On the uncertainty principle of neural networks
- URL: http://arxiv.org/abs/2205.01493v1
- Date: Tue, 3 May 2022 13:48:12 GMT
- Title: On the uncertainty principle of neural networks
- Authors: Jun-Jie Zhang, Dong-Xiao Zhang, Jian-Nan Chen, Long-Gang Pang
- Abstract summary: We show that the accuracy-robustness trade-off is an intrinsic property whose underlying mechanism is deeply related to the uncertainty principle in quantum mechanics.
We find that for a neural network to be both accurate and robust, it needs to resolve the features of the two parts $x$ (the inputs) and $Delta$ (the derivatives of the normalized loss function $J$ with respect to $x$)
- Score: 4.014046905033123
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Despite the successes in many fields, it is found that neural networks are
vulnerability and difficult to be both accurate and robust (robust means that
the prediction of the trained network stays unchanged for inputs with
non-random perturbations introduced by adversarial attacks). Various empirical
and analytic studies have suggested that there is more or less a trade-off
between the accuracy and robustness of neural networks. If the trade-off is
inherent, applications based on the neural networks are vulnerable with
untrustworthy predictions. It is then essential to ask whether the trade-off is
an inherent property or not. Here, we show that the accuracy-robustness
trade-off is an intrinsic property whose underlying mechanism is deeply related
to the uncertainty principle in quantum mechanics. We find that for a neural
network to be both accurate and robust, it needs to resolve the features of the
two conjugated parts $x$ (the inputs) and $\Delta$ (the derivatives of the
normalized loss function $J$ with respect to $x$), respectively. Analogous to
the position-momentum conjugation in quantum mechanics, we show that the inputs
and their conjugates cannot be resolved by a neural network simultaneously.
Related papers
- 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) - 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) - 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) - 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) - 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) - 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)
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.