arXiv subjects

Hamid Krim

Publications and source records attributed to Hamid Krim.

At least 19 recordsLinked to original sources

arXiv2026

Learning with Volterra Neural Networks: A System Theoretic Perspective

Higher-order interaction components are important for signal, image, and video modeling, but explicit high-order operators often suffer from rapidly increasing parameter and computational costs. This paper presents kVNN, a learnable kernelized Volterra Neural operator for compact higher-order filtering. The motivation is to use kernelization to improve the efficiency of Volterra-type neural operators while providing a structured interpretation of their higher-order components. The proposed formulation combines the order-wise structure of Volterra filtering with learnable polynomial-kernel atoms, allowing different interaction orders to be represented by separate learnable centers and coefficients. This order-decoupled representation avoids explicit high-order tensor parameterization and can be implemented as a CNN-compatible layer. Experiments on representative vision tasks show that kVNN achieves a favorable accuracy--efficiency trade-off.

cs.CV↗

arXiv2026

Counterfactual Reasoning for Fine-Grained Evidence Disentanglement in VideoQA

Recent advances in video multimodal models have significantly improved VideoQA performance. However, these systems often rely on spurious statistical correlations rather than answer-relevant causal evidence, resulting in unfaithful and brittle reasoning, especially in complex real-world scenarios. Existing methods either rely on cross-modality correlations, costly curated training resources, or insufficient causal assumptions and constraints, and typically operate at the time-interval level. As a result, they fail to explicitly disentangle causal visual cues from confounders and provide limited fine-grained evidence localization. To address this issue, we propose a Counterfactual Reasoning framework for fine-grained Evidence Disentanglement (CREDiT). CREDiT formulates the VideoQA process using a structural causal model and learns cross-modality representations that are explicitly decomposed into causal and non-causal components under independence and minimality constraints. To facilitate faithful disentanglement, we introduce feature-level causal interventions and construct counterfactual inputs that approximate causal effects while suppressing non-causal correlations. Extensive experiments on NExT-GQA, SportsQA, and SPORTU-video demonstrate that CREDiT consistently improves answer accuracy and reasoning reliability across both generic and complex sports scenarios, leading to more trustworthy VideoQA systems.

cs.CV↗

arXiv2026

KVNN: Learnable Multi-Kernel Volterra Neural Networks

Higher-order learning is fundamentally rooted in exploiting compositional features. It clearly hinges on enriching the representation by more elaborate interactions of the data which, in turn, tends to increase the model complexity of conventional large-scale deep learning models. In this paper, a kernelized Volterra Neural Network (kVNN) is proposed. The key to the achieved efficiency lies in using a learnable multi-kernel representation, where different interaction orders are modeled by distinct polynomial-kernel components with compact, learnable centers, yielding an order-adaptive parameterization. Features are learned by the composition of layers, each of which consists of parallel branches of different polynomial orders, enabling kVNN filters to directly replace standard convolutional kernels within existing architectures. The theoretical results are substantiated by experiments on two representative tasks: video action recognition and image denoising. The results demonstrate favorable performance-efficiency trade-offs: kVNN consistently yields reduced model (parameters) and computational (GFLOPs) complexity with competitive and often improved performance. These results are maintained even when trained from scratch without large-scale pretraining. In summary, we substantiate that structured kernelized higher-order layers offer a practical path to balancing expressivity and computational cost in modern deep networks.

cs.CV↗

arXiv2025

ViTCAE: ViT-based Class-conditioned Autoencoder

Vision Transformer (ViT) based autoencoders often underutilize the global Class token and employ static attention mechanisms, limiting both generative control and optimization efficiency. This paper introduces ViTCAE, a framework that addresses these issues by re-purposing the Class token into a generative linchpin. In our architecture, the encoder maps the Class token to a global latent variable that dictates the prior distribution for local, patch-level latent variables, establishing a robust dependency where global semantics directly inform the synthesis of local details. Drawing inspiration from opinion dynamics, we treat each attention head as a dynamical system of interacting tokens seeking consensus. This perspective motivates a convergence-aware temperature scheduler that adaptively anneals each head's influence function based on its distributional stability. This process enables a principled head-freezing mechanism, guided by theoretically-grounded diagnostics like an attention evolution distance and a consensus/cluster functional. This technique prunes converged heads during training to significantly improve computational efficiency without sacrificing fidelity. By unifying a generative Class token with an adaptive attention mechanism rooted in multi-agent consensus theory, ViTCAE offers a more efficient and controllable approach to transformer-based generation.

cs.LG↗

arXiv2025

Proximal Vision Transformer: Enhancing Feature Representation through Two-Stage Manifold Geometry

The Vision Transformer (ViT) architecture has become widely recognized in computer vision, leveraging its self-attention mechanism to achieve remarkable success across various tasks. Despite its strengths, ViT's optimization remains confined to modeling local relationships within individual images, limiting its ability to capture the global geometric relationships between data points. To address this limitation, this paper proposes a novel framework that integrates ViT with the proximal tools, enabling a unified geometric optimization approach to enhance feature representation and classification performance. In this framework, ViT constructs the tangent bundle of the manifold through its self-attention mechanism, where each attention head corresponds to a tangent space, offering geometric representations from diverse local perspectives. Proximal iterations are then introduced to define sections within the tangent bundle and project data from tangent spaces onto the base space, achieving global feature alignment and optimization. Experimental results confirm that the proposed method outperforms traditional ViT in terms of classification accuracy and data distribution.

cs.CV↗

arXiv2025

Boosting Adversarial Robustness and Generalization with Structural Prior

This work investigates a novel approach to boost adversarial robustness and generalization by incorporating structural prior into the design of deep learning models. Specifically, our study surprisingly reveals that existing dictionary learning-inspired convolutional neural networks (CNNs) provide a false sense of security against adversarial attacks. To address this, we propose Elastic Dictionary Learning Networks (EDLNets), a novel ResNet architecture that significantly enhances adversarial robustness and generalization. This novel and effective approach is supported by a theoretical robustness analysis using influence functions. Moreover, extensive and reliable experiments demonstrate consistent and significant performance improvement on open robustness leaderboards such as RobustBench, surpassing state-of-the-art baselines. To the best of our knowledge, this is the first work to discover and validate that structural prior can reliably enhance deep learning robustness under strong adaptive attacks, unveiling a promising direction for future research.

cs.LG↗

arXiv2024

Robustness Reprogramming for Representation Learning

This work tackles an intriguing and fundamental open challenge in representation learning: Given a well-trained deep learning model, can it be reprogrammed to enhance its robustness against adversarial or noisy input perturbations without altering its parameters? To explore this, we revisit the core feature transformation mechanism in representation learning and propose a novel non-linear robust pattern matching technique as a robust alternative. Furthermore, we introduce three model reprogramming paradigms to offer flexible control of robustness under different efficiency requirements. Comprehensive experiments and ablation studies across diverse learning models ranging from basic linear model and MLPs to shallow and modern deep ConvNets demonstrate the effectiveness of our approaches. This work not only opens a promising and orthogonal direction for improving adversarial defenses in deep learning beyond existing methods but also provides new insights into designing more resilient AI systems with robust statistics.

cs.LG↗

arXiv2024

Generative Expansion of Small Datasets: An Expansive Graph Approach

Limited data availability in machine learning significantly impacts performance and generalization. Traditional augmentation methods enhance moderately sufficient datasets. GANs struggle with convergence when generating diverse samples. Diffusion models, while effective, have high computational costs. We introduce an Expansive Synthesis model generating large-scale, information-rich datasets from minimal samples. It uses expander graph mappings and feature interpolation to preserve data distribution and feature relationships. The model leverages neural networks' non-linear latent space, captured by a Koopman operator, to create a linear feature space for dataset expansion. An autoencoder with self-attention layers and optimal transport refines distributional consistency. We validate by comparing classifiers trained on generated data to those trained on original datasets. Results show comparable performance, demonstrating the model's potential to augment training data effectively. This work advances data generation, addressing scarcity in machine learning applications.

cs.LG↗

arXiv2024

Accelerated Image-Aware Generative Diffusion Modeling

We propose in this paper an analytically new construct of a diffusion model whose drift and diffusion parameters yield an exponentially time-decaying Signal to Noise Ratio in the forward process. In reverse, the construct cleverly carries out the learning of the diffusion coefficients on the structure of clean images using an autoencoder. The proposed methodology significantly accelerates the diffusion process, reducing the required diffusion time steps from around 1000 seen in conventional models to 200-500 without compromising image quality in the reverse-time diffusion. In a departure from conventional models which typically use time-consuming multiple runs, we introduce a parallel data-driven model to generate a reverse-time diffusion trajectory in a single run of the model. The resulting collective block-sequential generative model eliminates the need for MCMC-based sub-sampling correction for safeguarding and improving image quality, to further improve the acceleration of image generation. Collectively, these advancements yield a generative model that is an order of magnitude faster than conventional approaches, while maintaining high fidelity and diversity in generated images, hence promising widespread applicability in rapid image synthesis tasks.

eess.IV↗

arXiv2024

Koopcon: A new approach towards smarter and less complex learning

In the era of big data, the sheer volume and complexity of datasets pose significant challenges in machine learning, particularly in image processing tasks. This paper introduces an innovative Autoencoder-based Dataset Condensation Model backed by Koopman operator theory that effectively packs large datasets into compact, information-rich representations. Inspired by the predictive coding mechanisms of the human brain, our model leverages a novel approach to encode and reconstruct data, maintaining essential features and label distributions. The condensation process utilizes an autoencoder neural network architecture, coupled with Optimal Transport theory and Wasserstein distance, to minimize the distributional discrepancies between the original and synthesized datasets. We present a two-stage implementation strategy: first, condensing the large dataset into a smaller synthesized subset; second, evaluating the synthesized data by training a classifier and comparing its performance with a classifier trained on an equivalent subset of the original data. Our experimental results demonstrate that the classifiers trained on condensed data exhibit comparable performance to those trained on the original datasets, thus affirming the efficacy of our condensation model. This work not only contributes to the reduction of computational resources but also paves the way for efficient data handling in constrained environments, marking a significant step forward in data-efficient machine learning.

cs.LG↗

arXiv2023

Volterra Neural Networks (VNNs)

The importance of inference in Machine Learning (ML) has led to an explosive number of different proposals in ML, and particularly in Deep Learning. In an attempt to reduce the complexity of Convolutional Neural Networks, we propose a Volterra filter-inspired Network architecture. This architecture introduces controlled non-linearities in the form of interactions between the delayed input samples of data. We propose a cascaded implementation of Volterra Filtering so as to significantly reduce the number of parameters required to carry out the same classification task as that of a conventional Neural Network. We demonstrate an efficient parallel implementation of this Volterra Neural Network (VNN), along with its remarkable performance while retaining a relatively simpler and potentially more tractable structure. Furthermore, we show a rather sophisticated adaptation of this network to nonlinearly fuse the RGB (spatial) information and the Optical Flow (temporal) information of a video sequence for action recognition. The proposed approach is evaluated on UCF-101 and HMDB-51 datasets for action recognition, and is shown to outperform state of the art CNN approaches.

cs.CV↗

arXiv2023

Recovery Bounds on Class-Based Optimal Transport: A Sum-of-Norms Regularization Framework

We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal algorithm with a closed-form projection and proximal operator scheme, thereby affording a more scalable algorithm for computing optimal transport plans. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer not only results in a better preservation of the class structure in the data but also yields additional robustness to the data geometry, compared to previous regularizers.

cs.LG↗

arXiv2023

Implicit Bayes Adaptation: A Collaborative Transport Approach

The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability distributions by some optimal metric, has been creatively exploited and shown to hold promise for many real-world data challenges. In a related theme in the present work, we posit that domain adaptation robustness is rooted in the intrinsic (latent) representations of the respective data, which are inherently lying in a non-linear submanifold embedded in a higher dimensional Euclidean space. We account for the geometric properties by refining the $l^2$ Euclidean metric to better reflect the geodesic distance between two distinct representations. We integrate a metric correction term as well as a prior cluster structure in the source data of the OT-driven adaptation. We show that this is tantamount to an implicit Bayesian framework, which we demonstrate to be viable for a more robust and better-performing approach to domain adaptation. Substantiating experiments are also included for validation purposes.

eess.IV↗

arXiv2022

Refining Self-Supervised Learning in Imaging: Beyond Linear Metric

We introduce in this paper a new statistical perspective, exploiting the Jaccard similarity metric, as a measure-based metric to effectively invoke non-linear features in the loss of self-supervised contrastive learning. Specifically, our proposed metric may be interpreted as a dependence measure between two adapted projections learned from the so-called latent representations. This is in contrast to the cosine similarity measure in the conventional contrastive learning model, which accounts for correlation information. To the best of our knowledge, this effectively non-linearly fused information embedded in the Jaccard similarity, is novel to self-supervision learning with promising results. The proposed approach is compared to two state-of-the-art self-supervised contrastive learning methods on three image datasets. We not only demonstrate its amenable applicability in current ML problems, but also its improved performance and training efficiency.

cs.CV↗

arXiv2022

Fast OT for Latent Domain Adaptation

In this paper, we address the problem of unsupervised Domain Adaptation. The need for such an adaptation arises when the distribution of the target data differs from that which is used to develop the model and the ground truth information of the target data is unknown. We propose an algorithm that uses optimal transport theory with a verifiably efficient and implementable solution to learn the best latent feature representation. This is achieved by minimizing the cost of transporting the samples from the target domain to the distribution of the source domain.

cs.LG↗

arXiv2022

Discovering Urban Functional Zones from Biased and Sparse Points of Interests and Sparse Human Activities

With rapid development of socio-economics, the task of discovering functional zones becomes critical to better understand the interactions between social activities and spatial locations. In this paper, we propose a framework to discover the real functional zones from the biased and extremely sparse Point of Interests (POIs). To cope with the bias and sparsity of POIs, the unbiased inner influences between spatial locations and human activities are introduced to learn a balanced and dense latent region representation. In addition, a spatial location based clustering method is also included to enrich the spatial information for latent region representation and enhance the region functionality consistency for the fine-grained region segmentation. Moreover, to properly annotate the various and fine-grained region functionalities, we estimate the functionality of the regions and rank them by the differences between the normalized POI distributions to reduce the inconsistency caused by the fine-grained segmentation. Thus, our whole framework is able to properly address the biased categories in sparse POI data and explore the true functional zones with a fine-grained level. To validate the proposed framework, a case study is evaluated by using very large real-world users GPS and POIs data from city of Raleigh. The results demonstrate that the proposed framework can better identify functional zones than the benchmarks, and, therefore, enhance understanding of urban structures with a finer granularity under practical conditions.

cs.SI↗

arXiv2022

Information Fusion: Scaling Subspace-Driven Approaches

In this work, we seek to exploit the deep structure of multi-modal data to robustly exploit the group subspace distribution of the information using the Convolutional Neural Network (CNN) formalism. Upon unfolding the set of subspaces constituting each data modality, and learning their corresponding encoders, an optimized integration of the generated inherent information is carried out to yield a characterization of various classes. Referred to as deep Multimodal Robust Group Subspace Clustering (DRoGSuRe), this approach is compared against the independently developed state-of-the-art approach named Deep Multimodal Subspace Clustering (DMSC). Experiments on different multimodal datasets show that our approach is competitive and more robust in the presence of noise.

cs.LG↗

arXiv2021

Deep Transform and Metric Learning Networks

Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer dictionaries, the recently improved Deep DL methods have also fallen short on a number of issues. We hence propose a novel Deep DL approach where each DL layer can be formulated and solved as a combination of one linear layer and a Recurrent Neural Network, where the RNN is flexibly regraded as a layer-associated learned metric. Our proposed work unveils new insights between the Neural Networks and Deep DL, and provides a novel, efficient and competitive approach to jointly learn the deep transforms and metrics. Extensive experiments are carried out to demonstrate that the proposed method can not only outperform existing Deep DL, but also state-of-the-art generic Convolutional Neural Networks.

cs.LG↗