Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem (1812.05720v2)

Abstract: Classifiers used in the wild, in particular for safety-critical systems, should not only have good generalization properties but also should know when they don't know, in particular make low confidence predictions far away from the training data. We show that ReLU type neural networks which yield a piecewise linear classifier function fail in this regard as they produce almost always high confidence predictions far away from the training data. For bounded domains like images we propose a new robust optimization technique similar to adversarial training which enforces low confidence predictions far away from the training data. We show that this technique is surprisingly effective in reducing the confidence of predictions far away from the training data while maintaining high confidence predictions and test error on the original classification task compared to standard training.

• The paper demonstrates that ReLU networks inherently yield high-confidence predictions on out-of-distribution inputs due to their piecewise affine structure.
• It introduces Adversarial Confidence Enhanced Training (ACET) and Confidence Enhancing Data Augmentation (CEDA) to enforce low confidence on synthetic noise data.
• Experimental results on MNIST, SVHN, CIFAR-10, and CIFAR-100 validate ACET’s effectiveness in reducing false positives and enhancing model robustness.

An Analysis of High-Confidence Predictions in ReLU Networks and Mitigation Techniques

The paper "Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem" addresses a critical issue in neural networks, particularly those utilizing ReLU activations. It explores the propensity of such networks to produce high-confidence predictions on inputs that are significantly different from the training data, posing potential risks in safety-critical applications.

Key Insights and Findings

ReLU networks, due to their architecture, yield a piecewise linear classifier function. The authors highlight that this structure leads to almost invariably high-confidence predictions on inputs outside the training domain, even when there is little to no basis for such confidence. This behavior can be problematic in applications like autonomous driving or medical diagnostics where the system must reliably recognize its limitations.

The theoretical underpinning is detailed through formal theorems and lemmas, characterizing the behavior of ReLU networks in terms of piecewise affine functions. A crucial theoretical result demonstrates that for any input direction, there exists a point at a sufficient distance where the network assigns nearly full confidence to one class, regardless of the data distribution within the training set. This inherent property of ReLU activations is independent of post-hoc methods attempting to calibrate confidence scores.

Proposed Mitigation Approach

To address this issue, the authors propose and evaluate a novel training methodology termed Adversarial Confidence Enhanced Training (ACET). Building on the principles of robust optimization akin to adversarial training, ACET enforces low confidence predictions for synthetic 'noise' inputs that are constructed to lie outside the input distribution. This method is shown to be surprisingly effective in reducing high-confidence erroneous predictions far from the training data while maintaining performance on the original task.

An alternative approach, Confidence Enhancing Data Augmentation (CEDA), involves training the model with additional noise data. While both CEDA and ACET are designed to lower confidence on out-of-distribution inputs, ACET proves superior in handling adversarial noise—synthetic inputs crafted to mislead the network's confidence assessment.

Experimental Evaluation

The paper presents an extensive experimental evaluation spanning various datasets like MNIST, SVHN, CIFAR-10, and CIFAR-100. Models were assessed based on several metrics, including mean maximum confidence (MMC), area under the ROC curve (AUROC), and false positive rates (FPR). Across these metrics, ACET consistently demonstrated enhanced robustness against overconfident out-of-distribution predictions compared to conventional training and CEDA.

Furthermore, a unique aspect of this paper is its investigation into adversarial examples—a domain traditionally focused on small perturbations rather than distant inputs. The results indicate that while ACET does not specifically target adversarial examples, it inadvertently provides some resilience against them, underscoring the broader applicability and utility of the method.

Implications and Future Directions

The findings have significant implications for the deployment of neural networks in real-world applications, highlighting the necessity of having classifiers that can indicate uncertainty when processing unfamiliar inputs. The theoretical results invite further exploration into neural network architectures that inherently avoid the pitfall of high-confidence predictions far from the training data.

In summary, this paper contributes both theoretical insights and practical solutions, fostering advances in developing more reliable AI systems. Future research directions may focus on refining these mitigation techniques and exploring alternative architectures that inherently reduce overconfident predictions without extensive post-training adjustments.