On the uncertainty principle of neural networks

• URL: http://arxiv.org/abs/2205.01493v4
• Date: Thu, 16 Jan 2025 11:16:40 GMT
• Title: On the uncertainty principle of neural networks
• Authors: Jun-Jie Zhang, Dong-Xiao Zhang, Jian-Nan Chen, Long-Gang Pang, Deyu Meng,
• Abstract summary: We show that neural networks are subject to an uncertainty relation, which manifests as a fundamental limitation in their ability to simultaneously achieve high accuracy and robustness against adversarial attacks.<n>Our findings reveal that the complementarity principle, a cornerstone of quantum physics, applies to neural networks, imposing fundamental limits on their capabilities in simultaneous learning of conjugate features.
• Score: 36.098205818550554
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: In this study, we explore the inherent trade-off between accuracy and robustness in neural networks, drawing an analogy to the uncertainty principle in quantum mechanics. We propose that neural networks are subject to an uncertainty relation, which manifests as a fundamental limitation in their ability to simultaneously achieve high accuracy and robustness against adversarial attacks. Through mathematical proofs and empirical evidence, we demonstrate that this trade-off is a natural consequence of the sharp boundaries formed between different class concepts during training. Our findings reveal that the complementarity principle, a cornerstone of quantum physics, applies to neural networks, imposing fundamental limits on their capabilities in simultaneous learning of conjugate features. Meanwhile, our work suggests that achieving human-level intelligence through a single network architecture or massive datasets alone may be inherently limited. Our work provides new insights into the theoretical foundations of neural network vulnerability and opens up avenues for designing more robust neural network architectures.

Related papers

• Emergent weight morphologies in deep neural networks [0.0]
  We show that training deep neural networks gives rise to emergent weight morphologies independent of the training data. Our work demonstrates emergence in the training of deep neural networks, which impacts the achievable performance of deep neural networks.
  arXiv  Detail & Related papers  (2025-01-09T19:48:51Z)
• Verified Neural Compressed Sensing [58.98637799432153]
  We develop the first (to the best of our knowledge) provably correct neural networks for a precise computational task. We show that for modest problem dimensions (up to 50), we can train neural networks that provably recover a sparse vector from linear and binarized linear measurements. We show that the complexity of the network can be adapted to the problem difficulty and solve problems where traditional compressed sensing methods are not known to provably work.
  arXiv  Detail & Related papers  (2024-05-07T12:20:12Z)
• Quantum-Inspired Analysis of Neural Network Vulnerabilities: The Role of Conjugate Variables in System Attacks [54.565579874913816]
  Neural networks demonstrate inherent vulnerability to small, non-random perturbations, emerging as adversarial attacks. A mathematical congruence manifests between this mechanism and the quantum physics' uncertainty principle, casting light on a hitherto unanticipated interdisciplinarity.
  arXiv  Detail & Related papers  (2024-02-16T02:11:27Z)
• The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning [71.14237199051276]
  We consider classical distribution-agnostic framework and algorithms minimising empirical risks. We show that there is a large family of tasks for which computing and verifying ideal stable and accurate neural networks is extremely challenging.
  arXiv  Detail & Related papers  (2023-09-13T16:33:27Z)
• Addressing caveats of neural persistence with deep graph persistence [54.424983583720675]
  We find that the variance of network weights and spatial concentration of large weights are the main factors that impact neural persistence. We propose an extension of the filtration underlying neural persistence to the whole neural network instead of single layers. This yields our deep graph persistence measure, which implicitly incorporates persistent paths through the network and alleviates variance-related issues.
  arXiv  Detail & Related papers  (2023-07-20T13:34:11Z)
• Semantic Strengthening of Neuro-Symbolic Learning [85.6195120593625]
  Neuro-symbolic approaches typically resort to fuzzy approximations of a probabilistic objective. We show how to compute this efficiently for tractable circuits. We test our approach on three tasks: predicting a minimum-cost path in Warcraft, predicting a minimum-cost perfect matching, and solving Sudoku puzzles.
  arXiv  Detail & Related papers  (2023-02-28T00:04:22Z)
• Certified Invertibility in Neural Networks via Mixed-Integer Programming [16.64960701212292]
  Neural networks are known to be vulnerable to adversarial attacks. There may exist large, meaningful perturbations that do not affect the network's decision. We discuss how our findings can be useful for invertibility certification in transformations between neural networks.
  arXiv  Detail & Related papers  (2023-01-27T15:40:38Z)
• Neural Bayesian Network Understudy [13.28673601999793]
  We show that a neural network can be trained to output conditional probabilities, providing approximately the same functionality as a Bayesian Network. We propose two training strategies that allow encoding the independence relations inferred from a given causal structure into the neural network.
  arXiv  Detail & Related papers  (2022-11-15T15:56:51Z)
• What Can the Neural Tangent Kernel Tell Us About Adversarial Robustness? [0.0]
  We study adversarial examples of trained neural networks through analytical tools afforded by recent theory advances connecting neural networks and kernel methods. We show how NTKs allow to generate adversarial examples in a training-free'' fashion, and demonstrate that they transfer to fool their finite-width neural net counterparts in the lazy'' regime.
  arXiv  Detail & Related papers  (2022-10-11T16:11:48Z)
• Consistency of Neural Networks with Regularization [0.0]
  This paper proposes the general framework of neural networks with regularization and prove its consistency. Two types of activation functions: hyperbolic function(Tanh) and rectified linear unit(ReLU) have been taken into consideration.
  arXiv  Detail & Related papers  (2022-06-22T23:33:39Z)
• Rank Diminishing in Deep Neural Networks [71.03777954670323]
  Rank of neural networks measures information flowing across layers. It is an instance of a key structural condition that applies across broad domains of machine learning. For neural networks, however, the intrinsic mechanism that yields low-rank structures remains vague and unclear.
  arXiv  Detail & Related papers  (2022-06-13T12:03:32Z)
• Searching for the Essence of Adversarial Perturbations [73.96215665913797]
  We show that adversarial perturbations contain human-recognizable information, which is the key conspirator responsible for a neural network's erroneous prediction. This concept of human-recognizable information allows us to explain key features related to adversarial perturbations.
  arXiv  Detail & Related papers  (2022-05-30T18:04:57Z)
• Quasi-orthogonality and intrinsic dimensions as measures of learning and generalisation [55.80128181112308]
  We show that dimensionality and quasi-orthogonality of neural networks' feature space may jointly serve as network's performance discriminants. Our findings suggest important relationships between the networks' final performance and properties of their randomly initialised feature spaces.
  arXiv  Detail & Related papers  (2022-03-30T21:47:32Z)
• The mathematics of adversarial attacks in AI -- Why deep learning is unstable despite the existence of stable neural networks [69.33657875725747]
  We prove that any training procedure based on training neural networks for classification problems with a fixed architecture will yield neural networks that are either inaccurate or unstable (if accurate) The key is that the stable and accurate neural networks must have variable dimensions depending on the input, in particular, variable dimensions is a necessary condition for stability. Our result points towards the paradox that accurate and stable neural networks exist, however, modern algorithms do not compute them.
  arXiv  Detail & Related papers  (2021-09-13T16:19:25Z)
• Non-Singular Adversarial Robustness of Neural Networks [58.731070632586594]
  Adrial robustness has become an emerging challenge for neural network owing to its over-sensitivity to small input perturbations. We formalize the notion of non-singular adversarial robustness for neural networks through the lens of joint perturbations to data inputs as well as model weights.
  arXiv  Detail & Related papers  (2021-02-23T20:59:30Z)
• Learning Connectivity of Neural Networks from a Topological Perspective [80.35103711638548]
  We propose a topological perspective to represent a network into a complete graph for analysis. By assigning learnable parameters to the edges which reflect the magnitude of connections, the learning process can be performed in a differentiable manner. This learning process is compatible with existing networks and owns adaptability to larger search spaces and different tasks.
  arXiv  Detail & Related papers  (2020-08-19T04:53:31Z)
• Bayesian Neural Networks [0.0]
  We show how errors in prediction by neural networks can be obtained in principle, and provide the two favoured methods for characterising these errors. We will also describe how both of these methods have substantial pitfalls when put into practice.
  arXiv  Detail & Related papers  (2020-06-02T09:43:00Z)
• Adversarial Robustness Guarantees for Random Deep Neural Networks [15.68430580530443]
  adversarial examples are incorrectly classified inputs that are extremely close to a correctly classified input. We prove that for any $pge1$, the $ellp$ distance of any given input from the classification boundary scales as one over the square root of the dimension of the input times the $ellp$ norm of the input. The results constitute a fundamental advance in the theoretical understanding of adversarial examples, and open the way to a thorough theoretical characterization of the relation between network architecture and robustness to adversarial perturbations.
  arXiv  Detail & Related papers  (2020-04-13T13:07:26Z)
• A neural network model of perception and reasoning [0.0]
  We show that a simple set of biologically consistent organizing principles confer these capabilities to neuronal networks. We implement these principles in a novel machine learning algorithm, based on concept construction instead of optimization, to design deep neural networks that reason with explainable neuron activity.
  arXiv  Detail & Related papers  (2020-02-26T06:26:04Z)

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.