Distributional Signatures

Handwritten signature verification is vital for personal authentication across commercial and financial applications. Although deep learning methods are widely adopted for online signature verification (OSV), they often struggle with capturing highly discriminative features and modelling long-range dependencies. To address these issues, we propose a novel framework that integrates the augmented path signature (APS) descriptor with the T-Mamba model. The APS descriptor first applies time and basepoint augmentations, then computes sliding-window path signatures. The path signature is a non-parametric feature map from rough path theory that effectively captures geometric structures and nonlinear inter-channel interactions. Inspired by the efficacy of state space models (SSMs) in sequence modelling, our T-Mamba model employs a hybrid design combining two temporal convolutional network (TCN) blocks with a time-scanning Mamba. This design enables the model to learn both local temporal patterns and global long-range dependencies, substantially improving verification accuracy. Our framework achieves state-of-the-art EERs on three public benchmark datasets (MCYT-100, SVC-2004 Task 2, DeepSignDB), validating its effectiveness and robustness, especially when the training data is limited. Our code is publicly available at https://github.com/DLRL04/OSV-using-APS-and-T-Mamba.

Bringing multiscale geometric analysis directly to irregular point clouds remains difficult: quantities such as local dimension, anisotropy, density variation, and geometric transitions are typically estimated through explicit neighborhood, manifold, or graph constructions, or left for neural networks to infer from coordinates. We introduce Heat Field Signatures (HFS), which lift a point cloud to a multiscale family of smooth ambient heat fields, providing a direct interface from discrete samples to geometric analysis. From this field, HFS computes closed-form global and local signatures directly from pairwise distances, capturing heat concentration, intrinsic dimension, anisotropy, and scale transitions. We further introduce the Heat Dimension Spectrum (HDS), a compact summary of multiscale geometric composition. HFS can be used as a closed-form descriptor, a lightweight learned representation, or a geometric feature channel for neural point-cloud models. Across synthetic and real-world benchmarks spanning subcellular, neuronal, tree, and protein data, HFS outperforms strong point-cloud and multiparameter-persistence baselines while substantially reducing end-to-end cost. On SCOP protein-fold classification, HFS improves over the strongest deep baseline by nearly $24$ percentage points using coordinates alone, while standalone HFS representations are exactly rotation-invariant by construction. More broadly, HFS turns a classical heat field into a practical interface for multiscale geometric analysis in modern point-cloud learning.

Token embeddings are the basic representational units that connect discrete tokens with continuous computation in language models. Although modern language models learn embeddings from random initialization through gradient-based training, the dynamical mechanism by which meaningful embedding structures emerge remains unclear. In this work, we identify that the evolving embedding structures are closely related to token-conditioned label and contextual distributions, which we formalize as probability signatures. We observe a progressive learning process, which we term Context Staircase: embeddings learn the low-order statistic signatures of the data before the high-order ones. More specifically, we observe that early in training they align with the simplest, context-free signature linking a token to its label, and as training proceeds, they progressively reflect signatures involving more and more context tokens. We then analyze the gradient flow of embeddings under small initialization to explain this phenomenon, deriving embedding evolution equations for feed-forward and self-attention architectures. We further extend these observations to real language-model training. Finally, we show that these embedding structures play an important role in both task learning and the incorporation of semantic structure into the embedding space. Overall, our results provide a dynamic explanation of how data statistics and architecture jointly shape token embeddings in language models, and reveal an implicit bias in the space of data statistics: training proceeds from simpler, low-order statistical relations toward increasingly complex, context-dependent ones.

Identifying individual learning styles optimizes pedagogical efficacy. While traditional questionnaires are structured, behavioral tracking methods require prolonged interaction log accumulation. To overcome these temporal constraints, this paper proposes an objective Electroencephalography (EEG) approach evaluating Phase Locking Value (PLV) connectivity against localized features across the Active-Reflective (AR) and Verbal-Visual (VV) Felder-Silverman dimensions. EEG signals were recorded from 28 participants during Raven's Advanced Progressive Matrices tasks. Support Vector Machine classification used Leave-One-Subject-Out Cross-Validation (LOSO-CV) alongside a 70:30 intra-subject split. The VV dimension achieved 70.00% subject-level accuracy driven by distinct fronto-occipital polarization. Conversely, the AR dimension yielded lower cross-subject generalizability (55.56%) due to overlapping executive networks and a "Systematic Neural Inversion" phenomenon, where stable individual connectivity signatures operated diametrically opposed to global boundaries (up to 20-0 voting margins). Ultimately, these outcomes demonstrate that rigid "one-size-fits-all" classifiers are bounded by biological diversity, emphasizing the need for future adaptive feature transformation techniques to bridge the cross-subject generalization gap.

Leak detection models for multiphase pipelines often degrade when deployed under flow regimes that differ from training. Existing evaluations typically assess performance under in-distribution operating conditions, masking failures caused by regime transitions such as bubble-to-slug flow. We propose the Manifold Gated Signature Bias (MGSB), a regime-aware architecture combining regime-conditioned feature fusion, a TT-RoughPath encoder, and Mean-Teacher consistency regularization to improve robustness under distribution shift. Under leave-one-group-out evaluation, MGSB achieves a detection F1 of 0.930 and an OOD F1 of 0.783, substantially outperforming CNN-LSTM and fully connected baselines under severe feature corruption. Ablations show the proposed architecture, not the training procedure, is the primary contributor to OOD robustness, while Mahalanobis-distance analysis confirms the held-out conditions are genuinely out-of-distribution. These results show that explicit regime-aware modelling is a practical path toward robust, sensor-agnostic leak detection in industrial multiphase pipelines.

When a language model fails on surface-perturbed input (typos, OCR noise, homophones), "which layer is responsible" has three natural operationalizations: where representations diverge most (sensitivity), where restoring clean activations recovers the prediction (causality), and where a small adapter can repair the damage (compensatory capacity) - and we show these three layer maps dissociate. Across a five-model panel we identify two propagation regimes - spike-and-suppress (Phi-3.5, Gemma-2-9B) and late-accumulation (Llama-3, Mistral, Qwen2.5-7B) - and on the two models meeting an 80% identity-patch gate, sensitivity and causality are anti-correlated (rho = -0.72 to -0.88). Within-family scaling on Qwen2.5 (1.5B to 14B) shows the late-accumulation signature strengthening monotonically with scale, corroborated on a second family. We propose cascade disruption as the mechanism behind the dissociation: adapters placed at causally implicated early layers break intact downstream computation, making diagnostic-flagged sites the worst adapter placements. A fixed-harness layer sweep across four models (3.8-8B) confirms the core prediction on chain-of-thought GSM8K - the flagged sites are the most damaging adapter windows on every adjudicable model - and is sign-consistent but strongly attenuated on a multiple-choice control, consistent with damage that compounds with generation length. The sweep yields practical guidance: a training-free LRD pre-screen and a default-deepest placement rule, though absolute gains over no-adapter baselines remain small. Finally, apparent gains from a representation-stability loss reverse under an adequate generation budget - truncated chain-of-thought had been scored as empty - a methodological warning for any intervention evaluated on chain-of-thought tasks.

The standard check for contamination in LLM backtests is simple: compare scores before and after the training cutoff. We show this check is uninformative. Four flagship models fail it on questions they cannot have memorized: every scored question resolved after their cutoffs. The reason is structural. Models legitimately know more about times near their cutoff, so recency mimics leakage, and we prove no passive backtest can separate the two from genuine skill. Measurement, not just detection, requires information from outside the backtest. We supply it in two forms. A known cutoff identifies leakage at the boundary; a matched clean control identifies it globally and yields a leakage-adjusted score. We also derive where leakage hides: it concentrates on outcomes that surprised the crowd and were well covered in training, and partial memorization is disproportionately rewarded. We validate the estimators against ground truth by planting leakage in twin models, where they recover the injected dose and return null on clean questions. Deployed on frontier models, they detect one cutoff-localized signature and, at the audit's power floor, clear five models whose apparent advantages were recency alone. Backtests need not be discarded; they need one defensible reference.

Accurate fault location is critical for distribution network reliability. However, increasing distributed energy resource (DER) penetration complicates fault location due to intermittent generation and bidirectional power flows that reshape fault signatures. Spatio-Temporal Graph Neural Networks (STGNNs) have shown promise by jointly modeling spatial and temporal dependencies, but their behavior under increasing DER penetration has not been studied rigorously. In this paper, we (i) systematically benchmark spatio-temporal graph attention network (STGATv2) against purely temporal (gated recurrent unit, GRU), purely spatial (GATv2) and traditional machine learning baselines, and (ii) evaluate how well models generalize across increasing DER penetration levels (10%, 25%, 50%) on a reconfigured IEEE 123-bus feeder with multiple DER injection points and moderate-to-high impedance faults. Results show that STGATv2 consistently outperforms neural baselines, achieving 92-94% macro F1 in-distribution. Notably, generalization across penetration levels is asymmetric: training at 50% penetration retains near in-distribution F1 score at lower levels, whereas training at 10% degrades considerably at 50% - with STGATv2 retaining 81-84% F1 under these drastic shifts, substantially higher than GATv2 and GRU which drop to 69-74% F1 and 73-75% F1 respectively. Under realistic measurement noise, STGATv2 maintains > 85% F1, while GRU drops as low as 33.5% F1, highlighting the critical role of topological awareness for robust fault location in active distribution networks.

Transformer adaptation is typically distributed across model depth, even when the intended change is narrow. We investigate how adaptation site shapes what a model learns, how well that learning generalizes, and how selectively it is applied. We introduce a controlled benchmark spanning five objectives (lexical binding, factual association, behavioral policy learning, causal mapping, and procedural reasoning) and define each objective's "adaptation geometry" as its profile of acquisition, transfer, and boundedness under full-stack and early-, middle-, or late-layer LoRA. The objectives exhibit distinct geometries. Lexical binding favors early-layer adaptation for acquisition and boundedness but requires broader updates for transfer; factual association favors later layers among localized adapters; behavioral learning separates late-layer action acquisition from middle-layer policy gating; and causal and procedural transfer benefit most from middle- or full-stack adaptation. These patterns largely persist under parameter-matched controls, and most corresponding directional contrasts replicate across five model families. These findings establish adaptation site as a key design variable for controlling what models learn, generalize, and leave unchanged.

The rapid advancement of generative models has spurred the critical need to evaluate the worst-case robustness of deepfake detectors. In this paper, we reveal a fundamental blind spot in current forensic paradigms: while existing detectors excel at capturing digital synthesis artifacts, their effectiveness drops drastically when AI-generated content is cloaked in authentic physical imaging characteristics. We posit that genuine photographs inherently possess hardware-intrinsic statistical signatures, which are imperceptible footprints imprinted by optical sensors and Image Signal Processing (ISP) pipelines, and are fundamentally absent in purely data-driven generative models. Driven by this insight, we propose ISPCloak, a novel optimization-free adversarial attack framework that explicitly weaponizes the ISP pipeline to mislead the judgment of deepfake detectors. Rather than relying on computationally expensive gradient perturbations, our method first employs an Invertible ISP network to project images into the RAW domain. Then, we seamlessly imprint the complex statistical priors of real cameras onto AI-generated images by injecting realistic Poisson-Gaussian sensor noise and conducting forward ISP reconstruction. Synergized with generative artifact suppression and adaptive masking, this streamlined physical simulation enables ultra-fast generation of adversarial examples. Extensive experiments show that embedding authentic physical perturbations fundamentally disrupts a broad range of current detection mechanisms, yielding universally evasive adversarial examples with imperceptible visual alterations.

Algebraic statistics characterizes statistical models through polynomial constraints, but it has mainly been used for analytically specified model classes. This paper studies the inverse problem: identifying probabilistic structure from vanishing binomials observed in empirical probability tensors. We treat the vanishing binomials of a toric model as its algebraic signature, and turn the ideal-variety correspondence of algebraic statistics into an operational procedure for structural learning that identifies a model by signature matching without parameter estimation. By restricting attention to a computationally tractable class of configuration matrices, which we call {\it the Kronecker-stack class}, we make these signatures explicitly enumerable. Within this class we define minimum invariant constraint (MIC) as the atomic unit characterizing each signature and generalizing the notion of independence. We tested this approach employing MICs on synthetic data as well as on corpus-scale real language data. The results suggested the utility of the method, revealing that the identified rank-one structures correspond to interpretable sets of words. These results open up a new avenue for applying algebraic statistics to computational linguistics.

TabPFN is a transformer-based foundation model for tabular prediction that performs inference without task-specific training by conditioning on a support set and query inputs. Despite its strong empirical performance, its internal behavior on structurally difficult tabular geometries remains poorly understood. We study this behavior using zigzag persistent homology, treating TabPFN layer representations as evolving point clouds. We construct a controlled benchmark of synthetic tabular tasks with known true probabilities and varied intrinsic topology, including warped circles, tori, spheres, Hopf links, trefoil knots, and Swiss rolls. Across these tasks, we find that the topology of TabPFN's internal representation geometry is strongly associated with dataset-level reliability; for example, the zeroth homology group $H_0$ fragmentation count correlates positively with mean absolute residual across controlled tasks, and this association strengthens in a high-resolution warped circle case study at large sample size. Harder geometries induce a dual topological signature: increased $H_1$ loop activity and increased $H_0$ fragmentation, while the $H_1$ persistence becomes shorter-lived. These descriptors correlate with Bayes error, mean absolute residuals, and overconfidence. Our results suggest that zigzag persistence diagnoses the reliability of the inferred in-context task geometry and provides a context-level view of when TabPFN operates in topologically stressed regimes.

Malware poses a critical and ever-evolving threat, and robust and effective systems for detecting and classifying malware are of essential importance. $n$-grams features are among the common static features used in effective machine learning systems for malware, but these features are inherently brittle. We propose an algorithm for constructing more robust features, hamm-grams, which are a special class of regular expressions having a fixed length and single-character wildcards. We devise an efficient algorithm for finding common hamm-grams using a new locality-sensitive hash designed to produce collisions among pairs of small Hamming distance and a clustering within hash buckets to place wildcards. We then demonstrate the advantages of these features in malware classification and detection tasks.

Singular learning theory characterises the complexity of a deep network through the geometry of its loss singularities. The local learning coefficient (LLC), the standard estimator of Watanabe's real log canonical threshold (RLCT, $λ$), reads this geometry as an integrated Bayesian scalar through SGLD, which needs per-task calibration and $10^4$-$10^6$ forward-backward passes per checkpoint. We introduce Dead-Direction Signatures (DDS), a family of cheap closed-form spectral readings of singular structure: each reads a network's activation matrix or per-sample-gradient Fisher-Gram at a chosen layer, replacing the SGLD posterior chain with spectral linear algebra. The readings rest on a dead-direction framework that predicts a structural correlation between activation- and Fisher-side spectra at any singular minimum, and a rank-multiplicative volume identity that single-eigenvalue monitors cannot produce: the active-volume $\log\det^{+}(G)$ slope counts the dead directions, tracking the rank-deficit $r$ across $r \in \{1,2,3,4\}$ (slope ratios $2.0, 3.1, 4.0$ at $r{=}2,3,4$ against the predicted $2,3,4$), where the smallest eigenvalue is rank-blind. On reduced-rank regression with closed-form $λ$, calibrated LLC recovers $λ$ at $99\%$ mean and the DDS observables rank-track it at the framework-predicted sign; on a non-linear modular-addition transformer DDS separates $d_{\mathrm{model}}$ across eighteen orders of magnitude where calibrated LLC at the protocol budget is rank-flat. Complementary to LLC's integrated posterior reading, DDS gives a directional, layer-local handle on a network's dead directions, read in closed form from its activation and gradient spectra.

Offline handwritten signature verification aims to distinguish genuine from forged signatures using static images. Since real forgeries are rarely available, negative samples are usually randomly drawn from genuine signatures of other users to create training data. However, this random selection often lacks diversity, increases redundancy, and escalates computational cost, leading to inefficient training. We propose a data-driven strategy to generate diverse, informative negative samples using prototypical signatures, which are compact, non-identifiable summaries of genuine signature features. Based on the experiments results, we conclude that (i) prototypical signatures yield more informative negative samples, improving the detection of skilled forgeries; (ii) the proposed approach is backbone-agnostic, showing robustness across architectures; and (iii) when combined with a primal-form linear SVM, it serves as an alternative to RBF-based models while significantly improving scalability and computational efficiency. Implementation of the method is available at https://github.com/kdmoura/proto_hsv.

When distributed agents exchange text across organizational boundaries, privacy leakage arises not only from explicit identifiers but also from distributional signatures such as formatting conventions, vocabulary choices, and syntactic patterns. We propose DiSan(Disentangled Sanitization), a privacy-preserving sanitization framework and a built-in component of Intern-Shannon for multi-agent collaboration. DiSan uses a two-stream encoder to factorize text into a source-invariant role subspace that preserves task semantics and a source-identifying style subspace that remains local. Federated proto-type alignment and adversarial regularization enable joint training without centralizing raw text. Experiments show that identifier-level masking is insufficient: masking 19.2% of tokens reduces TF-IDF stylometric attribution by only 18.6%. By contrast, DiSan reduces answer-level PII exposure by 20 times while maintaining 83% answer faithfulness on a distributed multi-agent RAG benchmark, and lowers Enron stylometric attribution by 73.2% under TF-IDF and 70.6% under a neural probe.

This short paper introduces a stylometric interpretation method inspired by genome-wide association studies (GWAS). Each "gene" token's association with "phenotype" authorship is tested using logistic regression with multiple-comparison correction. Applied to English, German, and Russian corpora, the method detects statistically significant lexical markers distinctive of individual authors.

Self-supervised learning (SSL) yields powerful, context-rich representations for speech emotion recognition (SER), yet aggregating these representations into holistic descriptors remains a bottleneck. Conventional first-order aggregation implicitly assumes feature independence, which overlooks the latent Riemannian geometry and discards higher-order relationships essential to the representational power of the backbone. To address this problem, this paper proposes a novel Second-Order Correlation (SOC) layer. Instead of treating features in isolation, SOC models feature correlations as covariance descriptors to capture synergistic co-occurrence patterns, which serve as discriminative signatures for robust emotion recognition. By mapping these descriptors from the Riemannian manifold to a Euclidean tangent space through Log-Euclidean mapping (LEM), the proposed method preserves geometric integrity while enabling direct linear discriminative learning. Extensive experiments on the ESD and RAVDESS datasets demonstrate that SOC recovers discriminative information lost in first-order pooling and effectively aggregates high-dimensional SSL features.

When post-trained language models fail on reasoning problems, the common test-time-scaling response is to spend more compute on additional attempts, and the failed traces play no further role. We argue this discards a crucial signal; some failures come from unlucky sampling, where more rollouts help, while others are structural and resist resampling regardless of budget. We propose that failed traces encode recoverability structure: the inference-time signature of which test-time interventions can rescue a given failure. Three problem-level trajectory features, derived from the structure of available interventions, recover this structure from the distributional signature of failed rollouts, not their text. They cluster failures into stable regimes, characterize the failure topography of different post-training methods ($84.3{\pm}4.3\%$ accuracy, $+20\%$ over a majority-class baseline), and support a training-free routing rule that lifts rescue by $+12.2\%$ on the deployment-relevant Steerable-Hard subset (failures where retry is insufficient and a bounded intervention is reachable). The features and the routing rule transfer across two cross-family probes. The same three features thus convert failed traces from discarded data into a diagnostic object, supporting test-time routing and post-training analysis without training-time or weight-space access.

We study risk-neutral control in Markov decision processes with an absorbing catastrophic state. Even though rewards are linear and the agent has no utility curvature, probability weighting, or framing dependence, standard Bellman optimality produces three prospect-theory-like signatures: an S-shaped value-function profile (convex near catastrophe, concave in the far field), an endogenous loss-sensitivity coefficient $λ^*(S) > 1$, and a reflection-effect policy reversal. Across 495 configurations, the optimal policy plays safe near catastrophe in positive-drift (growth) regimes despite the risky action's higher immediate expected value, and plays risky near catastrophe in negative-drift (decline) regimes despite the safe action's lower immediate expected loss. We derive a closed-form expression for the asymptotic loss-aversion plateau $\barλ$ that depends only on win probability $p$, payoff asymmetry $r = |Δ_\ell/Δ_w|$, and discount factor $β$, and matches numerical solutions to $R^2 = 0.999$. The mechanism does not require asymmetric payoffs. Across a sweep of $(p,β)$ at three asymmetry levels, the asymmetry share of $\barλ$ above unity has median 4.6% at $r = 1.25$ and rises to 13.9% at $r = 2$, with the boundary contribution exceeding the asymmetry contribution in every cell tested. The phenomena persist under tabular Q-learning (a model-free agent reproduces $V^*$ at correlation 0.98 in growth and 1.00 in decline) and under stochastic transitions with Gaussian, heavy-tailed Student-$t_3$, and asymmetric skew-normal noise up to 50% of the step size, where the asymptotic plateau tracks the closed-form prediction within 0.41% for safe-channel noise and within 9.6% for risky-channel or both-channel noise. These results identify absorbing failure states as a sufficient structural mechanism for prospect-theory-like behavior under optimal control.

Mechanistic interpretability often assumes that probes identifying a representational signature also identify the circuit executing the corresponding computation. We show that this assumption can fail systematically in Mamba-2. Studying the state sink (disproportionate Delta-gate activation on boundary tokens, analogous to the attention sink), we find that single-bucket probes recover only a small execution layer while missing a much larger detection layer with the same representational signature. In Mamba-2, the state sink decomposes into two functional head sets. Single-bucket BOS-specialist heads (about 5% of heads at 2.7B) causally support both BOS-context and newline-target predictions across model scales and corpora. Dual heads (27-35% of heads, recovered by multi-class aggregation of the same probe) show stronger BOS-newline representational similarity but substantially weaker causal effects under ablation. Representational similarity does not imply functional equivalence. This distinction matters for downstream behaviour: ablating BOS-specialist heads collapses RULER NIAH retrieval accuracy from 1.00 to 0.00 at 1024 context length in both Mamba-1 2.8B and Mamba-2 2.7B, while size-matched complements preserve baseline performance. A random channel-bucketing control rules out substrate granularity alone, implicating Mamba-2's head-shared Delta projection. Probe-derived specialty can identify execution circuits; at coarse granularity the same probe also recovers detection circuits, and separating them requires class-conditional ablation rather than class-conditional cosine.

Watermarking embeds statistical signatures in AI-generated text for detection and attribution. We reveal a fundamental vulnerability: when users access multiple models (today's reality), watermarks trivially fail. Watermarks perturb output distributions away from the original, and in competitive markets, these perturbations are typically independent across providers. We theoretically prove that averaging output probability distributions recovers the unwatermarked distribution with up to a second-order error term. Empirically, simply averaging 3-5 models cancels out these perturbations. We introduce WASH (Watermark Attenuation via Statistical Hybridisation), which solves practical challenges in ensemble generation: vocabulary misalignment and tokenisation differences across heterogeneous models. Experiments across six watermarking schemes and three LLMs show that averaging across 3 models suppresses detection z-scores from 5-300 to below 2 (below the detection threshold of 4) and reduces TPR at 5% FPR to below 50%, while improving quality by 27.5% and running 6 times faster than the best baseline on the long sequence generation. Our results suggest that robust AI-text detection via watermarking requires either accepting this fundamental vulnerability or unprecedented coordination among model providers.

Hyperdimensional (HD) computing offers an attractive alternative to deep networks for edge learning due to its simplicity, fast prototype-based inference, and compatibility with online updates. However, standard pixel-based HD encoders are brittle: small distribution shifts such as rotation, noise, or occlusion can drastically reduce accuracy. We extract discrete topological primitives-most notably holes-from binarized shapes and pair them with rotation/translation/scale (RTS)-invariant shape signatures. Our method constructs RTS-stable descriptors for (i) the outer shape using a spatial-pyramid variant of Zernike moments and (ii) each hole using an intrinsic Fourier descriptor of its radial signature together with RTS-canonical relative geometry. Each primitive is mapped to a bipolar hypervector via randomized projection and role binding, and variable-cardinality hole sets are aggregated by permutation-invariant bundling to form a single image hypervector. To avoid over-weighting any cue, we learn nonnegative reliability weights for the Zernike and hole channels on a validation set via late fusion of cosine similarities. Experiments on MNIST and EMNIST under controlled corruptions (rotation, Gaussian noise, salt-and-pepper, cutout, zoom) show that Topology-guided HD computing substantially improves robustness compared with a naive HD baseline, maintaining high accuracy across multiple corruption families and benefiting from lightweight online training. Compared with a compact CNN trained on clean data, our method achieves competitive clean accuracy while offering markedly stronger robustness to several pixel-level corruptions, demonstrating that explicit topological structure is a practical route to robust HD representations. The code is provided at https://github.com/arpan-kusari/Topological-HDC.

In this study, we tackle Generalized Category Discovery (GCD) via a Relational Retrieval perspective, explicitly coupling labeled and unlabeled data through bidirectional knowledge transfer. While existing methods treat these sources separately, missing valuable interaction opportunities, we propose Relational Pattern Consistency (RPC) that enables mutual enhancement. RPC employs One-vs-All classifiers for soft ID/OOD decomposition, then introduces two mechanisms: (i) for known-class preservation, we transfer semantic behavioral alignment; (ii) for category discovery, we leverage the insight that samples from the same category maintain invariant relationships with known-class prototypes, transforming unreliable pseudo-labeling into well-defined relational pattern matching. This bidirectional design allows labeled data to guide unlabeled learning while discovering novel categories through their collective relational signatures. Extensive experiments demonstrate RPC achieves state-of-the-art performance on both generic and fine-grained benchmarks.

In the mid-twentieth century, mathematician and polymath John von Neumann created a computational system on an array of cells as a simple model of the human brain, where each cell had one of a finite set of roles or states that he predicted would be modelled by a diffusion process. In this work, we show that such a system, when developed in a modern deep learning setting, enables the construction of an artificial neuron having specialized roles that can be learnt. We refer to this neuron as the Von Neumann neuron, and the resulting neural network from such neurons result in a self-engineered design whose architecture is only dependent on the structure and locations of its inputs and outputs on this cellular array. The mathematical framework for these Von Neumann Networks (VNNs) is also constructed and shows that they are based on the extension of neural operators and the learning of Green's functions with convolutions on a cellular topology having a diffusion signature. We also prove that these VNNs are part of a more general computational system called Cellular Machines that are computationally universal. Initial experiments show that VNN based multi-layered perceptrons outperform their equivalent deep learning variant on basic tasks, while being more parameter efficient and are capable of learning new types of tasks. This includes the ability to solve for and construct an extension of the Von Neumann (hardware) architecture common to all modern computers to cells and suggests new opportunities that could be explored.

In grokking, a model first fits the training data while test accuracy remains low, and only later begins to generalize. We ask whether this transition can be localized from observed training trajectories before the test accuracy rises, and formulate grokking transition localization as a diagnostic problem with an explicit threshold/FPR/lead-time trade-off. Task-dependent observables are summarized as empirical distributions, mapped to Wasserstein/quantile coordinates, and analyzed by Hankel dynamic mode decomposition (DMD); the resulting reconstruction residual, together with spectrum and effective rank, forms the diagnostic output. On held-out modular-addition Transformer runs, the residual achieves AUROC $\approx$ 0.93 for grokking-vs-non-grokking discrimination at the run level; under a fixed sustained-threshold operating rule, true-positive alarms can precede onset, with lead time reported jointly with false-alarm rate and uncertainty intervals. Perturbation experiments show that, in the tested $wd=1$ pool, high-residual windows exhibit about $3\times$ larger short-horizon perturbation deviation than low-residual windows. In a same-data norm-window control, perturbation sensitivity aligns with the residual ordering rather than total-parameter-norm ordering, suggesting that the residual is not merely a total-norm proxy at the window level in the studied $wd=1$ dynamics. Norm signals remain strong run-level regime indicators, and log-probability performs best among the observables tested under the current protocol. We position the residual as a window-level monitoring and localization signal in the studied modular-arithmetic Transformer settings, not a universal early-warning predictor or an intervention rule.

We introduce PLACE (Persistence-Landmark Analytic Classification Engine), a closed-form pipeline for classifying point clouds and graphs through their persistent-homology signatures. Three quantitative guarantees -- a margin-based excess-risk rate, a closed-form descriptor-selection rule, and a per-prediction certificate -- are derived from training labels alone, with no learned weights or held-out calibration. The embedding sums Mitra-Virk single-point coordinate functions over a sparse landmark grid; the closed-form weight rule $w_k^2 \propto (d_{k+1}^2 - d_k^2)/R_k^2$ maximizes the distortion slope in Mitra-Virk's affine certificate under $ν$-coherence. (i) An $O(kR/(Δ\sqrt{m_{\min}}))$ margin bound, driven by class-mean separation $Δ$ and embedding radius $R$, matched in the sample-starved regime $m \lesssim R/Δ$ by a Le Cam minimax lower bound. (ii) The Mahalanobis margin under Ledoit-Wolf-shrunk covariance is the strongest closed-form ranker on a 64-descriptor chemical-graph pool (mean Spearman $ρ= +0.56$ across 11 benchmarks, positive on 10 of 11); the isotropic surrogate $Δ/\sqrt{\ell}$ admits a closed-form selection-consistency rate on the homogeneous protein/social pools. (iii) A training-time-decided certificate, with no per-prediction overhead, in three concrete radii (Pinelis, Gaussian plug-in, and variance-aware Pinelis-Bernstein). Empirically, PLACE is the strongest diagram-based method on Orbit5k and matches the strongest topology-based baseline within statistical noise on MUTAG and COX2; remaining gaps fall into two diagnosable regimes (descriptor blindness on NCI1/NCI109; pool-coverage limits elsewhere). The Pinelis-Bernstein radius fires on 8 of the 12 benchmarks; on MUTAG the empirical and population nearest-centroid rules agree on every one of 940 held-out test predictions, validating the certificate's mechanism.

Training-free AI text detection methods primarily rely on model log-probabilities, achieving strong performance through approaches like Binoculars and DNA-DetectLLM. However, these methods face a fundamental ceiling as models are optimized through RLHF to produce human-like probability distributions. We introduce an alternative detection signal based on character distribution signatures. We provide theoretical foundations showing that AI models, trained on massive domain-balanced corpora, approximate global character patterns while humans exhibit domain-specialized distributions, creating a "Wall of Separation" where human-AI divergence significantly exceeds AI-AI divergence. To enable systematic evaluation, we construct the Models-Domains-Temperatures-Adversarials (MDTA) benchmark comprising 642,274 prompt-aligned samples across 4 models, 5 domains, 3 temperature settings, and 3 adversarial strategies, substantially expanding the HC3 dataset with modern model responses, temperature variation, and adversarial augmentation. We introduce the Letter Distribution Score (LD-Score), demonstrating low correlation (r = 0.08-0.13) with perplexity methods. When integrated with DNA-DetectLLM, Binoculars and FastDetectGPT via a non-linear classifier, LD-Score yields consistent improvements in AUROC and F1, with particularly pronounced gains in specialized domains where vocabulary constraints amplify the detection signal. The MDTA dataset can be accessed at: https://huggingface.co/datasets/nsp909/MDTA.

Graph Contrastive Learning (GCL) has emerged as a prominent framework for unsupervised graph representation learning. However, relying on augmentation design alone to define the invariances learned by GCL can be brittle under structural perturbations. To address this issue, we propose Cheeger--Hodge Contrastive Learning (CHCL), a framework that aligns a perturbation-stable Cheeger--Hodge joint signature across augmented views for robust graph representation learning. The proposed signature combines a Cheeger-inspired connectivity signature derived from the algebraic connectivity $λ_2$ with the low-frequency spectrum of the 1-Hodge Laplacian, thereby capturing both global connectivity and higher-order structural information. By aligning encoder representations with the proposed Cheeger--Hodge joint signature across augmented views, CHCL learns graph embeddings that are robust to local structural perturbations. Extensive experiments on standard benchmarks, transfer settings demonstrate that CHCL consistently improves performance, robustness, and generalization.

Reconstructing 3D Human-Object Interaction from an RGB image is essential for perceptive systems. Yet, this remains challenging as it requires capturing the subtle physical coupling between the body and objects. While current methods rely on sparse, binary contact cues, these fail to model the continuous proximity and dense spatial relationships that characterize natural interactions. We address this limitation via InterFields, a representation that encodes dense, continuous proximity across the entire body and object surfaces. However, inferring these fields from single images is inherently ill-posed. To tackle this, our intuition is that interaction patterns are characteristically structured by the action and object geometry. We capture this structure in LEXIS, a novel discrete manifold of interaction signatures learned via a VQ-VAE. We then develop LEXIS-Flow, a diffusion framework that leverages LEXIS signatures to estimate human and object meshes alongside their InterFields. Notably, these InterFields help in a guided refinement that ensures physically-plausible, proximity-aware reconstructions without requiring post-hoc optimization. Evaluation on Open3DHOI and BEHAVE shows that LEXIS-Flow significantly outperforms existing SotA baselines in reconstruction, contact, and proximity quality. Our approach not only improves generalization but also yields reconstructions perceived as more realistic, moving us closer to holistic 3D scene understanding. Code & models will be public at https://anticdimi.github.io/lexis.

Electroencephalography (EEG) signals have been promising for long-term braking intensity prediction but are prone to various artifacts that limit their reliability. Here, we propose a novel framework that models EEG signals as mixtures of independent blind sources and identifies those strongly correlated with braking action. Our method employs independent component analysis to decompose EEG into different components and combines time-frequency analysis with Pearson correlations to select braking-related components. Furthermore, we utilize hierarchical clustering to group braking-related components into two clusters, each characterized by a distinct spatial pattern. Additionally, these components exhibit trial-invariant temporal patterns and demonstrate stable and common neural signatures of the emergency braking process. Using power features from these components and historical braking data, we predict braking intensity at a 200 ms horizon. Evaluations on the open source dataset (O.D.) and human-in-the-loop simulation (H.S.) show that our method outperforms state-of-the-art approaches, achieving RMSE reductions of 8.0% (O.D.) and 23.8% (H.S.).

Efficient coding theory predicts that biological perceptual systems compress sensory input optimally under resource constraints, with the systematic structure of errors reflecting the geometry of that compression. Here we operationalize this principle using rate-distortion theory (RDT) to characterize how any system - biological or artificial - trades representational fidelity for informational efficiency. Treating stimulus-response behavior as an effective communication channel, we infer rate-distortion (RD) frontiers directly from confusion matrices and summarize each system with three geometric signatures: slope (beta), curvature (kappa), and area under the RD curve (AUC), capturing the marginal cost, abruptness, and overall efficiency of the accuracy-compression trade-off respectively. Applying this framework to human psychophysical data and 18 deep vision models across 12 families of controlled image perturbations at graded severities, we find that both biological and artificial systems follow a common lossy-compression principle but occupy systematically different regions of RD space. Humans exhibit smooth, flexible trade-offs characteristic of near-optimal efficient coding, while deep networks operate in steeper, more brittle regimes even at matched accuracy, with geometry dissociable from performance across training regimes. Critically, behavioral RD signatures track internal representational geometry, evidenced by the behaviorally inferred compression structure correlating with internal representational dissimilarity across all models. These results establish RD geometry as a compact diagnostic of perceptual compression strategy that recovers mechanistically interpretable structure in internal representations from behavioral input alone and extends naturally to the direct characterization of compression geometry in neural population activity.

Persistent entropy is a scalar summary of persistence barcodes widely used to detect regime changes, yet there is no account of when a structural change in a barcode must produce a detectable change in entropy. We establish a model-agnostic theorem supplying such conditions. Treating persistence diagrams as random objects indexed by a control parameter, we identify a dispersion-condensation mechanism in the normalized persistence weights and derive an explicit lower bound on the entropy difference between the two regimes, valid with high probability at finite sample size and insensitive to the absolute scale of bar lifetimes. We also give a procedure for verifying the hypotheses on empirical barcodes. Applied to convolutional networks, the criterion shows that the circular organization of learned filters reported by Gabrielsson and Carlsson emerges through a sharp topological phase transition, and locates its onset: within a few hundred iterations on MNIST, but an order of magnitude later on CIFAR-10. The same criterion detects the Kuramoto synchronization and Vicsek order-disorder transitions.

Online handwritten character recognition leverages stroke order and dynamic features, which generally provide higher accuracy and robustness compared with offline recognition. However, in practical applications, rotational deformations can disrupt the spatial layout of strokes, substantially reducing recognition accuracy. Extracting rotation-invariant features therefore remains a challenging open problem. In this work, we employ the Sliding Window Path Signature (SW-PS) to capture local structural features of characters, and introduce the lightweight Linear Recurrent Units (LRU) as the classifier. The LRU combine the fast incremental processing capability of recurrent neural networks (RNN) with the efficient parallel training of state space models (SSM), while reliably modelling dynamic stroke characteristics. We conducted recognition experiments with random rotation angle up to $\pm 180^{\circ}$ on three subsets of the CASIA-OLHWDB1.1 dataset: digits, English upper letters, and Chinese radicals. The accuracies achieved after ensemble learning were $99.62\%$, $96.67\%$, and $94.33\%$, respectively. Experimental results demonstrate that the proposed SW-PS+LRU framework consistently surpasses competing models in both convergence speed and test accuracy.

We propose Path Signatures Logistic Regression (PSLR), a semi-parametric framework for classifying vector-valued functional data with scalar covariates. Classical functional logistic regression models rely on linear assumptions and fixed basis expansions, which limit flexibility and degrade performance under irregular sampling. PSLR leverages the well-established properties of path signatures - basis-free representation, cross-channel dependency capture, and robustness to sampling irregularity - as an enabling tool. The key novelty, however, lies in two distinctive contributions: (i) a semi-parametric additive structure that preserves interpretable linear effects for scalar covariates, and (ii) a fully data-driven procedure for adaptively selecting the signature truncation order via a penalized empirical risk criterion. This selection mechanism is supported by rigorous non-asymptotic guarantees, including the existence of an optimal truncation order, its consistent estimation from finite samples, convergence rates for the classifier risk, a finite computable search bound, and an error propagation framework that formally quantifies PSLR's robustness under irregular sampling. Experiments on synthetic and real-world datasets demonstrate that PSLR with adaptive order selection consistently outperforms traditional functional classifiers and fixed-order signature baselines in accuracy, robustness, and interpretability. Our results highlight the practical and theoretical value of integrating rough path theory with adaptive model complexity control.

Respiratory activity is a direct and interpretable physiological channel for wearable stress and affective-state recognition, yet many studies emphasize classification accuracy without identifying which respiratory properties separate different states. Using the chest respiratory channel of the WESAD dataset, we analyze 60 s windows under leave-one-subject-out validation and combine two complementary branches: compact raw-signal one-dimensional convolutional neural networks (1D-CNNs) and physically grouped handcrafted respiratory signatures. The primary task is stress versus non-stress detection, while baseline, stress, amusement, and meditation are additionally analyzed in a one-vs-rest setting to reveal state-specific respiratory markers. The feature space is organized into respiratory timing, breath-to-breath variability, waveform statistics, spectral/time-frequency descriptors, and autocorrelation/nonlinear predictability descriptors, with the raw 60 s signal treated as a sixth representation for the CNN branch. We introduce autocorrelation transition lags (Zpm/Zmp) as interpretable markers of respiratory correlation scale and separately evaluate exploratory forecast-error-growth/Lyapunov-like descriptors. In the final CNN refit setting, the raw-signal model achieved the strongest stress-vs-rest performance (accuracy 96.72%, macro-F1 95.30%, MCC 90.61%). In contrast, compact feature models were stronger for baseline (MCC 65.34%), amusement (MCC 35.69%), and especially meditation (MCC 88.65%). Strict nested reanalysis of the auxiliary Top-20 stress search yielded mean MCC=82.29% versus 85.45% originally, indicating modest selection optimism. These results show that CNNs are most useful for the practical stress detector, whereas interpretable respiratory signatures provide stronger and more physiologically transparent state-specific markers for several non-stress conditions.