Neural oscillators, originating from the second-order ordinary differential equations (ODEs), have demonstrated competitive performance in stably learning causal mappings between long-term sequences or continuous temporal functions. However, theoretically quantifying the capacities of their neural network architectures remains a significant challenge. In this study, the neural oscillator consisting of a second-order ODE followed by a multilayer perceptron (MLP) is considered. Its upper approximation bound for approximating causal and uniformly continuous operators between continuous temporal function spaces and that for approximating uniformly asymptotically incrementally stable second-order dynamical systems are derived. The established proof method of the approximation bound for approximating the causal continuous operators can also be directly applied to state-space models consisting of a linear time-continuous complex recurrent neural network followed by an MLP. Theoretical results reveal that the approximation error of the neural oscillator for approximating the second-order dynamical systems scales polynomially with the reciprocals of the widths of two utilized MLPs, thus mitigating the curse of parametric complexity. The decay rates of two established approximation error bounds are validated through two numerical cases. These results provide a robust theoretical foundation for the effective application of the neural oscillator in science and engineering.

Agentic large language models are proposed as autonomous code generators for scientific computing, yet their reliability in high-stakes problems remains unclear. Developing computational scientific software from natural-language queries remains challenging broadly due to (a) sparse representation of domain codes during training and (b) the limited feasibility of RLHF with a small expert community. To address these limitations, this work conceptualizes an inverse approach to code design, embodied in the Chain of Unit-Physics framework: a first-principles (or primitives)-centric, multi-agent system in which human expert knowledge is encoded as unit-physics tests that explicitly constrain code generation. The framework is evaluated on a nontrivial combustion task, used here as a representative benchmark for scientific problem with realistic physical constraints. Closed-weight systems and code-focused agentic variants fail to produce correct end-to-end solvers, despite tool and web access, exhibiting four recurrent error classes: interface (syntax/API) hallucinations, overconfident assumptions, numerical/physical incoherence, and configuration fragility. Open-weight models with chain-of-thought (CoT) decoding reduce interface errors but still yield incorrect solutions. On the benchmark task, the proposed framework converges within 5-6 iterations, matches the human-expert implementation (mean error of $3.1\times10^{-3}$ %), with a $\sim$33.4 % faster runtime and a $\sim$30 % efficient memory usage at a cost comparable to mid-sized commercial APIs, yielding a practical template for physics-grounded scientific code generation. As datasets and models evolve, zero-shot code accuracy will improve; however, the Chain of Unit-Physics framework goes further by embedding first-principles analysis that is foundational to scientific codes.

Abstract-- This paper addresses the Object Goal Navigation problem, where a robot must efficiently find a target object in an unknown environment. Existing implicit memory-based methods struggle with long-term memory retention and planning, while explicit map-based approaches lack rich semantic information. T o address these challenges, we propose FOM-Nav, a modular framework that enhances exploration efficiency through Frontier-Object Maps and vision-language models. Our Frontier-Object Maps are built online and jointly encode spatial frontiers and fine-grained object information. Using this representation, a vision-language model performs multimodal scene understanding and high-level goal prediction, which is executed by a low-level planner for efficient trajectory generation. T o train FOM-Nav, we automatically construct large-scale navigation datasets from real-world scanned environments. Extensive experiments validate the effectiveness of our model design and constructed dataset. FOM-Nav achieves state-of-the-art performance on the MP3D and HM3D benchmarks, particularly in navigation efficiency metric SPL, and yields promising results on a real robot. Autonomous navigation has been a long-standing challenge in robotics [1], dating back to the pioneering work on the robot Shakey [2] in the 1960s. While early work focused on navigating to specific points [3], [4] with a preconstructed map [5], [6], recent research has progressively shifted towards navigation in unknown environments using textual [7], [8] or visual [9] goals, which is an essential capability for enabling mobile manipulation systems [10], [11] to perform diverse real-world tasks. In this work, we focus on the object goal navigation task (ObjectNav) [8], where an agent must navigate to a target object category in an unknown environment using RGB-D observations. This task requires long-horizon multimodal scene understanding and efficient exploration. The robot should not only recognize objects within its current field of view but also use previous observations to develop more accurate scene understanding.

Medical imaging is essential for clinical diagnosis, yet real-world data frequently suffers from corruption, noise, and potential tampering, challenging the reliability of AI-assisted interpretation. Conventional reconstruction techniques prioritize pixel-level recovery and may produce visually plausible outputs while compromising anatomical fidelity, an issue that can directly impact clinical outcomes. We propose a semantic-aware medical image reconstruction framework that integrates high-level latent embeddings with a hybrid U-Net architecture to preserve clinically relevant structures during restoration. To ensure trust and accountability, we incorporate a lightweight blockchain-based provenance layer using scale-free graph design, enabling verifiable recording of each reconstruction event without imposing significant overhead. Extensive evaluation across multiple datasets and corruption types demonstrates improved structural consistency, restoration accuracy, and provenance integrity compared with existing approaches. By uniting semantic-guided reconstruction with secure traceability, our solution advances dependable AI for medical imaging, enhancing both diagnostic confidence and regulatory compliance in healthcare environments.

We introduce IndiMathBench, a human-verified benchmark designed to evaluate mathematical theorem proving, curated using an AI-powered human-assisted pipeline for formalizing natural language problems in Lean. IndiMathBench is composed of 312 formal Lean 4 theorems paired with their corresponding informal problem statements, sourced from Indian Mathematics Olympiads. Through category-based retrieval, iterative compiler feedback, and multi-model ensembles, our pipeline generates candidate formalizations that experts efficiently validate via an interactive dashboard with automated quality summaries. Evaluation across multiple frontier models demonstrates that autoformalization remains challenging, with substantial gaps between syntactic validity and semantic correctness, while theorem proving success rates remain low even with iterative refinement, demonstrating that \benchmark~presents a challenging testbed for mathematical reasoning. IndiMathBench is available at https://github.com/prmbiy/IndiMathBench.

Most evaluations of large language models focus on standard tasks such as factual question answering or short summarization. This research expands that scope in two directions: first, by comparing two retrieval strategies, Graph RAG, structured knowledge-graph based, and Advanced RAG, hybrid keyword-semantic search, for QA; and second, by evaluating whether LLMs can generate high quality non-traditional academic outputs, specifically slide decks and podcast scripts. We implemented a prototype combining Meta's LLaMA 3 70B open weight and OpenAI's GPT 4o mini API based. QA performance was evaluated using both human ratings across eleven quality dimensions and large language model judges for scalable cross validation. GPT 4o mini with Advanced RAG produced the most accurate responses. Graph RAG offered limited improvements and led to more hallucinations, partly due to its structural complexity and manual setup. Slide and podcast generation was tested with document grounded retrieval. GPT 4o mini again performed best, though LLaMA 3 showed promise in narrative coherence. Human reviewers were crucial for detecting layout and stylistic flaws, highlighting the need for combined human LLM evaluation in assessing emerging academic outputs.

The transition to prescriptive maintenance in manufacturing is critically constrained by a dependence on predictive models. These models tend to rely on spurious correlations rather than identifying the true causal drivers of failures, often leading to costly misdiagnoses and ineffective interventions. This fundamental limitation results in a key-challenge: while we can predict that a failure may occur, we lack a systematic method to understand why a failure occurs, thereby providing the basis for identifying the most effective intervention. This paper proposes a model based on causal machine learning to bridge this gap. Our objective is to move beyond diagnosis to active prescription by simulating and evaluating potential fixes toward optimizing KPIs such as Overall Equipment Effectiveness (OEE). For this purpose a pre-trained causal foundation model is used as a "what-if" model to estimate the effects of potential fixes. By measuring the causal effect of each intervention on system-level KPIs, it provides a data-driven ranking of actions to recommend at the production line. This process not only identifies root causes but also quantifies their operational impact. The model is evaluated using semi-synthetic manufacturing data and compared with a baseline machine learning model. This paper sets the technical basis for a robust prescriptive maintenance framework, allowing engineers to test potential solutions in a causal environment to make more effective operational decisions and reduce costly downtimes.

Organisms constantly pivot between tasks such as evading predators, foraging, traversing rugged terrain, and socializing, often within milliseconds. Remarkably, they preserve knowledge of once-learned environments sans catastrophic forgetting, a phenomenon neuroscientists hypothesize, is due to a singular neural circuitry dynamically overlayed by neuromodulatory agents such as dopamine and acetylcholine. In parallel, deep learning research addresses analogous challenges via domain generalization (DG) and continual learning (CL), yet these methods remain siloed, despite the brains ability to perform them seamlessly. In particular, prior work has not explored architectures involving associative memories (AMs), which are an integral part of biological systems, to jointly address these tasks. We propose Memory-Integrated Reconfigurable Adapters (MIRA), a unified framework that integrates Hopfield-style associative memory modules atop a shared backbone. Associative memory keys are learned post-hoc to index and retrieve an affine combination of stored adapter updates for any given task or domain on a per-sample basis. By varying only the task-specific objectives, we demonstrate that MIRA seamlessly accommodates domain shifts and sequential task exposures under one roof. Empirical evaluations on standard benchmarks confirm that our AM-augmented architecture significantly enhances adaptability and retention: in DG, MIRA achieves SoTA out-of-distribution accuracy, and in incremental learning settings, it outperforms architectures explicitly designed to handle catastrophic forgetting using generic CL algorithms. By unifying adapter-based modulation with biologically inspired associative memory, MIRA delivers rapid task switching and enduring knowledge retention in a single extensible architecture, charting a path toward more versatile and memory-augmented AI systems.

Transformer models have significantly advanced Natural Language Processing (NLP), demonstrating strong performance in English. However, their effectiveness in Arabic, particularly for Named Entity Recognition (NER), remains limited, even with larger pre-trained models. This performance gap stems from multiple factors, including tokenisation, dataset quality, and annotation inconsistencies. Existing studies often analyze these issues in isolation, failing to capture their joint effect on system behaviour and performance. We introduce DeformAr (Debugging and Evaluation Framework for Transformer-based NER Systems), a novel framework designed to investigate and explain the performance discrepancy between Arabic and English NER systems. DeformAr integrates a data extraction library and an interactive dashboard, supporting two modes of evaluation: cross-component analysis and behavioural analysis. The framework divides each language into dataset and model components to examine their interactions. The analysis proceeds in two stages. First, cross-component analysis provides systematic diagnostic measures across data and model subcomponents, addressing the "what," "how," and "why" behind observed discrepancies. The second stage applies behavioural analysis by combining interpretability techniques with token-level metrics, interactive visualisations, and representation space analysis. These stages enable a component-aware diagnostic process that detects model behaviours and explains them by linking them to underlying representational patterns and data factors. DeformAr is the first Arabic-specific, component-based interpretability tool, offering a crucial resource for advancing model analysis in under-resourced languages.

Large Language Models (LLMs) have shown remarkable abilities in a wide variety of reasoning and factual knowledge tasks (Achiam et al., 2023; Bubeck et al., 2023; Katz et al., 2024), but their large size makes inference expensive. With the advent of agentic systems that interact with the external world, LLMs are poised to become even more ubiquitous in science, technology, and society, but the tremendous inference cost presents a challenge for realizing the full potential of these agents. One way to quell the computational expense associated with LLM inference is to use small language models (SLMs). With orders of magnitude fewer parameters, SLMs are faster, cheaper, and easier to finetune for specialised skills like tool use, making them natural specialists using proprietary data or within agentic systems (Belcak et al., 2025). Training language models typically involves three stages: pre-training on large general-purpose corpora, supervised finetuning (SFT), and reinforcement learning from human feedback (RLHF) or from verifiable rewards (RLVR) (Ouyang et al., 2022).