression spaces for different business objectives. It further constructs pairwise preferences from multi-stage behavioral feedback, supplementing the relative preference information in exposed-but-unclicked samples and strengthening the relative advantage of clicked candidates in the generation distribution. At inference, UniPolicy supports parallel, business-customizable multi-policy beam search, flexibly allocating candidate quotas across objectives under a fixed retrieval budget. Large-scale offline experiments show that UniPolicy delivers balanced improvements across multiple metrics while preserving retrieval quality, outperforming single-objective reinforcement learning and naive reward-fusion baselines. In a 7-day online A/B test on a real search advertising system, UniPolicy improves CTR by 0.71%, RPS by 1.58%, and advertising revenue by 1.32%, while maintaining stable serving latency.
Large language model responses are non-deterministic, so failures in LLM agents are hard to reproduce: a failure depends on inference that is not bitwise reproducible, on tools that read changing state, and on a multi-step trajectory that a re-run rarely repeats. Record-and-replay makes a run reproducible, but existing agent tooling records runs only to trace or score them, not to test a code change against them. We present Chronicle, which records an agent run at its non-deterministic boundaries as immutable envelopes and replays it from the record. Its central operation, cut-point replay, serves a chosen subset of boundaries from the record and executes the complementary subset live with new code, turning a recorded incident into a regression test that runs in continuous integration. On a benchmark of 6 recorded failures with simulated model boundaries, recording adds 23 μs per crossing (0.008% of an assumed 300 ms model call), full replay issues zero model calls and is bit-stable across 20 repetitions, and cut-point tests fail on faulty code and pass on guarded and benign changes for all 6 incidents. In a mutation study of the guarded tools, cut-point tests catch every mutant that lets the recorded unsafe action through, while a baseline that stubs every boundary, using the same assertion, catches none. Chronicle and the benchmark are publicly available at https://github.com/theagentplane/chronicle.
Autonomous underwater vehicles (AUVs) operating beyond reliable communications must recover from failures without human intervention. We investigate an architecture in which conventional deterministic layered control autonomy manages normal operations, while an invokable large language model (LLM) serves as a diagnostic and recovery planner when onboard anomaly detection identifies performance outside expected limits. Because language models are stochastic, rigorous evaluation requires ensemble testing rather than individual demonstrations. We present a closed-loop simulation architecture that couples real-time C vehicle software with a higher-level orchestration layer for physics-based fault injection, structured prompting, language-model interaction, mission file generation, validation, execution, and LLM-judge scoring. The framework, which we call SPAR (Simulation Platform for AUV Recovery), supports evaluation across fault realizations, prompt structures, reasoning models, and mission conditions. We vary these for a mass-shift fault over 480 SPAR trials, evaluating a frontier model and three off-the-shelf locally deployable LLMs. Model choice dominates diagnosis: the frontier model places the CG-shift mechanism in its top three hypotheses in 85-90% of trials, versus 60-78% for the best local model. Reasoning analysis indicates that local-model success is associated with following the complete diagnostic procedure, whereas weaker models often commit prematurely to elevator failure even though the actuator tracks its command. Diagnosis and operational decision performance do not appear to be coupled in this dataset. The contributions are an architecture extending unanticipated-fault recovery from detection to mitigation and an ensemble methodology for evaluating LLM-assisted mission management on low-power AUVs.
Frontier AI models are rapidly gaining the ability to exploit vulnerabilities in complex pieces of software. The risk is not theoretical, as evidenced by recent sandbox escapes performed by frontier models at OpenAI and Anthropic. Discussions of how to sandbox inference stack components often focus on components other than the inference engine itself (e.g., network proxies or code execution environments). However, the inference engine is an attractive target for a misaligned model. For example, if a model can trigger exploits in that engine merely by generating specially-crafted output tokens, the model can initiate a multi-step, to-the-bare-metal exploit chain in the engine, without relying on vulnerabilities in other components of the inference stack, and without assistance from externally-provided, maliciously-crafted input tokens. In this paper, we show that a misaligned model can perform inference engine fingerprinting to determine the specific engine (e.g., vLLM, SGLang) which executes the model. Once the engine has been fingerprinted, the model can leverage engine-specific exploits to take control of the engine using only carefully-selected output tokens. We provide concrete examples of model fingerprints in five popular engines, and demonstrate how realistic agentic harnesses allow a model to leverage those fingerprints to identify the local engine. We also describe a proof-of-concept, to-the-bare-metal exploit chain that originates from a fingerprinted (and subsequently compromised) inference engine. We conclude by discussing several ways that inference engines could be changed to make fingerprinting attacks more difficult.
On-policy self-distillation (OPSD) lets a language model learn from a frozen copy of itself that sees an answer or a worked solution. Giving the teacher this extra information seems to offer the student more to learn, but how much does it add beyond distillation itself? To isolate that contribution, we construct AMPLE-Math, a reusable suite of 5,319 mathematical problems with six reasoning views that share the same answer, and compare each view with matched reference-free distillation. With a thinking-enabled teacher supervising direct-response rollouts, reference-free distillation accounts for much of Qwen3-1.7B's improvement under thinking-enabled evaluation, both in domain and on external benchmarks. Evidence for an additional reference benefit is modest in Qwen, strongest for a polished solution, whereas complete traces add two percentage points in SmolLM3-3B at step 50. These benefits depend on the student being trained. At the same checkpoint, replacing short direct-response rollouts with long thinking-enabled rollouts turns gains into losses in both families while the problems, references, and evaluation stay fixed. Teacher profiles and matched loss interventions in Qwen further show that changing token-level supervision can leave student behavior largely unchanged. Together, these findings suggest that OPSD can improve access to existing reasoning capabilities through parameters shared by direct-response and thinking-enabled inference. The value of a privileged reference is what it adds to this cross-mode transfer, not how much of the solution it reveals.
Choosing the right vector store for your Amazon Bedrock Knowledge Bases RAG application affects performance and cost. This post compares Amazon OpenSearch Service, Amazon Aurora PostgreSQL with pgvector, and Amazon S3 Vectors across three RAG use cases, with benchmarks and a practical selection framework.
In this paper, we tackle the problem of jointly estimating the system states and partially unknown dynamics within distributed sensor-equipped networks, particularly in scenarios where only partial state observations are available. To address this issue, we propose an observer-based dynamic cooperative learning framework incorporating online distributed Gaussian Process (GP) regression, which enables accurate estimation despite incomplete in measurements and deficient GP models. In addition, a novel data collection strategy is introduced, with theoretical conditions ensuring feasible data acquisition. Moreover, we also derive an error upper bound encompassing state estimation and model estimation, leveraging the deterministic error bounds of GPs. Empirical simulations demonstrate the superiority of our approach compared to existing distributed GP-based methods.
Quantum long short-term memory (QLSTM) models extend recurrent sequence learning with variational quantum circuits, but their optimization behavior can vary substantially across random initializations and temporal contexts. This paper evaluates a recursive QLSTM architecture against a standard QLSTM for one-step-ahead prediction of daily minimum and maximum temperature. Using daily weather observations from Toronto and identical training settings, we compare convergence, predictive accuracy, and generalization across input windows of 8, 16, and 32 days over 20 random seeds. The recursive model consistently reaches a near-optimal test loss earlier, reduces mean absolute error and root mean squared error, and exhibits a smaller generalization gap. These results indicate that recursive quantum feature transformations can improve stability and out-of-sample performance for compact hybrid quantum--classical temporal models.
Word-in-Context (WiC) remains challenging for language models, despite recent progress on lexical-semantic tasks. We hypothesise that this difficulty arises not only from comparing two contextual uses of a word, but also from the absence of an explicit sense inventory that specifies the relevant level of semantic granularity. We evaluate open LLMs on WiC and traditional Word Sense Disambiguation (WSD) under similar settings. We find that providing candidate senses, similar to what is done in traditional WSD, improves WiC performance in all settings. In general, explicit sense information helps models make more consistent and targeted judgements. Human evaluation further shows that many apparent WiC errors reflect label ambiguity or mismatches between model and annotator sense boundaries rather than simple failures of lexical understanding. In particular, results show that LLMs overthink the sense distinction often leading to errors based on overly fine-grained distinctions.
Learn how to build a fully serverless pipeline that automatically collects Git metrics from GitHub and GitLab and visualizes them in interactive Amazon Quick Sight dashboards, giving engineering teams near-real-time delivery analytics at low cost.
Wood Mackenzie built APEX, a shared agentic AI platform on Amazon Bedrock AgentCore so every team can ship production agents without rebuilding runtime, identity, observability, and guardrails from scratch. Learn why they chose AgentCore, how APEX Studio operates it, and where multi-agent systems go next.
