ClaudesLens: Uncertainty Quantification in Computer Vision Models

TL;DR

ClaudesLens introduces an entropy-based framework to quantify uncertainty in computer vision models by perturbing network weights with Gaussian noise and analyzing resulting prediction distributions. It formalizes two metrics, the Perturbation Index $\pi_\sigma$ and Perturbation Stability Index $\psi_\sigma$, and computes entropy-conditioned accuracy to connect uncertainty with performance. The method is demonstrated on three model families—Naïve multinomial regression, ConvNeXt, and Vision Transformer—trained on MNIST, revealing that Shannon entropy can capture prediction uncertainty and that sensitivity to perturbations varies by architecture. This approach provides a principled, quantifiable lens for uncertainty in AI systems and suggests a path toward integrating entropy-based uncertainty into future state-of-the-art uncertainty quantification techniques.

Abstract

In a world where more decisions are made using artificial intelligence, it is of utmost importance to ensure these decisions are well-grounded. Neural networks are the modern building blocks for artificial intelligence. Modern neural network-based computer vision models are often used for object classification tasks. Correctly classifying objects with \textit{certainty} has become of great importance in recent times. However, quantifying the inherent \textit{uncertainty} of the output from neural networks is a challenging task. Here we show a possible method to quantify and evaluate the uncertainty of the output of different computer vision models based on Shannon entropy. By adding perturbation of different levels, on different parts, ranging from the input to the parameters of the network, one introduces entropy to the system. By quantifying and evaluating the perturbed models on the proposed PI and PSI metrics, we can conclude that our theoretical framework can grant insight into the uncertainty of predictions of computer vision models. We believe that this theoretical framework can be applied to different applications for neural networks. We believe that Shannon entropy may eventually have a bigger role in the SOTA (State-of-the-art) methods to quantify uncertainty in artificial intelligence. One day we might be able to apply Shannon entropy to our neural systems.

Figures (15)

• Figure 1: A picture of a dog and the same image but perturbed.
• Figure 2: A single neuron with $n$ inputs and one output, showcasing the summation and activation components in a neuron.
• Figure 3: The sigmoid, ReLU, and GELU activation functions and their graphical representations.
• Figure 4: A one-layer neural network with $n$ inputs and $n$ outputs, featuring a hidden layer with $n$ neurons, mathematically represented as $\mathbf{a} = f.(\mathbf{W}_1 \mathbf{x} + \mathbf{b}_1) \rightarrow \mathbf{y} = f.(\mathbf{W}_2 \mathbf{a} + \mathbf b_2)$.
• Figure 5: An image ($4 \times 4 \times 1$) with no padding, convolved by a $(2 \times 2 \times 1)$ kernel with 2 in stride, producing a $(2\times 2)$ feature map.