Understanding the quantum control landscape (QCL) is important for designing effective quantum control strategies. In this study, we analyze the QCL for a single two-level quantum system (qubit) using various control strategies. We employ Principal Component Analysis (PCA), to visualize and analyze the QCL for higher dimensional control parameters. Our results indicate that dimensionality reduction techniques such as PCA, can play an important role in understanding the complex nature of quantum control in higher dimensions. Evaluations of traditional control techniques and machine learning algorithms reveal that Genetic Algorithms (GA) outperform Stochastic Gradient Descent (SGD), while Q-learning (QL) shows great promise compared to Deep Q-Networks (DQN) and Proximal Policy Optimization (PPO). Additionally, our experiments highlight the importance of reward function design in DQN and PPO demonstrating that using immediate reward results in improved performance rather than delayed rewards for systems with short time steps. A study of solution space complexity was conducted by using Cluster Density Index (CDI) as a key metric for analyzing the density of optimal solutions in the landscape. The CDI reflects cluster quality and helps determine whether a given algorithm generates regions of high fidelity or not. Our results provide insights into effective quantum control strategies, emphasizing the significance of parameter selection and algorithm optimization.

The business processes of organizations may deviate from normal control flow due to disruptive anomalies, including unknown, skipped, and wrongly-ordered activities. To identify these control-flow anomalies, process mining can check control-flow correctness against a reference process model through conformance checking, an explainable set of algorithms that allows linking any deviations with model elements. However, the effectiveness of conformance checking-based techniques is negatively affected by noisy event data and low-quality process models. To address these shortcomings and support the development of competitive and explainable conformance checking-based techniques for control-flow anomaly detection, we propose a novel process mining-based feature extraction approach with alignment-based conformance checking. This variant aligns the deviating control flow with a reference process model; the resulting alignment can be inspected to extract additional statistics such as the number of times a given activity caused mismatches. We integrate this approach into a flexible and explainable framework for developing techniques for control-flow anomaly detection. The framework combines process mining-based feature extraction and dimensionality reduction to handle high-dimensional feature sets, achieve detection effectiveness, and support explainability. The results show that the framework techniques implementing our approach outperform the baseline conformance checking-based techniques while maintaining the explainable nature of conformance checking. We also provide an explanation of why existing conformance checking-based techniques may be ineffective.

Stochastic reaction networks (SRNs) model stochastic effects for various applications, including intracellular chemical or biological processes and epidemiology. A typical challenge in practical problems modeled by SRNs is that only a few state variables can be dynamically observed. Given the measurement trajectories, one can estimate the conditional probability distribution of unobserved (hidden) state variables by solving a stochastic filtering problem. In this setting, the conditional distribution evolves over time according to an extensive or potentially infinite-dimensional system of coupled ordinary differential equations with jumps, known as the filtering equation. The current numerical filtering techniques, such as the Filtered Finite State Projection (DAmbrosio et al., 2022), are hindered by the curse of dimensionality, significantly affecting their computational performance. To address these limitations, we propose to use a dimensionality reduction technique based on the Markovian projection (MP), initially introduced for forward problems (Ben Hammouda et al., 2024). In this work, we explore how to adapt the existing MP approach to the filtering problem and introduce a novel version of the MP, the Filtered MP, that guarantees the consistency of the resulting estimator. The novel method combines a particle filter with reduced variance and solving the filtering equations in a low-dimensional space, exploiting the advantages of both approaches. The analysis and empirical results highlight the superior computational efficiency of projection methods compared to the existing filtered finite state projection in the large dimensional setting.

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that 2K projection vectors are sufficient for the independence preservation of any K class data sampled from a union of independent subspaces. It is this non-trivial observation that we use for designing our dimensionality reduction technique. In this paper, we propose a novel dimensionality reduction algorithm that theoretically preserves this structure for a given dataset. We support our theoretical analysis with empirical results on both synthetic and real world data achieving state-of-the-art results compared to popular dimensionality reduction techniques.

Supervised dimensionality reduction aims to map labeled data to a low-dimensional feature space while maximizing class discriminability. Despite the availability of methods for learning complex non-linear features (e.g. Deep Learning), there is an enduring demand for dimensionality reduction methods that learn linear features due to their interpretability, low computational cost, and broad applicability. However, there is a gap between methods that optimize linear separability (e.g. LDA), and more flexible but computationally expensive methods that optimize over arbitrary class boundaries (e.g. metric-learning methods). Here, we present Supervised Quadratic Feature Analysis (SQFA), a dimensionality reduction method for learning linear features that maximize the differences between class-conditional first- and second-order statistics, which allow for quadratic discrimination. SQFA exploits the information geometry of second-order statistics in the symmetric positive definite manifold. We show that SQFA features support quadratic discriminability in real-world problems. We also provide a theoretical link, based on information geometry, between SQFA and the Quadratic Discriminant Analysis (QDA) classifier.

Weaknesses: I have the following critical concerns about this paper: 1. The used datasets are too simple. More complex datasets such as SculptFaces in NeRV paper are required to evaluate the performance of the proposed algorithm. As detailed above, ClassNeRV could be seen as a variation of NeRV through penalizing within-class missed neighbors and between-class false neighbors with class information. Therefore, in my opinion, it is not a significant contribution. According to Sec 3.2, they derived the ClassNeRV Stress Function from NeRV Stress Function by splitting Eq. 2 into within-class and between-class relations.

Three referees indicate accept, one indicates that the paper is marginally below threshold. I agree with reviewers 1, 2 and 4 that the presented approach is insightful and useful to NeurIPS applications, and support an accept after reading the rebuttal. However, when revising the paper, please take into account reviewers' concerns about improving quantitative comparisons with other similar methods as well as providing further discussion. Please consider adding experimental support with more complex data to the the main paper or Supplementary Materials.

This work achieves an improved bound on the sample complexity of random tensor projection and it is argued that this bound is tight and nearly optimal. A key observation is to view the random sketch as a bilinear form of a random matrix. It makes the analysis suitable to apply general matrix concentration inequalities. The authors can obtain better bounds by analyzing both operator and Frobenius norm of the random matrix, which is the key challenges of this work. Their proof techniques are different from previous approaches but very impressive.

This paper presents tight bounds on the dimension of random projection for tensor product of vectors, achieving exponential improvement on sketch dimension compared to the prior work. The reviewers found the work solid and of high significance.

Originality As far as I can tell, the authors' claim that this is the first such work is correct. Previous work has been done is describing heuristics or empirical understandings of such behaviour, but the work is nonetheless original in proving a theoretical basis for this. Quality The authors' exposition of the problem and the solution is well thought out and expertly laid out in a logical and convincing form. However, the excellent technical contribution is somewhat lacking in discussion, particularly given the authors aim to bridge the gap between theory and practice; such claims as "This new consequence may serve an important guide for practical considerations" warrant a standalone discussion section which is not provided. Further, the results predicted in theory could have been compared to empirical experiments to show tightness in practice, and phase transitions could be shown in experiments as a demonstration.