Shaping Attacks: How Geometry Reveals Neural Network Weaknesses

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Author: Denis Avetisyan

A new method uses the language of shapes to expose vulnerabilities and interpret the inner workings of deep learning models.

Even with minimal initial structure, a generative model can synthesize shapes that consistently fool image classification networks into confidently identifying specific objects—achieving over 90% success across diverse architectures and the entire ImageNet dataset when complexity increases beyond a threshold of 20, and demonstrating that increasingly detailed, algorithmically-generated forms reliably reinforce semantic understanding within those networks, as evidenced by the monotonic increase in target confidence from 1.14% to 98.86% for a single ice bear shape.
Even with minimal initial structure, a generative model can synthesize shapes that consistently fool image classification networks into confidently identifying specific objects—achieving over 90% success across diverse architectures and the entire ImageNet dataset when complexity increases beyond a threshold of 20, and demonstrating that increasingly detailed, algorithmically-generated forms reliably reinforce semantic understanding within those networks, as evidenced by the monotonic increase in target confidence from 1.14% to 98.86% for a single ice bear shape.

Researchers demonstrate a framework for generating adversarial examples by optimizing object geometry using Fourier series, offering insights into network decision-making.

Despite advances in visual recognition, deep neural networks remain relatively unexplored regarding their understanding of geometric cues. This is addressed in ‘Learning Fourier shapes to probe the geometric world of deep neural networks’, which introduces a framework for directly optimizing object geometry using Fourier series to generate potent semantic carriers, high-fidelity interpretability tools, and a novel adversarial paradigm. By unifying differentiable graphics with DNN optimization, this work demonstrates that shape alone can drive high-confidence classifications and reveal salient model regions. Could this approach unlock a more robust and interpretable machine perception, bridging the gap between how networks and humans ‘see’ the world?

Fragile Visions: The Limits of Deep Learning

Deep Neural Networks (DNNs) achieve remarkable success in image recognition, yet remain surprisingly vulnerable to adversarial attacks. These attacks, often imperceptible, reveal a fundamental fragility in how networks ‘understand’ visual information, extending beyond misclassification to include confidently identifying nonexistent objects or failing to detect present ones.

Current DNNs primarily detect texture and shape correlations, lacking a robust understanding of underlying visual forms. This reliance on surface-level features easily fools them. Despite advances in object detection frameworks like YOLOv3 and RetinaNet, they struggle with perturbations preserving semantic content while altering pixel values.

By optimizing adversarial shapes represented as Fourier coefficients, the study demonstrates a generalizable attack paradigm for object detection, successfully reducing detection confidence to 15.9% compared to 93.2%-94.9% with simple geometric occlusions.
By optimizing adversarial shapes represented as Fourier coefficients, the study demonstrates a generalizable attack paradigm for object detection, successfully reducing detection confidence to 15.9% compared to 93.2%-94.9% with simple geometric occlusions.

The pursuit of perfect machine vision reveals a simple truth: architecture isn’t a diagram, it’s a compromise.

Fourier’s Revenge: Shaping Adversarial Attacks

Learnable Fourier Shapes represents and manipulates image shapes using Fourier Series, offering a mathematically rigorous framework for shape control. This addresses limitations of prior techniques by operating in the frequency domain, enabling precise shape manipulation. The innovation lies in establishing a differentiable mapping between Fourier coefficients and pixel space via the Winding Number Theorem.

This differentiability enables gradient-based optimization of shape parameters, integrating seamlessly with DNNs for end-to-end training. Incorporating Signal Energy Theory ensures generated shapes are physically plausible, avoiding undesirable high-frequency artifacts.

Through a differentiable shape learning pipeline, the research enables three experimental frameworks—class-specific shape generation, shape-based interpretability, and a generalizable adversarial paradigm—demonstrating the capability of shapes to both represent semantics and manipulate model predictions.
Through a differentiable shape learning pipeline, the research enables three experimental frameworks—class-specific shape generation, shape-based interpretability, and a generalizable adversarial paradigm—demonstrating the capability of shapes to both represent semantics and manipulate model predictions.

The research extends adversarial attacks by targeting the fundamental shape representation learned by the DNN, enabling robust and targeted attacks, and developing shape-based defenses.

Probing the Void: Shape-Based Attacks and Interpretability

Experiments using ResNet-50 demonstrate the efficacy of Learnable Fourier Shapes in generating visually plausible adversarial examples that consistently induce misclassification. Analysis reveals these examples challenge interpretability techniques; saliency maps often fail to highlight introduced shapes, suggesting the model relies on features unrelated to discernible form.

This method extends beyond image classification to object detection tasks like FCOS. Using only generated Fourier shapes, a classification accuracy exceeding 90% is achieved across diverse ImageNet classes and architectures, underscoring the representational capacity of this approach.

Auditing the Algorithm: Towards Robust Visual AI

Learnable Fourier Shapes present a novel method for auditing DNNs and identifying vulnerabilities related to shape perception. This constructs adversarial perturbations by optimizing shape features in the Fourier domain, directly addressing network sensitivity to geometric forms.

Experiments demonstrate a high success rate in generating adversarial examples, revealing a significant decrease in Precision-Recall curves when subjected to these shape-based attacks. This offers a complementary approach to texture-based attacks, enhancing robustness against a wider range of threats.

Understanding critical shape features can inform the design of more efficient and interpretable architectures. By identifying vulnerabilities related to shape perception, researchers can improve the reliability of DNN-based systems. Ultimately, every elegant architecture yields to edge cases.

The pursuit of elegant geometric priors in deep networks, as explored in this study, feels predictably fragile. The paper details a method for crafting adversarial shapes through Fourier analysis, a mathematically beautiful approach. Yet, one anticipates the inevitable: production data, with its inherent noise and edge cases, will expose limitations in even the most refined Fourier-based attack. As Yann LeCun aptly stated, “Everything we deploy will eventually crash.” This is not a condemnation of the work—the exploration of shape optimization and its impact on interpretability is valuable—but a quiet acknowledgment that theoretical elegance often encounters the brutal reality of deployment, where abstractions, no matter how carefully constructed, ultimately succumb to the chaos of real-world input.

What’s Next?

The pursuit of adversarial shapes, elegantly rendered through Fourier series, feels… predictably complex. It’s a neat trick, translating perturbations into geometric space, but anyone who’s spent time in production knows that ‘geometric’ rapidly devolves into ‘a mess of intersecting polygons that somehow broke the classifier.’ The current work establishes a baseline – a beautifully differentiable one, admittedly – but it doesn’t address the fundamental issue: these attacks, like all attacks, will be patched, countered, and then circumvented in ways the authors haven’t imagined. It’s a constant escalation, and the only certainty is increasing computational cost.

The notion of ‘interpretable’ adversarial examples, though, deserves scrutiny. Finding shapes that reliably fool a network and reveal something about its decision boundaries is a tantalizing prospect. However, it’s likely these ‘interpretations’ are simply artifacts of the chosen representation – a Fourier basis isn’t inherently meaningful to a convolutional net, it’s just a convenient way to parameterize a perturbation. The real challenge isn’t generating these shapes, it’s building a system that isn’t fooled by them – a task that consistently proves more difficult than generating the attacks themselves.

Ultimately, this work feels like another step in building increasingly elaborate tools to probe systems that are, at their core, fundamentally opaque. The authors leave notes for future digital archaeologists, detailing how to break things in a slightly more sophisticated way. If a system crashes consistently, at least it’s predictable. One suspects the next innovation won’t be in the attack itself, but in the inevitable defense—or, more realistically, in the next layer of obfuscation.

Original article: https://arxiv.org/pdf/2511.04970.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-11-11 02:30