The growing prevalence of real-world deepfakes presents a critical challenge for existing detection systems, which are often evaluated on datasets collected just for scientific purposes. To address this gap, we introduce a novel dataset of real-world audio deepfakes. Our analysis reveals that these real-world examples pose significant challenges, even for the most performant detection models. Rather than increasing model complexity or exhaustively search for a better alternative, in this work we focus on a data-centric paradigm, employing strategies like dataset curation, pruning, and augmentation to improve model robustness and generalization. Through these methods, we achieve a 55% relative reduction in EER on the In-the-Wild dataset, reaching an absolute EER of 1.7%, and a 63% reduction on our newly proposed real-world deepfakes dataset, AI4T. These results highlight the transformative potential of data-centric approaches in enhancing deepfake detection for real-world applications. Code and data available at: this https URL.

Deepfake detection has gained significant attention across audio, text, and image modalities, with high accuracy in distinguishing real from fake. However, identifying the exact source--such as the system or model behind a deepfake--remains a less studied problem. In this paper, we take a significant step forward in audio deepfake model attribution or source tracing by proposing a training-free, green AI approach based entirely on k-Nearest Neighbors (kNN). Leveraging a pre-trained self-supervised learning (SSL) model, we show that grouping samples from the same generator is straightforward--we obtain an 0.93 F1-score across five deepfake datasets. The method also demonstrates strong out-of-domain (OOD) detection, effectively identifying samples from unseen models at an F1-score of 0.84. We further analyse these results in a multi-dimensional approach and provide additional insights. All code and data protocols used in this work are available in our open repository: this https URL.

This paper considers smooth convex optimization problems with many functional constraints. To solve this general class of problems we propose a new stochastic perturbed augmented Lagrangian method, called SGDPA, where a perturbation is introduced in the augmented Lagrangian function by multiplying the dual variables with a subunitary parameter. Essentially, we linearize the objective and one randomly chosen functional constraint within the perturbed augmented Lagrangian at the current iterate and add a quadratic regularization that leads to a stochastic gradient descent update for the primal variables, followed by a perturbed random coordinate ascent step to update the dual variables. We provide a convergence analysis in both optimality and feasibility criteria for the iterates of SGDPA algorithm using basic assumptions on the problem. In particular, when the dual updates are assumed to be bounded, we prove sublinear rates of convergence for the iterates of algorithm SGDPA of order $\mathcal{O} (k^{-1/2})$ when the objective is convex and of order $\mathcal{O} (k^{-1})$ when the objective is strongly convex, where $k$ is the iteration counter. Under some additional assumptions, we prove that the dual iterates are bounded and in this case we obtain convergence rates of order $\mathcal{O} (k^{-1/4})$ and $\mathcal{O} (k^{-1/2})$ when the objective is convex and strongly convex, respectively. Preliminary numerical experiments on problems with many quadratic constraints demonstrate the viability and performance of our method when compared to some existing state-of-the-art optimization methods and software.

Generalisation -- the ability of a model to perform well on unseen data -- is crucial for building reliable deepfake detectors. However, recent studies have shown that the current audio deepfake models fall short of this desideratum. In this work we investigate the potential of pretrained self-supervised representations in building general and calibrated audio deepfake detection models. We show that large frozen representations coupled with a simple logistic regression classifier are extremely effective in achieving strong generalisation capabilities: compared to the RawNet2 model, this approach reduces the equal error rate from 30.9% to 8.8% on a benchmark of eight deepfake datasets, while learning less than 2k parameters. Moreover, the proposed method produces considerably more reliable predictions compared to previous approaches making it more suitable for realistic use.

In this paper we propose a distributed version of a randomized block-coordinate descent method for minimizing the sum of a partially separable smooth convex function and a fully separable non-smooth convex function. Under the assumption of block Lipschitz continuity of the gradient of the smooth function, this method is shown to have a sublinear convergence rate. Linear convergence rate of the method is obtained for the newly introduced class of generalized error bound functions. We prove that the new class of generalized error bound functions encompasses both global/local error bound functions and smooth strongly convex functions. We also show that the theoretical estimates on the convergence rate depend on the number of blocks chosen randomly and a natural measure of separability of the objective function.

In this paper we present the solver DuQuad specialized for solving general convex quadratic problems arising in many engineering applications. When it is difficult to project on the primal feasible set, we use the (augmented) Lagrangian relaxation to handle the complicated constraints and then, we apply dual first order algorithms based on inexact dual gradient information for solving the corresponding dual problem. The iteration complexity analysis is based on two types of approximate primal solutions: the primal last iterate and an average of primal iterates. We provide computational complexity estimates on the primal suboptimality and feasibility violation of the generated approximate primal solutions. Then, these algorithms are implemented in the programming language C in DuQuad, and optimized for low iteration complexity and low memory footprint. DuQuad has a dynamic Matlab interface which make the process of testing, comparing, and analyzing the algorithms simple. The algorithms are implemented using only basic arithmetic and logical operations and are suitable to run on low cost hardware. It is shown that if an approximate solution is sufficient for a given application, there exists problems where some of the implemented algorithms obtain the solution faster than state-of-the-art commercial solvers.

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum of two terms satisfying a stochastic bounded gradient condition, with or without strong convexity type properties. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets, in this paper we consider that each constraint set is given as the level set of a convex but not necessarily differentiable function. Based on the flexibility offered by our general optimization model we consider a stochastic subgradient method with random feasibility updates. At each iteration, our algorithm takes a stochastic proximal (sub)gradient step aimed at minimizing the objective function and then a subsequent subgradient step minimizing the feasibility violation of the observed random constraint. We analyze the convergence behavior of the proposed algorithm for diminishing stepsizes and for the case when the objective function is convex or strongly convex, unifying the nonsmooth and smooth cases. We prove sublinear convergence rates for this stochastic subgradient algorithm, which are known to be optimal for subgradient methods on this class of problems. When the objective function has a linear least-square form and the constraints are polyhedral, it is shown that the algorithm converges linearly. Numerical evidence supports the effectiveness of our method in real problems.

In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a linearized augmented Lagrangian method, i.e., we linearize the objective function and the functional constraints in a Gauss-Newton fashion at the current iterate within the augmented Lagrangian function and add a quadratic regularization, yielding a subproblem that is easy to solve, and whose solution is the next primal iterate. The update of the dual multipliers is also based on the linearization of functional constraints. Under a novel dynamic regularization parameter choice, we prove boundedness and global asymptotic convergence of the iterates to a first-order solution of the problem. We also derive convergence guarantees for the iterates of our method to an $\epsilon$-first-order solution in $\mathcal{O}(\sqrt{\rho} \epsilon^{-2})$ Jacobian evaluations, where $\rho$ is the penalty parameter. Moreover, when the problem exhibits a benign nonconvex property, we derive improved convergence results to an $\epsilon$-second-order solution. Finally, we validate the performance of the proposed algorithm by numerically comparing it with the existing methods and software from the literature.

In this paper we develop a higher-order method for solving composite (non)convex minimization problems with smooth (non)convex functional constraints. At each iteration our method approximates the smooth part of the objective function and of the constraints by higher-order Taylor approximations, leading to a moving Taylor approximation method (MTA). We present convergence guarantees for MTA algorithm for both, nonconvex and convex problems. In particular, when the objective and the constraints are nonconvex functions, we prove that the sequence generated by MTA algorithm converges globally to a KKT point. Moreover, we derive convergence rates in the iterates when the problem data satisfy the Kurdyka-Lojasiewicz (KL) property. Further, when the objective function is (uniformly) convex and the constraints are also convex, we provide (linear/superlinear) sublinear convergence rates for our algorithm. Finally, we present an efficient implementation of the proposed algorithm and compare it with existing methods from the literature.

In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain acceleration we build on the fact that the Kaczmarz method is dual to a coordinate descent method. We use a recently proposed acceleration method for the randomized coordinate descent and transfer it to the primal space. This method inherits many of the attractive features of the accelerated coordinate descent method, including its worst-case convergence rates. A theoretical analysis of the convergence of the proposed method is given. Numerical experiments show that the proposed method is more efficient and faster than the existing methods for solving the same problem.

We study the worst-case behavior of Block Coordinate Descent (BCD) type algorithms for unconstrained minimization of coordinate-wise smooth convex functions. This behavior is indeed not completely understood, and the practical success of these algorithms is not fully explained by current convergence analyses. We extend the recently proposed Performance Estimation Problem (PEP) approach to convex coordinate-wise smooth functions by proposing necessary interpolation conditions. We then exploit this to obtain improved numerical upper bounds on the worst-case convergence rate of three different BCD algorithms, namely Cyclic Coordinate Descent (CCD), Alternating Minimization (AM), and a Cyclic version of the Random Accelerated Coordinate Descent introduced in Fercoq and Richtárik (2015) (CACD), substantially outperforming the best current bounds in some situations. In addition, we show the convergence of the CCD algorithm with more natural assumptions in the context of convex optimization than those typically made in the literature. Our methodology uncovers a number of phenomena, some of which can be formally established. These include a scale-invariance property of the worst case of CCD with respect to the coordinate-wise smoothness constants and a lower bound on the worst-case performance of CCD which is equal to the number of blocks times the worst-case of full gradient descent over the class of smooth convex functions. We also adapt our framework to the analysis of random BCD algorithms, and present numerical results showing that the standard acceleration scheme in Fercoq and Richtárik (2015) appears to be inefficient for deterministic algorithms.

Deep neural networks have revolutionized many fields, including image processing, inverse problems, text mining and more recently, give very promising results in systems and control. Neural networks with hidden layers have a strong potential as an approximation framework of predictive control laws as they usually yield better approximation quality and smaller memory requirements than existing explicit (multi-parametric) approaches. In this paper, we first show that neural networks with HardTanh activation functions can exactly represent predictive control laws of linear time-invariant systems. We derive theoretical bounds on the minimum number of hidden layers and neurons that a HardTanh neural network should have to exactly represent a given predictive control law. The choice of HardTanh deep neural networks is particularly suited for linear predictive control laws as they usually require less hidden layers and neurons than deep neural networks with ReLU units for representing exactly continuous piecewise affine (or equivalently min-max) maps. In the second part of the paper we bring the physics of the model and standard optimization techniques into the architecture design, in order to eliminate the disadvantages of the black-box HardTanh learning. More specifically, we design trainable unfolded HardTanh deep architectures for learning linear predictive control laws based on two standard iterative optimization algorithms, i.e., projected gradient descent and accelerated projected gradient descent. We also study the performance of the proposed HardTanh type deep neural networks on a linear model predictive control application.

In this paper we consider finite sum composite convex optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the other is amenable to proximal evaluations. We assume a generalized bounded gradient condition on the objective which allows us to simultaneously tackle both smooth and nonsmooth problems. We also consider the cases of both with and without a strong convexity property. Further, we assume that each constraint set is given as the level set of a convex but not necessarily differentiable function. We reformulate the constrained finite sum problem into a stochastic optimization problem for which the stochastic subgradient projection method from [17] specializes to a collection of mini-batch variants, with different mini-batch sizes for the objective function and functional constraints, respectively. More specifically, at each iteration, our algorithm takes a mini-batch stochastic proximal subgradient step aimed at minimizing the objective function and then a subsequent mini-batch subgradient projection step minimizing the feasibility violation. By specializing different mini-batching strategies, we derive exact expressions for the stepsizes as a function of the mini-batch size and in some cases we also derive insightful stepsize-switching rules which describe when one should switch from a constant to a decreasing stepsize regime. We also prove sublinear convergence rates for the mini-batch subgradient projection algorithm which depend explicitly on the mini-batch sizes and on the properties of the objective function. Numerical results also show a better performance of our mini-batch scheme over its single-batch counterpart.

Hyperspectral Imaging comprises excessive data consequently leading to significant challenges for data processing, storage and transmission. Compressive Sensing has been used in the field of Hyperspectral Imaging as a technique to compress the large amount of data. This work addresses the recovery of hyperspectral images 2.5x compressed. A comparative study in terms of the accuracy and the performance of the convex FISTA/ADMM in addition to the greedy gOMP/BIHT/CoSaMP recovery algorithms is presented. The results indicate that the algorithms recover successfully the compressed data, yet the gOMP algorithm achieves superior accuracy and faster recovery in comparison to the other algorithms at the expense of high dependence on unknown sparsity level of the data to recover.

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known. Further, we consider both cases: unconstrained and linearly constrained nonconvex problems. For optimization problems of the above structure, we propose random coordinate descent algorithms and analyze their convergence properties. For the general case, when the objective function is nonconvex and composite we prove asymptotic convergence for the sequences generated by our algorithms to stationary points and sublinear rate of convergence in expectation for some optimality measure. Additionally, if the objective function satisfies an error bound condition we derive a local linear rate of convergence for the expected values of the objective function. We also present extensive numerical experiments for evaluating the performance of our algorithms in comparison with state-of-the-art methods.

We develop a method of driving a Markov processes through a continuous flow. In particular, at the level of the transition functions we investigate an approach of adding a first order operator to the generator of a Markov process, when the two generators commute. A relevant example is a measure-valued superprocess having a continuous flow as spatial motion and a branching mechanism which does not depend on the spatial variable. We prove that any flow is actually continuous in a convenient topology and we show that a Markovian multiplicative semigroup on an Lp space is generated by a continuous flow, completing the answer to the question whether it is enough to have a measurable structure, like a C0-semigroup of Markovian contractions on an $L^p$-space with no fixed topology, in order to ensure the existence of a right Markov process associated to the given semigroup. We extend from bounded to unbounded functions the weak generator (in the sense of Dynkin) and the corresponding martingale problem

In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is differentiable but nonseparable. Under these general settings we derive and analyze two new coordinate descent methods. The first algorithm, referred to as coordinate proximal gradient method, considers the composite form of the objective function, while the other algorithm disregards the composite form of the objective and uses the partial gradient of the full objective, yielding a coordinate gradient descent scheme with novel adaptive stepsize rules. We prove that these new stepsize rules make the coordinate gradient scheme a descent method, provided that additional assumptions hold for the second term in the objective function. We present a complete worst-case complexity analysis for these two new methods in both, convex and nonconvex settings, provided that the (block) coordinates are chosen random or cyclic. Preliminary numerical results also confirm the efficiency of our two algorithms on practical problems.

This paper deals with composite optimization problems having the objective function formed as the sum of two terms, one has Lipschitz continuous gradient along random subspaces and may be nonconvex and the second term is simple and differentiable, but possibly nonconvex and nonseparable. Under these settings we design a stochastic coordinate proximal gradient method which takes into account the nonseparable composite form of the objective function. This algorithm achieves scalability by constructing at each iteration a local approximation model of the whole nonseparable objective function along a random subspace with user-determined dimension. We outline efficient techniques for selecting the random subspace, yielding an implementation that has low cost per-iteration while also achieving fast convergence rates. We present a probabilistic worst-case complexity analysis for our stochastic coordinate proximal gradient method in convex and nonconvex settings, in particular we prove high-probability bounds on the number of iterations before a given optimality is achieved. Extensive numerical results also confirm the efficiency of our algorithm.

In this paper we consider large-scale composite nonconvex optimization problems having the objective function formed as a sum of three terms, first has block coordinate-wise Lipschitz continuous gradient, second is twice differentiable but nonseparable and third is the indicator function of some separable closed convex set. Under these general settings we derive and analyze a new cyclic coordinate descent method, which uses the partial gradient of the differentiable part of the objective, yielding a coordinate gradient descent scheme with a novel adaptive stepsize rule. We prove that this stepsize rule makes the coordinate gradient scheme a descent method, provided that additional assumptions hold for the second term in the objective function. We also present a worst-case complexity analysis for this new method in the nonconvex settings. Numerical results on orthogonal nonnegative matrix factorization problem also confirm the efficiency of our algorithm.

In this paper, we consider a modified projected Gauss-Newton method for solving constrained nonlinear least-squares problems. We assume that the functional constraints are smooth and the the other constraints are represented by a simple closed convex set. We formulate the nonlinear least-squares problem as an optimization problem using the Euclidean norm as a merit function. In our method, at each iteration we linearize the functional constraints inside the merit function at the current point and add a quadratic regularization, yielding a strongly convex subproblem that is easy to solve, whose solution is the next iterate. We present global convergence guarantees for the proposed method under mild assumptions. In particular, we prove stationary point convergence guarantees and under Kurdyka-Lojasiewicz (KL) property for the objective function we derive convergence rates depending on the KL parameter. Finally, we show the efficiency of this method on the power flow analysis problem using several IEEE bus test cases.