Visual encoders have become fundamental components in modern computer vision pipelines. However, ensuring robustness against adversarial perturbations remains a critical challenge. Recent efforts have explored both supervised and unsupervised adversarial fine-tuning strategies. We identify two key limitations in these approaches: (i) they often suffer from instability, especially during the early stages of fine-tuning, resulting in suboptimal convergence and degraded performance on clean data, and (ii) they exhibit a suboptimal trade-off between robustness and clean data accuracy, hindering the simultaneous optimization of both objectives. To overcome these challenges, we propose **L**agrangian-**O**ptimized **R**obust **E**mbeddings (LORE), a novel unsupervised adversarial fine-tuning framework. LORE utilizes constrained optimization, which offers a principled approach to balancing competing goals, such as improving robustness while preserving nominal performance. By enforcing embedding-space proximity constraints, LORE effectively maintains clean data performance throughout adversarial fine-tuning. Extensive experiments show that LORE stabilizes training and significantly improves zero-shot adversarial robustness with minimal degradation in clean data accuracy. Furthermore, we demonstrate the effectiveness of the adversarially fine-tuned image encoder in out-of-distribution generalization and enhancing the interpretability of image embeddings. The code is available on [GitHub](https://github.com/Theborna/LORE-Lagrangian-Optimized-Robust-Embeddings).

Transformer networks, originally developed in the community of machine translation to eliminate sequential nature of recurrent neural networks, have shown impressive results in other natural language processing and machine vision tasks. Self-attention is the core module behind visual transformers which globally mixes the image information. This module drastically reduces the intrinsic inductive bias imposed by CNNs, such as locality, while encountering insufficient robustness against some adversarial attacks. In this paper we introduce K-sparse attention to preserve low inductive bias, while robustifying transformers against adversarial attacks. We show that standard transformers attend values with dense set of weights, while the sparse attention, automatically selected by an optimization algorithm, can preserve generalization performance of the transformer and, at the same time, improve its robustness.

Compressed Sensing is targeted at reconstructing a signal from a small set of measurements, if the signal is sparse in some domains. In this respect, a low coherent measurement matrix plays an important role. In this letter, an efficient approximation of ℓ∞-norm based on the soft maximum is introduced to design a low coherent measurement matrix with a controllable spectral norm. The proposed approximation, called Logarithm of Sum of Exponential Absolute values (LSEAp), is convex (similar to ℓ∞-norm) and almost smooth. We design a low coherent measurement matrix with a small spectral norm via minimization of the ℓ∞-norm of the Gram matrix. The resulting problem is not convex but our simulations show that the LSEAp leads to an improved design of the measurement matrix, as compared to current methods.

Deep neural networks have presented superlative performance in many machine learning based perception and recognition tasks, where they have even outperformed human precision in some applications. However, it has been found that human perception system is much more robust to adversarial perturbation, as compared to these artificial networks. It has been shown that a deep architecture with a lower Lipschitz constant can generalize better and tolerate higher level of adversarial perturbation. Smooth regularization has been proposed to control the Lipschitz constant of a deep architecture and in this work, we show how a deep convolutional neural network (CNN), based on non-smooth regularization of convolution and fully connected layers, can present enhanced generalization and robustness to adversarial perturbation, simultaneously. We propose two non-smooth regularizers that present specific features for adversarial samples with different levels of signal-to-noise ratios. The regularizers build direct interconnections for the weight matrices in each layer, through which they control the Lipschitz constant of architecture and improve the consistency of input-output mapping of the network. This leads to more reliable and interpretable network mapping and reduces abrupt changes in the networks output. We develop an efficient algorithm to solve the non-smooth learning problems, which presents a gradual complexity addition property. Our simulation results over three benchmark datasets signify the superiority of the proposed formulations over previously reported methods for improving the robustness of deep architecture, towards human robustness to adversarial samples.

Classification of video events based on frame-level descriptors is a common approach to video recognition. In the meanwhile, proper encoding of the frame-level descriptors is vital to the whole event classification procedure. While there are some pretty efficient video descriptor encoding methods, temporal ordering of the descriptors is often ignored in these encoding algorithms. In this paper, we show that by taking into account the temporal inter-frame dependencies and tracking the chronological order of video sub-events, accuracy of event recognition is further improved. First, the frame-level descriptors are extracted using convolutional neural networks (CNNs) pre-trained on ImageNet, which are fine-tuned on a portion of training video frames. Then, a spatio-temporal encoding is applied to the derived descriptors. The proposed spatio-temporal encoding, as the main contribution of this work, is inspired from the well-known vector of locally aggregated descriptors (VLAD) encoding in spatial domain and from total variation de-noising (TVD) in temporal domain. The proposed unified spatio-temporal encoding is then shown to be in the form of a convex optimization problem which is solved efficiently with alternating direction method of multipliers (ADMM) algorithm. The experimental results show superiority of the proposed encoding method in terms of recognition accuracy over both frame-level video encoding approaches and spatio-temporal video representations. As compared to the state-of-the-art approaches, our encoding method improves the mean average precision (mAP) over both Columbia consumer video (CCV), unstructured social activity attribute (USAA), YouTube-8M, and Kinetics datasets and is very competitive on FCVID dataset.