Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all tokens, thereby overlooking the intrinsic information heterogeneity along reasoning chains. We show that this coarse-grained credit assignment leads to premature entropy collapse and encourages the model to generate redundant, low-quality reasoning paths. Through systematic empirical analysis, we identify Critical Decision Pivots (CDPs): transient high-entropy states where the policy's trajectory is most sensitive to perturbations. These pivots represent the "forks in the road" where effective multi-path exploration is most crucial yet often suppressed by uniform advantage signals. Building on these insights, we propose Entropy-Regulated Policy Optimization (ERPO), which transitions the optimization focus from coarse sequences to fine-grained token dynamics. ERPO introduces three synergistic components: (i) Entropy-aware Gating, which adaptively amplifies exploration at CDPs to facilitate diverse path discovery; (ii) Bucket-based Implicit Normalization, which mitigates difficulty bias by aligning token progress windows; and (iii) Result-anchored Advantage Synthesis, which re-weights token-level signals via outcome-driven anchors. Extensive experiments on competitive mathematical benchmarks demonstrate that ERPO significantly outperforms GRPO. Notably, ERPO not only boosts reasoning accuracy but also yields significantly more concise and robust derivation paths, while achieving performance comparable to large models with orders of magnitude more parameters.

Reconstructing accurate 3D models of large-scale real-world scenes from unstructured, in-the-wild imagery remains a core challenge in computer vision, especially when the input views have little or no overlap. In such cases, existing reconstruction pipelines often produce multiple disconnected partial reconstructions or erroneously merge non-overlapping regions into overlapping geometry. In this work, we propose a framework that grounds each partial reconstruction to a complete reference model of the scene, enabling globally consistent alignment even in the absence of visual overlap. We obtain reference models from dense, geospatially accurate pseudo-synthetic renderings derived from Google Earth Studio. These renderings provide full scene coverage but differ substantially in appearance from real-world photographs. Our key insight is that, despite this significant domain gap, both domains share the same underlying scene semantics. We represent the reference model using 3D Gaussian Splatting, augmenting each Gaussian with semantic features, and formulate alignment as an inverse feature-based optimization scheme that estimates a global 6DoF pose and scale while keeping the reference model fixed. Furthermore, we introduce the WikiEarth dataset, which registers existing partial 3D reconstructions with pseudo-synthetic reference models. We demonstrate that our approach consistently improves global alignment when initialized with various classical and learning-based pipelines, while mitigating failure modes of state-of-the-art end-to-end models.

We propose Process-Aware Policy Optimization (PAPO), a method that integrates process-level evaluation into Group Relative Policy Optimization (GRPO) through decoupled advantage normalization, to address two limitations of existing reward designs. Outcome reward models (ORM) evaluate only final-answer correctness, treating all correct responses identically regardless of reasoning quality, and gradually lose the advantage signal as groups become uniformly correct. Process reward models (PRM) offer richer supervision, but directly using PRM scores causes reward hacking, where models exploit verbosity to inflate scores while accuracy collapses. PAPO resolves both by composing the advantage from an outcome component Aout, derived from ORM and normalized over all responses, and a process component Aproc, derived from a rubric-based PRM and normalized exclusively among correct responses. This decoupled design ensures that Aout anchors training on correctness while Aproc differentiates reasoning quality without distorting the outcome signal. Experiments across multiple model scales and six benchmarks demonstrate that PAPO consistently outperforms ORM, reaching 51.3% vs.\ 46.3% on OlympiadBench while continuing to improve as ORM plateaus and declines.

Vision Foundation Models (VFMs) have become the cornerstone of modern computer vision, offering robust representations across a wide array of tasks. While recent advances allow these models to handle varying input sizes during training, inference typically remains restricted to a single, fixed scale. This prevalent single-scale paradigm overlooks a fundamental property of visual perception: varying resolutions offer complementary inductive biases, where low-resolution views excel at global semantic recognition and high-resolution views are essential for fine-grained refinement. In this work, we propose Multi-Resolution Fusion (MuRF), a simple yet universally effective strategy to harness this synergy at inference time. Instead of relying on a single view, MuRF constructs a unified representation by processing an image at multiple resolutions through a frozen VFM and fusing the resulting features. The universality of MuRF is its most compelling attribute. It is not tied to a specific architecture, serving instead as a fundamental, training-free enhancement to visual representation. We empirically validate this by applying MuRF to a broad spectrum of critical computer vision tasks across multiple distinct VFM families - primarily DINOv2, but also demonstrating successful generalization to contrastive models like SigLIP2.

Document parsing is a fine-grained task where image resolution significantly impacts performance. While advanced research leveraging vision-language models benefits from high-resolution input to boost model performance, this often leads to a quadratic increase in the number of vision tokens and significantly raises computational costs. We attribute this inefficiency to substantial visual regions redundancy in document images, like background. To tackle this, we propose PaddleOCR-VL, a novel coarse-to-fine architecture that focuses on semantically relevant regions while suppressing redundant ones, thereby improving both efficiency and performance. Specifically, we introduce a lightweight Valid Region Focus Module (VRFM) which leverages localization and contextual relationship prediction capabilities to identify valid vision tokens. Subsequently, we design and train a compact yet powerful 0.9B vision-language model (PaddleOCR-VL-0.9B) to perform detailed recognition, guided by VRFM outputs to avoid direct processing of the entire large image. Extensive experiments demonstrate that PaddleOCR-VL achieves state-of-the-art performance in both page-level parsing and element-level recognition. It significantly outperforms existing solutions, exhibits strong competitiveness against top-tier VLMs, and delivers fast inference while utilizing substantially fewer vision tokens and parameters, highlighting the effectiveness of targeted coarse-to-fine parsing for accurate and efficient document understanding. The source code and models are publicly available at https://github.com/PaddlePaddle/PaddleOCR.

Unsupervised medical anomaly detection is severely limited by the scarcity of normal training samples. Existing methods typically train dedicated models for each dataset or disease, requiring hundreds of normal images per task and lacking cross-modality generalization. We propose Semantic Iterative Reconstruction (SIR), a framework that enables a single universal model to detect anomalies across diverse medical domains using extremely few normal samples. SIR leverages a pretrained teacher encoder to extract multi-scale deep features and employs a compact up-then-down decoder with multi-loop iterative refinement to enforce robust normality priors in deep feature space. The framework adopts a one-shot universal design: a single model is trained by mixing exactly one normal sample from each of nine heterogeneous datasets, enabling effective anomaly detection on all corresponding test sets without task-specific retraining. Extensive experiments on nine medical benchmarks demonstrate that SIR achieves state-of-the-art under all four settings -- one-shot universal, full-shot universal, one-shot specialized, and full-shot specialized -- consistently outperforming previous methods. SIR offers an efficient and scalable solution for multi-domain clinical anomaly detection.

Large language models are increasingly consulted for Islamic knowledge, yet no comprehensive benchmark evaluates their performance across core Islamic disciplines. We introduce IslamicMMLU, a benchmark of 10,013 multiple-choice questions spanning three tracks: Quran (2,013 questions), Hadith (4,000 questions), and Fiqh (jurisprudence, 4,000 questions). Each track is formed of multiple types of questions to examine LLMs capabilities handling different aspects of Islamic knowledge. The benchmark is used to create the IslamicMMLU public leaderboard for evaluating LLMs, and we initially evaluate 26 LLMs, where their averaged accuracy across the three tracks varied between 39.8% to 93.8% (by Gemini 3 Flash). The Quran track shows the widest span (99.3% to 32.4%), while the Fiqh track includes a novel madhab (Islamic school of jurisprudence) bias detection task revealing variable school-of-thought preferences across models. Arabic-specific models show mixed results, but they all underperform compared to frontier models. The evaluation code and leaderboard are made publicly available.

Event cameras provide robust visual signals under fast motion and challenging illumination conditions thanks to their microsecond latency and high dynamic range. However, their unique sensing characteristics and limited labeled data make it challenging to train event-based visual foundation models (VFMs), which are crucial for learning visual features transferable across tasks. To tackle this problem, we propose GEP (Generative Event Pretraining), a two-stage framework that transfers semantic knowledge learned from internet-scale image datasets to event data while learning event-specific temporal dynamics. First, an event encoder is aligned to a frozen VFM through a joint regression-contrastive objective, grounding event features in image semantics. Second, a transformer backbone is autoregressively pretrained on mixed event-image sequences to capture the temporal structure unique to events. Our approach outperforms state-of-the-art event pretraining methods on a diverse range of downstream tasks, including object recognition, segmentation, and depth estimation. Together, VFM-guided alignment and generative sequence modeling yield a semantically rich, temporally aware event model that generalizes robustly across domains.

Although Large Language Models (LLMs) have evolved from text generators into the cognitive core of modern AI systems, their inherent lack of authorization awareness exposes these systems to catastrophic risks, ranging from unintentional data leakage to unauthorized command execution. Existing defense mechanisms are fundamentally decoupled from internal reasoning, rendering them insufficient for the complex security demands of dynamic AI systems. Here, we propose the Chain-of-Authorization (CoA) framework, a paradigm that internalizes access control as a foundational cognitive capability. By systematically redesigning the input-output format and fine-tuning the model on synthesized data with complex permission topologies, CoA forces the model to generate a structured authorization trajectory as a causal prerequisite for any substantive response or action, thereby enabling LLMs to internalize access boundaries within dynamic reasoning environments. CoA maintains high utility in authorized scenarios while achieving high rejection rates of unauthorized prompts and robust defense against diverse adversarial attacks. By embedding authorization directly into the reasoning process, CoA provides a principled architectural blueprint for deploying secure LLMs as the cognitive cores of modern AI systems.

Gaussian Error Linear Unit (GELU) is a widely used smooth alternative to Rectifier Linear Unit (ReLU), yet many deployment, compression, and analysis toolchains are most naturally expressed for piecewise-linear (ReLU-type) networks. We study a hardness-parameterized formulation of GELU, f(x;λ)=xΦ(λ x), where Φ is the Gaussian CDF and λ \in [1, infty) controls gate sharpness, with the goal of turning smooth gated training into a controlled path toward ReLU-compatible models. Learning λ is non-trivial: naive updates yield unstable dynamics and effective gradient attenuation, so we introduce a constrained reparameterization and an optimizer-aware update scheme. Empirically, across a diverse set of model--dataset pairs spanning MLPs, CNNs, and Transformers, we observe structured layerwise hardness profiles and assess their robustness under different initializations. We further study a deterministic ReLU-ization strategy in which the learned gates are progressively hardened toward a principled target, enabling a post-training substitution of λ-GELU by ReLU with reduced disruption. Overall, λ-GELU provides a minimal and interpretable knob to profile and control gating hardness, bridging smooth training with ReLU-centric downstream pipelines.

Designing urban spaces that provide pedestrian wind comfort and safety requires time-resolved Computational Fluid Dynamics (CFD) simulations, but their current computational cost makes extensive design exploration impractical. We introduce WinDiNet (Wind Diffusion Network), a pretrained video diffusion model that is repurposed as a fast, differentiable surrogate for this task. Starting from LTX-Video, a 2B-parameter latent video transformer, we fine-tune on 10,000 2D incompressible CFD simulations over procedurally generated building layouts. A systematic study of training regimes, conditioning mechanisms, and VAE adaptation strategies, including a physics-informed decoder loss, identifies a configuration that outperforms purpose-built neural PDE solvers. The resulting model generates full 112-frame rollouts in under a second. As the surrogate is end-to-end differentiable, it doubles as a physics simulator for gradient-based inverse optimization: given an urban footprint layout, we optimize building positions directly through backpropagation to improve wind safety as well as pedestrian wind comfort. Experiments on single- and multi-inlet layouts show that the optimizer discovers effective layouts even under challenging multi-objective configurations, with all improvements confirmed by ground-truth CFD simulations.

Joint Vision-Language Embedding models such as CLIP typically fail at understanding negation in text queries, for example, failing to distinguish "no" in the query: "a plain blue shirt with no logos". Prior work has largely addressed this limitation through data-centric approaches, fine-tuning CLIP on large-scale synthetic negation datasets. However, these efforts are commonly evaluated using retrieval-based metrics that cannot reliably reflect whether negation is actually understood. In this paper, we identify two key limitations of such evaluation metrics and investigate an alternative evaluation framework based on Multimodal LLMs-as-a-judge, which typically excel at understanding simple yes/no questions about image content, providing a fair evaluation of negation understanding in CLIP models. We then ask whether there already exists a direction in the CLIP embedding space associated with negation. We find evidence that such a direction exists, and show that it can be manipulated through test-time intervention via representation engineering to steer CLIP toward negation-aware behavior without any fine-tuning. Finally, we test negation understanding on non-common image-text samples to evaluate generalization under distribution shifts. Code is at https://github.com/fawazsammani/negation-steering

Despite the rapid advancements in Artificial Intelligence (AI), Stochastic Differential Equations (SDEs) remain the gold-standard formalism for modeling systems under uncertainty. However, applying SDEs in practice is fraught with challenges: modeling risk is high, calibration is often brittle, and high-fidelity simulations are computationally expensive. This technical report introduces JointFM, a foundation model that inverts this paradigm. Instead of fitting SDEs to data, we sample an infinite stream of synthetic SDEs to train a generic model to predict future joint probability distributions directly. This approach establishes JointFM as the first foundation model for distributional predictions of coupled time series - requiring no task-specific calibration or finetuning. Despite operating in a purely zero-shot setting, JointFM reduces the energy loss by 21.1% relative to the strongest baseline when recovering oracle joint distributions generated by unseen synthetic SDEs.

Most existing text-to-speech (TTS) systems either synthesize speech sentence by sentence and stitch the results together, or drive synthesis from plain-text dialogues alone. Both approaches leave models with little understanding of global context or paralinguistic cues, making it hard to capture real-world phenomena such as multi-speaker interactions (interruptions, overlapping speech), evolving emotional arcs, and varied acoustic environments. We introduce the Borderless Long Speech Synthesis framework for agent-centric, borderless long audio synthesis. Rather than targeting a single narrow task, the system is designed as a unified capability set spanning VoiceDesigner, multi-speaker synthesis, Instruct TTS, and long-form text synthesis. On the data side, we propose a "Labeling over filtering/cleaning" strategy and design a top-down, multi-level annotation schema we call Global-Sentence-Token. On the model side, we adopt a backbone with a continuous tokenizer and add Chain-of-Thought (CoT) reasoning together with Dimension Dropout, both of which markedly improve instruction following under complex conditions. We further show that the system is Native Agentic by design: the hierarchical annotation doubles as a Structured Semantic Interface between the LLM Agent and the synthesis engine, creating a layered control protocol stack that spans from scene semantics down to phonetic detail. Text thereby becomes an information-complete, wide-band control channel, enabling a front-end LLM to convert inputs of any modality into structured generation commands, extending the paradigm from Text2Speech to borderless long speech synthesis.

Medical vision--language models (MVLMs) are increasingly used as perceptual backbones in radiology pipelines and as the visual front end of multimodal assistants, yet their reliability under real clinical workflows remains underexplored. Prior robustness evaluations often assume clean, curated inputs or study isolated corruptions, overlooking routine acquisition, reconstruction, display, and delivery operations that preserve clinical readability while shifting image statistics. To address this gap, we propose CoDA, a chain-of-distribution framework that constructs clinically plausible pipeline shifts by composing acquisition-like shading, reconstruction and display remapping, and delivery and export degradations. Under masked structural-similarity constraints, CoDA jointly optimizes stage compositions and parameters to induce failures while preserving visual plausibility. Across brain MRI, chest X-ray, and abdominal CT, CoDA substantially degrades the zero-shot performance of CLIP-style MVLMs, with chained compositions consistently more damaging than any single stage. We also evaluate multimodal large language models (MLLMs) as technical-authenticity auditors of imaging realism and quality rather than pathology. Proprietary multimodal models show degraded auditing reliability and persistent high-confidence errors on CoDA-shifted samples, while the medical-specific MLLMs we test exhibit clear deficiencies in medical image quality auditing. Finally, we introduce a post-hoc repair strategy based on teacher-guided token-space adaptation with patch-level alignment, which improves accuracy on archived CoDA outputs. Overall, our findings characterize a clinically grounded threat surface for MVLM deployment and show that lightweight alignment improves robustness in deployment.

Autonomous driving technologies have achieved significant advances in recent years, yet their real-world deployment remains constrained by data scarcity, safety requirements, and the need for generalization across diverse environments. In response, synthetic data and virtual environments have emerged as powerful enablers, offering scalable, controllable, and richly annotated scenarios for training and evaluation. This survey presents a comprehensive review of recent developments at the intersection of autonomous driving, simulation technologies, and synthetic datasets. We organize the landscape across three core dimensions: (i) the use of synthetic data for perception and planning, (ii) digital twin-based simulation for system validation, and (iii) domain adaptation strategies bridging synthetic and real-world data. We also highlight the role of vision-language models and simulation realism in enhancing scene understanding and generalization. A detailed taxonomy of datasets, tools, and simulation platforms is provided, alongside an analysis of trends in benchmark design. Finally, we discuss critical challenges and open research directions, including Sim2Real transfer, scalable safety validation, cooperative autonomy, and simulation-driven policy learning, that must be addressed to accelerate the path toward safe, generalizable, and globally deployable autonomous driving systems.

Retrieval-Augmented Generation (RAG) improves factual grounding by incorporating external knowledge into language model generation. However, when retrieved context is noisy, unreliable, or inconsistent with the model's parametric knowledge, it introduces retrieval-prior conflicts that can degrade generation quality. While this problem has been studied in autoregressive language models, it remains largely unexplored in diffusion-based language models, where the iterative denoising process introduces unique challenges for integrating retrieved context. In this work, we propose Adaptive Retrieval-Augmented Masked Diffusion (ARAM), a training-free adaptive guidance framework for Masked Diffusion Models (MDMs) in RAG settings. ARAM dynamically calibrates the guidance scale during denoising according to the Signal-to-Noise Ratio (SNR) of the distributional shift induced by retrieved context. Intuitively, the model strengthens guidance when the retrieved context provides reliable corrective evidence and suppresses it when the contextual signal is noisy or non-supportive. Extensive experiments on multiple knowledge-intensive QA benchmarks show that ARAM improves overall QA performance over competitive RAG baselines.

Falls in wet bathroom environments are a major safety risk for seniors living alone. Recent work has shown that mmWave-only, vibration-only, and existing multimodal schemes, such as vibration-triggered radar activation, early feature concatenation, and decision-level score fusion, can support privacy-preserving, non-intrusive fall detection. However, these designs still treat motion and impact as loosely coupled streams, depending on coarse temporal alignment and amplitude thresholds, and do not explicitly encode the causal link between radar-observed collapse and floor impact or address timing drift, object drop confounders, and latency and energy constraints on low-power edge devices. To this end, we propose a two-stream architecture that encodes radar signals with a Motion--Mamba branch for long-range motion patterns and processes floor vibration with an Impact--Griffin branch that emphasizes impact transients and cross-axis coupling. Cross-conditioned fusion uses low-rank bilinear interaction and a Switch--MoE head to align motion and impact tokens and suppress object-drop confounders. The model keeps inference cost suitable for real-time execution on a Raspberry Pi 4B gateway. We construct a bathroom fall detection benchmark dataset with frame-level annotations, comprising more than 3~h of synchronized mmWave radar and triaxial vibration recordings across eight scenarios under running water, together with subject-independent training, validation, and test splits. On the test split, our model attains 96.1% accuracy, 94.8% precision, 88.0% recall, a 91.1% macro F1 score, and an AUC of 0.968. Compared with the strongest baseline, it improves accuracy by 2.0 percentage points and fall recall by 1.3 percentage points, while reducing latency from 35.9 ms to 15.8 ms and lowering energy per 2.56 s window from 14200 mJ to 10750 mJ on the Raspberry Pi 4B gateway.

Video dubbing requires content accuracy, expressive prosody, high-quality acoustics, and precise lip synchronization, yet existing approaches struggle on all four fronts. To address these issues, we propose DiFlowDubber, the first video dubbing framework built upon a discrete flow matching backbone with a novel two-stage training strategy. In the first stage, a zero-shot text-to-speech (TTS) system is pre-trained on large-scale corpora, where a deterministic architecture captures linguistic structures, and the Discrete Flow-based Prosody-Acoustic (DFPA) module models expressive prosody and realistic acoustic characteristics. In the second stage, we propose the Content-Consistent Temporal Adaptation (CCTA) to transfer TTS knowledge to the dubbing domain: its Synchronizer enforces cross-modal alignment for lip-synchronized speech. Complementarily, the Face-to-Prosody Mapper (FaPro) conditions prosody on facial expressions, whose outputs are then fused with those of the Synchronizer to construct rich, fine-grained multimodal embeddings that capture prosody-content correlations, guiding the DFPA to generate expressive prosody and acoustic tokens for content-consistent speech. Experiments on two benchmark datasets demonstrate that DiFlowDubber outperforms prior methods across multiple evaluation metrics.

This paper studies unsupervised cross-domain image retrieval (UCDIR), which aims to retrieve images of the same category across different domains without relying on labeled data. Existing methods typically utilize pseudo-labels, derived from clustering algorithms, as supervisory signals for intra-domain representation learning and cross-domain feature alignment. However, these discrete pseudo-labels often fail to provide accurate and comprehensive semantic guidance. Moreover, the alignment process frequently overlooks the entanglement between domain-specific and semantic information, leading to semantic degradation in the learned representations and ultimately impairing retrieval performance. This paper addresses the limitations by proposing a Text-Phase Synergy Network with Dual Priors(TPSNet). Specifically, we first employ CLIP to generate a set of class-specific prompts per domain, termed as domain prompt, serving as a text prior that offers more precise semantic supervision. In parallel, we further introduce a phase prior, represented by domain-invariant phase features, which is integrated into the original image representations to bridge the domain distribution gaps while preserving semantic integrity. Leveraging the synergy of these dual priors, TPSNet significantly outperforms state-of-the-art methods on UCDIR benchmarks.

Locomotion on granular slopes such as sand dunes remains a fundamental challenge for legged robots due to reduced shear strength and gravity-induced anisotropic yielding of granular media. Using a hexapedal robot on a tiltable granular bed, we systematically measure locomotion speed together with slope-dependent normal and shear granular resistive forces. While normal penetration resistance remains nearly unchanged with inclination, shear resistance decreases substantially as slope angle increases. Guided by these measurements, we develop a simple robot-terrain interaction model that predicts anchoring timing, step length, and resulting robot speed, as functions of terrain strength and slope angle. The model reveals that slope-induced performance loss is primarily governed by delayed anchoring and increased backward slip rather than excessive sinkage. By extending the model to generalized terrain conditions, we construct failure phase diagrams that identify sinkage- and slippage-induced failure regimes, enabling quantitative risk estimation for locomotion on granular slopes. This physics-informed framework provides predictive insight into terrain-dependent failure mechanisms and offers guidance for safer and more robust robot operation on deformable inclines.

Zero-shot depth completion has gained attention for its ability to generalize across environments without sensor-specific datasets or retraining. However, most existing approaches rely on diffusion-based test-time optimization, which is computationally expensive due to iterative denoising. Recent visual-prompt-based methods reduce training cost but still require repeated forward--backward passes through the full frozen network to optimize input-level prompts, resulting in slow inference. In this work, we show that adapting only the decoder is sufficient for effective test-time optimization, as depth foundation models concentrate depth-relevant information within a low-dimensional decoder subspace. Based on this insight, we propose a lightweight test-time adaptation method that updates only this low-dimensional subspace using sparse depth supervision. Our approach achieves state-of-the-art performance, establishing a new Pareto frontier between accuracy and efficiency for test-time adaptation. Extensive experiments on five indoor and outdoor datasets demonstrate consistent improvements over prior methods, highlighting the practicality of fast zero-shot depth completion.

The success of large language models (LLMs) in scientific domains has heightened safety concerns, prompting numerous benchmarks to evaluate their scientific safety. Existing benchmarks often suffer from limited risk coverage and a reliance on subjective evaluation. To address these problems, we introduce SafeSci, a comprehensive framework for safety evaluation and enhancement in scientific contexts. SafeSci comprises SafeSciBench, a multi-disciplinary benchmark with 0.25M samples, and SafeSciTrain, a large-scale dataset containing 1.5M samples for safety enhancement. SafeSciBench distinguishes between safety knowledge and risk to cover extensive scopes and employs objective metrics such as deterministically answerable questions to mitigate evaluation bias. We evaluate 24 advanced LLMs, revealing critical vulnerabilities in current models. We also observe that LLMs exhibit varying degrees of excessive refusal behaviors on safety-related issues. For safety enhancement, we demonstrate that fine-tuning on SafeSciTrain significantly enhances the safety alignment of models. Finally, we argue that knowledge is a double-edged sword, and determining the safety of a scientific question should depend on specific context, rather than universally categorizing it as safe or unsafe. Our work provides both a diagnostic tool and a practical resource for building safer scientific AI systems.

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work introduces a physics-informed training framework that addresses these limitations by decomposing PDEs using operator splitting methods, training separate neural operators to learn individual non-linear physical operators while approximating linear operators with fixed finite-difference convolutions. This modular mixture-of-experts architecture enables generalisation to novel physical regimes by explicitly encoding the underlying operator structure. We formulate the modelling task as a neural ordinary differential equation (ODE) where these learned operators constitute the right-hand side, enabling continuous-in-time predictions through standard ODE solvers and implicitly enforcing PDE constraints. Demonstrated on incompressible and compressible Navier--Stokes equations, our approach achieves better convergence and superior performance when generalising to unseen physics. The method remains parameter-efficient, enabling temporal extrapolation beyond training horizons, and provides interpretable components whose behaviour can be verified against known physics.

Low-Rank Adaptation (LoRA) dominates parameter-efficient fine-tuning (PEFT). However, it faces a ``linear ceiling'': increasing the rank yields diminishing returns in expressive capacity due to intrinsic linear constraints. We introduce CeRA (Capacity-enhanced Rank Adaptation), a weight-level parallel adapter that injects SiLU gating and dropout to induce non-linear capacity expansion. We demonstrate a fundamental relationship between adapter expressivity and task complexity. In basic arithmetic (GSM8K), CeRA matches standard linear baselines, but on the complex MATH dataset, it demonstrates high parameter efficiency in downstream reasoning (Exact Match). CeRA at rank 64 (pass@1 16.36\%) outperforms both a high-rank LoRA at rank 512 (15.72\%) and the state-of-the-art linear variant, DoRA, at rank 64 (14.44\%), achieving higher exact-match accuracy with only 1/8 of the parameter budget. Empirical spectral analysis shows that CeRA activates the lower-variance tail of the singular value spectrum, preventing the rank collapse observed in linear methods and providing the representation capacity required for complex logical reasoning.

Grokking -- the abrupt transition from memorization to generalization long after near-zero training loss -- has been studied mainly in single-task settings. We extend geometric analysis to multi-task modular arithmetic, training shared-trunk Transformers on dual-task (mod-add + mod-mul) and tri-task (mod-add + mod-mul + mod-sq) objectives across a systematic weight decay sweep. Five consistent phenomena emerge. (1) Staggered grokking order: multiplication generalizes first, followed by squaring, then addition, with consistent delays across seeds. (2) Universal integrability: optimization trajectories remain confined to an empirically invariant low-dimensional execution manifold; commutator defects orthogonal to this manifold reliably precede generalization. (3) Weight decay phase structure: grokking timescale, curvature depth, reconstruction threshold, and defect lead covary systematically with weight decay, revealing distinct dynamical regimes and a sharp no-decay failure mode. (4) Holographic incompressibility: final solutions occupy only 4--8 principal trajectory directions yet are distributed across full-rank weights and destroyed by minimal perturbations; SVD truncation, magnitude pruning, and uniform scaling all fail to preserve performance. (5) Transverse fragility and redundancy: removing less than 10% of orthogonal gradient components eliminates grokking, yet dual-task models exhibit partial recovery under extreme deletion, suggesting redundant center manifolds enabled by overparameterization. Together, these results support a dynamical picture in which multi-task grokking constructs a compact superposition subspace in parameter space, with weight decay acting as compression pressure and excess parameters supplying geometric redundancy in optimization pathways.

Grokking -- the abrupt transition from memorization to generalization after prolonged training -- has been linked to confinement on low-dimensional execution manifolds in modular arithmetic. Whether this mechanism extends beyond arithmetic remains open. We study two sequence-learning benchmarks: SCAN compositional generalization and Dyck-1 depth prediction. Across both tasks and a wide range of learning rates, the commutator defect -- a curvature measure derived from non-commuting gradient updates -- rises well before generalization, with lead times following a superlinear power law (alpha approximately 1.18 for SCAN, approximately 1.13 for Dyck), consistent with prior results on modular arithmetic. Weight-space PCA reveals that spectral concentration is not a universal precursor; the commutator defect is. Causal interventions demonstrate a mechanistic role: amplifying non-commutativity accelerates grokking (roughly 32% on SCAN, roughly 50% on Dyck), while suppressing orthogonal gradient flow delays or prevents it. The three task families form a spectrum of causal sensitivity -- modular arithmetic is rigid, Dyck is responsive, SCAN is intermediate -- yet suppression delays or prevents grokking in all cases, establishing necessity as a universal finding. These results identify the commutator defect as a robust, architecture-agnostic, causally implicated early-warning signal for delayed generalization in transformers.

Grokking -- the delayed transition from memorization to generalization in small algorithmic tasks -- remains poorly understood. We present a geometric analysis of optimization dynamics in transformers trained on modular arithmetic. PCA of attention weight trajectories reveals that training evolves predominantly within a low-dimensional execution subspace, with a single principal component capturing 68-83% of trajectory variance. To probe loss-landscape geometry, we measure commutator defects -- the non-commutativity of successive gradient steps -- and project them onto this learned subspace. We find that curvature grows sharply in directions orthogonal to the execution subspace while the trajectory remains largely confined to it. Importantly, curvature growth consistently precedes generalization across learning rates and hyperparameter regimes, with the lead time obeying a power law in the grokking timescale. Causal intervention experiments show that motion along the learned subspace is necessary for grokking, while artificially increasing curvature is insufficient. Together, these results support a geometric account in which grokking reflects escape from a metastable regime characterized by low-dimensional confinement and transverse curvature accumulation. All findings replicate across this learning-rate range, a qualitatively different slow regime (lr=5e-5, wd=0.1, 3 layers), and three random seeds, though alignment dynamics differ quantitatively between regimes. Causal intervention experiments establish that orthogonal gradient flow is necessary but not sufficient for grokking: suppressing it prevents generalization with a monotonic dose-response across four operations, while artificially boosting curvature defects has no effect.

We introduce GoogleFontsBench, the first public benchmark for classifying open-source web fonts, addressing a gap left by existing benchmarks that cover only commercial typefaces. GoogleFontsBench comprises 394 font variants across 32 Google Fonts families, a reproducible synthetic data generation pipeline (~575 images per variant, ~226K total), and a typographically-grounded evaluation metric (SWER) that weights errors by visual severity. We establish baselines using six fine-tuning strategies on a DINOv2 Vision Transformer backbone. Parameter-efficient adaptation with LoRA achieves 99.0% top-1 accuracy while training only 1% of the model's 87.2M parameters, with errors 140x less severe than random guessing. We release the benchmark, all trained models, and the full training pipeline as open-source resources.

Audio-driven 3D talking avatar generation is increasingly important in virtual communication, digital humans, and interactive media, where avatars must preserve identity, synchronize lip motion with speech, express emotion, and exhibit lifelike spatial dynamics, collectively defining a broader objective of expressivity. However, achieving this remains challenging due to insufficient training data with limited subject identities, narrow audio representations, and restricted explicit controllability. In this paper, we propose 3DXTalker, an expressive 3D talking avatar through data-curated identity modeling, audio-rich representations, and spatial dynamics controllability. 3DXTalker enables scalable identity modeling via 2D-to-3D data curation pipeline and disentangled representations, alleviating data scarcity and improving identity generalization. Then, we introduce frame-wise amplitude and emotional cues beyond standard speech embeddings, ensuring superior lip synchronization and nuanced expression modulation. These cues are unified by a flow-matching-based transformer for coherent facial dynamics. Moreover, 3DXTalker also enables natural head-pose motion generation while supporting stylized control via prompt-based conditioning. Extensive experiments show that 3DXTalker integrates lip synchronization, emotional expression, and head-pose dynamics within a unified framework, achieves superior performance in 3D talking avatar generation.