Nonsmooth Nonnegative Matrix Factorization (nsNMF) is capable of producing more localized, less overlapped feature representations than other variants of NMF while keeping satisfactory fit to data. However, nsNMF as well as other existing NMF methods is incompetent to learn hierarchical features of complex data due to its shallow structure. To fill this gap, we propose a deep nsNMF method coined by the fact that it possesses a deeper architecture compared with standard nsNMF. The deep nsNMF not only gives parts-based features due to the nonnegativity constraints, but also creates higher-level, more abstract features by combing lower-level ones. The in-depth description of how deep architecture can help to efficiently discover abstract features in dnsNMF is presented. And we also show that the deep nsNMF has close relationship with the deep autoencoder, suggesting that the proposed model inherits the major advantages from both deep learning and NMF. Extensive experiments demonstrate the standout performance of the proposed method in clustering analysis.

We study the problem of synthesizing a controller for a robot with a surveillance objective, that is, the robot is required to maintain knowledge of the location of a moving, possibly adversarial target. We formulate this problem as a one-sided partial-information game in which the winning condition for the agent is specified as a temporal logic formula. The specification formalizes the surveillance requirement given by the user, including additional non-surveillance tasks. In order to synthesize a surveillance strategy that meets the specification, we transform the partial-information game into a perfect-information one, using abstraction to mitigate the exponential blow-up typically incurred by such transformations. This enables the use of off-the-shelf tools for reactive synthesis. We use counterexample-guided refinement to automatically achieve abstraction precision that is sufficient to synthesize a surveillance strategy. We evaluate the proposed method on two case-studies, demonstrating its applicability to large state-spaces and diverse requirements.

This work shows that policies with simple linear and RBF parameterizations can be trained to solve a variety of continuous control tasks, including the OpenAI gym benchmarks. The performance of these trained policies are competitive with state of the art results, obtained with more elaborate parameterizations such as fully connected neural networks. Furthermore, existing training and testing scenarios are shown to be very limited and prone to over-fitting, thus giving rise to only trajectory-centric policies. Training with a diverse initial state distribution is shown to produce more global policies with better generalization. This allows for interactive control scenarios where the system recovers from large on-line perturbations; as shown in the supplementary video.

Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a notion of Tensor Train subspace and in this paper we propose a TT-PCA algorithm for estimating this structured subspace from the given data. By maintaining low rank tensor structure, TT-PCA is more robust to noise comparing with PCA or Tucker-PCA. This is borne out numerically by testing the proposed approach on the Extended YaleFace Dataset B.

This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal is to learn a weighted graph (a graph Laplacian matrix) and a graph-based filter (a function of graph Laplacian matrices). In order to solve the proposed problem, an algorithm is developed to jointly identify a graph and a graph-based filter (GBF) from multiple signal/data observations. Our algorithm is valid under the assumption that GBFs are one-to-one functions. The proposed approach can be applied to learn diffusion (heat) kernels, which are popular in various fields for modeling diffusion processes. In addition, for specific choices of graph-based filters, the proposed problem reduces to a graph Laplacian estimation problem. Our experimental results demonstrate that the proposed algorithm outperforms the current state-of-the-art methods. We also implement our framework on a real climate dataset for modeling of temperature signals.

This paper presents a learning-based approach for impromptu trajectory tracking for non-minimum phase systems, i.e., systems with unstable inverse dynamics. Inversion-based feedforward approaches are commonly used for improving tracking performance; however, these approaches are not directly applicable to non-minimum phase systems due to their inherent instability. In order to resolve the instability issue, existing methods have assumed that the system model is known and used pre-actuation or inverse approximation techniques. In this work, we propose an approach for learning a stable, approximate inverse of a non-minimum phase baseline system directly from its input-output data. Through theoretical discussions, simulations, and experiments on two different platforms, we show the stability of our proposed approach and its effectiveness for high-accuracy, impromptu tracking. Our approach also shows that including more information in the training, as is commonly assumed to be useful, does not lead to better performance but may trigger instability and impact the effectiveness of the overall approach.

In this note we propose a method based on artificial neural network to study the transition between states governed by stochastic processes. In particular, we aim for numerical schemes for the committor function, the central object of transition path theory, which satisfies a high-dimensional Fokker-Planck equation. By working with the variational formulation of such partial differential equation and parameterizing the committor function in terms of a neural network, approximations can be obtained via optimizing the neural network weights using stochastic algorithms. The numerical examples show that moderate accuracy can be achieved for high-dimensional problems.

We consider the problem of tracking an intruder using a network of wireless sensors. For tracking the intruder at each instant, the optimal number and the right configuration of sensors has to be powered. As powering the sensors consumes energy, there is a trade off between accurately tracking the position of the intruder at each instant and the energy consumption of sensors. This problem has been formulated in the framework of Partially Observable Markov Decision Process (POMDP). Even for the state-of-the-art algorithm in the literature, the curse of dimensionality renders the problem intractable. In this paper, we formulate the Intrusion Detection (ID) problem with a suitable state-action space in the framework of POMDP and develop a Reinforcement Learning (RL) algorithm utilizing the Upper Confidence Tree Search (UCT) method to solve the ID problem. Through simulations, we show that our algorithm performs and scales well with the increasing state and action spaces.

We propose a reliable intersection control mechanism for strategic autonomous and connected vehicles (agents) in non-cooperative environments. Each agent has access to his/her earliest possible and desired passing times, and reports a passing time to the intersection manager, who allocates the intersection temporally to the agents in a First-Come-First-Serve basis. However, the agents might have conflicting interests and can take actions strategically. To this end, we analyze the strategic behaviors of the agents and formulate Nash equilibria for all possible scenarios. Furthermore, among all Nash equilibria we identify a socially optimal equilibrium that leads to a fair intersection allocation, and correspondingly we describe a strategy-proof intersection mechanism, which achieves reliable intersection control such that the strategic agents do not have any incentive to misreport their passing times strategically.

This paper describes a novel communication-spare cooperative localization algorithm for a team of mobile unmanned robotic vehicles. Exploiting an event-based estimation paradigm, robots only send measurements to neighbors when the expected innovation for state estimation is high. Since agents know the event-triggering condition for measurements to be sent, the lack of a measurement is thus also informative and fused into state estimates. The robots use a Covariance Intersection (CI) mechanism to occasionally synchronize their local estimates of the full network state. In addition, heuristic balancing dynamics on the robots' CI-triggering thresholds ensure that, in large diameter networks, the local error covariances remains below desired bounds across the network. Simulations on both linear and nonlinear dynamics/measurement models show that the event-triggering approach achieves nearly optimal state estimation performance in a wide range of operating conditions, even when using only a fraction of the communication cost required by conventional full data sharing. The robustness of the proposed approach to lossy communications, as well as the relationship between network topology and CI-based synchronization requirements, are also examined.

Living organisms intertwine soft (e.g., muscle) and hard (e.g., bones) materials, giving them an intrinsic flexibility and resiliency often lacking in conventional rigid robots. The emerging field of soft robotics seeks to harness these same properties in order to create resilient machines. The nature of soft materials, however, presents considerable challenges to aspects of design, construction, and control -- and up until now, the vast majority of gaits for soft robots have been hand-designed through empirical trial-and-error. This manuscript describes an easy-to-assemble tensegrity-based soft robot capable of highly dynamic locomotive gaits and demonstrating structural and behavioral resilience in the face of physical damage. Enabling this is the use of a machine learning algorithm able to discover effective gaits with a minimal number of physical trials. These results lend further credence to soft-robotic approaches that seek to harness the interaction of complex material dynamics in order to generate a wealth of dynamical behaviors.

Both humans and the sensors on an autonomous vehicle have limited sensing capabilities. When these limitations coincide with scenarios involving vulnerable road users, it becomes important to account for these limitations in the motion planner. For the scenario of an occluded pedestrian crosswalk, the speed of the approaching vehicle should be a function of the amount of uncertainty on the roadway. In this work, the longitudinal controller is formulated as a partially observable Markov decision process and dynamic programming is used to compute the control policy. The control policy scales the speed profile to be used by a model predictive steering controller.

The rise of connected personal devices together with privacy concerns call for machine learning algorithms capable of leveraging the data of a large number of agents to learn personalized models under strong privacy requirements. In this paper, we introduce an efficient algorithm to address the above problem in a fully decentralized (peer-to-peer) and asynchronous fashion, with provable convergence rate. We show how to make the algorithm differentially private to protect against the disclosure of information about the personal datasets, and formally analyze the trade-off between utility and privacy. Our experiments show that our approach dramatically outperforms previous work in the non-private case, and that under privacy constraints, we can significantly improve over models learned in isolation.

The proven efficacy of learning-based control schemes strongly motivates their application to robotic systems operating in the physical world. However, guaranteeing correct operation during the learning process is currently an unresolved issue, which is of vital importance in safety-critical systems. We propose a general safety framework based on Hamilton-Jacobi reachability methods that can work in conjunction with an arbitrary learning algorithm. The method exploits approximate knowledge of the system dynamics to guarantee constraint satisfaction while minimally interfering with the learning process. We further introduce a Bayesian mechanism that refines the safety analysis as the system acquires new evidence, reducing initial conservativeness when appropriate while strengthening guarantees through real-time validation. The result is a least-restrictive, safety-preserving control law that intervenes only when (a) the computed safety guarantees require it, or (b) confidence in the computed guarantees decays in light of new observations. We prove theoretical safety guarantees combining probabilistic and worst-case analysis and demonstrate the proposed framework experimentally on a quadrotor vehicle. Even though safety analysis is based on a simple point-mass model, the quadrotor successfully arrives at a suitable controller by policy-gradient reinforcement learning without ever crashing, and safely retracts away from a strong external disturbance introduced during flight.

We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix. The algorithm extends the recently introduced technique of spectral filtering, previously applied only to systems with a symmetric transition matrix, using a novel convex relaxation to allow for the efficient identification of phases.

Wiatowski and Bölcskei, 2015, proved that deformation stability and vertical translation invariance of deep convolutional neural network-based feature extractors are guaranteed by the network structure per se rather than the specific convolution kernels and non-linearities. While the translation invariance result applies to square-integrable functions, the deformation stability bound holds for band-limited functions only. Many signals of practical relevance (such as natural images) exhibit, however, sharp and curved discontinuities and are, hence, not band-limited. The main contribution of this paper is a deformation stability result that takes these structural properties into account. Specifically, we establish deformation stability bounds for the class of cartoon functions introduced by Donoho, 2001.

Adversarial neural networks solve many important problems in data science, but are notoriously difficult to train. These difficulties come from the fact that optimal weights for adversarial nets correspond to saddle points, and not minimizers, of the loss function. The alternating stochastic gradient methods typically used for such problems do not reliably converge to saddle points, and when convergence does happen it is often highly sensitive to learning rates. We propose a simple modification of stochastic gradient descent that stabilizes adversarial networks. We show, both in theory and practice, that the proposed method reliably converges to saddle points, and is stable with a wider range of training parameters than a non-prediction method. This makes adversarial networks less likely to "collapse," and enables faster training with larger learning rates.

Time awareness is critical to a broad range of emerging applications -- in Cyber-Physical Systems and Internet of Things -- running on commodity platforms and operating systems. Traditionally, time is synchronized across devices through a best-effort background service whose performance is neither observable nor controllable, thus consuming system resources independently of application needs while not allowing the applications and OS services to adapt to changes in uncertainty in system time. We advocate for rethinking how time is managed in a system stack. In this paper, we propose a new clock model that characterizes various sources of timing uncertainties in true time. We then present a Kalman filter based time synchronization protocol that adapts to the uncertainties exposed by the clock model. Our realization of a uncertainty-aware clock model and synchronization protocol is based on a standard embedded Linux platform.

In this paper four iterative algorithms for learning analysis operators are presented. They are built upon the same optimisation principle underlying both Analysis K-SVD and Analysis SimCO. The Forward and Sequential Analysis Operator Learning (FAOL and SAOL) algorithms are based on projected gradient descent with optimally chosen step size. The Implicit AOL (IAOL) algorithm is inspired by the implicit Euler scheme for solving ordinary differential equations and does not require to choose a step size. The fourth algorithm, Singular Value AOL (SVAOL), uses a similar strategy as Analysis K-SVD while avoiding its high computational cost. All algorithms are proven to decrease or preserve the target function in each step and a characterisation of their stationary points is provided. Further they are tested on synthetic and image data, compared to Analysis SimCO and found to give better recovery rates and faster decay of the objective function respectively. In a final denoising experiment the presented algorithms are again shown to perform similar to or better than the state-of-the-art algorithm ASimCO.

Optimizing measures of the observability Gramian as a surrogate for the estimation performance may provide irrelevant or misleading trajectories for planning under observation uncertainty.

We study two important SVM variants: hard-margin SVM (for linearly separable cases) and $ν$-SVM (for linearly non-separable cases). We propose new algorithms from the perspective of saddle point optimization. Our algorithms achieve $(1-ε)$-approximations with running time $\tilde{O}(nd+n\sqrt{d / ε})$ for both variants, where $n$ is the number of points and $d$ is the dimensionality. To the best of our knowledge, the current best algorithm for $ν$-SVM is based on quadratic programming approach which requires $Ω(n^2 d)$ time in worst case~\cite{joachims1998making,platt199912}. In the paper, we provide the first nearly linear time algorithm for $ν$-SVM. The current best algorithm for hard margin SVM achieved by Gilbert algorithm~\cite{gartner2009coresets} requires $O(nd / ε)$ time. Our algorithm improves the running time by a factor of $\sqrt{d}/\sqrtε$. Moreover, our algorithms can be implemented in the distributed settings naturally. We prove that our algorithms require $\tilde{O}(k(d +\sqrt{d/ε}))$ communication cost, where $k$ is the number of clients, which almost matches the theoretical lower bound. Numerical experiments support our theory and show that our algorithms converge faster on high dimensional, large and dense data sets, as compared to previous methods.

The Particle Swarm Optimization Policy (PSO-P) has been recently introduced and proven to produce remarkable results on interacting with academic reinforcement learning benchmarks in an off-policy, batch-based setting. To further investigate the properties and feasibility on real-world applications, this paper investigates PSO-P on the so-called Industrial Benchmark (IB), a novel reinforcement learning (RL) benchmark that aims at being realistic by including a variety of aspects found in industrial applications, like continuous state and action spaces, a high dimensional, partially observable state space, delayed effects, and complex stochasticity. The experimental results of PSO-P on IB are compared to results of closed-form control policies derived from the model-based Recurrent Control Neural Network (RCNN) and the model-free Neural Fitted Q-Iteration (NFQ). Experiments show that PSO-P is not only of interest for academic benchmarks, but also for real-world industrial applications, since it also yielded the best performing policy in our IB setting. Compared to other well established RL techniques, PSO-P produced outstanding results in performance and robustness, requiring only a relatively low amount of effort in finding adequate parameters or making complex design decisions.

We establish the link between Mathematical Morphology and the map of Asplund's distances between a probe and a grey scale function, using the Logarithmic Image Processing scalar multiplication. We demonstrate that the map is the logarithm of the ratio between a dilation and an erosion of the function by a structuring function: the probe. The dilations and erosions are mappings from the lattice of the images into the lattice of the positive functions. Using a flat structuring element, the expression of the map of Asplund's distances can be simplified with a dilation and an erosion of the image; these mappings stays in the lattice of the images. We illustrate our approach by an example of pattern matching with a non-flat structuring function.

Data association, the reasoning over correspondence between targets and measurements, is a problem of fundamental importance in target tracking. Recently, belief propagation (BP) has emerged as a promising method for estimating the marginal probabilities of measurement to target association, providing fast, accurate estimates. The excellent performance of BP in the particular formulation used may be attributed to the convexity of the underlying free energy which it implicitly optimises. This paper studies multiple scan data association problems, i.e., problems that reason over correspondence between targets and several sets of measurements, which may correspond to different sensors or different time steps. We find that the multiple scan extension of the single scan BP formulation is non-convex and demonstrate the undesirable behaviour that can result. A convex free energy is constructed using the recently proposed fractional free energy (FFE). A convergent, BP-like algorithm is provided for the single scan FFE, and employed in optimising the multiple scan free energy using primal-dual coordinate ascent. Finally, based on a variational interpretation of joint probabilistic data association (JPDA), we develop a sequential variant of the algorithm that is similar to JPDA, but retains consistency constraints from prior scans. The performance of the proposed methods is demonstrated on a bearings only target localisation problem.

Numerous algorithms are used for nonnegative matrix factorization under the assumption that the matrix is nearly separable. In this paper, we show how to make these algorithms efficient for data matrices that have many more rows than columns, so-called "tall-and-skinny matrices". One key component to these improved methods is an orthogonal matrix transformation that preserves the separability of the NMF problem. Our final methods need a single pass over the data matrix and are suitable for streaming, multi-core, and MapReduce architectures. We demonstrate the efficacy of these algorithms on terabyte-sized synthetic matrices and real-world matrices from scientific computing and bioinformatics.

The radial basis function neural network (RBFN) trained with a gradient descending algorithm provides an effective fully connected structure in both shallow and deep networks. The error correction (ErrCor), a state-of-the-art gradient-based training method, selects optimal hidden units to improve accuracy. Alternatively, as a population-based algorithm, the particle swarm optimization algorithm (PSO) uses the swarm experience to optimize RBFN parameters, offering global search and robustness to local minima. Adaptive PSO (APSO) has emerged as an improved variant of PSO. APSO algorithm improves convergence speed by dynamically adjusting swarm parameters during optimization. Both ErrCor and PSO demonstrate improved results and competitive convergence. However, with large datasets, these methods face scalability challenges such as excessive kernel computations and large hidden layer structures. A recent multi-column RBFN approach (MCRN) improves ErrCor performance by deploying small RBFNs in a parallel system. Inspired by MCRN's success, we propose two novel approaches to improve PSO performance: the multi-column RBFN with PSO (MC-PSO) and the multi-column RBFN with APSO (MC-APSO). These methods introduce parallel RBFN structures trained using evolutionary swarm methods. Each RBFN is independently trained on a specific spatial subset of the dataset using either PSO or APSO algorithms. These resulting specialist-trained RBFNs are tailored to their respective subsets. During testing, only selected RBFNs, where the test instance neighbors are located, contribute to the multi-column output. This specialization improves accuracy, while parallelism enhances speed. We evaluate the proposed methods on various benchmark datasets. The MC-PSO and MC-APSO outperform ErrCor, PSO, APSO, and MCRN in terms of accuracy and recall. They also demonstrate faster training and testing times in most experiments.

Preserving data privacy is an important topic in structural data management and data mining. However, the issue of privacy leakage in distributed causal structure learning is a persistent challenge, especially in cases where data transmission and computation are required. In this paper, we propose a method based on fully homomorphic encryption (FHE) that performs calculations on ciphertexts, keeping data encrypted in transition and computation. Nevertheless, adopting FHE to causal structure learning is challenging due to the high computation cost and limited support on division as well as logarithm operations in FHE. To tackle this challenge, we propose a series of novel techniques including (i) circuit simplification for better efficiency, (ii) approximation of division and logarithm through Newton-Raphson Reciprocal and Taylor expansion, and (iii) a batching technique with SIMD-acceleration to enhance the whole learning process. Additionally, our method can be easily extended beyond FHE by demonstration of its portability to support differential privacy. Empirical results show that our method achieves high consistency and comparable causal structure with the plaintext version in the datasets tested. Last, our method is efficient and practical to complete learning causal structures in tens of minutes even under the privacy protection of FHE.

After the success of 3D Gaussian Splatting (3DGS) for novel view synthesis, many works have explored how to also use it for geometric surface representation. However, extracting accurate geometric information directly from 3DGS remains challenging and can often reduce the appearance rendering quality. In this work, we show that 3DGS in its default form is inheritedly unsuited to represent texture and geometry at the same time, by training with complete ground-truth texture and geometry information. We also propose a simple solution by applying a single additional geometry opacity parameter to each splat, together with an optional transparency-curated optimization pipeline. Our experiments, both with ground-truth and vision foundation model geometric input, show that this change leads to improved rendering and geometry performance on a wide variety of dataset, and especially complex scenes with transparent objects benefit significantly from our method.

We present in this paper a framework for the identification of control-affine reduced-order models (ROMs). The proposed method utilizes autoencoders (AEs) to transform the high-dimensional states, and potentially the high-dimensional inputs, into reduced latent ones suitable for control-affine state-space dynamics. This is achieved by simultaneous training of the AE and the state-space model. In addition, we extend the discrete ROM formulation to a sequence-based model, which processes state and input histories to improve prediction accuracy while preserving the control-affine structure. We motivate our framework by applying feedback linearization to the derived models, and we present guidelines for its efficient use. The proposed framework is assessed on two numerical examples and its performance is compared to a baseline model, where the AE identifies a latent space with linear state-space dynamics. The assessment involves evaluating the prediction accuracy of the ROM on test data and its effectiveness in controlling the system to a desired state or trajectory.

When an AI agent calls an API and hits a validation error, it needs more than what went wrong -- it needs what to do next. A self-reflective API returns, on validation failure, a machine-readable recovery\_feedback.suggestions[] payload sufficient for the agent to repair the request and retry without external reasoning. On a leak-audited pilot ($N{=}30$ per cell, 3 LLMs, 10 adversarial tasks), structured suggestions lift task-completion rate by $+36.7$--$40.0$pp over plain-English diagnoses on Anthropic models (Fisher's exact $p \le 0.0022$), at $1.8$--$2.2\times$ better per-success token efficiency. The lift is not significant on gpt-4o-mini ($p{=}0.435$); a second-domain replication on a billing API confirms the pattern. The comparison only holds after auditing two undocumented classes of answer leakage in LLM benchmarks. We shipaudit\_prompt\_leakage.py as reusable CI infrastructure. Code and data: https://github.com/arquicanedo/self-reflective-apis.