Neural networks often contain polysemantic neurons that respond to multiple, sometimes unrelated, features, complicating mechanistic interpretability. We introduce the Polysemanticity Index (PSI), a null-calibrated metric that quantifies when a neuron's top activations decompose into semantically distinct clusters. PSI multiplies three independently calibrated components: geometric cluster quality (S), alignment to labeled categories (Q), and open-vocabulary semantic distinctness via CLIP (D). On a pretrained ResNet-50 evaluated with Tiny-ImageNet images, PSI identifies neurons whose activation sets split into coherent, nameable prototypes, and reveals strong depth trends: later layers exhibit substantially higher PSI than earlier layers. We validate our approach with robustness checks (varying hyperparameters, random seeds, and cross-encoder text heads), breadth analyses (comparing class-only vs. open-vocabulary concepts), and causal patch-swap interventions. In particular, aligned patch replacements increase target-neuron activation significantly more than non-aligned, random, shuffled-position, or ablate-elsewhere controls. PSI thus offers a principled and practical lever for discovering, quantifying, and studying polysemantic units in neural networks.

Deformable retinal image registration is notoriously difficult due to large homogeneous regions and sparse but critical vascular features, which cause limited gradient signals in standard learning-based frameworks. In this paper, we introduce Gaussian Primitive Optimization (GPO), a novel iterative framework that performs structured message passing to overcome these challenges. After an initial coarse alignment, we extract keypoints at salient anatomical structures (e.g., major vessels) to serve as a minimal set of descriptor-based control nodes (DCN). Each node is modelled as a Gaussian primitive with trainable position, displacement, and radius, thus adapting its spatial influence to local deformation scales. A K-Nearest Neighbors (KNN) Gaussian interpolation then blends and propagates displacement signals from these information-rich nodes to construct a globally coherent displacement field; focusing interpolation on the top (K) neighbors reduces computational overhead while preserving local detail. By strategically anchoring nodes in high-gradient regions, GPO ensures robust gradient flow, mitigating vanishing gradient signal in textureless areas. The framework is optimized end-to-end via a multi-term loss that enforces both keypoint consistency and intensity alignment. Experiments on the FIRE dataset show that GPO reduces the target registration error from 6.2\,px to ~2.4\,px and increases the AUC at 25\,px from 0.770 to 0.938, substantially outperforming existing methods. The source code can be accessed via https://github.com/xintian-99/GPOreg.

This paper investigates false positive constructions: grammatical structures which an LLM hallucinates as distinct constructions but which human introspection does not support. Both a behavioural probing task using contextual embeddings and a meta-linguistic probing task using prompts are included, allowing us to distinguish between implicit and explicit linguistic knowledge. Both methods reveal that models do indeed hallucinate constructions. We then simulate hypothesis testing to determine what would have happened if a linguist had falsely hypothesized that these hallucinated constructions do exist. The high accuracy obtained shows that such false hypotheses would have been overwhelmingly confirmed. This suggests that construction probing methods suffer from a confirmation bias and raises the issue of what unknown and incorrect syntactic knowledge these models also possess.

Regression under uncertainty is fundamental across science and engineering. We present an Anchored Mixture of Experts (Anchor-MoE), a model that handles both probabilistic and point regression. For simplicity, we use a tuned gradient-boosting model to furnish the anchor mean; however, any off-the-shelf point regressor can serve as the anchor. The anchor prediction is projected into a latent space, where a learnable metric-window kernel scores locality and a soft router dispatches each sample to a small set of mixture-density-network experts; the experts produce a heteroscedastic correction and predictive variance. We train by minimizing negative log-likelihood, and on a disjoint calibration split fit a post-hoc linear map on predicted means to improve point accuracy. On the theory side, assuming a Hölder smooth regression function of order~$α$ and fixed Lipschitz partition-of-unity weights with bounded overlap, we show that Anchor-MoE attains the minimax-optimal $L^2$ risk rate $O\!\big(N^{-2α/(2α+d)}\big)$. In addition, the CRPS test generalization gap scales as $\widetilde{O}\!\Big(\sqrt{(\log(Mh)+P+K)/N}\Big)$; it is logarithmic in $Mh$ and scales as the square root in $P$ and $K$. Under bounded-overlap routing, $K$ can be replaced by $k$, and any dependence on a latent dimension is absorbed into $P$. Under uniformly bounded means and variances, an analogous $\widetilde{O}\!\big(\sqrt{(\log(Mh)+P+K)/N}\big)$ scaling holds for the test NLL up to constants. Empirically, across standard UCI regressions, Anchor-MoE consistently matches or surpasses the strong NGBoost baseline in RMSE and NLL; on several datasets it achieves new state-of-the-art probabilistic regression results on our benchmark suite. Code is available at https://github.com/BaozhuoSU/Probabilistic_Regression.

Understanding the factors that shape students' mathematics performance is vital for designing effective educational policies. This study applies explainable artificial intelligence (XAI) techniques to PISA 2018 data to predict math achievement and identify key predictors across ten countries (67,329 students). We tested four models: Multiple Linear Regression (MLR), Random Forest (RF), CATBoost, and Artificial Neural Networks (ANN), using student, family, and school variables. Models were trained on 70% of the data (with 5-fold cross-validation) and tested on 30%, stratified by country. Performance was assessed with R^2 and Mean Absolute Error (MAE). To ensure interpretability, we used feature importance, SHAP values, and decision tree visualizations. Non-linear models, especially RF and ANN, outperformed MLR, with RF balancing accuracy and generalizability. Key predictors included socio-economic status, study time, teacher motivation, and students' attitudes toward mathematics, though their impact varied across countries. Visual diagnostics such as scatterplots of predicted vs actual scores showed RF and CATBoost aligned closely with actual performance. Findings highlight the non-linear and context-dependent nature of achievement and the value of XAI in educational research. This study uncovers cross-national patterns, informs equity-focused reforms, and supports the development of personalized learning strategies.

Traditional neural embeddings represent concepts as points, excelling at similarity but struggling with higher-level reasoning and asymmetric relationships. We introduce a novel paradigm: embedding concepts as linear subspaces. This framework inherently models generality via subspace dimensionality and hierarchy through subspace inclusion. It naturally supports set-theoretic operations like intersection (conjunction), linear sum (disjunction) and orthogonal complements (negations), aligning with classical formal semantics. To enable differentiable learning, we propose a smooth relaxation of orthogonal projection operators, allowing for the learning of both subspace orientation and dimension. Our method achieves state-of-the-art results in reconstruction and link prediction on WordNet. Furthermore, on natural language inference benchmarks, our subspace embeddings surpass bi-encoder baselines, offering an interpretable formulation of entailment that is both geometrically grounded and amenable to logical operations.

Accurate and timely traffic flow forecasting is crucial for intelligent transportation systems. This paper presents a novel deep learning model, the Spatial-Temporal Unified Graph Attention Network (STGAtt). By leveraging a unified graph representation and an attention mechanism, STGAtt effectively captures complex spatial-temporal dependencies. Unlike methods relying on separate spatial and temporal dependency modeling modules, STGAtt directly models correlations within a Spatial-Temporal Unified Graph, dynamically weighing connections across both dimensions. To further enhance its capabilities, STGAtt partitions traffic flow observation signal into neighborhood subsets and employs a novel exchanging mechanism, enabling effective capture of both short-range and long-range correlations. Extensive experiments on the PEMS-BAY and SHMetro datasets demonstrate STGAtt's superior performance compared to state-of-the-art baselines across various prediction horizons. Visualization of attention weights confirms STGAtt's ability to adapt to dynamic traffic patterns and capture long-range dependencies, highlighting its potential for real-world traffic flow forecasting applications.

With the advent of wearable Internet of Things (IoT) devices, remote patient monitoring (RPM) emerged as a promising solution for managing heart failure. However, the heart rate can fluctuate significantly due to various factors, and without correlating it to the patient's actual physical activity, it becomes difficult to assess whether changes are significant. Although Artificial Intelligence (AI) models may enhance the accuracy and contextual understanding of remote heart rate monitoring, the integration of activity data is still rarely addressed. In this paper, we propose a Transformer model combined with a Laplace diffusion technique to model heart rate fluctuations driven by physical activity of the patient. Unlike prior models that treat activity as secondary, our approach conditions the entire modeling process on activity context using specialized embeddings and attention mechanisms to prioritize activity specific historical patents. The model captures both long-term patterns and activity-specific heart rate dynamics by incorporating contextualized embeddings and dedicated encoder. The Transformer model was validated on a real-world dataset collected from 29 patients over a 4-month period. Experimental results show that our model outperforms current state-of-the-art methods, achieving a 43% reduction in mean absolute error compared to the considered baseline models. Moreover, the coefficient of determination R2 is 0.97 indicating the model predicted heart rate is in strong agreement with actual heart rate values. These findings suggest that the proposed model is a practical and effective tool for supporting both healthcare providers and remote patient monitoring systems.

--Graph signal processing has become an essential tool for analyzing data structured on irregular domains. While conventional graph shift operators (GSOs) are effective for certain tasks, they inherently lack flexibility in modeling dependencies between non-adjacent nodes, limiting their ability to represent complex graph structures. T o address this limitation, this paper proposes the unified extended matrix (UEM) framework, which integrates the extended-adjacency matrix and the unified graph representation matrix through parametric design, so as to be able to flexibly adapt to different graph structures and reveal more graph signal information. Theoretical analysis of the UEM is conducted, demonstrating positive semi-definiteness and eigenvalue monotonicity under specific conditions. Then, we propose graph Fourier transform based on UEM (UEM-GFT), which can adaptively tune spectral properties to enhance signal processing performance. Experimental results on synthetic and real-world datasets demonstrate that the UEM-GFT outperforms existing GSO-based methods in anomaly detection tasks, achieving superior performance across varying network topologies. Index T erms --Graph shift operator, unified extended matrix, graph signal processing, graph Fourier transform based on unified extended matrix.

Outlier detection holds significant importance in the realm of data mining, particularly with the growing pervasiveness of data acquisition methods. The ability to identify outliers in data streams is essential for maintaining data quality and detecting faults. However, dealing with data streams presents challenges due to the non-stationary nature of distributions and the ever-increasing data volume. While numerous methods have been proposed to tackle this challenge, a common drawback is the lack of straightforward parameterization in many of them. This article introduces two novel methods: DyCF and DyCG. DyCF leverages the Christoffel function from the theory of approximation and orthogonal polynomials. Conversely, DyCG capitalizes on the growth properties of the Christoffel function, eliminating the need for tuning parameters. Both approaches are firmly rooted in a well-defined algebraic framework, meeting crucial demands for data stream processing, with a specific focus on addressing low-dimensional aspects and maintaining data history without memory cost. A comprehensive comparison between DyCF, DyCG, and state-of-the-art methods is presented, using both synthetic and real industrial data streams. The results show that DyCF outperforms fine-tuning methods, offering superior performance in terms of execution time and memory usage. DyCG performs less well, but has the considerable advantage of requiring no tuning at all.