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 Statistical Learning


Can Linear Probes Measure LLM Uncertainty?

arXiv.org Artificial Intelligence

Effective Uncertainty Quantification (UQ) represents a key aspect for reliable deployment of Large Language Models (LLMs) in automated decision-making and beyond. Yet, for LLM generation with multiple choice structure, the state-of-the-art in UQ is still dominated by the naive baseline given by the maximum softmax score. To address this shortcoming, we demonstrate that taking a principled approach via Bayesian statistics leads to improved performance despite leveraging the simplest possible model, namely linear regression. More precisely, we propose to train multiple Bayesian linear models, each predicting the output of a layer given the output of the previous one. Based on the obtained layer-level posterior distributions, we infer the global uncertainty level of the LLM by identifying a sparse combination of distributional features, leading to an efficient UQ scheme. Numerical experiments on various LLMs show consistent improvement over state-of-the-art baselines.


Why Cannot Neural Networks Master Extrapolation? Insights from Physical Laws

arXiv.org Artificial Intelligence

Motivated by the remarkable success of Foundation Models (FMs) in language modeling, there has been growing interest in developing FMs for time series prediction, given the transformative power such models hold for science and engineering. This culminated in significant success of FMs in short-range forecasting settings. However, extrapolation or long-range forecasting remains elusive for FMs, which struggle to outperform even simple baselines. This contrasts with physical laws which have strong extrapolation properties, and raises the question of the fundamental difference between the structure of neural networks and physical laws. In this work, we identify and formalize a fundamental property characterizing the ability of statistical learning models to predict more accurately outside of their training domain, hence explaining performance deterioration for deep learning models in extrapolation settings. In addition to a theoretical analysis, we present empirical results showcasing the implications of this property on current deep learning architectures. Our results not only clarify the root causes of the extrapolation gap but also suggest directions for designing next-generation forecasting models capable of mastering extrapolation.


Hierarchical Generalized Category Discovery for Brain Tumor Classification in Digital Pathology

arXiv.org Artificial Intelligence

Accurate brain tumor classification is critical for intra-operative decision making in neuro-oncological surgery. However, existing approaches are restricted to a fixed set of predefined classes and are therefore unable to capture patterns of tumor types not available during training. Unsupervised learning can extract general-purpose features, but it lacks the ability to incorporate prior knowledge from labelled data, and semi-supervised methods often assume that all potential classes are represented in the labelled data. Generalized Category Discovery (GCD) aims to bridge this gap by categorizing both known and unknown classes within unlabelled data. To reflect the hierarchical structure of brain tumor taxonomies, in this work, we introduce Hierarchical Generalized Category Discovery for Brain Tumor Classification (HGCD-BT), a novel approach that integrates hierarchical clustering with contrastive learning. Our method extends contrastive learning based GCD by incorporating a novel semi-supervised hierarchical clustering loss. We evaluate HGCD-BT on OpenSRH, a dataset of stimulated Raman histology brain tumor images, achieving a +28% improvement in accuracy over state-of-the-art GCD methods for patch-level classification, particularly in identifying previously unseen tumor categories. Furthermore, we demonstrate the generalizability of HGCD-BT on slide-level classification of hematoxylin and eosin stained whole-slide images from the Digital Brain Tumor Atlas, confirming its utility across imaging modalities.


MSCoD: An Enhanced Bayesian Updating Framework with Multi-Scale Information Bottleneck and Cooperative Attention for Structure-Based Drug Design

arXiv.org Artificial Intelligence

Structure-Based Drug Design (SBDD) is a powerful strategy in computational drug discovery, utilizing three-dimensional protein structures to guide the design of molecules with improved binding affinity. However, capturing complex protein-ligand interactions across multiple scales remains challenging, as current methods often overlook the hierarchical organization and intrinsic asymmetry of these interactions. To address these limitations, we propose MSCoD, a novel Bayesian updating-based generative framework for structure-based drug design. In our MSCoD, Multi-Scale Information Bottleneck (MSIB) was developed, which enables semantic compression at multiple abstraction levels for efficient hierarchical feature extraction. Furthermore, a multi-head cooperative attention (MHCA) mechanism was developed, which employs asymmetric protein-to-ligand attention to capture diverse interaction types while addressing the dimensionality disparity between proteins and ligands. Empirical studies showed that MSCoD outperforms state-of-the-art methods on the benchmark dataset. Its real-world applicability is confirmed by case studies on difficult targets like KRAS G12D (7XKJ). Additionally, the MSIB and MHCA modules prove transferable, boosting the performance of GraphDTA on standard drug target affinity prediction benchmarks (Davis and Kiba). The code and data underlying this article are freely available at https://github.com/xulong0826/MSCoD.


Echo Flow Networks

arXiv.org Artificial Intelligence

At the heart of time-series forecasting (TSF) lies a fundamental challenge: how can models efficiently and effectively capture long-range temporal dependencies across ever-growing sequences? While deep learning has brought notable progress, conventional architectures often face a trade-off between computational complexity and their ability to retain accumulative information over extended horizons. Echo State Networks (ESNs), a class of reservoir computing models, have recently regained attention for their exceptional efficiency, offering constant memory usage and per-step training complexity regardless of input length. This makes them particularly attractive for modeling extremely long-term event history in TSF. However, traditional ESNs fall short of state-of-the-art performance due to their limited nonlinear capacity, which constrains both their expressiveness and stability. We introduce Echo Flow Networks (EFNs), a framework composed of a group of extended Echo State Networks (X-ESNs) with MLP readouts, enhanced by our novel Matrix-Gated Composite Random Activation (MCRA), which enables complex, neuron-specific temporal dynamics, significantly expanding the network's representational capacity without compromising computational efficiency. In addition, we propose a dual-stream architecture in which recent input history dynamically selects signature reservoir features from an infinite-horizon memory, leading to improved prediction accuracy and long-term stability. Extensive evaluations on five benchmarks demonstrate that EFNs achieve up to 4x faster training and 3x smaller model size compared to leading methods like PatchTST, reducing forecasting error from 43% to 35%, a 20% relative improvement. One instantiation of our framework, EchoFormer, consistently achieves new state-of-the-art performance across five benchmark datasets: ETTh, ETTm, DMV, Weather, and Air Quality.


Nearest Neighbor Projection Removal Adversarial Training

arXiv.org Artificial Intelligence

Deep neural networks have exhibited impressive performance in image classification tasks but remain vulnerable to adversarial examples. Standard adversarial training enhances robustness but typically fails to explicitly address inter-class feature overlap, a significant contributor to adversarial susceptibility. In this work, we introduce a novel adversarial training framework that actively mitigates inter-class proximity by projecting out inter-class dependencies from adversarial and clean samples in the feature space. Specifically, our approach first identifies the nearest inter-class neighbors for each adversarial sample and subsequently removes projections onto these neighbors to enforce stronger feature separability. Theoretically, we demonstrate that our proposed logits correction reduces the Lipschitz constant of neural networks, thereby lowering the Rademacher complexity, which directly contributes to improved generalization and robustness. Extensive experiments across standard benchmarks including CIF AR-10, CIF AR-100, SVHN, and TinyImagenet show that our method demonstrates strong performance that is competitive with leading adversarial training techniques, highlighting significant achievements in both robust and clean accuracy. Our findings reveal the importance of addressing inter-class feature proximity explicitly to bolster adversarial robustness in DNNs. The code is available in the supplementary material.


UMATO: Bridging Local and Global Structures for Reliable Visual Analytics with Dimensionality Reduction

arXiv.org Artificial Intelligence

Due to the intrinsic complexity of high-dimensional (HD) data, dimensionality reduction (DR) techniques cannot preserve all the structural characteristics of the original data. Therefore, DR techniques focus on preserving either local neighborhood structures (local techniques) or global structures such as pairwise distances between points (global techniques). However, both approaches can mislead analysts to erroneous conclusions about the overall arrangement of manifolds in HD data. For example, local techniques may exaggerate the compactness of individual manifolds, while global techniques may fail to separate clusters that are well-separated in the original space. In this research, we provide a deeper insight into Uniform Manifold Approximation with Two-phase Optimization (UMATO), a DR technique that addresses this problem by effectively capturing local and global structures. UMATO achieves this by dividing the optimization process of UMAP into two phases. In the first phase, it constructs a skeletal layout using representative points, and in the second phase, it projects the remaining points while preserving the regional characteristics. Quantitative experiments validate that UMATO outperforms widely used DR techniques, including UMAP, in terms of global structure preservation, with a slight loss in local structure. We also confirm that UMATO outperforms baseline techniques in terms of scalability and stability against initialization and subsampling, making it more effective for reliable HD data analysis. Finally, we present a case study and a qualitative demonstration that highlight UMATO's effectiveness in generating faithful projections, enhancing the overall reliability of visual analytics using DR.


ReviewGraph: A Knowledge Graph Embedding Based Framework for Review Rating Prediction with Sentiment Features

arXiv.org Artificial Intelligence

In the hospitality industry, understanding the factors that drive customer review ratings is critical for improving guest satisfaction and business performance. This work proposes ReviewGraph for Review Rating Prediction (RRP), a novel framework that transforms textual customer reviews into knowledge graphs by extracting (subject, predicate, object) triples and associating sentiment scores. Using graph embeddings (Node2Vec) and sentiment features, the framework predicts review rating scores through machine learning classifiers. We compare ReviewGraph performance with traditional NLP baselines (such as Bag of Words, TF-IDF, and Word2Vec) and large language models (LLMs), evaluating them in the HotelRec dataset. In comparison to the state of the art literature, our proposed model performs similar to their best performing model but with lower computational cost (without ensemble). While ReviewGraph achieves comparable predictive performance to LLMs and outperforms baselines on agreement-based metrics such as Cohen's Kappa, it offers additional advantages in interpretability, visual exploration, and potential integration into Retrieval-Augmented Generation (RAG) systems. This work highlights the potential of graph-based representations for enhancing review analytics and lays the groundwork for future research integrating advanced graph neural networks and fine-tuned LLM-based extraction methods. We will share ReviewGraph output and platform open-sourced on our GitHub page https://github.com/aaronlifenghan/ReviewGraph


Graph Learning Metallic Glass Discovery from Wikipedia

arXiv.org Artificial Intelligence

Synthesizing new materials efficiently is highly demanded in various research fields. However, this process is usually slow and expensive, especially for metallic glasses, whose formation strongly depends on the optimal combinations of multiple elements to resist crystallization. This constraint renders only several thousands of candidates explored in the vast material space since 1960. Recently, data-driven approaches armed by advanced machine learning techniques provided alternative routes for intelligent materials design. Due to data scarcity and immature material encoding, the conventional tabular data is usually mined by statistical learning algorithms, giving limited model predictability and generalizability. Here, we propose sophisticated data learning from material network representations. The node elements are encoded from the Wikipedia by a language model. Graph neural networks with versatile architectures are designed to serve as recommendation systems to explore hidden relationships among materials. By employing Wikipedia embeddings from different languages, we assess the capability of natural languages in materials design. Our study proposes a new paradigm to harvesting new amorphous materials and beyond with artificial intelligence.


Lightweight Model for Poultry Disease Detection from Fecal Images Using Multi-Color Space Feature Optimization and Machine Learning

arXiv.org Artificial Intelligence

Poultry farming is a vital component of the global food supply chain, yet it remains highly vulnerable to infectious diseases such as coccidiosis, salmonellosis, and Newcastle disease. This study proposes a lightweight machine learning-based approach to detect these diseases by analyzing poultry fecal images. We utilize multi-color space feature extraction (RGB, HSV, LAB) and explore a wide range of color, texture, and shape-based descriptors, including color histograms, local binary patterns (LBP), wavelet transforms, and edge detectors. Through a systematic ablation study and dimensionality reduction using PCA and XGBoost feature selection, we identify a compact global feature set that balances accuracy and computational efficiency. An artificial neural network (ANN) classifier trained on these features achieved 95.85% accuracy while requiring no GPU and only 638 seconds of execution time in Google Colab. Compared to deep learning models such as Xception and MobileNetV3, our proposed model offers comparable accuracy with drastically lower resource usage. This work demonstrates a cost-effective, interpretable, and scalable alternative to deep learning for real-time poultry disease detection in low-resource agricultural settings.