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Alexandre Araujo

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15 papers

2 author rows

TMLR Journal 2025 Journal Article

EMMA: Efficient Visual Alignment in Multi-Modal LLMs

Sara Ghazanfari
Alexandre Araujo
Prashanth Krishnamurthy
Siddharth Garg
Farshad Khorrami

Multi-modal Large Language Models (MLLMs) have recently exhibited impressive general- purpose capabilities by leveraging vision foundation models to encode the core concepts of images into representations. These are then combined with instructions and processed by the language model to generate high-quality responses. Despite significant progress in enhancing the language component, challenges persist in optimally fusing visual encodings within the language model for task-specific adaptability. Recent research has focused on improving this fusion through modality adaptation modules but at the cost of significantly increased model complexity and training data needs. In this paper, we propose EMMA (Efficient Multi-Modal Adaptation), a lightweight cross-modality module designed to efficiently fuse visual and textual encodings, generating instruction-aware visual representations for the language model. Our key contributions include: (1) an efficient early fusion mechanism that integrates vision and language representations with minimal added parameters (less than 0.2% increase in model size), (2) an in-depth interpretability analysis that sheds light on the internal mechanisms of the proposed method; (3) comprehensive experiments that demonstrate notable improvements on both specialized and general benchmarks for MLLMs. Empirical results show that EMMA boosts performance across multiple tasks by up to 9.3% while significantly improving robustness against hallucinations.

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ICML Conference 2024 Conference Paper

Fine-grained Local Sensitivity Analysis of Standard Dot-Product Self-Attention

Aaron J. Havens
Alexandre Araujo
Huan Zhang
Bin Hu 0002

Self-attention has been widely used in various machine learning models, such as vision transformers. The standard dot-product self-attention is arguably the most popular structure, and there is a growing interest in understanding the mathematical properties of such attention mechanisms. This paper presents a fine-grained local sensitivity analysis of the standard dot-product self-attention, leading to new non-vacuous certified robustness results for vision transformers. Despite the well-known fact that dot-product self-attention is not (globally) Lipschitz, we develop new theoretical analysis of Local Fine-grained Attention Sensitivity (LoFAST) quantifying the effect of input feature perturbations on the attention output. Our analysis reveals that the local sensitivity of dot-product self-attention to $\ell_2$ perturbations can actually be controlled by several key quantities associated with the attention weight matrices and the unperturbed input. We empirically validate our theoretical findings by computing non-vacuous certified $\ell_2$-robustness for vision transformers on CIFAR-10 and SVHN datasets. The code for LoFAST is available at https: //github. com/AaronHavens/LoFAST.

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ICLR Conference 2024 Conference Paper

LipSim: A Provably Robust Perceptual Similarity Metric

Sara Ghazanfari
Alexandre Araujo
Prashanth Krishnamurthy
Farshad Khorrami
Siddharth Garg

Recent years have seen growing interest in developing and applying perceptual similarity metrics. Research has shown the superiority of perceptual metrics over pixel-wise metrics in aligning with human perception and serving as a proxy for the human visual system. On the other hand, as perceptual metrics rely on neural networks, there is a growing concern regarding their resilience, given the established vulnerability of neural networks to adversarial attacks. It is indeed logical to infer that perceptual metrics may inherit both the strengths and shortcomings of neural networks. In this work, we demonstrate the vulnerability of state-of-the-art perceptual similarity metrics based on an ensemble of ViT-based feature extractors to adversarial attacks. We then propose a framework to train a robust perceptual similarity metric called LipSim (Lipschitz Similarity Metric) with provable guarantees. By leveraging 1-Lipschitz neural networks as the backbone, LipSim provides guarded areas around each data point and certificates for all perturbations within an $\ell_2$ ball. Finally, a comprehensive set of experiments shows the performance of LipSim in terms of natural and certified scores and on the image retrieval application.

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ICLR Conference 2024 Conference Paper

Novel Quadratic Constraints for Extending LipSDP beyond Slope-Restricted Activations

Patricia Pauli
Aaron J. Havens
Alexandre Araujo
Siddharth Garg
Farshad Khorrami
Frank Allgöwer
Bin Hu 0002

Recently, semidefinite programming (SDP) techniques have shown great promise in providing accurate Lipschitz bounds for neural networks. Specifically, the LipSDP approach (Fazlyab et al., 2019) has received much attention and provides the least conservative Lipschitz upper bounds that can be computed with polynomial time guarantees. However, one main restriction of LipSDP is that its formulation requires the activation functions to be slope-restricted on $[0,1]$, preventing its further use for more general activation functions such as GroupSort, MaxMin, and Householder. One can rewrite MaxMin activations for example as residual ReLU networks. However, a direct application of LipSDP to the resultant residual ReLU networks is conservative and even fails in recovering the well-known fact that the MaxMin activation is 1-Lipschitz. Our paper bridges this gap and extends LipSDP beyond slope-restricted activation functions. To this end, we provide novel quadratic constraints for GroupSort, MaxMin, and Householder activations via leveraging their underlying properties such as sum preservation. Our proposed analysis is general and provides a unified approach for estimating $\ell_2$ and $\ell_\infty$ Lipschitz bounds for a rich class of neural network architectures, including non-residual and residual neural networks and implicit models, with GroupSort, MaxMin, and HouseHolder activations. Finally, we illustrate the utility of our approach with a variety of experiments and show that our proposed SDPs generate less conservative Lipschitz bounds in comparison to existing approaches.

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ICLR Conference 2024 Conference Paper

On the Scalability and Memory Efficiency of Semidefinite Programs for Lipschitz Constant Estimation of Neural Networks

Zi Wang 0016
Bin Hu 0002
Aaron J. Havens
Alexandre Araujo
Yang Zheng 0001
Yudong Chen
Somesh Jha

Lipschitz constant estimation plays an important role in understanding generalization, robustness, and fairness in deep learning. Unlike naive bounds based on the network weight norm product, semidefinite programs (SDPs) have shown great promise in providing less conservative Lipschitz bounds with polynomial-time complexity guarantees. However, due to the memory consumption and running speed, standard SDP algorithms cannot scale to modern neural network architectures. In this paper, we transform the SDPs for Lipschitz constant estimation into an eigenvalue optimization problem, which aligns with the modern large-scale optimization paradigms based on first-order methods. This is amenable to autodiff frameworks such as PyTorch and TensorFlow, requiring significantly less memory than standard SDP algorithms. The transformation also allows us to leverage various existing numerical techniques for eigenvalue optimization, opening the way for further memory improvement and computational speedup. The essential technique of our eigenvalue-problem transformation is to introduce redundant quadratic constraints and then utilize both Lagrangian and Shor's SDP relaxations under a certain trace constraint. Notably, our numerical study successfully scales the SDP-based Lipschitz constant estimation to address large neural networks on ImageNet. Our numerical examples on CIFAR10 and ImageNet demonstrate that our technique is more scalable than existing approaches. Our code is available at https://github.com/z1w/LipDiff.

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ICLR Conference 2024 Conference Paper

The Lipschitz-Variance-Margin Tradeoff for Enhanced Randomized Smoothing

Blaise Delattre
Alexandre Araujo
Quentin Barthélemy
Alexandre Allauzen

Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However how to design an efficient classifier with an associated certified radius? Randomized smoothing provides a promising framework by relying on noise injection into the inputs to obtain a smoothed and robust classifier. In this paper, we first show that the variance introduced by the Monte-Carlo sampling in the randomized smoothing procedure estimate closely interacts with two other important properties of the classifier, \textit{i.e.} its Lipschitz constant and margin. More precisely, our work emphasizes the dual impact of the Lipschitz constant of the base classifier, on both the smoothed classifier and the empirical variance. To increase the certified robust radius, we introduce a different way to convert logits to probability vectors for the base classifier to leverage the variance-margin trade-off. We leverage the use of Bernstein's concentration inequality along with enhanced Lipschitz bounds for randomized smoothing. Experimental results show a significant improvement in certified accuracy compared to current state-of-the-art methods. Our novel certification procedure allows us to use pre-trained models with randomized smoothing, effectively improving the current certification radius in a zero-shot manner.

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ICLR Conference 2023 Conference Paper

A Unified Algebraic Perspective on Lipschitz Neural Networks

Alexandre Araujo
Aaron J. Havens
Blaise Delattre
Alexandre Allauzen
Bin Hu 0002

Important research efforts have focused on the design and training of neural networks with a controlled Lipschitz constant. The goal is to increase and sometimes guarantee the robustness against adversarial attacks. Recent promising techniques draw inspirations from different backgrounds to design 1-Lipschitz neural networks, just to name a few: convex potential layers derive from the discretization of continuous dynamical systems, Almost-Orthogonal-Layer proposes a tailored method for matrix rescaling. However, it is today important to consider the recent and promising contributions in the field under a common theoretical lens to better design new and improved layers. This paper introduces a novel algebraic perspective unifying various types of 1-Lipschitz neural networks, including the ones previously mentioned, along with methods based on orthogonality and spectral methods. Interestingly, we show that many existing techniques can be derived and generalized via finding analytical solutions of a common semidefinite programming (SDP) condition. We also prove that AOL biases the scaled weight to the ones which are close to the set of orthogonal matrices in a certain mathematical manner. Moreover, our algebraic condition, combined with the Gershgorin circle theorem, readily leads to new and diverse parameterizations for 1-Lipschitz network layers. Our approach, called SDP-based Lipschitz Layers (SLL), allows us to design non-trivial yet efficient generalization of convex potential layers. Finally, the comprehensive set of experiments on image classification shows that SLLs outperform previous approaches on certified robust accuracy. Code is available at https://github.com/araujoalexandre/Lipschitz-SLL-Networks.

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NeurIPS Conference 2023 Conference Paper

Diffusion-Based Adversarial Sample Generation for Improved Stealthiness and Controllability

Haotian Xue
Alexandre Araujo
Bin Hu
Yongxin Chen

Neural networks are known to be susceptible to adversarial samples: small variations of natural examples crafted to deliberatelymislead the models. While they can be easily generated using gradient-based techniques in digital and physical scenarios, they often differ greatly from the actual data distribution of natural images, resulting in a trade-off between strength and stealthiness. In this paper, we propose a novel framework dubbed Diffusion-Based Projected Gradient Descent (Diff-PGD) for generating realistic adversarial samples. By exploiting a gradient guided by a diffusion model, Diff-PGD ensures that adversarial samples remain close to the original data distribution while maintaining their effectiveness. Moreover, our framework can be easily customized for specific tasks such as digital attacks, physical-world attacks, and style-based attacks. Compared with existing methods for generating natural-style adversarial samples, our framework enables the separation of optimizing adversarial loss from other surrogate losses (e. g. content/smoothness/style loss), making it more stable and controllable. Finally, we demonstrate that the samples generated using Diff-PGD have better transferability and anti-purification power than traditional gradient-based methods.

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ICML Conference 2023 Conference Paper

Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration

Blaise Delattre
Quentin Barthélemy
Alexandre Araujo
Alexandre Allauzen

Since the control of the Lipschitz constant has a great impact on the training stability, generalization, and robustness of neural networks, the estimation of this value is nowadays a real scientific challenge. In this paper we introduce a precise, fast, and differentiable upper bound for the spectral norm of convolutional layers using circulant matrix theory and a new alternative to the Power iteration. Called the Gram iteration, our approach exhibits a superlinear convergence. First, we show through a comprehensive set of experiments that our approach outperforms other state-of-the-art methods in terms of precision, computational cost, and scalability. Then, it proves highly effective for the Lipschitz regularization of convolutional neural networks, with competitive results against concurrent approaches.

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NeurIPS Conference 2023 Conference Paper

Exploiting Connections between Lipschitz Structures for Certifiably Robust Deep Equilibrium Models

Aaron Havens
Alexandre Araujo
Siddharth Garg
Farshad Khorrami
Bin Hu

Recently, deep equilibrium models (DEQs) have drawn increasing attention from the machine learning community. However, DEQs are much less understood in terms of certified robustness than their explicit network counterparts. In this paper, we advance the understanding of certified robustness of DEQs via exploiting the connections between various Lipschitz network parameterizations for both explicit and implicit models. Importantly, we show that various popular Lipschitz network structures, including convex potential layers (CPL), SDP-based Lipschitz layers (SLL), almost orthogonal layers (AOL), Sandwich layers, and monotone DEQs (MonDEQ) can all be reparameterized as special cases of the Lipschitz-bounded equilibrium networks (LBEN) without changing the prescribed Lipschitz constant in the original network parameterization. A key feature of our reparameterization technique is that it preserves the Lipschitz prescription used in different structures. This opens the possibility of achieving improved certified robustness of DEQs via a combination of network reparameterization, structure-preserving regularization, and LBEN-based fine-tuning. We also support our theoretical understanding with new empirical results, which show that our proposed method improves the certified robust accuracy of DEQs on classification tasks. All codes and experiments are made available at \url{https: //github. com/AaronHavens/ExploitingLipschitzDEQ}.

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UAI Conference 2023 Conference Paper

Towards better certified segmentation via diffusion models

Othmane Laousy
Alexandre Araujo
Guillaume Chassagnon
Marie-Pierre Revel
Siddharth Garg
Farshad Khorrami
Maria Vakalopoulou

The robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached production-level accuracy. However, like classification models, segmentation models can be vulnerable to adversarial perturbations, which hinders their use in critical-decision systems like healthcare or autonomous driving. Recently, randomized smoothing has been proposed to certify segmentation predictions by adding Gaussian noise to the input to obtain theoretical guarantees. However, this method exhibits a trade-off between the amount of added noise and the level of certification achieved. In this paper, we address the problem of certifying segmentation prediction using a combination of randomized smoothing and diffusion models. Our experiments show that combining randomized smoothing and diffusion models significantly improves certified robustness, with results indicating a mean improvement of 21 points in accuracy compared to previous state-of-the-art methods on Pascal-Context and Cityscapes public datasets. Our method is independent of the selected segmentation model and does not need any additional specialized training procedure.

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ICML Conference 2022 Conference Paper

A Dynamical System Perspective for Lipschitz Neural Networks

Laurent Meunier
Blaise Delattre
Alexandre Araujo
Alexandre Allauzen

The Lipschitz constant of neural networks has been established as a key quantity to enforce the robustness to adversarial examples. In this paper, we tackle the problem of building $1$-Lipschitz Neural Networks. By studying Residual Networks from a continuous time dynamical system perspective, we provide a generic method to build $1$-Lipschitz Neural Networks and show that some previous approaches are special cases of this framework. Then, we extend this reasoning and show that ResNet flows derived from convex potentials define $1$-Lipschitz transformations, that lead us to define the Convex Potential Layer (CPL). A comprehensive set of experiments on several datasets demonstrates the scalability of our architecture and the benefits as an $\ell_2$-provable defense against adversarial examples. Our code is available at \url{https: //github. com/MILES-PSL/Convex-Potential-Layer}

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AAAI Conference 2021 Conference Paper

On Lipschitz Regularization of Convolutional Layers using Toeplitz Matrix Theory

Alexandre Araujo
Benjamin Negrevergne
Yann Chevaleyre
Jamal Atif

This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization, robustness against adversarial examples, etc. However, computing the exact value of the Lipschitz constant of a neural network is known to be NP-hard. Recent attempts from the literature introduce upper-bounds to approximate this constant that are either efficient but loose or accurate but computationally expensive. In this work, by leveraging the theory of Toeplitz matrices, we introduce a new upper-bound for convolutional layers that is both tight and easy to compute. Based on this result we devise an algorithm to train Lipschitz regularized Convolutional Neural Networks.

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ECAI Conference 2020 Conference Paper

Understanding and Training Deep Diagonal Circulant Neural Networks

Alexandre Araujo
Benjamin Négrevergne
Yann Chevaleyre
Jamal Atif

In this paper, we study deep diagonal circulant neural networks, which are deep neural networks in which weight matrices are the product of diagonal and circulant ones. Besides making a theoretical analysis of their expressivity, we introduce principled techniques for training these models: we devise an initialization scheme and propose a smart use of non-linearity functions in order to train deep diagonal circulant networks. Furthermore, we show that these networks outperform recently introduced deep networks with other types of structured layers. We conduct a thorough experimental study to compare the performance of deep diagonal circulant networks with state-of-the-art models based on structured matrices and with dense models. We show that our models achieve better accuracy than other structured approaches while requiring 2x fewer weights than the next best approach. Finally, we train compact and accurate deep diagonal circulant networks on a real world video classification dataset with over 3. 8 million training examples.

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NeurIPS Conference 2019 Conference Paper

Theoretical evidence for adversarial robustness through randomization

Rafael Pinot
Laurent Meunier
Alexandre Araujo
Hisashi Kashima
Florian Yger
Cedric Gouy-Pailler
Jamal Atif

This paper investigates the theory of robustness against adversarial attacks. It focuses on the family of randomization techniques that consist in injecting noise in the network at inference time. These techniques have proven effective in many contexts, but lack theoretical arguments. We close this gap by presenting a theo- retical analysis of these approaches, hence explaining why they perform well in practice. More precisely, we make two new contributions. The first one relates the randomization rate to robustness to adversarial attacks. This result applies for the general family of exponential distributions, and thus extends and unifies the previous approaches. The second contribution consists in devising a new upper bound on the adversarial risk gap of randomized neural networks. We support our theoretical claims with a set of experiments.

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