# Unlocking Feature Visualization for Deeper Networks with MAgnitude Constrained Optimization

arXiv: https://arxiv.org/abs/2306.06805 · HTML: https://mlsanity.com/paper/2306.06805/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 71 references that are in the map.
- First posted on arXiv 11 Jun 2023.

## Builds on (most cited first, 30 of 50)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Understanding Deep Image Representations by Inverting Them](https://mlsanity.com/paper/1412.0035/) (2014)
- [Evaluating Explainable AI: Which Algorithmic Explanations Help Users Predict Model Behavior?](https://mlsanity.com/paper/2005.01831/) (2020)
- [Synthesizing the preferred inputs for neurons in neural networks via deep generator networks](https://mlsanity.com/paper/1605.09304/) (2016)
- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [Formalizing Trust in Artificial Intelligence: Prerequisites, Causes and Goals of Human Trust in AI](https://mlsanity.com/paper/2010.07487/) (2020)
- [FlexiViT: One Model for All Patch Sizes](https://mlsanity.com/paper/2212.08013/) (2022)

## Built on by (most cited first, 27 of 27)

- [Universal Sparse Autoencoders: Interpretable Cross-Model Concept Alignment](https://mlsanity.com/paper/2502.03714/) (2025)
- [Labeling Neural Representations with Inverse Recognition](https://mlsanity.com/paper/2311.13594/) (2023)
- [CoSy: Evaluating Textual Explanations of Neurons](https://mlsanity.com/paper/2405.20331/) (2024)
- [Understanding Visual Feature Reliance through the Lens of Complexity](https://mlsanity.com/paper/2407.06076/) (2024)
- [Better artificial intelligence does not mean better models of biology](https://mlsanity.com/paper/2504.16940/) (2025)
- [Intrinsic User-Centric Interpretability through Global Mixture of Experts](https://mlsanity.com/paper/2402.02933/) (2024)
- [AttributionScanner: A Visual Analytics System for Model Validation with Metadata-Free Slice Finding](https://mlsanity.com/paper/2401.06462/) (2024)
- [Disentangling Polysemantic Channels in Convolutional Neural Networks](https://mlsanity.com/paper/2504.12939/) (2025)
- [Feature Accentuation: Revealing 'What' Features Respond to in Natural Images](https://mlsanity.com/paper/2402.10039/) (2024)
- [Bi-Orthogonal Factor Decomposition for Vision Transformers](https://mlsanity.com/paper/2601.05328/) (2026)
- [Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifolds](https://mlsanity.com/paper/2606.25234/) (2026)
- [Concept-Centric Token Interpretation for Vector-Quantized Generative Models](https://mlsanity.com/paper/2506.00698/) (2025)
- [Manipulating Feature Visualizations with Gradient Slingshots](https://mlsanity.com/paper/2401.06122/) (2024)
- [VITAL: More Understandable Feature Visualization through Distribution Alignment and Relevant Information Flow](https://mlsanity.com/paper/2503.22399/) (2025)
- [Efficient and Flexible Neural Network Training through Layer-wise Feedback Propagation](https://mlsanity.com/paper/2308.12053/) (2023)
- [Ensuring Medical AI Safety: Interpretability-Driven Detection and Mitigation of Spurious Model Behavior and Associated Data](https://mlsanity.com/paper/2501.13818/) (2025)
- [Flow AM: Generating Point Cloud Global Explanations by Latent Alignment](https://mlsanity.com/paper/2404.18760/) (2024)
- [Backdooring CLIP through Concept Confusion](https://mlsanity.com/paper/2503.09095/) (2025)
- [Back to the Baseline: Examining Baseline Effects on Explainability Metrics](https://mlsanity.com/paper/2512.11433/) (2025)
- [A Unifying Framework for Concept-Based Representational Similarity](https://mlsanity.com/paper/2606.09653/) (2026)
- [Understanding Inhibition Through Maximally Tense Images](https://mlsanity.com/paper/2406.05598/) (2024)
- [Stretching Beyond the Obvious: A Gradient-Free Framework to Unveil the Hidden Landscape of Visual Invariance](https://mlsanity.com/paper/2506.17040/) (2025)
- [Semantic Prioritization in Visual Counterfactual Explanations with Weighted Segmentation and Auto-Adaptive Region Selection](https://mlsanity.com/paper/2511.12992/) (2025)
- [Capability neq Interpretability: Human Interpretability of Vision Foundation Models](https://mlsanity.com/paper/2605.20337/) (2026)
- [Interpretability Without Tradeoffs: Disentangling Polysemanticity At Equal Predictive Performance](https://mlsanity.com/paper/2605.31304/) (2026)
- [From Interpretability Methods to Interpretable Models](https://mlsanity.com/paper/2609.05399/) (2026)
- [Discriminative Score Function: Turning Pretrained Models into Functional Generative Priors](https://mlsanity.com/paper/2610.19743/) (2026)

## Abstract (arXiv)

Feature visualization has gained substantial popularity, particularly after the influential work by Olah et al. in 2017, which established it as a crucial tool for explainability. However, its widespread adoption has been limited due to a reliance on tricks to generate interpretable images, and corresponding challenges in scaling it to deeper neural networks. Here, we describe MACO, a simple approach to address these shortcomings. The main idea is to generate images by optimizing the phase spectrum while keeping the magnitude constant to ensure that generated explanations lie in the space of natural images. Our approach yields significantly better results (both qualitatively and quantitatively) and unlocks efficient and interpretable feature visualizations for large state-of-the-art neural networks. We also show that our approach exhibits an attribution mechanism allowing us to augment feature visualizations with spatial importance. We validate our method on a novel benchmark for comparing feature visualization methods, and release its visualizations for all classes of the ImageNet dataset on https://serre-lab.github.io/Lens/. Overall, our approach unlocks, for the first time, feature visualizations for large, state-of-the-art deep neural networks without resorting to any parametric prior image model.