User modeling is a critical task in a variety of personalized systems. Recognizing their effectiveness in learning from graph-structured data, Graph Neural Networks (GNNs), particularly Graph Convolutional Networks (GCNs), are increasingly employed for user modeling. However, existing approaches typically treat different relation types in a graph as homogeneous, limiting their ability to capture richer semantics and construct more informative user models. While multi-relational GNNs (MR-GNNs) have been adopted for representation learning and recommendation, their application for user modeling remains unexplored. Moreover, existing GNN-based user modeling approaches ignore the user interaction sequence. To address these research gaps, in this work we propose MR-ConceptGCN, a novel fully unsupervised approach focused on concept-based sequential learner modeling using multi-relational GCNs (MR-GCNs). MR-ConceptGCN effecively combines Personal Knowledge Graphs (PKGs), MR-GCNs, and the pre-trained language model SBERT to obtain enhanced relation- and semantic-aware representations of the PKG items. The enriched embeddings of the knowledge concepts that a learner did not understand when interacting with learning materials in CourseMapper are then used to construct a sequential learner model that combines long-term and short-term learner interactions. We report the results of an online user study (n = 31), demonstrating the benefits of MR-ConceptGCN in terms of several important user-centric aspects including accuracy, usefulness, diversity, and satisfaction with an educational recommender system.
https://arxiv.org/abs/2607.19253
A central aim of unsupervised learning is to uncover latent factors that explain dependencies among observations. Probabilistic models typically achieve this by introducing multiple latent variables linked through a graph of conditional relationships, with distributional parameters and their dependence learnt from data. Learning relies either on distributional choices that allow tractable belief propagation, or on approximations that scale poorly with model size and complexity. We build on the recently developed recognition-parametrised modelling paradigm to propose an alternative approach: RAMP, a method that implicitly defines latent structure by learning a flexible, nonlinear, amortised message-passing framework. We show that RAMP enables efficient likelihood-based recovery of latent-variable distributions within expressive nonlinear models acting on complex high-dimensional data.
https://arxiv.org/abs/2607.18883
Intelligence appears under different names in different fields: as data compression in statistics and machine learning, as universal computation in dynamical systems, and as adaptive behavior in agents. Each field carries its own objective, and the two most influential drives often fail in mirror image: novelty search, which seeks surprise, is transfixed by a noisy television screen, while the free-energy principle, which avoids surprise, is most content in a dark room. Both failures have a single cause: each objective treats as one quantity the surprise a learner can convert into knowledge and the surprise it never can. Here we show that the learnable part of that information, which we call learnable novelty, yields the seemingly disparate projections of intelligence, and we give a closed-form estimator of it built on a cheap and differentiable reservoir computer. Used as a measure, with no supervision of any kind, the estimator recovers decades of complexity classification, ranking the Turing-complete rule~110 highest among the elementary cellular automata. Used as an objective, its gradient carries a neural cellular automaton from simple dynamics into a regime of solitons, the traveling, colliding structures by which rule~110 computes, as well as organizes the representation of an image encoder around the ten digit classes of MNIST, fully unsupervised: no label ever enters training. Handed to a reinforcement-learning agent as an intrinsic reward, it supplies the exploration that task rewards lack, improving on the task baseline in nine of ten environments and collapsing in none. Complexity generation, abstraction, and exploration, ordinarily pursued with unrelated objectives in separate fields, thus emerge from ascent on one differentiable quantity, and the projections of intelligence gain a common quantitative footing.
https://arxiv.org/abs/2607.18433
Deep neural networks have become a promising approach for IMU-based sensing, but their scalability is fundamentally limited by costly labeled data and poor robustness to heterogeneous devices, placements, and users. Existing unsupervised and self-supervised methods reduce but do not remove this dependence, still requiring labeled data for domain adaptation and largely ignoring known physical structure. We propose physical self-supervised learning, an autoencoder-style paradigm for label-free IMU sensing. We replace the conventional neural decoder with an auto-adaptive physics decoder, a learnable family of kinematic equations that enforces explicit physical structure while adapting across environments, and adopt a hybrid two-stage IMU encoder with reconstruction in a structured latent space to mitigate sensor noise. Our framework further introduces probabilistic frequency-spatial constraints to disentangle sensor and object motion, a multi-view kinematic tree to exploit sparse physical self-supervised signals, and an uncertainty-aware formulation to handle the inherent ambiguity of IMU inference. Evaluated on inertial tracking and full-body motion capture over public datasets and realistic deployments, physical self-supervised learning reduces errors by up to 5x for tracking and 4x for motion capture in challenging generalization scenarios, consistently outperforming state-of-the-art supervised and self-supervised baselines without any labels.
https://arxiv.org/abs/2607.18361
Financial statements (FS) such as Balance Sheet (BS), Income Statement (IS) and Cash-flow Statement (CS) summarize the annual financial performance of a company. FS are widely used for evaluating corporate governance, credit appraisal, risk analysis, validate taxation, make investment decisions etc. Financial auditing is a complex and knowledge-intensive discipline whose one important aim is ensuring integrity, accuracy, fairness and absence of material misstatement in the published FS. Given the importance of FS, there are incentives to hide, omit or falsify information to misrepresent the true financial health of the company; e.g., reduce tax liabilities, or increase investor confidence. Given the complex, time-consuming and expertise-dependent nature of auditing, auditors would benefit from an AI-assisted system that automatically detects instances of misinformation in the given FS and identify likely sources of this misinformation in the financial data. In this paper, we present unsupervised techniques to identify misinformation in FS, and also generate explanations as to the financial variables that are likely sources of misinformation. The auditor can then explore in more detail the associated data sources and business processes to validate these suggestions. A crucial feature of our approach is the use of past corpus of FS and associated audit reports to generate insights, which help in providing assistance. We demonstrate the efficacy of these techniques on a large corpus of 11,460 FS over 5 years and associated audit reports. This paper integrates and adds more novel contributions over the previously reported research (Shinde et al., 2022)\cite{SVAP22}, (Vaishampayan et al., 2022)\cite{VSPP22}, (Pawar et al., 2023)\cite{PAPV23}, which we have used as the foundation for our AI-assisted Auditor Assistance system.
https://arxiv.org/abs/2607.17797
Unsupervised Graph Domain Adaptation (UGDA) aims to facilitate knowledge transfer from a labeled source graph to an unlabeled target graph by mitigating cross-domain distribution shifts. Existing methods primarily focus on node-level feature alignment in latent spaces, relying on the implicit assumption that all source nodes contribute positively to the alignment. However, this assumption often fails because a node's semantic information is intrinsically coupled with its topological graph structure. Due to structural shifts, source nodes with severe structural deviations (e.g., structural outliers) lack semantic counterparts in the target graph, and forcing alignment on them introduces severe noise and causes negative transfer. To bridge this gap, we argue that selective source node utilization is superior to full-graph training, thereby shifting the research paradigm from feature-level alignment to data-level refinement. To this end, we propose Source Node Influence Pruning (SNIP), a novel model-agnostic, data-centric refinement framework. Specifically, SNIP quantifies the structural discrepancy between individual source nodes and the target domain by integrating multiple centrality measures, assigning each source node an influence score. A rank-based normalization mechanism is further employed to eliminate scale variations across different measures, allowing SNIP to effectively identify and filter out structurally incompatible nodes with low influence scores. As a plug-and-play method, SNIP constructs a refined "sub-source" graph that is inherently more beneficial for subsequent alignment. Comprehensive experiments across eight transfer scenarios on five real-world datasets demonstrate that SNIP consistently outperforms competitive baselines and significantly enhances adaptation performance, validating the superiority of selective node utilization over full-graph training.
https://arxiv.org/abs/2607.17668
Across environments with mixed sources of uncertainty, unsupervised reinforcement learning requires intrinsic motivation that does not precommit to a particular direction of surprise. Surprise minimization is scoped by design to ``unstable'' environments. Prediction-error curiosity rewards total expected surprise, including irreducible noise. Bandit or mixture switching between surprise-minimizing and surprise-maximizing rewards reintroduces non-stationarity by construction. We propose a single intrinsic reward, stationary within each window, derived from the novelty contribution of a preference-free Expected Free Energy objective, expressed in reward-maximization form. Our claim is that parameter information gain, the expected surprise of the next state minus its irreducible part, is the appropriate intrinsic signal in both high-entropy and low-entropy components of the state space. Maximizing it seeks exactly the surprise the model can explain away. In regions of unresolved dynamics, this epistemic term drives exploration. As dynamics become resolved, the epistemic term vanishes, while an aleatoric penalty favors lower-variance transitions, all without fitting an explicit next-state predictor. A pseudocount supplies epistemic value, a probe-based penalty captures aleatoric variance, and a short-horizon gate protects informative successors. A window-based freeze of all reward-defining objects yields a stationary Bellman operator, explicit bounds on learning targets, and a conditional uniform-concentration result for the nonparametric estimators under mixing, smoothness, bandwidth, and capacity assumptions. In active-inference terms, the agent is preference-free where novelty is retained, standard likelihood ambiguity vanishes under full observability, a nonstandard transition-entropy penalty is added, and surprise minimization emerges in resolved regions of the state space.
https://arxiv.org/abs/2607.16858
Deep functional map frameworks (DFM) for shape correspondence are powerful, yet fundamentally limited by their reliance on end-to-end differentiability. This constraint prevents the integration of highly accurate, non-differentiable refinement techniques, capping their overall performance, especially on challenging non-isometric shapes. To overcome this, we introduce MDND, a novel DFM paradigm built on the principle of merging differentiable and non-differentiable components. Our framework facilitates unsupervised learning guided by an internal, non-differentiable refinement. Specifically, MDND employs a dual-branch architecture: a non-differentiable refinement branch leverages a novel, multiscale iterative solver to produce highly robust correspondences, acting as a refined target. Concurrently, a fully differentiable branch learns to predict correspondences from features. The entire system is trained end-to-end without supervision by enforcing a consistency loss that compels the differentiable branch to learn from the superior, refined results of the non-differentiable branch. Extensive experiments show that MDND sets a new state-of-the-art, demonstrating remarkable robustness on shapes with non-isometric deformations and topological noise.
https://arxiv.org/abs/2607.15887
Metaphor in Arabic is a culturally grounded mechanism for constructing meaning, encoding cultural knowledge that shapes interpretation. Yet current Arabic language models typically collapse lexical, cultural, and metaphorical information into a single representational space, a phenomenon we term "semantic smearing". We introduce CAMMAR (Culture-Aware Matryoshka for Metaphorical Arabic Representations), a representation learning framework that organizes meaning into nested lexical, cultural, and metaphorical embedding subspaces through a staged semantic curriculum. The design implements compositional principles of Al-Jurjani's theory of nazum, modeling figurative meaning as compositionally grounded in prior semantic relations, and yields a training-free geometric measure of metaphoricity based on the distance between lexical and metaphorical representations. Evaluated on a new span-annotated Arabic metaphor set as word-matched figurative/literal pairs, the geometric readout detects metaphor well above chance when the inter-layer geometry is shaped by paired supervision (AUC up to 0.84; figurative outscores its literal counterpart for the same word in 82.6\% of pairs), but sits at chance under an unsupervised domain contrast alone, a clean separation between a legible-under-supervision regime and a non-emergent one. A controlled ablation shows that grounding the lexical layer in morphological roots gives a small but consistent gain, an effect absent from direct probing that reflects the layer's quality as a measurement anchor. We will release the datasets, cultural concept inventory, and code upon acceptance.
https://arxiv.org/abs/2607.15847
3D CT vision-language models (VLMs) classify abnormalities from text prompts in a zero-shot manner, enabling cross-institution deployment where labels are scarce and clinical tasks shift faster than supervised models can be retrained. A real CT scan, however, typically contains several co-occurring abnormalities, and the reliability of zero-shot multi-label prediction under distribution shift remains poorly understood. Test-time adaptation (TTA) updates a model on unlabeled target scans without source data or target annotations, yet existing TTA methods target multi-class softmax prediction on natural images or 2D medical segmentation, and none addresses unsupervised multi-label adaptation for zero-shot 3D CT VLMs. We study when TTA helps zero-shot 3D CT VLMs. A controlled diagnostic analysis shows that TTA is conditional: the volumetric input must preserve the encoder's depth structure, and the base representation must transfer to the target cohort, with depth reduction alone lowering internal AUROC by more than 0.12. We then focus on the regime where the base model already separates present from absent abnormalities. We introduce CARVE (Cardinality-Aware Retained-View Entropy), the first TTA method for this setting. CARVE estimates a sample-specific positive-label cardinality $\hat{k}$, optimizes a top-$\hat{k}$ objective to preserve co-occurring abnormalities, and performs memory-efficient multi-view adaptation by scoring weak 3D views without gradients before updating on a retained subset. Across contrastive CT-CLIP and anatomy-aware fVLM, CARVE provides the most consistent improvements across multi-label, three-class, and binary CT tasks when the base model is already discriminative. These results establish multi-label TTA for zero-shot 3D CT VLMs as a distinct problem and CARVE as a cardinality-aware solution.
https://arxiv.org/abs/2607.15556
Serverless computing provides automatic resource management and pay-per-use execution, but effective autoscaling remains challenging because of dynamic workloads, cold-start latency, and dependencies among functions. We present a dependency-aware autoscaling framework that integrates graph-based bottleneck identification, short-term workload forecasting, multi-model consensus, and cost-aware scaling control. Serverless applications are represented as directed dependency graphs, and structurally important functions are identified using weighted degree centrality. Resource demand is predicted using lightweight MLP, LSTM, and CNN models. Their outputs are combined through a performance-weighted probabilistic ensemble inspired by Bayesian model averaging. The controller further incorporates cold-start awareness and cost comparison to select among scale-up, scale-down, and hold actions. Experiments using real workload traces show that supervised forecasting substantially outperforms unsupervised clustering for autoscaling decision generation. The proposed ensemble achieves 99.88 percent prediction accuracy and reduces prediction error compared with representative hybrid forecasting methods. Evaluations across multiple cloud pricing models also demonstrate consistent infrastructure cost reductions while maintaining performance targets. The results show that combining dependency analysis, multi-expert forecasting, and cost-aware control provides a robust and practical solution for serverless autoscaling.
https://arxiv.org/abs/2607.15511
Recent works have explored ways to handle uncertainty in dynamic time warping (DTW) alignment paths through the use of differentiable variants of DTW like Soft-DTW. In this paper, we approach the issue of uncertainty in DTW alignment paths in a different way. Given a DTW alignment path, we propose a metric that indicates how reliable a local segment of the alignment path is. The intuition for our metric is based on the idea of circumstantial evidence. If DTW has found a very prominent path, then if we re-run the alignment with relaxed boundary conditions, it will still pick the same path. If, on the other hand, DTW has found a "weak" path, then re-running the alignment with relaxed boundary conditions will likely yield a different path. Accordingly, our reliability metric is computed by picking a local section of the DTW alignment path, re-estimating the alignment with FlexDTW (which allows flexibility in the boundary conditions), and then measuring how well the DTW and FlexDTW paths agree. We assess the proposed reliability metric on DTW alignment paths containing both matching and non-matching regions across a range of scenarios on an audio-audio alignment task. We find that the reliability metric correctly identifies reliable regions of the alignment path with an aggregate AUROC of 0.97. This approach provides an unsupervised method for estimating the reliability of a DTW alignment path.
https://arxiv.org/abs/2607.15443
Falls among older adults are a major safety challenge, but continuous monitoring is difficult to sustain. Video captures fall-related posture and motion, yet deployment is limited by privacy, computation, and bandwidth. Supervised pose estimation is anatomically interpretable but vulnerable to occlusion and partial body visibility. We propose a privacy-preserving framework that replaces RGB transmission with compact motion representations based on unsupervised keypoints and predictive temporal modeling. Local processing performs segmentation and keypoint extraction; variational recurrent prediction and sequence classification then detect falls from observed and forecasted motion. We evaluate the framework on the UR Fall Detection and Human Fall datasets using random, subject-disjoint, and occlusion-based splits. Under random splits, neither representation consistently dominates, suggesting that standard protocols may hide meaningful differences. Under subject-disjoint evaluation, supervised keypoints show a statistically significant advantage, but performance varies by subject: they perform better when anatomical landmarks are visible, whereas unsupervised keypoints are more robust to occlusion and partial visibility, though they produce more false positives for complex activities. Under occlusion-based evaluation, supervised keypoints miss nearly half of all falls, while unsupervised keypoints retain strong sensitivity and substantially outperform them. Their anatomical independence allows spatial anchors to adapt to visible body structure rather than fail on absent landmarks. The gap widens under bandwidth constraints, where supervised localization errors compound through the temporal model. These findings show that representation choice should reflect expected visual conditions and that unsupervised keypoints offer an advantage when body visibility is compromised.
https://arxiv.org/abs/2607.15400
Unsupervised visible-infrared person re-identification (USVI-ReID) is challenging due to the large modality gap and the lack of cross-modal identity annotations. Progressive association paradigms have been proposed to gradually bridge the gap, but they suffer from two critical bottlenecks: reliance on ambiguous global representations and unchecked propagation of pseudo-label noise in an open-loop manner. To address these issues, we propose Structural-Semantic Reciprocal Learning (SSRL), a framework that transforms open-loop association into a self-correcting closed-loop system. Structurally, we introduce Fine-grained Structural Decoupling (FSD) to extract discriminative body-part primitives as reliable spatial anchors, complementing ambiguous holistic silhouettes with spatially consistent structural details. Semantically, we design a Closed-loop Semantic Calibration (CSC) mechanism that reconstructs shared semantic prototypes at each epoch and feeds them back into the training loop, effectively filtering pseudo-label noise before the next clustering cycle. Through the reciprocal interaction between structural and semantic learning, SSRL achieves robust cross-modal representation. Extensive experiments demonstrate the competitive performance of SSRL against state-of-the-art USVI-ReID methods on both SYSU-MM01 and RegDB, notably surpassing several supervised counterparts on RegDB.
https://arxiv.org/abs/2607.15220
Industrial anomaly detection aims to identify and localize defective regions without relying on exhaustive annotations of all possible defect types. Although recent unsupervised methods have achieved strong performance, most are primarily designed for single-class settings and often struggle in multi-class scenarios, where diverse normal patterns may lead to over-generalization and reduce the discriminative capability between normal and anomalous regions. In this paper, we propose SwinAD, a reconstruction-based framework for multi-class unsupervised anomaly detection that leverages a frozen pretrained Swin Transformer V2 encoder and a feature diversity-preserving reconstruction decoder. The hierarchical encoder provides semantically rich multi-scale features, while stage-wise bottleneck modules with dropout prevent trivial identity mapping and encourage robust reconstruction of normal patterns. To further improve localization, we introduce a feature diversity-preserving reconstruction framework that maintains complementary reconstruction hypotheses instead of relying on a single decoding branch. The discrepancies between encoder features and the two reconstructed features are then aggregated across multiple scales to produce the final anomaly map. Experiments conducted on three industrial anomaly detection benchmarks, including MVTec AD, VisA, and Real-IAD, demonstrate that SwinAD achieves competitive image-level performance and strong pixel-level localization accuracy, with particularly notable improvements in pixel-level AP and 1 on MVTec AD. These results indicate that combining hierarchical Swin features with diverse multi-scale reconstruction substantially improve pixel-level localization in multi-class unsupervised anomaly setting.
https://arxiv.org/abs/2607.14534
Arrhythmogenic left ventricular cardiomyopathy is a genetic myocardial disease difficult to diagnose due to the lack of gold standard criteria. Simultaneous PET/MR imaging, combined with multiparametric quantitative analysis, could facilitate the identification of different profiles related to the phenotype and progression of cardiomyopathy. This preliminary study focuses on a methodological strategy for dealing with PET/MRI data, including inter-patient data linkage and regional analysis. Two-step clustering was applied to T1 and T2 maps, LGE, and 18F-FDG-PET images of 99 patients genetically diagnosed with arrhythmogenic left ventricular cardiomyopathy. Each patient's images were independently z-scored and summed into a single volume, which was clustered into supervoxels. Thirty-two inter-patient groups of supervoxels were obtained by spectral clustering. An "abnormality" score was assigned to each cluster and modality, and used to visualise abnormal regions likely associated with disease. They enabled the generation of automated textual and bullseye health reports for each patient, which were compared with cardiac imager assessments using balanced accuracy in repeated nested cross-validation. This approach was further validated on a larger cohort of 167 numerical phantoms. The reports generated by clustering accurately identified most of the cardiac physicians' observations (BA = 0.76 $\pm$ 0.04 in repeated nested cross-validation on patients, and BA $\ge$ 0.8 on phantoms). Furthermore, the identified abnormal clusters closely matched their visual observations, facilitating the identification of varying degrees of fibrosis or inflammation on the images. This approach enables a more systematic handling of multimodal PET/MRI data to characterise myocardial heterogeneity in arrhythmogenic left ventricular cardiomyopathy patients.
https://arxiv.org/abs/2607.13936
Centroid neural network (CentNN) is an unsupervised competitive learning algorithm in which centroid splitting is triggered only after strict local stabilization, often leading to prolonged low-movement training phases before model expansion. This report proposes FastCentNN, an accelerated variant that addresses this inefficiency by introducing an early splitting strategy based on the total centroid movement per epoch, which serves as a training entropy proxy. As a result, FastCentNN reduces unnecessary reassignment epochs while preserving the original winner-loser learning dynamics. FastCentNN supports both absolute and stage-relative movement thresholds, allowing the splitting criterion to remain either fixed or adaptive throughout training. Experiments on some benchmark datasets show that FastCentNN consistently achieves clustering quality comparable to CentNN while reducing runtime by up to 16% on synthetic 2D datasets and about 5% on high-dimensional datasets. FastCentNN therefore provides a practical and efficient drop-in replacement for CentNN, retaining its online adaptive learning behavior while offering a simple and interpretable speed-stability trade-off through configurable splitting thresholds.
https://arxiv.org/abs/2607.13613
Spiking Neural Networks (SNNs) trained through unsupervised Spike-Timing-Dependent Plasticity (STDP) have been explored as solutions to visual loop closure problems, driven by the prospect of efficient on-device inference on neuromorphic devices. State-of-the-art STDP-based models deliver high classification accuracy but fail to reach the high Recall at 100% Precision (R@100P) needed for reliable autonomous navigation. We present a discrete, tensor-native implementation of the STDP-based SNN-VPR pipeline using PyTorch with snnTorch and evaluate it on a 100-place Nordland dataset using 15 independently-trained networks. The contribution of three decisions in the implementation is investigated. First, we show how to perform neuron assignment with a closed-form, deterministic tensor pipeline and show that it provides significantly higher R@100P than a standard argmax procedure. However, some of this gain comes from implementation differences compared to prior continuous-time models, which we measure independently. Second, ablation in isolation shows that state reset after each query helps improve R@100P regardless of the way neurons are assigned. Third, velocity-compensated sliding window aggregation over k consecutive frames reaches R@100P = 100.00% at k = 5 for constant-velocity traversal and an additional 0.20 ms latency. Taken together, these findings show the impact of inference stage design decisions in STDP-based SNN-VPR on recall precision, although the separate contribution of each mechanism and implementation differences is only partially disentangled and needs further examination.
https://arxiv.org/abs/2607.13584
The banking sector increasingly relies on automated systems to monitor electronic transactions for signs of fraud, yet conventional rule-based approaches struggle with high false-positive rates and offer no justification for their outputs, limiting their utility for compliance teams. This paper introduces an Explainable Artificial Intelligence (XAI) framework tailored for banking transaction anomaly detection within internal audit workflows. An Isolation Forest (iForest) model performs unsupervised anomaly scoring, while a SHAP (SHapley Additive exPlanations) layer provides transaction-level, feature-attributed explanations grounded in cooperative game theory [8]. A lightweight Streamlit dashboard renders these outputs in a form accessible to audit professionals without machine learning expertise. Evaluation on a synthetic banking dataset yields 0.91 precision and 0.88 recall, outperforming three unsupervised baselines. Expert feedback confirms that feature-level explanations measurably improve auditor confidence and decision quality. The framework advances the practical deployment of accountable, transparent AI in regulated financial environments.
https://arxiv.org/abs/2607.13469
Automated visual inspection of steel surface defects is a recurring quality control task in which labeled defect data is scarce and costly to obtain, while unlabeled surface images are abundant, which motivates self supervised methods that learn useful representations without class labels. A Transformer based Masked Autoencoder is used here to learn representations of steel surface defects for unsupervised grouping. During pretraining, 75% of the input image patches are randomly masked, and a lightweight decoder reconstructs the masked regions from the visible 25%. The encoder is trained jointly with an auxiliary defect localization objective, used only as a training signal and not evaluated as a detector. The decoder reaches a structural similarity score of 0.92 and a mean squared error of 0.47. Features from the pretrained encoder are then clustered using UMAP for dimensionality reduction and Agglomerative clustering, reaching a Hungarian matched accuracy of 91.3% against the six known defect categories.
https://arxiv.org/abs/2607.13178