Miguel R. D. Rodrigues

Reem I. Masoud, Ziquan Liu, Martin Ferianc et al.

The deployment of large language models (LLMs) raises concerns regarding their cultural misalignment and potential ramifications on individuals and societies with diverse cultural backgrounds. While the discourse has focused mainly on political and social biases, our research proposes a Cultural Alignment Test (Hoftede's CAT) to quantify cultural alignment using Hofstede's cultural dimension framework, which offers an explanatory cross-cultural comparison through the latent variable analysis. We apply our approach to quantitatively evaluate LLMs, namely Llama 2, GPT-3.5, and GPT-4, against the cultural dimensions of regions like the United States, China, and Arab countries, using different prompting styles and exploring the effects of language-specific fine-tuning on the models' behavioural tendencies and cultural values. Our results quantify the cultural alignment of LLMs and reveal the difference between LLMs in explanatory cultural dimensions. Our study demonstrates that while all LLMs struggle to grasp cultural values, GPT-4 shows a unique capability to adapt to cultural nuances, particularly in Chinese settings. However, it faces challenges with American and Arab cultures. The research also highlights that fine-tuning LLama 2 models with different languages changes their responses to cultural questions, emphasizing the need for culturally diverse development in AI for worldwide acceptance and ethical use. For more details or to contribute to this research, visit our GitHub page https://github.com/reemim/Hofstedes_CAT/

Jonathan Scarlett, Reinhard Heckel, Miguel R. D. Rodrigues et al.

In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven by practical algorithms and experiments, it has also given rise to a variety of intriguing theoretical problems. In this paper, we survey some of the prominent theoretical developments in this line of works, focusing in particular on generative priors, untrained neural network priors, and unfolding algorithms. In addition to summarizing existing results in these topics, we highlight several ongoing challenges and open problems.

Shaik Basheeruddin Shah, Pradyumna Pradhan, Wei Pu et al.

Solving linear inverse problems plays a crucial role in numerous applications. Algorithm unfolding based, model-aware data-driven approaches have gained significant attention for effectively addressing these problems. Learned iterative soft-thresholding algorithm (LISTA) and alternating direction method of multipliers compressive sensing network (ADMM-CSNet) are two widely used such approaches, based on ISTA and ADMM algorithms, respectively. In this work, we study optimization guarantees, i.e., achieving near-zero training loss with the increase in the number of learning epochs, for finite-layer unfolded networks such as LISTA and ADMM-CSNet with smooth soft-thresholding in an over-parameterized (OP) regime. We achieve this by leveraging a modified version of the Polyak-Lojasiewicz, denoted PL$^*$, condition. Satisfying the PL$^*$ condition within a specific region of the loss landscape ensures the existence of a global minimum and exponential convergence from initialization using gradient descent based methods. Hence, we provide conditions, in terms of the network width and the number of training samples, on these unfolded networks for the PL$^*$ condition to hold. We achieve this by deriving the Hessian spectral norm of these networks. Additionally, we show that the threshold on the number of training samples increases with the increase in the network width. Furthermore, we compare the threshold on training samples of unfolded networks with that of a standard fully-connected feed-forward network (FFNN) with smooth soft-thresholding non-linearity. We prove that unfolded networks have a higher threshold value than FFNN. Consequently, one can expect a better expected error for unfolded networks than FFNN.

Avner Shultzman, Eyar Azar, Miguel R. D. Rodrigues et al.

Model-based neural networks provide unparalleled performance for various tasks, such as sparse coding and compressed sensing problems. Due to the strong connection with the sensing model, these networks are interpretable and inherit prior structure of the problem. In practice, model-based neural networks exhibit higher generalization capability compared to ReLU neural networks. However, this phenomenon was not addressed theoretically. Here, we leverage complexity measures including the global and local Rademacher complexities, in order to provide upper bounds on the generalization and estimation errors of model-based networks. We show that the generalization abilities of model-based networks for sparse recovery outperform those of regular ReLU networks, and derive practical design rules that allow to construct model-based networks with guaranteed high generalization. We demonstrate through a series of experiments that our theoretical insights shed light on a few behaviours experienced in practice, including the fact that ISTA and ADMM networks exhibit higher generalization abilities (especially for small number of training samples), compared to ReLU networks.

Martin Ferianc, Ondrej Bohdal, Timothy Hospedales et al.

Enhancing the generalisation abilities of neural networks (NNs) through integrating noise such as MixUp or Dropout during training has emerged as a powerful and adaptable technique. Despite the proven efficacy of noise in NN training, there is no consensus regarding which noise sources, types and placements yield maximal benefits in generalisation and confidence calibration. This study thoroughly explores diverse noise modalities to evaluate their impacts on NN's generalisation and calibration under in-distribution or out-of-distribution settings, paired with experiments investigating the metric landscapes of the learnt representations across a spectrum of NN architectures, tasks, and datasets. Our study shows that AugMix and weak augmentation exhibit cross-task effectiveness in computer vision, emphasising the need to tailor noise to specific domains. Our findings emphasise the efficacy of combining noises and successful hyperparameter transfer within a single domain but the difficulties in transferring the benefits to other domains. Furthermore, the study underscores the complexity of simultaneously optimising for both generalisation and calibration, emphasising the need for practitioners to carefully consider noise combinations and hyperparameter tuning for optimal performance in specific tasks and datasets.

Gholamali Aminian, Saeed Masiha, Laura Toni et al.

Generalization error bounds are essential for comprehending how well machine learning models work. In this work, we suggest a novel method, i.e., the Auxiliary Distribution Method, that leads to new upper bounds on expected generalization errors that are appropriate for supervised learning scenarios. We show that our general upper bounds can be specialized under some conditions to new bounds involving the $α$-Jensen-Shannon, $α$-Rényi ($0< α< 1$) information between a random variable modeling the set of training samples and another random variable modeling the set of hypotheses. Our upper bounds based on $α$-Jensen-Shannon information are also finite. Additionally, we demonstrate how our auxiliary distribution method can be used to derive the upper bounds on excess risk of some learning algorithms in the supervised learning context {\blue and the generalization error under the distribution mismatch scenario in supervised learning algorithms, where the distribution mismatch is modeled as $α$-Jensen-Shannon or $α$-Rényi divergence between the distribution of test and training data samples distributions.} We also outline the conditions for which our proposed upper bounds might be tighter than other earlier upper bounds.

Chen Feng, Minghe Shen, Ananth Balashankar et al.

Reliable certification of Large Language Models (LLMs)-verifying that failure rates are below a safety threshold-is critical yet challenging. While "LLM-as-a-Judge" offers scalability, judge imperfections, noise, and bias can invalidate statistical guarantees. We introduce a "Noisy but Valid" hypothesis testing framework to address this. By leveraging a small human-labelled calibration set to estimate the judge's True Positive and False Positive Rates (TPR/FPR), we derive a variance-corrected critical threshold applied to a large judge-labelled dataset. Crucially, our framework theoretically guarantees finite-sample Type-I error control (validity) despite calibration uncertainty. This distinguishes our work from Prediction-Powered Inference (PPI), positioning our method as a diagnostic tool that explicitly models judge behavior rather than a black-box estimator. Our contributions include: (1) Theoretical Guarantees: We derive the exact conditions under which noisy testing yields higher statistical power than direct evaluation; (2) Empirical Validation: Experiments on Jigsaw Comment, Hate Speech and SafeRLHF confirm our theory; (3) The Oracle Gap: We reveal a significant performance gap between practical methods and the theoretical "Oracle" (perfectly known judge parameters), quantifying the cost of estimation. Specifically, we provide the first systematic treatment of the imperfect-judge setting, yielding interpretable diagnostics of judge reliability and clarifying how evaluation power depends on judge quality, dataset size, and certification levels. Together, these results sharpen understanding of statistical evaluation with LLM judges, and highlight trade-offs among competing inferential tools.

Zhuo Zhi, Chen Feng, Adam Daneshmend et al.

Multimodal large language models (MLLMs) show promise in tasks like visual question answering (VQA) but still face challenges in multimodal reasoning. Recent works adapt agentic frameworks or chain-of-thought (CoT) reasoning to improve performance. However, CoT-based multimodal reasoning often demands costly data annotation and fine-tuning, while agentic approaches relying on external tools risk introducing unreliable output from these tools. In this paper, we propose Seeing and Reasoning with Confidence (SRICE), a training-free multimodal reasoning framework that integrates external vision models with uncertainty quantification (UQ) into an MLLM to address these challenges. Specifically, SRICE guides the inference process by allowing MLLM to autonomously select regions of interest through multi-stage interactions with the help of external tools. We propose to use a conformal prediction-based approach to calibrate the output of external tools and select the optimal tool by estimating the uncertainty of an MLLM's output. Our experiment shows that the average improvement of SRICE over the base MLLM is 4.6% on five datasets and the performance on some datasets even outperforms fine-tuning-based methods, revealing the significance of ensuring reliable tool use in an MLLM agent.

Reem I. Masoud, Martin Ferianc, Philip Treleaven et al.

Large Language Model (LLM) alignment conventionally relies on supervised fine-tuning or reinforcement learning based alignment frameworks. These methods typically require labeled or preference datasets and involve updating model weights to align the LLM with the training objective or reward model. Meanwhile, in social sciences such as cross-cultural studies, factor analysis is widely used to uncover underlying dimensions or latent variables that explain observed patterns in survey data. The non-differentiable nature of these measurements deriving from survey data renders the former alignment methods infeasible for alignment with cultural dimensions. To overcome this, we propose a parameter efficient strategy that combines soft prompt tuning, which freezes the model parameters while modifying the input prompt embeddings, with Differential Evolution (DE), a black-box optimization method for cases where a differentiable objective is unattainable. This strategy ensures alignment consistency without the need for preference data or model parameter updates, significantly enhancing efficiency and mitigating overfitting. Our method demonstrates significant improvements in LLama-3-8B-Instruct's cultural dimensions across multiple regions, outperforming both the Naive LLM and the In-context Learning (ICL) baseline, and effectively bridges computational models with human cultural nuances.

Chen Feng, Ziquan Liu, Zhuo Zhi et al.

It is widely known that state-of-the-art machine learning models, including vision and language models, can be seriously compromised by adversarial perturbations. It is therefore increasingly relevant to develop capabilities to certify their performance in the presence of the most effective adversarial attacks. Our paper offers a new approach to certify the performance of machine learning models in the presence of adversarial attacks with population level risk guarantees. In particular, we introduce the notion of $(α,ζ)$-safe machine learning model. We propose a hypothesis testing procedure, based on the availability of a calibration set, to derive statistical guarantees providing that the probability of declaring that the adversarial (population) risk of a machine learning model is less than $α$ (i.e. the model is safe), while the model is in fact unsafe (i.e. the model adversarial population risk is higher than $α$), is less than $ζ$. We also propose Bayesian optimization algorithms to determine efficiently whether a machine learning model is $(α,ζ)$-safe in the presence of an adversarial attack, along with statistical guarantees. We apply our framework to a range of machine learning models - including various sizes of vision Transformer (ViT) and ResNet models - impaired by a variety of adversarial attacks, such as PGDAttack, MomentumAttack, GenAttack and BanditAttack, to illustrate the operation of our approach. Importantly, we show that ViT's are generally more robust to adversarial attacks than ResNets, and large models are generally more robust than smaller models. Our approach goes beyond existing empirical adversarial risk-based certification guarantees. It formulates rigorous (and provable) performance guarantees that can be used to satisfy regulatory requirements mandating the use of state-of-the-art technical tools.

Reem I. Masoud, Chen Feng, Shunta Asano et al.

The global deployment of large language models (LLMs) has raised concerns about cultural misalignment, yet the linguistic properties of fine-tuning datasets used for cultural adaptation remain poorly understood. We adopt a dataset-centric view of cultural alignment and ask which linguistic properties of fine-tuning data are associated with cultural performance, whether these properties are predictive prior to training, and how these effects vary across models. We compute lightweight linguistic, semantic, and structural metrics for Arabic, Chinese, and Japanese datasets and apply principal component analysis separately within each language. This design ensures that the resulting components capture variation among datasets written in the same language rather than differences between languages. The resulting components correspond to broadly interpretable axes related to semantic coherence, surface-level lexical and syntactic diversity, and lexical or structural richness, though their composition varies across languages. We fine-tune three major LLM families (LLaMA, Mistral, DeepSeek) and evaluate them on benchmarks of cultural knowledge, values, and norms. While PCA components correlate with downstream performance, these associations are strongly model-dependent. Through controlled subset interventions, we show that lexical-oriented components (PC3) are the most robust, yielding more consistent performance across models and benchmarks, whereas emphasizing semantic or diversity extremes (PC1-PC2) is often neutral or harmful.

Martin Ferianc, Hongxiang Fan, Miguel Rodrigues

Ensembles of separate neural networks (NNs) have shown superior accuracy and confidence calibration over single NN across tasks. To improve the hardware efficiency of ensembles of separate NNs, recent methods create ensembles within a single network via adding early exits or considering multi input multi output approaches. However, it is unclear which of these methods is the most effective for a given task, needing a manual and separate search through each method. Our novel Single Architecture Ensemble (SAE) framework enables an automatic and joint search through the early exit and multi input multi output configurations and their previously unobserved in-between combinations. SAE consists of two parts: a scalable search space that generalises the previous methods and their in-between configurations, and an optimisation objective that allows learning the optimal configuration for a given task. Our image classification and regression experiments show that with SAE we can automatically find diverse configurations that fit the task, achieving competitive accuracy or confidence calibration to baselines while reducing the compute operations or parameter count by up to $1.5{\sim}3.7\times$.

Gholamali Aminian, Mahed Abroshan, Mohammad Mahdi Khalili et al.

A common assumption in semi-supervised learning is that the labeled, unlabeled, and test data are drawn from the same distribution. However, this assumption is not satisfied in many applications. In many scenarios, the data is collected sequentially (e.g., healthcare) and the distribution of the data may change over time often exhibiting so-called covariate shifts. In this paper, we propose an approach for semi-supervised learning algorithms that is capable of addressing this issue. Our framework also recovers some popular methods, including entropy minimization and pseudo-labeling. We provide new information-theoretical based generalization error upper bounds inspired by our novel framework. Our bounds are applicable to both general semi-supervised learning and the covariate-shift scenario. Finally, we show numerically that our method outperforms previous approaches proposed for semi-supervised learning under the covariate shift.

Wei Pu, Jun-Jie Huang, Barak Sober et al.

In this paper, we focus on X-ray images of paintings with concealed sub-surface designs (e.g., deriving from reuse of the painting support or revision of a composition by the artist), which include contributions from both the surface painting and the concealed features. In particular, we propose a self-supervised deep learning-based image separation approach that can be applied to the X-ray images from such paintings to separate them into two hypothetical X-ray images. One of these reconstructed images is related to the X-ray image of the concealed painting, while the second one contains only information related to the X-ray of the visible painting. The proposed separation network consists of two components: the analysis and the synthesis sub-networks. The analysis sub-network is based on learned coupled iterative shrinkage thresholding algorithms (LCISTA) designed using algorithm unrolling techniques, and the synthesis sub-network consists of several linear mappings. The learning algorithm operates in a totally self-supervised fashion without requiring a sample set that contains both the mixed X-ray images and the separated ones. The proposed method is demonstrated on a real painting with concealed content, Doña Isabel de Porcel by Francisco de Goya, to show its effectiveness.

Yuheng Bu, Gholamali Aminian, Laura Toni et al.

We provide an information-theoretic analysis of the generalization ability of Gibbs-based transfer learning algorithms by focusing on two popular transfer learning approaches, $α$-weighted-ERM and two-stage-ERM. Our key result is an exact characterization of the generalization behaviour using the conditional symmetrized KL information between the output hypothesis and the target training samples given the source samples. Our results can also be applied to provide novel distribution-free generalization error upper bounds on these two aforementioned Gibbs algorithms. Our approach is versatile, as it also characterizes the generalization errors and excess risks of these two Gibbs algorithms in the asymptotic regime, where they converge to the $α$-weighted-ERM and two-stage-ERM, respectively. Based on our theoretical results, we show that the benefits of transfer learning can be viewed as a bias-variance trade-off, with the bias induced by the source distribution and the variance induced by the lack of target samples. We believe this viewpoint can guide the choice of transfer learning algorithms in practice.

Wei Pu, Chao Zhou, Yonina C. Eldar et al.

In this paper, we consider deep neural networks for solving inverse problems that are robust to forward model mis-specifications. Specifically, we treat sensing problems with model mismatch where one wishes to recover a sparse high-dimensional vector from low-dimensional observations subject to uncertainty in the measurement operator. We then design a new robust deep neural network architecture by applying algorithm unfolding techniques to a robust version of the underlying recovery problem. Our proposed network - named Robust lEarned Shrinkage-Thresholding (REST) - exhibits an additional normalization processing compared to Learned Iterative Shrinkage-Thresholding Algorithm (LISTA), leading to reliable recovery of the signal under sample-wise varying model mismatch. The proposed REST network is shown to outperform state-of-the-art model-based and data-driven algorithms in both compressive sensing and radar imaging problems wherein model mismatch is taken into consideration.

Afroditi Papadaki, Natalia Martinez, Martin Bertran et al.

Federated learning is an increasingly popular paradigm that enables a large number of entities to collaboratively learn better models. In this work, we study minmax group fairness in paradigms where different participating entities may only have access to a subset of the population groups during the training phase. We formally analyze how this fairness objective differs from existing federated learning fairness criteria that impose similar performance across participants instead of demographic groups. We provide an optimization algorithm -- FedMinMax -- for solving the proposed problem that provably enjoys the performance guarantees of centralized learning algorithms. We experimentally compare the proposed approach against other methods in terms of group fairness in various federated learning setups.

Gholamali Aminian, Yuheng Bu, Laura Toni et al.

Bounding the generalization error of a supervised learning algorithm is one of the most important problems in learning theory, and various approaches have been developed. However, existing bounds are often loose and lack of guarantees. As a result, they may fail to characterize the exact generalization ability of a learning algorithm. Our main contribution is an exact characterization of the expected generalization error of the well-known Gibbs algorithm in terms of symmetrized KL information between the input training samples and the output hypothesis. Such a result can be applied to tighten existing expected generalization error bound. Our analysis provides more insight on the fundamental role the symmetrized KL information plays in controlling the generalization error of the Gibbs algorithm.

Hongxiang Fan, Martin Ferianc, Miguel Rodrigues et al.

Neural networks (NNs) have demonstrated their potential in a wide range of applications such as image recognition, decision making or recommendation systems. However, standard NNs are unable to capture their model uncertainty which is crucial for many safety-critical applications including healthcare and autonomous vehicles. In comparison, Bayesian neural networks (BNNs) are able to express uncertainty in their prediction via a mathematical grounding. Nevertheless, BNNs have not been as widely used in industrial practice, mainly because of their expensive computational cost and limited hardware performance. This work proposes a novel FPGA-based hardware architecture to accelerate BNNs inferred through Monte Carlo Dropout. Compared with other state-of-the-art BNN accelerators, the proposed accelerator can achieve up to 4 times higher energy efficiency and 9 times better compute efficiency. Considering partial Bayesian inference, an automatic framework is proposed, which explores the trade-off between hardware and algorithmic performance. Extensive experiments are conducted to demonstrate that our proposed framework can effectively find the optimal points in the design space.

Martin Ferianc, Partha Maji, Matthew Mattina et al.

Bayesian neural networks (BNNs) are making significant progress in many research areas where decision-making needs to be accompanied by uncertainty estimation. Being able to quantify uncertainty while making decisions is essential for understanding when the model is over-/under-confident, and hence BNNs are attracting interest in safety-critical applications, such as autonomous driving, healthcare, and robotics. Nevertheless, BNNs have not been as widely used in industrial practice, mainly because of their increased memory and compute costs. In this work, we investigate quantisation of BNNs by compressing 32-bit floating-point weights and activations to their integer counterparts, that has already been successful in reducing the compute demand in standard pointwise neural networks. We study three types of quantised BNNs, we evaluate them under a wide range of different settings, and we empirically demonstrate that a uniform quantisation scheme applied to BNNs does not substantially decrease their quality of uncertainty estimation.

Gholamali Aminian, Laura Toni, Miguel R. D. Rodrigues

Generalization error bounds are critical to understanding the performance of machine learning models. In this work, building upon a new bound of the expected value of an arbitrary function of the population and empirical risk of a learning algorithm, we offer a more refined analysis of the generalization behaviour of a machine learning models based on a characterization of (bounds) to their generalization error moments. We discuss how the proposed bounds -- which also encompass new bounds to the expected generalization error -- relate to existing bounds in the literature. We also discuss how the proposed generalization error moment bounds can be used to construct new generalization error high-probability bounds.

Gholamali Aminian, Laura Toni, Miguel R. D. Rodrigues

Generalization error bounds are critical to understanding the performance of machine learning models. In this work, we propose a new information-theoretic based generalization error upper bound applicable to supervised learning scenarios. We show that our general bound can specialize in various previous bounds. We also show that our general bound can be specialized under some conditions to a new bound involving the Jensen-Shannon information between a random variable modelling the set of training samples and another random variable modelling the hypothesis. We also prove that our bound can be tighter than mutual information-based bounds under some conditions.

Wei Pu, Barak Sober, Nathan Daly et al.

X-radiography (X-ray imaging) is a widely used imaging technique in art investigation. It can provide information about the condition of a painting as well as insights into an artist's techniques and working methods, often revealing hidden information invisible to the naked eye. In this paper, we deal with the problem of separating mixed X-ray images originating from the radiography of double-sided paintings. Using the visible color images (RGB images) from each side of the painting, we propose a new Neural Network architecture, based upon 'connected' auto-encoders, designed to separate the mixed X-ray image into two simulated X-ray images corresponding to each side. In this proposed architecture, the convolutional auto encoders extract features from the RGB images. These features are then used to (1) reproduce both of the original RGB images, (2) reconstruct the hypothetical separated X-ray images, and (3) regenerate the mixed X-ray image. The algorithm operates in a totally self-supervised fashion without requiring a sample set that contains both the mixed X-ray images and the separated ones. The methodology was tested on images from the double-sided wing panels of the \textsl{Ghent Altarpiece}, painted in 1432 by the brothers Hubert and Jan van Eyck. These tests show that the proposed approach outperforms other state-of-the-art X-ray image separation methods for art investigation applications.

Martin Ferianc, Hongxiang Fan, Miguel Rodrigues

In recent years, neural architecture search (NAS) has received intensive scientific and industrial interest due to its capability of finding a neural architecture with high accuracy for various artificial intelligence tasks such as image classification or object detection. In particular, gradient-based NAS approaches have become one of the more popular approaches thanks to their computational efficiency during the search. However, these methods often experience a mode collapse, where the quality of the found architectures is poor due to the algorithm resorting to choosing a single operation type for the entire network, or stagnating at a local minima for various datasets or search spaces. To address these defects, we present a differentiable variational inference-based NAS method for searching sparse convolutional neural networks. Our approach finds the optimal neural architecture by dropping out candidate operations in an over-parameterised supergraph using variational dropout with automatic relevance determination prior, which makes the algorithm gradually remove unnecessary operations and connections without risking mode collapse. The evaluation is conducted through searching two types of convolutional cells that shape the neural network for classifying different image datasets. Our method finds diverse network cells, while showing state-of-the-art accuracy with up to almost 2 times fewer non-zero parameters.

Jaweria Amjad, Zhaoyan Lyu, Miguel R. D. Rodrigues

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask whether such knowledge of the forward operator can be exploited in deep learning approaches increasingly used to solve inverse problems. In this paper, we provide one such way via an analysis of the generalisation error of deep learning methods applicable to inverse problems. In particular, by building on the algorithmic robustness framework, we offer a generalisation error bound that encapsulates key ingredients associated with the learning problem such as the complexity of the data space, the size of the training set, the Jacobian of the deep neural network and the Jacobian of the composition of the forward operator with the neural network. We then propose a 'plug-and-play' regulariser that leverages the knowledge of the forward map to improve the generalization of the network. We likewise also propose a new method allowing us to tightly upper bound the Lipschitz constants of the relevant functions that is much more computational efficient than existing ones. We demonstrate the efficacy of our model-aware regularised deep learning algorithms against other state-of-the-art approaches on inverse problems involving various sub-sampling operators such as those used in classical compressed sensing setup and accelerated Magnetic Resonance Imaging (MRI).

Daniel Jakubovitz, Miguel R. D. Rodrigues, Raja Giryes

Transfer learning is a very important tool in deep learning as it allows propagating information from one "source dataset" to another "target dataset", especially in the case of a small number of training examples in the latter. Yet, discrepancies between the underlying distributions of the source and target data are commonplace and are known to have a substantial impact on algorithm performance. In this work we suggest a novel information theoretic approach for the analysis of the performance of deep neural networks in the context of transfer learning. We focus on the task of semi-supervised transfer learning, in which unlabeled samples from the target dataset are available during the network training on the source dataset. Our theory suggests that one may improve the transferability of a deep neural network by imposing a Lautum information based regularization that relates the network weights to the target data. We demonstrate the effectiveness of the proposed approach in various transfer learning experiments.

Jaweria Amjad, Zhaoyan Lyu, Miguel R. D. Rodrigues

Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their solution. This paper instead studies the use of deep learning approaches to approximate the solution of inverse problems. In particular, the paper provides a new generalization bound, depending on key quantity associated with a deep neural network -- its Jacobian matrix -- that also leads to a number of computationally efficient regularization strategies applicable to inverse problems. The paper also tests the proposed regularization strategies in a number of inverse problems including image super-resolution ones. Our numerical results conducted on various datasets show that both fully connected and convolutional neural networks regularized using the regularization or proxy regularization strategies originating from our theory exhibit much better performance than deep networks regularized with standard approaches such as weight-decay.

Daniel Jakubovitz, Raja Giryes, Miguel R. D. Rodrigues

Deep learning models have lately shown great performance in various fields such as computer vision, speech recognition, speech translation, and natural language processing. However, alongside their state-of-the-art performance, it is still generally unclear what is the source of their generalization ability. Thus, an important question is what makes deep neural networks able to generalize well from the training set to new data. In this article, we provide an overview of the existing theory and bounds for the characterization of the generalization error of deep neural networks, combining both classical and more recent theoretical and empirical results.

Pingfan Song, Miguel R. D. Rodrigues

In real-world scenarios, many data processing problems often involve heterogeneous images associated with different imaging modalities. Since these multimodal images originate from the same phenomenon, it is realistic to assume that they share common attributes or characteristics. In this paper, we propose a multi-modal image processing framework based on coupled dictionary learning to capture similarities and disparities between different image modalities. In particular, our framework can capture favorable structure similarities across different image modalities such as edges, corners, and other elementary primitives in a learned sparse transform domain, instead of the original pixel domain, that can be used to improve a number of image processing tasks such as denoising, inpainting, or super-resolution. Practical experiments demonstrate that incorporating multimodal information using our framework brings notable benefits.

Martin Bertran, Natalia Martinez, Afroditi Papadaki et al.

It is becoming increasingly clear that users should own and control their data. Utility providers are also becoming more interested in guaranteeing data privacy. As such, users and utility providers should collaborate in data privacy, a paradigm that has not yet been developed in the privacy research community. We introduce this concept and present explicit architectures where the user controls what characteristics of the data she/he wants to share and what she/he wants to keep private. This is achieved by collaborative learning a sensitization function, either a deterministic or a stochastic one, that retains valuable information for the utility tasks but it also eliminates necessary information for the privacy ones. As illustration examples, we implement them using a plug-and-play approach, where no algorithm is changed at the system provider end, and an adversarial approach, where minor re-training of the privacy inferring engine is allowed. In both cases the learned sanitization function keeps the data in the original domain, thereby allowing the system to use the same algorithms it was using before for both original and privatized data. We show how we can maintain utility while fully protecting private information if the user chooses to do so, even when the first is harder than the second, as in the case here illustrated of identity detection while hiding gender.

Jure Sokolic, Qiang Qiu, Miguel R. D. Rodrigues et al.

Security, privacy, and fairness have become critical in the era of data science and machine learning. More and more we see that achieving universally secure, private, and fair systems is practically impossible. We have seen for example how generative adversarial networks can be used to learn about the expected private training data; how the exploitation of additional data can reveal private information in the original one; and how what looks like unrelated features can teach us about each other. Confronted with this challenge, in this paper we open a new line of research, where the security, privacy, and fairness is learned and used in a closed environment. The goal is to ensure that a given entity (e.g., the company or the government), trusted to infer certain information with our data, is blocked from inferring protected information from it. For example, a hospital might be allowed to produce diagnosis on the patient (the positive task), without being able to infer the gender of the subject (negative task). Similarly, a company can guarantee that internally it is not using the provided data for any undesired task, an important goal that is not contradicting the virtually impossible challenge of blocking everybody from the undesired task. We design a system that learns to succeed on the positive task while simultaneously fail at the negative one, and illustrate this with challenging cases where the positive task is actually harder than the negative one being blocked. Fairness, to the information in the negative task, is often automatically obtained as a result of this proposed approach. The particular framework and examples open the door to security, privacy, and fairness in very important closed scenarios, ranging from private data accumulation companies like social networks to law-enforcement and hospitals.

Jure Sokolic, Raja Giryes, Guillermo Sapiro et al.

This paper studies the generalization error of invariant classifiers. In particular, we consider the common scenario where the classification task is invariant to certain transformations of the input, and that the classifier is constructed (or learned) to be invariant to these transformations. Our approach relies on factoring the input space into a product of a base space and a set of transformations. We show that whereas the generalization error of a non-invariant classifier is proportional to the complexity of the input space, the generalization error of an invariant classifier is proportional to the complexity of the base space. We also derive a set of sufficient conditions on the geometry of the base space and the set of transformations that ensure that the complexity of the base space is much smaller than the complexity of the input space. Our analysis applies to general classifiers such as convolutional neural networks. We demonstrate the implications of the developed theory for such classifiers with experiments on the MNIST and CIFAR-10 datasets.

Hugo Reboredo, Francesco Renna, Robert Calderbank et al.

This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the probability of misclassification to zero in the low-noise regime, both for random measurements and designed ones. Such bounds reveal two important operational regimes that are a function of the characteristics of the source: i) when the number of classes is less than or equal to the dimension of the space spanned by signals in each class, reliable classification is possible in the low-noise regime by using a one-vs-all measurement design; ii) when the dimension of the spaces spanned by signals in each class is lower than the number of classes, reliable classification is guaranteed in the low-noise regime by using a simple random measurement design. Simulation results both with synthetic and real data show that our analysis is sharp, in the sense that it is able to gauge the number of measurements required to drive the misclassification probability to zero in the low-noise regime.

Jure Sokolic, Raja Giryes, Guillermo Sapiro et al.

The generalization error of deep neural networks via their classification margin is studied in this work. Our approach is based on the Jacobian matrix of a deep neural network and can be applied to networks with arbitrary non-linearities and pooling layers, and to networks with different architectures such as feed forward networks and residual networks. Our analysis leads to the conclusion that a bounded spectral norm of the network's Jacobian matrix in the neighbourhood of the training samples is crucial for a deep neural network of arbitrary depth and width to generalize well. This is a significant improvement over the current bounds in the literature, which imply that the generalization error grows with either the width or the depth of the network. Moreover, it shows that the recently proposed batch normalization and weight normalization re-parametrizations enjoy good generalization properties, and leads to a novel network regularizer based on the network's Jacobian matrix. The analysis is supported with experimental results on the MNIST, CIFAR-10, LaRED and ImageNet datasets.

Jure Sokolic, Francesco Renna, Robert Calderbank et al.

This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned on a given class is Gaussian with a zero mean and a low-rank covariance matrix. We also assume that the classifier knows only a mismatched version of the parameters of input distribution in lieu of the true parameters. By constructing an asymptotic low-noise expansion of an upper bound to the error probability of such a mismatched classifier, we provide sufficient conditions for reliable classification in the low-noise regime that are able to sharply predict the absence of a classification error floor. Such conditions are a function of the geometry of the true signal distribution, the geometry of the mismatched signal distributions as well as the interplay between such geometries, namely, the principal angles and the overlap between the true and the mismatched signal subspaces. Numerical results demonstrate that our conditions for reliable classification can sharply predict the behavior of a mismatched classifier both with synthetic data and in a motion segmentation and a hand-written digit classification applications.

Joao F. C. Mota, Nikos Deligiannis, Aswin C. Sankaranarayanan et al.

We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear dynamical model. Our algorithm, based on recent theoretical results for $\ell_1$-$\ell_1$ minimization, is recursive and computes the number of measurements to be taken at each time on-the-fly. As an example, we apply the algorithm to compressive video background subtraction, a problem that can be stated as follows: given a set of measurements of a sequence of images with a static background, simultaneously reconstruct each image while separating its foreground from the background. The performance of our method is illustrated on sequences of real images: we observe that it allows a dramatic reduction in the number of measurements with respect to state-of-the-art compressive background subtraction schemes.

Francesco Renna, Liming Wang, Xin Yuan et al.

This paper offers a characterization of fundamental limits on the classification and reconstruction of high-dimensional signals from low-dimensional features, in the presence of side information. We consider a scenario where a decoder has access both to linear features of the signal of interest and to linear features of the side information signal; while the side information may be in a compressed form, the objective is recovery or classification of the primary signal, not the side information. The signal of interest and the side information are each assumed to have (distinct) latent discrete labels; conditioned on these two labels, the signal of interest and side information are drawn from a multivariate Gaussian distribution. With joint probabilities on the latent labels, the overall signal-(side information) representation is defined by a Gaussian mixture model. We then provide sharp sufficient and/or necessary conditions for these quantities to approach zero when the covariance matrices of the Gaussians are nearly low-rank. These conditions, which are reminiscent of the well-known Slepian-Wolf and Wyner-Ziv conditions, are a function of the number of linear features extracted from the signal of interest, the number of linear features extracted from the side information signal, and the geometry of these signals and their interplay. Moreover, on assuming that the signal of interest and the side information obey such an approximately low-rank model, we derive expansions of the reconstruction error as a function of the deviation from an exactly low-rank model; such expansions also allow identification of operational regimes where the impact of side information on signal reconstruction is most relevant. Our framework, which offers a principled mechanism to integrate side information in high-dimensional data problems, is also tested in the context of imaging applications.

João F. C. Mota, Nikos Deligiannis, Miguel R. D. Rodrigues

We address the problem of Compressed Sensing (CS) with side information. Namely, when reconstructing a target CS signal, we assume access to a similar signal. This additional knowledge, the side information, is integrated into CS via L1-L1 and L1-L2 minimization. We then provide lower bounds on the number of measurements that these problems require for successful reconstruction of the target signal. If the side information has good quality, the number of measurements is significantly reduced via L1-L1 minimization, but not so much via L1-L2 minimization. We provide geometrical interpretations and experimental results illustrating our findings.

Liming Wang, Miguel Rodrigues, Lawrence Carin

We investigate connections between information-theoretic and estimation-theoretic quantities in vector Poisson channel models. In particular, we generalize the gradient of mutual information with respect to key system parameters from the scalar to the vector Poisson channel model. We also propose, as another contribution, a generalization of the classical Bregman divergence that offers a means to encapsulate under a unifying framework the gradient of mutual information results for scalar and vector Poisson and Gaussian channel models. The so-called generalized Bregman divergence is also shown to exhibit various properties akin to the properties of the classical version. The vector Poisson channel model is drawing considerable attention in view of its application in various domains: as an example, the availability of the gradient of mutual information can be used in conjunction with gradient descent methods to effect compressive-sensing projection designs in emerging X-ray and document classification applications.

Minhua Chen, William Carson, Miguel Rodrigues et al.

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label (based on a Shannon entropy measure). By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely related methods (Linear Discriminant Analysis and Information Discriminant Analysis), and comparisons are also made with a method in which Renyi entropy is used to define the mutual information (in this case the gradient may be computed simply, under a special parameter setting). Relative to these alternative approaches, the proposed method achieves promising results on real datasets.