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We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established analytically.

In this letter, the achievable rate maximization problem is considered for intelligent reflecting surface (IRS) assisted multiple-input multiple-output (MIMO) systems in an underlay spectrum sharing scenario, subject to interference power constraints at the primary users. The formulated non-convex optimization problem is challenging to solve due to its non-convexity as well as coupling design variables in the constraints. Different from existing works that are mostly based on alternating optimization (AO), we propose a penalty dual decomposition based gradient projection (PDDGP) algorithm to solve this problem. We also provide a convergence proof and a complexity analysis for the proposed algorithm. We benchmark the proposed algorithm against two known solutions, namely a minimum mean-square error based AO algorithm and an inner approximation method with block coordinate descent. Specifically, the complexity of the proposed algorithm grows linearly with respect to the number of reflecting elements at the IRS, while that of the two benchmark methods grows with the third power of the number of IRS elements. Moreover, numerical results show that the proposed PDDGP algorithm yields considerably higher achievable rate than the benchmark solutions.

Gradient Descent (GD) is a powerful workhorse of modern machine learning thanks to its scalability and efficiency in high-dimensional spaces. Its ability to find local minimisers is only guaranteed for losses with Lipschitz gradients, where it can be seen as a 'bona-fide' discretisation of an underlying gradient flow. Yet, many ML setups involving overparametrised models do not fall into this problem class, which has motivated research beyond the so-called "Edge of Stability", where the step-size crosses the admissibility threshold inversely proportional to the Lipschitz constant above. Perhaps surprisingly, GD has been empirically observed to still converge regardless of local instability. In this work, we study a local condition for such an unstable convergence around a local minima in a low dimensional setting. We then leverage these insights to establish global convergence of a two-layer single-neuron ReLU student network aligning with the teacher neuron in a large learning rate beyond the Edge of Stability under population loss. Meanwhile, while the difference of norms of the two layers is preserved by gradient flow, we show that GD above the edge of stability induces a balancing effect, leading to the same norms across the layers.

We present a systematic refactoring of the conventional treatment of privacy analyses, basing it on mathematical concepts from the framework of Quantitative Information Flow (QIF). The approach we suggest brings three principal advantages: it is flexible, allowing for precise quantification and comparison of privacy risks for attacks both known and novel; it can be computationally tractable for very large, longitudinal datasets; and its results are explainable both to politicians and to the general public. We apply our approach to a very large case study: the Educational Censuses of Brazil, curated by the governmental agency INEP, which comprise over 90 attributes of approximately 50 million individuals released longitudinally every year since 2007. These datasets have only very recently (2018-2021) attracted legislation to regulate their privacy -- while at the same time continuing to maintain the openness that had been sought in Brazilian society. INEP's reaction to that legislation was the genesis of our project with them. In our conclusions here we share the scientific, technical, and communication lessons we learned in the process.

We present an empirical study on the use of continual learning (CL) methods in a reinforcement learning (RL) scenario, which, to the best of our knowledge, has not been described before. CL is a very active recent research topic concerned with machine learning under non-stationary data distributions. Although this naturally applies to RL, the use of dedicated CL methods is still uncommon. This may be due to the fact that CL methods often assume a decomposition of CL problems into disjoint sub-tasks of stationary distribution, that the onset of these sub-tasks is known, and that sub-tasks are non-contradictory. In this study, we perform an empirical comparison of selected CL methods in a RL problem where a physically simulated robot must follow a racetrack by vision. In order to make CL methods applicable, we restrict the RL setting and introduce non-conflicting subtasks of known onset, which are however not disjoint and whose distribution, from the learner's point of view, is still non-stationary. Our results show that dedicated CL methods can significantly improve learning when compared to the baseline technique of "experience replay".

In this paper we elaborate an extension of rotation-based iterative Gaussianization, RBIG, which makes image Gaussianization possible. Although RBIG has been successfully applied to many tasks, it is limited to medium dimensionality data (on the order of a thousand dimensions). In images its application has been restricted to small image patches or isolated pixels, because rotation in RBIG is based on principal or independent component analysis and these transformations are difficult to learn and scale. Here we present the \emph{Convolutional RBIG}: an extension that alleviates this issue by imposing that the rotation in RBIG is a convolution. We propose to learn convolutional rotations (i.e. orthonormal convolutions) by optimising for the reconstruction loss between the input and an approximate inverse of the transformation using the transposed convolution operation. Additionally, we suggest different regularizers in learning these orthonormal convolutions. For example, imposing sparsity in the activations leads to a transformation that extends convolutional independent component analysis to multilayer architectures. We also highlight how statistical properties of the data, such as multivariate mutual information, can be obtained from \emph{Convolutional RBIG}. We illustrate the behavior of the transform with a simple example of texture synthesis, and analyze its properties by visualizing the stimuli that maximize the response in certain feature and layer.

In this paper, we are concerned with the numerical solution for the two-dimensional time fractional Fokker-Planck equation with tempered fractional derivative of order $\alpha$. Although some of its variants are considered in many recent numerical analysis papers, there are still some significant differences. Here we first provide the regularity estimates of the solution. And then a modified $L$1 scheme inspired by the middle rectangle quadrature formula on graded meshes is employed to compensate for the singularity of the solution at $t\rightarrow 0^{+}$, while the five-point difference scheme is used in space. Stability and convergence are proved in the sence of $L^{\infty}$ norm, then a sharp error estimate $\mathscr{O}(\tau^{\min\{2-\alpha, r\alpha\}})$ is derived on graded meshes. Furthermore, unlike the bounds proved in the previous works, the constant multipliers in our analysis do not blow up as the Caputo fractional derivative $\alpha$ approaches the classical value of 1. Finally, we perform the numerical experiments to verify the effectiveness and convergence order of the presented algorithms.

Fuzzing has proven to be a fundamental technique to automated software testing but also a costly one. With the increased adoption of CI/CD practices in software development, a natural question to ask is `What are the best ways to integrate fuzzing into CI/CD pipelines considering the velocity in code changes and the automated delivery/deployment practices?'. Indeed, a recent study by B\"ohme and Zhu shows that four in every five bugs have been introduced by recent code changes (i.e. regressions). In this paper, we take a close look at the integration of fuzzers to CI/CD pipelines from both automated software testing and continuous development angles. Firstly, we study an optimization opportunity to triage commits that do not require fuzzing and find, through experimental analysis, that the average fuzzing effort in CI/CD can be reduced by ~63% in three of the nine libraries we analyzed (>40% for six libraries). Secondly, we investigate the impact of fuzzing campaign duration on the CI/CD process: A shorter fuzzing campaign such as 15 minutes (as opposed to the wisdom of 24 hours in the field) facilitates a faster pipeline and can still uncover important bugs, but may also reduce its capability to detect sophisticated bugs. Lastly, we discuss a prioritization strategy that automatically assigns resources to fuzzing campaigns based on a set of predefined priority strategies. Our findings suggest that continuous fuzzing (as part of the automated testing in CI/CD) is indeed beneficial and there are many optimization opportunities to improve the effectiveness and scalability of fuzz testing.

Democratization of AI involves training and deploying machine learning models across heterogeneous and potentially massive environments. Diversity of data opens up a number of possibilities to advance AI systems, but also introduces pressing concerns such as privacy, security, and equity that require special attention. This work shows that it is theoretically impossible to design a rational learning algorithm that has the ability to successfully learn across heterogeneous environments, which we decoratively call collective intelligence (CI). By representing learning algorithms as choice correspondences over a hypothesis space, we are able to axiomatize them with essential properties. Unfortunately, the only feasible algorithm compatible with all of the axioms is the standard empirical risk minimization (ERM) which learns arbitrarily from a single environment. Our impossibility result reveals informational incomparability between environments as one of the foremost obstacles for researchers who design novel algorithms that learn from multiple environments, which sheds light on prerequisites for success in critical areas of machine learning such as out-of-distribution generalization, federated learning, algorithmic fairness, and multi-modal learning.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.