Explaining Anomalies with Tensor Networks

• URL: http://arxiv.org/abs/2505.03911v1
• Date: Tue, 06 May 2025 18:35:05 GMT
• Title: Explaining Anomalies with Tensor Networks
• Authors: Hans Hohenfeld, Marius Beuerle, Elie Mounzer,
• Abstract summary: We introduce tree tensor networks for the task of explainable anomaly detection.<n>We show adequate predictive performance compared to several baseline models.<n>We thereby extend the application of tensor networks to a broader class of potential problems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Tensor networks, a class of variational quantum many-body wave functions have attracted considerable research interest across many disciplines, including classical machine learning. Recently, Aizpurua et al. demonstrated explainable anomaly detection with matrix product states on a discrete-valued cyber-security task, using quantum-inspired methods to gain insight into the learned model and detected anomalies. Here, we extend this framework to real-valued data domains. We furthermore introduce tree tensor networks for the task of explainable anomaly detection. We demonstrate these methods with three benchmark problems, show adequate predictive performance compared to several baseline models and both tensor network architectures' ability to explain anomalous samples. We thereby extend the application of tensor networks to a broader class of potential problems and open a pathway for future extensions to more complex tensor network architectures.

Related papers

• Transfer entropy and O-information to detect grokking in tensor network multi-class classification problems [0.6222849132943892]
  We study the training dynamics of Matrix Product State (MPS) classifiers applied to three-class problems.<n>We investigate the phenomenon of grokking, where generalization emerges suddenly after memorization.<n>Our results show that grokking in the fashion MNIST task coincides with a sharp entanglement transition and a peak in redundant information, whereas the overfitted hyper-spectral model retains synergistic, disordered behavior.
  arXiv  Detail & Related papers  (2025-07-31T08:53:04Z)
• No-Free-Lunch Theories for Tensor-Network Machine Learning Models [4.410253346975833]
  We focus on the rigorous formulation of their no-free-lunch theorem -- essential yet notoriously challenging to formalize for specific tensor network machine learning models.<n>We first prove a no-free-lunch theorem for machine learning models based on matrix product states, i.e., the one-dimensional tensor network states.<n>We circumvent the challenging issue of calculating the partition function for two-dimensional Ising model, and prove the no-free-lunch theorem for the case of two-dimensional entangled-pair state.
  arXiv  Detail & Related papers  (2024-12-07T14:41:24Z)
• Towards Scalable and Versatile Weight Space Learning [51.78426981947659]
  This paper introduces the SANE approach to weight-space learning. Our method extends the idea of hyper-representations towards sequential processing of subsets of neural network weights.
  arXiv  Detail & Related papers  (2024-06-14T13:12:07Z)
• Do We Need an Encoder-Decoder to Model Dynamical Systems on Networks? [18.92828441607381]
  We show that embeddings induce a model that fits observations well but simultaneously has incorrect dynamical behaviours. We propose a simple embedding-free alternative based on parametrising two additive vector-field components.
  arXiv  Detail & Related papers  (2023-05-20T12:41:47Z)
• Theory on variational high-dimensional tensor networks [2.0307382542339485]
  We investigate the emergent statistical properties of random high-dimensional-network states and the trainability of tensoral networks. We prove that variational high-dimensional networks suffer from barren plateaus for global loss functions. Our results pave a way for their future theoretical studies and practical applications.
  arXiv  Detail & Related papers  (2023-03-30T15:26:30Z)
• Bayesian Attention Belief Networks [59.183311769616466]
  Attention-based neural networks have achieved state-of-the-art results on a wide range of tasks. This paper introduces Bayesian attention belief networks, which construct a decoder network by modeling unnormalized attention weights. We show that our method outperforms deterministic attention and state-of-the-art attention in accuracy, uncertainty estimation, generalization across domains, and adversarial attacks.
  arXiv  Detail & Related papers  (2021-06-09T17:46:22Z)
• A neural anisotropic view of underspecification in deep learning [60.119023683371736]
  We show that the way neural networks handle the underspecification of problems is highly dependent on the data representation. Our results highlight that understanding the architectural inductive bias in deep learning is fundamental to address the fairness, robustness, and generalization of these systems.
  arXiv  Detail & Related papers  (2021-04-29T14:31:09Z)
• Tensor Networks for Multi-Modal Non-Euclidean Data [24.50116388903113]
  We introduce a novel Multi-Graph Network (MGTN) framework, which leverages on the desirable properties of graphs, tensors and neural networks in a physically meaningful and compact manner. This equips MGTNs with the ability to exploit local information in irregular data sources at a drastically reduced parameter complexity. The benefits of the MGTN framework, especially its ability to avoid overfitting through the inherent low-rank regularization properties of tensor networks, are demonstrated.
  arXiv  Detail & Related papers  (2021-03-27T21:33:46Z)
• Explainable Adversarial Attacks in Deep Neural Networks Using Activation Profiles [69.9674326582747]
  This paper presents a visual framework to investigate neural network models subjected to adversarial examples. We show how observing these elements can quickly pinpoint exploited areas in a model.
  arXiv  Detail & Related papers  (2021-03-18T13:04:21Z)
• Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning [50.24174211654775]
  We present a novel contrastive self-supervised learning framework for anomaly detection on attributed networks. Our framework fully exploits the local information from network data by sampling a novel type of contrastive instance pair. A graph neural network-based contrastive learning model is proposed to learn informative embedding from high-dimensional attributes and local structure.
  arXiv  Detail & Related papers  (2021-02-27T03:17:20Z)
• Understanding Generalization in Deep Learning via Tensor Methods [53.808840694241]
  We advance the understanding of the relations between the network's architecture and its generalizability from the compression perspective. We propose a series of intuitive, data-dependent and easily-measurable properties that tightly characterize the compressibility and generalizability of neural networks.
  arXiv  Detail & Related papers  (2020-01-14T22:26:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.