Dimensionality Reduction for Cyberattack Classification: A Comparative Evaluation of PCA and Linear Predictive Coding

Despite the success of convolutional neural networks in image classification tasks and their general application in multi-modal models, their susceptibility to out-of-distribution and adversarial attack samples raises concerns regarding trustworthiness and safety. Among the approaches to tackle such issues, detection methods that analyze the model's intermediate activations to estimate a confidence score are a promising family that evaluates the decision process, relying on a dimensionality reduction step to enable efficient downstream processing of the high-dimensional activations. However, when considering convolutional layers, the dimensionality reduction methods in the literature either lack a mechanism to control the compression/information-loss trade-off or yield large representations. In this paper, we carefully analyze two state-of-the-art detection methods and their dimensionality reductions for convolutional layers and develop a novel reduction method with a controllable high-compression level. We extend these two state-of-the-art detection methods, enabling the usage of any dimensionality reduction, and evaluate their performance on out-of-distribution and adversarial attack detection. Results show that the detection methods with the proposed dimensionality reduction consistently perform better than, or comparable to, the strongest alternative. Furthermore, the proposed method is shown to reduce computation and memory footprints, given that it has the highest compression among the compared methods.

Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this work, we attempt to unveil this mystery by investigating the structures of intermediate features. Motivated by our empirical findings that linear layers mimic the roles of deep layers in nonlinear networks for feature learning, we explore how deep linear networks transform input data into output by investigating the output (i.e., features) of each layer after training in the context of multi-class classification problems. Toward this goal, we first define metrics to measure within-class compression and between-class discrimination of intermediate features, respectively. Through theoretical analysis of these two metrics, we show that the evolution of features follows a simple and quantitative pattern from shallow to deep layers when the input data is nearly orthogonal and the network weights are minimum-norm, balanced, and approximate low-rank: Each layer of the linear network progressively compresses within-class features at a geometric rate and discriminates between-class features at a linear rate with respect to the number of layers that data have passed through. To the best of our knowledge, this is the first quantitative characterization of feature evolution in hierarchical representations of deep linear networks. Empirically, our extensive experiments not only validate our theoretical results numerically but also reveal a similar pattern in deep nonlinear networks which aligns well with recent empirical studies. Moreover, we demonstrate the practical implications of our results in transfer learning. Our code is available at https://github.com/Heimine/PNC_DLN.

Large language and sentence-embedding models provide rich semantic representations, but their high dimensionality poses a challenge for near-term quantum machine learning (QML), where quantum circuits can process only a limited number of input features. We investigate a hybrid quantum-classical pipeline that transforms high-dimensional sentence embeddings into compact representations for variational quantum classification. The workflow combines a pretrained sentence-embedding model, dimensionality reduction, angle encoding, a variational quantum circuit (VQC), and a classical decision layer. We systematically compare principal component analysis (PCA), neighborhood components analysis (NCA), and linear discriminant analysis (LDA), covering both unsupervised and supervised dimensionality reduction. Using the TREC question-classification dataset, we study the relationship between representation dimensionality, information retention, qubit count, and classification performance. Preliminary PCA experiments reveal a strong information bottleneck: reducing 768-dimensional embeddings to 3, 4, 5, and 8 dimensions retains about 8.2%, 10.2%, 11.9%, and 16.4% of the variance, with corresponding classification accuracies of 50.3%, 51.2%, 57.9%, and 63.4%. In contrast, supervised reduction is substantially more efficient. LDA reaches 85.3% accuracy and NCA reaches 83.1% using only 5 dimensions, under a leakage-free cross-validation protocol, compared with 85.1% for a full 384-dimensional classical baseline. These results indicate that supervised dimensionality reduction can preserve task-relevant information far more effectively than variance-based compression, making compact representations a promising route toward practical hybrid quantum-classical NLP models.