Quantum Spectral Reasoning: A Non-Neural Architecture for Interpretable Machine Learning

• URL: http://arxiv.org/abs/2508.03170v1
• Date: Tue, 05 Aug 2025 07:16:45 GMT
• Title: Quantum Spectral Reasoning: A Non-Neural Architecture for Interpretable Machine Learning
• Authors: Andrew Kiruluta,
• Abstract summary: We propose a novel machine learning architecture that departs from conventional neural network paradigms.<n>We use quantum spectral methods, specifically Pade approximants and the Lanczos algorithm, for interpretable signal analysis and symbolic reasoning.<n>Our results show that this spectral-symbolic architecture achieves competitive accuracy while maintaining interpretability and data efficiency.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a novel machine learning architecture that departs from conventional neural network paradigms by leveraging quantum spectral methods, specifically Pade approximants and the Lanczos algorithm, for interpretable signal analysis and symbolic reasoning. The core innovation of our approach lies in its ability to transform raw time-domain signals into sparse, physically meaningful spectral representations without the use of backpropagation, high-dimensional embeddings, or data-intensive black-box models. Through rational spectral approximation, the system extracts resonant structures that are then mapped into symbolic predicates via a kernel projection function, enabling logical inference through a rule-based reasoning engine. This architecture bridges mathematical physics, sparse approximation theory, and symbolic artificial intelligence, offering a transparent and physically grounded alternative to deep learning models. We develop the full mathematical formalism underlying each stage of the pipeline, provide a modular algorithmic implementation, and demonstrate the system's effectiveness through comparative evaluations on time-series anomaly detection, symbolic classification, and hybrid reasoning tasks. Our results show that this spectral-symbolic architecture achieves competitive accuracy while maintaining interpretability and data efficiency, suggesting a promising new direction for physically-informed, reasoning-capable machine learning.

Related papers

• Symbolic Neural Ordinary Differential Equations [11.69943926220929]
  We propose a novel learning framework of symbolic continuous-depth neural networks, termed Symbolic Neural Ordinary Differential Equations (SNODEs)<n>Our framework can be further applied to a wide range of scientific problems, such as system bifurcation and control, reconstruction and forecasting, as well as the discovery of new equations.
  arXiv  Detail & Related papers  (2025-03-11T05:38:22Z)
• Circuit-tuning: A Mechanistic Approach for Identifying Parameter Redundancy and Fine-tuning Neural Networks [11.906779308433723]
  We develop an interpretable fine-tuning method for analyzing the mechanism behind learning.<n>We first introduce the concept of node-level intrinsic dimensionality to describe the learning process of a model in a computational graph.<n>Based on our theory, we propose circuit-tuning, a two-stage algorithm that iteratively builds the minimal subgraph for a specific task.
  arXiv  Detail & Related papers  (2025-02-10T02:35:53Z)
• Mechanistic Neural Networks for Scientific Machine Learning [58.99592521721158]
  We present Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential equations as representations. Central to our approach is a novel Relaxed Linear Programming solver (NeuRLP) inspired by a technique that reduces solving linear ODEs to solving linear programs.
  arXiv  Detail & Related papers  (2024-02-20T15:23:24Z)
• Neural Harmonium: An Interpretable Deep Structure for Nonlinear Dynamic System Identification with Application to Audio Processing [4.599180419117645]
  Interpretability helps us understand a model's ability to generalize and reveal its limitations. We introduce a causal interpretable deep structure for modeling dynamic systems. Our proposed model makes use of the harmonic analysis by modeling the system in a time-frequency domain.
  arXiv  Detail & Related papers  (2023-10-10T21:32:15Z)
• Discrete, compositional, and symbolic representations through attractor dynamics [51.20712945239422]
  We introduce a novel neural systems model that integrates attractor dynamics with symbolic representations to model cognitive processes akin to the probabilistic language of thought (PLoT) Our model segments the continuous representational space into discrete basins, with attractor states corresponding to symbolic sequences, that reflect the semanticity and compositionality characteristic of symbolic systems through unsupervised learning, rather than relying on pre-defined primitives. This approach establishes a unified framework that integrates both symbolic and sub-symbolic processing through neural dynamics, a neuroplausible substrate with proven expressivity in AI, offering a more comprehensive model that mirrors the complex duality of cognitive operations
  arXiv  Detail & Related papers  (2023-10-03T05:40:56Z)
• LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoning [73.98142349171552]
  LOGICSEG is a holistic visual semantic that integrates neural inductive learning and logic reasoning with both rich data and symbolic knowledge. During fuzzy logic-based continuous relaxation, logical formulae are grounded onto data and neural computational graphs, hence enabling logic-induced network training. These designs together make LOGICSEG a general and compact neural-logic machine that is readily integrated into existing segmentation models.
  arXiv  Detail & Related papers  (2023-09-24T05:43:19Z)
• A Recursive Bateson-Inspired Model for the Generation of Semantic Formal Concepts from Spatial Sensory Data [77.34726150561087]
  This paper presents a new symbolic-only method for the generation of hierarchical concept structures from complex sensory data. The approach is based on Bateson's notion of difference as the key to the genesis of an idea or a concept. The model is able to produce fairly rich yet human-readable conceptual representations without training.
  arXiv  Detail & Related papers  (2023-07-16T15:59:13Z)
• Spectral Decomposition Representation for Reinforcement Learning [100.0424588013549]
  We propose an alternative spectral method, Spectral Decomposition Representation (SPEDER), that extracts a state-action abstraction from the dynamics without inducing spurious dependence on the data collection policy. A theoretical analysis establishes the sample efficiency of the proposed algorithm in both the online and offline settings. An experimental investigation demonstrates superior performance over current state-of-the-art algorithms across several benchmarks.
  arXiv  Detail & Related papers  (2022-08-19T19:01:30Z)
• Gaussian Process Surrogate Models for Neural Networks [6.8304779077042515]
  In science and engineering, modeling is a methodology used to understand complex systems whose internal processes are opaque. We construct a class of surrogate models for neural networks using Gaussian processes. We demonstrate our approach captures existing phenomena related to the spectral bias of neural networks, and then show that our surrogate models can be used to solve practical problems.
  arXiv  Detail & Related papers  (2022-08-11T20:17:02Z)
• Deep Equilibrium Assisted Block Sparse Coding of Inter-dependent Signals: Application to Hyperspectral Imaging [71.57324258813675]
  A dataset of inter-dependent signals is defined as a matrix whose columns demonstrate strong dependencies. A neural network is employed to act as structure prior and reveal the underlying signal interdependencies. Deep unrolling and Deep equilibrium based algorithms are developed, forming highly interpretable and concise deep-learning-based architectures.
  arXiv  Detail & Related papers  (2022-03-29T21:00:39Z)
• Data Assimilation Networks [1.5545257664210517]
  Data assimilation aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations. We propose a fully data driven deep learning architecture generalizing recurrent Elman networks and data assimilation algorithms. Our architecture achieves comparable performance to EnKF on both the analysis and the propagation of probability density functions of the system state at a given time without using any explicit regularization technique.
  arXiv  Detail & Related papers  (2020-10-19T17:35:36Z)
• Equivalence in Deep Neural Networks via Conjugate Matrix Ensembles [0.0]
  A numerical approach is developed for detecting the equivalence of deep learning architectures. The empirical evidence supports the it phenomenon that difference between spectral densities of neural architectures and corresponding it conjugate circular ensemble are vanishing.
  arXiv  Detail & Related papers  (2020-06-14T12:34:13Z)

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.