HYDRA: Hyperbolic Dynamic Representation Architecture for Kolmogorov-Arnold Networks

Kolmogorov-Arnold Networks (KANs) enhance nonlinear function approximation by replacing scalar weights with learnable univariate functions. However, assigning an independent function to every connection results in substantial parameter redundancy, limiting their scalability and efficiency. To reduce this redundancy, we introduce \textbf{HY}perbolic \textbf{D}ynamic \textbf{R}epresentation \textbf{A}rchitecture (HYDRA), a parameter-efficient hyperbolic extension of KAN that combines spline-based functional learning with representations in the Poincaré ball. HYDRA maps vector-valued inputs into a bounded hyperbolic latent space, performs KAN-style updates in tangent space, and employs a low-rank prototype block to share functional transformations across hidden dimensions. The resulting hyperbolic representations provide a structured radial coordinate for interpretation, while radius control improves training stability by preventing boundary saturation. Extensive experiments across eight benchmark datasets demonstrate that HYDRA consistently achieves competitive or superior predictive performance while improving parameter efficiency and representation interpretability.

HyperANFIS: Enhancing Rule Representation and Interpretability in Adaptive Neuro-Fuzzy Systems via Hyperbolic Geometry

The adaptive neuro-fuzzy inference system (ANFIS) is an interpretable reasoning framework capable of generating explicit IF-THEN fuzzy rules, making it suitable for tasks requiring transparent reasoning. However, existing ANFIS models generally construct rule antecedents and perform inference in Euclidean space, limiting their representational capacity and predictive performance. To address this issue, we propose Hyperbolic ANFIS (HyperANFIS), a hyperbolic extension of ANFIS. HyperANFIS preserves the fuzzy semantics and core architecture of conventional ANFIS while performing rule-prototype learning, rule activation, and consequent aggregation in hyperbolic space. It also retains the ability to generate interpretable IF-THEN rules. By exploiting the representational properties of hyperbolic geometry, HyperANFIS strengthens the fuzzy inference process, thereby improving predictive accuracy, inter-rule collaboration, and the credibility of its interpretable rules. Experimental results show that HyperANFIS consistently outperforms the standard ANFIS baseline and various ANFIS variants across all datasets, while also generating higher-quality fuzzy rules.

CausalNav: Reliability-Certified Causal World Models for Control under Physical-Parameter Shift

A world model is only useful for physical AI if it changes what the agent does, and only safe if it declines to do so when it is wrong. We study both halves of that requirement with CausalNav, a controller built around a signed, action-conditioned transition graph over identified state coordinates. At deployment CausalNav simulates a small library of intervention sequences, converts their objective error into policy-logit advice, and admits that advice only when a scale-free predictive-reliability certificate, a policy-margin gate, and an argmax-agreement gate all pass; otherwise it falls back exactly to its own model-based base controller. We evaluate against nine controlled baselines (transformer, recurrent, split-latent, graph, causal-induction, and three recent model-based reasoning modules) on CartPole-v1 and discretized Pendulum-v1 with physical-parameter shifts, under one shared PPO trainer, one interaction budget, and ten held-out seeds (200 runs). CausalNav attains the best average rank (1.25 of ten). The diagnostic result is more informative than the ranking: the learned graph recovers structure well above chance (CartPole F1 = 0.59 +/- 0.09), yet per-seed structural fidelity is uncorrelated with per-seed control benefit (r = -0.15, p = 0.67), and the certificate abstains on 10/10 Pendulum seeds, where forcing the planner on costs return. Model fidelity did not predict downstream control utility in our setting; certified abstention, not better prediction, is what made the world model safe to deploy.

When the Judge Should Not Decide: Evidence-Locked, Non-Compensatory Selection Bounds LLM-Judge Failure in Reasoning Pipelines

An LLM judge deployed inside a reasoning pipeline does not merely measure quality, it decides which answer ships. We show that the cost of that decision depends less on judge accuracy than on the decision rule the judge is embedded in. On frozen candidate pools from four GRPO policies, an unconstrained scalar DeepSeek-R1-7B judge buys almost nothing over answer-level majority vote (+1.0 pp on 500 GSM8K questions, +0.34 EM on 300 HotpotQA questions), and on a frozen-rule 30-question confirmation split it is 10 points worse than majority, a judge that destroys accuracy while scoring candidates confidently. We then subordinate the same judge to Evidence-Locked Derive-Gate-Repair (EL-DGR), a task-adaptive non-compensatory rule under which a judge preference may override evidence-supported consensus only with an extractive evidence certificate, and a repair only when neither alternative is certified and the repair is. With no change to the judge, the candidates, or the budget, EL-DGR reaches 58.2% on GSM8K (vs. 56.8% judge, 55.8% majority, 55.4% first candidate) and 17.33 EM / 25.46 F1 on HotpotQA (vs. 15.67/23.49, 15.33/23.19, 15.33/22.97), improving on first-candidate GRPO by +2.8 pp (exact McNemar p=0.0026) and +2.00 EM (p=0.070, borderline). A decision audit shows why: EL-DGR overturns consensus on only 8 of 30 pilot questions and never converts a correct consensus into an incorrect answer. We also report what did not work: the same seven-channel decomposition used as a step-level gated training reward is null, and corrected channel-drop ablations show no channel is individually necessary (p=1.0 throughout). The practitioner-facing finding is negative about judges and positive about admissibility, bound the judge's blast radius rather than trying to make it accurate.

What Transfers Under Source Shift? Definitions, Examples, and Fine-Tuning for Climate Disclosure Classification

Climate disclosure classification is a fundamental task for analysing corporate climate disclosures, yet such disclosures appear in many different sources -- annual reports, press releases, and earnings calls -- that differ in length, purpose, and writing style. Existing evaluations are mostly conducted within a single source, leaving open whether common LLM adaptation strategies remain effective under source shift. We reframe climate disclosure classification as a cross-source adaptation problem and study three widely used adaptation strategies -- definitions, examples, and fine-tuning -- across eleven open- and closed-source LLMs, using two corpora that share the same label space but come from different sources. We find that all strategies bring positive cross-source gains on average, but the strongest in-source strategies are not the strongest cross-source ones: similarity-based retrieval and LoRA fine-tuning gain most in-source but lose most of that advantage under source shift; randomly selected few-shot examples, a weaker in-source baseline, retain their advantage more reliably; definitions transfer most consistently, though only when their granularity matches the target text. Across these strategies, when the source changes, simpler is often safer.

TGHE: Template-based Graph Homomorphic Encryption for Privacy-Preserving GNN Inference in Edge-Cloud Systems

Existing homomorphic encryption (HE)-based GNN systems adopt a graph-centric paradigm that couples per-query cost to global graph size, limiting evaluations to at most ~20k nodes and making them incompatible with dynamic, large-scale financial graphs. We propose TGHE (Template-based Graph Homomorphic Encryption), an ego-centric framework that resolves this by exploiting a template phenomenon: local computation trees in transaction graphs converge into a small set of structural shapes. TGHE canonicalizes ego-graphs at the edge and packs structurally identical trees into shared CKKS ciphertexts for SIMD-parallel encrypted inference, with two long-tail optimizers (Approximate Template Fitting and Topology Collapse) ensuring full SIMD coverage. On DGraphFin (3.7M nodes, 4.3M edges), TGHE-Collapse achieves a 66.9x speedup over the sequential encrypted baseline with less than 0.002 AUC loss.

Beyond Normal References: Discriminative Few-Shot Anomaly Detection

This paper considers a practical few-shot anomaly detection (FSAD) setting, termed discriminative FSAD, where a limited number of both normal and anomalous examples are available as references during inference. Existing FSAD methods rely on normal-only references through normality matching, ignoring the discriminative clues in anomalous references, while directly fitting both references can overfit to the seen anomalies. We introduce IDEAL, an intrinsic deviation learning framework that leverages both reference types to learn intrinsic deviation patterns characterizing generalizable abnormality as deviations from normality. IDEAL decomposes the learning process into two novel components: 1) a Normal Variation Eraser to suppress nuisance normal variations that may lead to noisy deviations from normality, thereby highlighting anomaly-relevant deviation representations; 2) an Intrinsic Deviation Encoder to decompose these denoised deviation representations into intrinsic deviation vectors capturing the most discriminative orthogonal deviation directions. At inference, IDEAL scores query-to-normal deviations preserved after projection onto the learned intrinsic deviation vectors, enabling generalization for both seen and unseen anomalies. Extensive experiments on eight real-world datasets show that IDEAL generalizes effectively to unseen anomalies and consistently outperforms existing state-of-the-art FSAD methods. Code and data will be available at \href{https://github.com/mala-lab/IDEAL}{https://github.com/mala-lab/IDEAL}.

FedHPro: Federated Hyper-Prototype Learning via Gradient Matching

Federated Learning (FL) enables collaborative training of distributed clients while protecting privacy. To enhance generalization capability in FL, prototype-based FL is in the spotlight, since shared global prototypes offer semantic anchors for aligning client-specific local prototypes. However, existing methods update global prototypes at the prototype-level via averaging local prototypes or refining global anchors, which often leads to semantic drift across clients and subsequently yields a misaligned global signal. To alleviate this issue, we introduce hyper-prototypes, defined by a set of learnable global class-wise prototypes to preserve underlying semantic knowledge across clients. The hyper-prototypes are optimized via gradient matching to align with class-relevant characteristics distilled directly from clients' real samples, rather than prototype-level descriptors. We further propose FedHPro, a Federated Hyper-Prototype Learning framework, to leverage hyper-prototypes to promote inter-class separability via mutual-contrastive learning with client-specific margin, while encouraging intra-class uniformity through a consistency penalty. Comprehensive experiments under diverse heterogeneous scenarios confirm that 1) hyper-prototypes produce a more semantically consistent global signal, and 2) FedHPro achieves state-of-the-art performance on several benchmark datasets. Code is available at \href{https://github.com/mala-lab/FedHPro}{https://github.com/mala-lab/FedHPro}.

A Cross-graph Tuning-free GNN Prompting Framework

GNN prompting aims to adapt models across tasks and graphs without requiring extensive retraining. However, most existing graph prompt methods still require task-specific parameter updates and face the issue of generalizing across graphs, limiting their performance and undermining the core promise of prompting. In this work, we introduce a Cross-graph Tuning-free Prompting Framework (CTP), which supports both homogeneous and heterogeneous graphs, can be directly deployed to unseen graphs without further parameter tuning, and thus enables a plug-and-play GNN inference engine. Extensive experiments on few-shot prediction tasks show that, compared to SOTAs, CTP achieves an average accuracy gain of 30.8% and a maximum gain of 54%, confirming its effectiveness and offering a new perspective on graph prompt learning.

Domain-Skewed Federated Learning with Feature Decoupling and Calibration

Federated learning (FL) allows distributed clients to collaboratively train a global model in a privacy-preserving manner. However, one major challenge is domain skew, where clients' data originating from diverse domains may hinder the aggregated global model from learning a consistent representation space, resulting in poor generalizable ability in multiple domains. In this paper, we argue that the domain skew is reflected in the domain-specific biased features of each client, causing the local model's representations to collapse into a narrow low-dimensional subspace. We then propose Federated Feature Decoupling and Calibration ($F^2$DC), which liberates valuable class-relevant information by calibrating the domain-specific biased features, enabling more consistent representations across domains. A novel component, Domain Feature Decoupler (DFD), is first introduced in $F^2$DC to determine the robustness of each feature unit, thereby separating the local features into domain-robust features and domain-related features. A Domain Feature Corrector (DFC) is further proposed to calibrate these domain-related features by explicitly linking discriminative signals, capturing additional class-relevant clues that complement the domain-robust features. Finally, a domain-aware aggregation of the local models is performed to promote consensus among clients. Empirical results on three popular multi-domain datasets demonstrate the effectiveness of the proposed $F^2$DC and the contributions of its two modules. Code is available at https://github.com/mala-lab/F2DC.