Computer Science (arXiv)

Learning real-world dynamics from visual observations is crucial for various domains. A common strategy is to calibrate simulators by estimating physical parameters, yet accuracy is ultimately bounded by the underlying physical models, which often assume materials are homogeneous and isotropic. Even if reasonable, real-world objects typically exhibit mild anisotropy and heterogeneity. After the near-isotropic backbone is well calibrated, these residual effects become the key bottleneck for further closing the real-to-sim gap. Although neural networks can fit dynamics end-to-end, such black-box modeling discards strong physical priors, leading to poor data efficiency and overfitting. Therefore, we propose MoSA, a motion-constrained stress adaptation framework that targets these residual effects to further improve real-to-sim dynamics learning. MoSA uses an isotropic model as a physics prior and learns residual stress operators to capture mild anisotropy and heterogeneity. It progressively adapts stresses via microplane-constrained redistribution in a physics-informed cascaded network. We further impose motion constraints by supervising temporal and spatial derivatives of the deformation field. Experimentally, our learned dynamics achieves superior accuracy, generalization, and robustness, while learning physically meaningful residual anisotropy. Finally, we validate MoSA in a robot manipulation setting, showing that better real-to-sim dynamics modeling translates into more reliable sim-to-real transfer. Project Page is available at https://mercerai.github.io/MoSA/.

Robotic tasks are typically specified by a tuple of factors, such as the object to be grasped, the obstacles to be avoided, the color of the target, and so on. Collecting expert demonstrations for every combination of factor values grows combinatorially. We present factored diffusion policies: a single shared diffusion network trained with per-factor null-token dropout, whose score decomposes additively across factors at inference. Under approximate conditional independence between factors given the action-observation pair, this composition approximates the true joint score with a bounded uniform error, reducing the training-task budget from a product of factor cardinalities to a sum. A trajectory-tube certificate chains this score-level bound through the reverse-time sampling ODE and a contracting tracking controller into a closed-loop state-trajectory tube whose radius factors into an ODE-sensitivity constant and a per-factor score-error budget. Unlike compositional-diffusion methods for control that combine separately trained networks, we use one shared network. Drone racing experiments confirm both the generalization bound and the certificate. On state-based multi-gate racing, the factored policy passes 90% of held-out gates -- matching an oracle -- while a K-network composition baseline collapses to 3%; on vision-based single-gate traversal, it transfers zero-shot to an unseen venue with +11.7pp success-rate gain and 2.4X crash-rate reduction.

While deep ensembles are widely considered to be the default method for uncertainty quantification in deep learning, their effectiveness for graph-structured data is often simply assumed based on successes in domains like computer vision. We investigate standard deep ensembles specifically for message-passing graph neural networks. Benchmarking across seven datasets representing varied tasks and complexities, we reveal that ensembles provide surprisingly little improvement over a single model. Instead, the observed marginal gains stem primarily from stabilizing optimization noise in point predictions rather than yielding meaningfully better uncertainty estimates. Through an aleatoric-epistemic decomposition, we identify epistemic collapse: independently trained networks consistently converge to overly similar predictions. Because disagreement is the fundamental mechanism through which ensembles capture epistemic uncertainty, this lack of diversity neutralizes their key advantage. Analyzing this phenomenon further, we suggest this collapse is driven by functional rather than weight-space convexity, where distinct parameter solutions induce almost identical behavior. Our results suggest that deep ensemble success does not seamlessly transfer to graph machine learning.

Frozen Vision Foundation Models (VFMs) with lightweight classification heads are increasingly used in medical imaging because they offer efficient and reproducible deployment. Yet noisy-label learning methods for this frozen-feature regime remain poorly understood, and most existing methods still rely on a small-loss assumption inherited from end-to-end training. We present a controlled benchmark of eight noisy-label methods across five medical datasets, three backbones, two noise types, and five noise rates (150 conditions, 6,000 training runs), evaluated with balanced accuracy. The benchmark shows that there is no universal winner: Friedman ranking over the 150 conditions yields $χ^2 = 333.2$ ($p = 4.77 \times 10^{-68}$), ELR wins the most conditions (49/150), while CUFIT attains the best mean rank (2.51). The practical cost of method choice grows sharply with noise severity, from 4.5pp on clean data to 18.8pp at asymmetric 40\% noise. To explain these benchmark-level patterns, we revisit the small-loss assumption in a representative high-risk regime. Under frozen DINOv2 features, clean and noisy loss distributions overlap by 53--61\%, and matched-rate clean-sample detection shows that prediction agreement is markedly more stable than loss ranking under asymmetric noise (3pp vs.\ 13pp precision drop). On ISIC2019 with asymmetric 40\% noise, Co-Teaching reaches 68\% overall accuracy while collapsing to 35.1\% balanced accuracy with zero recall on three minority classes. Together, these results recast noisy-label learning for frozen VFMs as a regime-aware method-selection problem rather than a search for a single dominant algorithm. We conclude with evidence-based guidance and a low-regret feature-space selector for practical recommendation.

Information Technology (IT) security professionals have ready access to open-source platforms such as Kali Linux. But no such platform exists for Operational Technology (OT) that underpins Industrial Control Systems. We discuss experiences of architecting, building and releasing LINICS, an open-source platform for OT pentesting and security analysis.

Federated Unlearning (FU) is emerging as a powerful tool that enables the selective removal of client data to effectively address data contamination and meet strict privacy regulations in mobile edge computing (MEC) systems. Although FU has recently drawn attention in the AI community, existing approaches suffer from low unlearning precision and lack temporal information reflection, which results in suboptimal forgetting performance. To address these issues, we propose SCALE, a dual-level unlearning framework combining historical contribution analysis with information freshness-aware adaptive sparsification. Our framework first employs a historical contribution-based layer sensitivity analysis to identify layers most influenced by target clients, then performs fine-grained unlearning through adaptive sparsification at the weight sub-group level to balance information freshness with forgetting effectiveness. Through theoretical analysis, the proposed framework demonstrates the convergence properties and acceleration advantages. Our experiments and testbed results demonstrate superior unlearning effectiveness compared to state-of-the-art baselines, with significantly improved forgetting performance.

This tutorial develops diffusion models from the viewpoint of differential equations. We begin with the conditional Gaussian forward process and show that this path admits both an ordinary differential equation (ODE) representation and a stochastic differential equation (SDE) representation. Averaging the conditional process over the data distribution then yields marginalized forward ODE and SDE formulations that transport the data distribution $p_0=p_{\mathrm{data}}$ to a Gaussian prior $p_1=\mathcal{N}(0,I)$. We next derive the corresponding reverse-time dynamics, namely the reverse SDE and the reverse probability-flow ODE, both of which are governed by the marginal score $\grad\log p_t(x)$. This leads to a training objective for score estimation and shows that the standard noise-prediction objective is equivalent to score matching up to an additive constant independent of the model parameters. We then discuss sampling methods for the learned reverse dynamics, including DPM-Solver, as well as guided sampling through classifier guidance and classifier-free guidance. Finally, we compare DDPM and DDIM with the reverse SDE/ODE framework and show that they share the same training objective, while DDPM sampling corresponds to discrete reverse-SDE sampling and DDIM sampling corresponds to reverse-ODE sampling.

Many public buildings provide floorplans with a "you are here" indicator to help visitors orient themselves. Floorplan localization seeks to computationally replicate this capability by determining where visual observations were captured within a floorplan. However, existing methods typically assume controlled small-scale environments and precise vectorized floorplans, limiting their ability to operate in large-scale buildings and rasterized floorplans. In this work, we present an approach for performing floorplan localization in the wild by grounding the task in a reconstructed 3D representation of the scene. Given an unconstrained image collection, our method reconstructs a gravity-aligned 3D scene and projects it into a 2D density map that serves as a floorplan proxy. Floorplan localization is then formulated as aligning this proxy with the input floorplan via a 2D similarity transform. To bridge the appearance gap between density maps and architectural floorplans, we adapt a 2D foundation model to learn cross-modal correspondences, introducing a fine-tuning scheme that encourages semantically aligned matches while preserving structural consistency. Extensive experiments demonstrate substantial improvements over prior methods, including in extremely sparse settings with as little as a single input image. Our code and data will be publicly available.

Recent work has identified a counterintuitive phenomenon termed "Hyperfitting", where fine-tuning Large Language Models (LLMs) to near-zero training loss on small datasets surprisingly enhances open-ended generation quality and mitigates repetition in greedy decoding. While effective, the underlying mechanism remains poorly understood, with the extremely low-entropy output distributions suggesting a potential equivalence to simple temperature scaling. In this work, we demonstrate that this phenomenon is fundamentally distinct from distribution sharpening; entropy-matched control experiments reveal that temperature scaling fails to replicate the diversity gains of hyperfitting. Furthermore, we falsify the hypothesis of static vocabulary reweighting, showing through ablation studies that hyperfitting relies on a dynamic, context-dependent rank reordering mechanism. Layer-wise analysis localizes this effect to a "Terminal Expansion" in the final transformer block, where a substantial geometric expansion of the feature space (Delta Dim approx +80.8) facilitates the promotion of deep-tail tokens. Additionally, we introduce Late-Stage LoRA, a targeted fine-tuning strategy that updates only the final 5 layers, yielding robust generation with minimal parameter updates

Online map estimation is a crucial component of autonomous driving systems that reduces the reliance on costly high-definition maps. State-of-the-art (SOTA) methods commonly predict map elements as ordered sequences of points that form polylines and polygons. The evaluation of these methods relies predominantly on mean average precision (mAP) based on thresholded Chamfer distance (CD). This framework lacks sensitivity to point ordering and provides limited granularity in assessing geometric quality, making it difficult to distinguish which methods truly excel over others. In this work, we address these limitations on two fronts. For the single-instance similarity measure, we introduce sequence optimal sub-pattern assignment (SOSPA), an order-aware metric that enables fine-grained evaluation of individual geometries while satisfying all metric axioms. For the multi-instance evaluation framework, we propose polyline localisation and detection (PLD), a soft metric that jointly captures detection quality and geometric accuracy, replacing the hard thresholding of mAP with a principled soft assignment. Through evaluations on nuScenes, we demonstrate that PLD effectively ranks SOTA online mapping methods (MapTRv2, StreamMapNet, MapTracker) while providing a decomposed error analysis. This analysis identifies detection capability as the dominant bottleneck in current methods, revealing a performance trend that mAP fails to capture. Code for evaluation using our metrics will be released.

Accurate segmentation of brain tumour sub-regions from multi-parametric MRI is critical for treatment planning yet remains challenging due to morphological variability, class imbalance, and overlapping appearances of tumour regions across imaging sequences. We propose SegGuidedNet, a three-dimensional residual encoder--decoder network introducing a novel SegAttentionGate module that explicitly supervises the decoder to produce spatially discriminative attention maps for each tumour sub-region necrotic core, peritumoral oedema, and enhancing tumour via a lightweight auxiliary loss, adding less than 0.2% parameter overhead. This sub-region supervision maintains decoder discriminability between visually ambiguous classes while providing free-of-cost spatial interpretability at inference without any post-hoc explanation method. Evaluated independently on BraTS2021 and BraTS2023 GLI across 251 held-out subjects each, SegGuidedNet achieves mean Dice of 0.905 (ET= 0.873, TC=0.906, WT=0.935) and 0.897 (ET=0.859, TC=0.902, WT=0.931) respectively, surpassing ensemble-based nnU-Net and HNF-Netv2 as a single model and approaching Swin UNETR a 10-model ensemble within 2--4 Dice points at a fraction of the inference cost. The consistency of results across two benchmark editions further confirms the generalisability of the proposed approach, offering competitive accuracy with built-in interpretability in a lightweight, clinically practical framework.

Spatio-temporal reasoning is a core capability for Multimodal Large Language Models (MLLMs) operating in the real world. As such, evaluating it precisely has become an essential challenge. However, existing spatio-temporal reasoning benchmark datasets primarily rely on static image sets or passively curated video data, which limits the evaluation of fine-grained reasoning capabilities. In this paper, we introduce VGenST-Bench, a video benchmark that employs generative models to actively synthesize highly controlled and diverse evaluation scenarios. To construct VGenST-Bench, we propose a multi-agent pipeline incorporating a human quality control stage, ensuring the quality of all generated videos and QA pairs. We establish a comprehensive 3x2x2 video taxonomy, encompassing Spatial Scale, Perspective, and Scene Dynamics to span diverse scenarios. Furthermore, we design a hierarchical task suite that decouples low-level visual perception from high-level spatio-temporal reasoning. By shifting the paradigm from passive curation to active synthesis, VGenST-Bench enables fine-grained diagnosis of spatio-temporal understanding in MLLMs.

An adversary copies your encrypted traffic today and waits for a quantum computer to decrypt it later. How exposed are you? We show that the functional form of the answer is not merely a calibration choice -- it is structurally justified by three assumptions about adversarial production and value-decay dynamics. Under those assumptions, the HNDL compromise probability factorises into a temporal hazard, a multiplicative cryptographic-vulnerability and operational-exposure term, and a saturation denominator governed by the defense-attack intensity ratio; the marginal sensitivity to each dimension is endogenous to the organisation's position in the vulnerability-exposure plane, not a fixed global constant. Additive scoring frameworks cannot reproduce this structure because the interaction between cryptographic vulnerability and operational exposure is absent by construction, regardless of calibration. The resulting framework provides a structurally grounded basis for operational HNDL exposure prioritisation under partial observability.

The benchmarks used to evaluate AI agents in security-critical roles suffer from crucial weaknesses. Building on recent empirical evidence, we characterize three core challenges that undermine security evaluations: benchmark vulnerabilities, temporal staleness, and runtime uncertainty. We then outline practical directions toward building more robust and trustworthy evaluation frameworks.

Reinforcement learning has proven effective for enhancing multi-step reasoning in large language models (LLMs), yet its benefits have not fully translated to multilingual contexts. Existing methods struggle with a fundamental trade-off: prioritizing input-language consistency severely hampers reasoning quality, while prioritizing reasoning often leads to unintended language drift toward English. We address this challenge with LANG, a novel framework that leverages language-conditioned hints to guide exploration in non-English reasoning tasks. Our method incorporates two key mechanisms to prevent dependency on these hints: a progressive decay schedule that gradually withdraws scaffolding, and a language-adaptive switch that tailors learning horizons to specific language difficulties. Empirical results on challenging multilingual mathematical benchmarks reveal that LANG substantially enhances reasoning performance without compromising language consistency. Moreover, we show that our framework generalizes beyond mathematics, fostering more consistent language alignment across model layers

Large Language Model (LLM)-based agents demonstrate strong reasoning and execution capabilities on complex tasks when guided by structured instructions, commonly referred to as workflows. However, existing workflow-assisted agent serving systems typically rely on predefined templates and shallow matching mechanisms, which limit their ability to capture deep semantic relationships and generalize to previously unseen tasks. To address these limitations, we propose a new workflow management paradigm that represents workflows using a unified graph, termed wGraph, where each node corresponds to an atomic operation. wGraph serves as a shared substrate from which task-specific workflows are dynamically instantiated. Building on wGraph primitives, we introduce GraphFlow, a system that efficiently integrates workflows into agent serving through two key designs. First, adaptive workflow generation dynamically constructs workflows from wGraph based on task semantics and constraint requirements. Second, workflow state management exploits wGraph structure to efficiently manage Key-Value (KV) caches, reducing redundant computation during agent serving. Extensive experiments across five benchmark datasets show that GraphFlow consistently outperforms state-of-the-art methods, yielding an average performance improvement of approximately 4.95 percentage points, while achieving an approximately 4$\times$ reduction in memory footprint.

Today, tool-calling agents are commonly evaluated or tested on static datasets of execution traces, including input commands, agent responses, and associated tool calls. However, internal production datasets are often insufficient or unusable for testing; for example, they may contain sensitive or proprietary data, or they may be too sparse to support comprehensive testing (especially pre-deployment). In these settings, practitioners are increasingly replacing or augmenting real datasets with synthetic ones for evaluation purposes. A key challenge is quantifying the relation between these synthetic datasets and the real data. We introduce SynAE, an evaluation framework for assessing how well synthetic benchmarks for multi-turn, tool-calling agents replicate and augment the characteristics of real data trajectories. SynAE assesses the validity, fidelity, and diversity of synthetic data across four metric categories: (i) task instructions and intermediate responses, (ii) tool calls, (iii) final outputs, and (iv) downstream evaluation. We evaluate SynAE using recent agent benchmarks and test common synthetic data failure modes via realistic and controlled generation schemes. SynAE detects fine-grained variations in data validity, fidelity and diversity, and shows that no single metric is sufficient to fully characterize synthetic data quality, motivating a multi-axis evaluation of synthetic data for agent testing. A demo of SynAE is available at https://synae-2026-synae-demo.static.hf.space/index.html, with code at https://github.com/wsqwsq/SynAE.

Training Deep Neural Networks for tracking individual cells in biomedical videos requires a large amount of annotated data. The annotation of videos for cell tracking is very time consuming and often requires domain expertise; this explains the limited availability of public annotated data to address important medical problems like tissue repair or cancer treatment. Generating synthetic videos along with their Ground Truth annotations is a promising solution that relies, as a foundational first step, on the synthesis of single cell annotations (or phantoms). Phantoms need to be time consistent, as they have to replicate biological processes that are specific to the cell types. In this work, we propose a novel framework for generating videos of cell phantoms in the Elliptical Fourier Descriptors (EFDs) domain, a compact and geometrically interpretable representation for 2D closed contours. We represent the cell phantom evolution as a multivariate time series of EFD coefficients, introducing a strong prior for cell morphology and enabling the efficient generation of sequences that evolve coherently in time. Our experimental validation proves that modelling the temporal evolution in EFD space enables the generation of biologically plausible phantom videos. Our method can be used in generative pipelines for synthesizing annotated data for cell tracking, thus strongly mitigating the annotation effort for creating new datasets. Our code is available for download here: https://github.com/FrancescoBenedetto99/efd-cell-video-gen.

Bayesian optimization (BO) is a widely used iterative black-box optimization method that utilizes Gaussian process (GP) surrogate models. In practice, BO is typically terminated after a fixed evaluation budget is exhausted, which can incur unnecessary cost and provides no optimality guarantee on solution quality. Recent research in developing a practical stopping criterion has made empirical progress, yet a theoretically sound stopping criterion remains a work in progress. In this work, we present provably tighter instantaneous regret bounds for GP upper confidence bound (GP-UCB) at any given iteration. Then, we propose stopping criteria for GP-UCB based on this tighter bound that ensures an $ε$-optimal solution with high probability $1-δ$ upon termination. Numerical experiments are performed to validate and demonstrate the effectiveness and efficiency of our stopping criteria.

Spatio-temporal reasoning in vision-language models requires visual representations that preserve physical geometry rather than merely semantic appearance. Recent multimodal models incorporate geometric information through structural branches, 3D-aware supervision, reasoning-stage fusion, or long-horizon memory. While these approaches demonstrate the importance of geometry for spatial intelligence, they typically treat geometric cues as a shared signal across all visual tokens. We note that this overlooks a finer-grained challenge: different visual tokens require different geometric evidence depending on their spatial roles. To address this limitation, we introduce GeoWeaver, a pre-reasoning geometric grounding framework that treats geometry as a representational prerequisite for spatio-temporal reasoning. GeoWeaver constructs a multi-level geometry bank from a frozen geometry encoder and performs token-adaptive geometric evidence allocation, enabling each visual token to retrieve the most relevant geometric abstractions. The selected evidence is incorporated into visual tokens via a residual grounding operation prior to language modeling, yielding geometry-grounded representations for downstream reasoning. Extensive evaluations on spatial reasoning benchmarks demonstrate that GeoWeaver consistently enhances geometry-aware reasoning while retaining general multimodal capabilities. This indicates that geometric information yields the greatest benefit not as a late-fusion auxiliary signal but as a fundamental prerequisite that shapes the representational foundation on which large language models perform reasoning. All source code and models will be released at https://github.com/yahooo-m/GeoWeaver .

We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition and separation structures, and covers both finite-dimensional function approximation and infinite-dimensional operator approximation. We prove well-posedness and universal approximation properties for the corresponding neural flows, including, to the best of our knowledge, the first universal approximation result for flow-based models between infinite-dimensional spaces. We also obtain universal approximation results for convolutional neural flow models. Through suitable time discretizations, the composition structure recovers ResNet-type architectures, while the separation structure, via a splitting-based discretization, yields plain architectures. This gives a unified flow-based route to both residual and plain architectures for neural networks and neural operators with fully connected or convolutional linear layers.

Digital elevation models (DEMs) underpin terrain analysis in Geographic Information Systems (GIS), but in their common raster form, they rely on interpolation for off-grid sampling and finite-difference operators for derivative-based analysis. Implicit neural representations (INRs) offer a continuous alternative, but prior terrain INRs lack explicit frequency control, neglect the gradient structure of terrain, and remain too large and costly to train for practical deployment. We present ImplicitTerrainV2, which advances terrain INRs toward a compact, efficient neural terrain data format by combining a spectral control mechanism with wavelet-guided spatial adaptivity, derivative-aware supervision, and post-training model compression. At its core, a wavelet complexity field (WCF) derives spatially-adaptive frequency masks from analytically computed wavelet coefficients, localizing high-frequency capacity to complex terrain regions. The same field guides complexity-aware adaptive sampling that concentrates training in high-complexity regions, while gradient matching applies extra supervision to enforce the smooth manifold structure of terrain DEMs for improved derivative fidelity. Post-training mixed-precision quantization and entropy coding reduce storage to 1.23 bpp with a 0.28 dB PSNR drop. On 50 Swiss terrain tiles, ImplicitTerrainV2 reaches 66.25 dB end-to-end PSNR, improving over the prior work by 5.70 dB while using 3.2x fewer parameters and training in 55 s per tile on a single GPU. Our compressed neural format is competitive with several established DEM codecs in rate-distortion performance, while additionally supporting off-grid point queries, closed-form derivative evaluation, and resolution-independent reconstruction, which may benefit many downstream GIS applications.

Fashion image retrieval is a cornerstone of modern e-commerce systems. A unified framework that supports diverse query formats and search intentions is highly desired in practice. However, existing approaches focus on narrow retrieval tasks and do not fully capture such diversity. Therefore, in this work, we aim to develop a unified framework capable of handling diverse realistic fashion retrieval scenarios, achieving truly versatile fashion image retrieval. To establish a data foundation, we first introduce U-FIRE, a comprehensive benchmark that consolidates fragmented fashion datasets into a unified collection, supplemented by two manually curated datasets for testing generalization. Building upon this, we propose FashionLens, a unified framework based on Multimodal Large Language Models. To handle divergent matching objectives, we design a Proposal-Guided Spherical Query Calibrator that dynamically shifts query representations into task-aligned metric spaces via adaptive spherical linear interpolation. Additionally, to mitigate the optimization imbalance caused by varying task complexities and data scales, we develop a Gradient-Guided Adaptive Sampling strategy that automatically re-weights tasks based on realtime learning difficulty and the data scale prior. Experiments on U-FIRE show that FashionLens achieves state-of-the-art performance across diverse retrieval scenarios and generalizes robustly to unseen tasks. The data and code are publicly released at https://github.com/haokunwen/FashionLens.

Two-wheelers account for a disproportionately high share of road fatalities in the Global South. Research on two-wheeler rider behavior, however, lags far behind four-wheelers, where multimodal datasets have driven major advances in Advanced Driver Assistance Systems (ADAS). To address this gap, we present the MOtorized TwO-wheeler Rider (MOTOR) dataset, the first large-scale, multi-view, multimodal resource dedicated to two-wheelers in dense, unstructured traffic. MOTOR comprises 1,629 sequences (25+ hours of video data) collected from 16 riders and integrates synchronized front, rear, and helmet videos, rider eye-gaze from wearable trackers, on-road audio, and telemetry (GPS, accelerometer, gyroscope). Rich annotations capture traffic context, rider state, 12 riding maneuvers spanning conventional and unconventional behaviors, and legality labels (Legal, Illegal, Unspecified). We benchmark rider behavior recognition and maneuver legality classification using state-of-the-art video action recognition backbones (CNN and Transformer-based), extended with multimodal fusion, and find that combining RGB, gaze, and telemetry consistently yields the best performance. MOTOR thus provides a unique foundation for advancing safety-critical understanding of two-wheeler riding. It offers the research community a benchmark to develop and evaluate models for behavior analysis, legality-aware prediction, and intelligent transportation systems. Dataset and code is available at https: //varuniiith.github.io/MOTOR-Dataset/

The Hilbert-Schmidt Independence Criterion (HSIC) and its joint-independence extension $d\mathrm{HSIC}$ are degenerate $V$-statistics whose data-dependent weighted-$χ^2$ null limits force a permutation calibration that multiplies the per-test cost by the number of permutations, in practice two orders of magnitude. Adapting the recent martingale MMD construction for two-sample testing to the (joint) independence problem, we introduce two studentised statistics whose null distributions are standard normal regardless of the data law, so that a single normal-quantile lookup replaces the permutation step entirely. The first, $m\mathrm{HSIC}$, is a self-normalised lower-triangular sum of the Hadamard product of two empirically centred Gram matrices. Under independence and bounded-fourth-moment kernels it converges to a standard normal. It is consistent against every fixed alternative, and runs at quadratic cost in the sample size without any sample split, matching the biased HSIC $V$-statistic. Our second statistic, $md\mathrm{HSIC}$, achieves finite-sample consistency with a single half-sample split: the centring is estimated on one half and the lower-triangular self-normalised martingale is run on the other, shrinking the conditional-mean residual to a quantity that is exponentially small in $d$, so the statistic is asymptotically standard normal at every fixed number of jointly tested variables, with a per-test cost that grows only linearly in $d$. On synthetic data with per-variable input dimension from $1$ to $500$ and between $2$ and $10$ jointly tested variables, both statistics match the empirical type-I error rate and test power of permutation-calibrated baselines while running $25$ to $60\times$ faster.