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The More the Merrier:On Evolving Five-Valued Spectra Boolean Functions
No full textEvolving Boolean functions with specific properties is an interesting optimization problem since, depending on the combination of properties and Boolean function size, the problem can range from very simple to (almost) impossible to solve. Some problems are more interesting as there may be only a few options for generating the required Boolean functions. This paper investigates one such problem: evolving five-valued spectra Boolean functions, the functions whose Walsh-Hadamard coefficients can only take five distinct values. We experimented with three solution encodings, two fitness functions, and 12 Boolean function sizes and showed that the tree encoding is superior to other choices, as we can obtain five-valued Boolean functions with high nonlinearity.</p
Free-Space Characterization Setup for Low-Loss UV-261nm Waveguides in Aluminum Oxide
Get PDFHere, we report a characterization setup for low-loss integrated photonic waveguides in aluminum oxide, tailored for deep UV applications. The setup includes a 261nm UV light source, objective lenses for free-space coupling, an automated stage, and a UV camera. The measured losses for the aluminum oxide waveguides in the UV-261nm range were calculated to be 4.9485 dB/cm. These results demonstrate the effectiveness of the setup in achieving low-loss characterization of integrated photonics waveguides for deep UV applications
T-Graph:Enhancing Sparse-view Camera Pose Estimation by Pairwise Translation Graph
Get PDFSparse-view camera pose estimation, which aims to estimate the 6-Degree-of-Freedom (6-DoF) poses from a limited number of images captured from different viewpoints, is a fundamental yet challenging problem in remote sensing applications. Existing methods often overlook the translation information between each pair of viewpoints, leading to suboptimal performance in sparse-view scenarios. To address this limitation, we introduce T-Graph, a lightweight, plug-and-play module to enhance camera pose estimation in sparse-view settings. T-graph takes paired image features as input and maps them through a Multilayer Perceptron (MLP). It then constructs a fully connected translation graph, where nodes represent cameras and edges encode their translation relationships. It can be seamlessly integrated into existing models as an additional branch in parallel with the original prediction, maintaining efficiency and ease of use. Furthermore, we introduce two pairwise translation representations, relative-t and pair-t, formulated under different local coordinate systems. While relative-t captures intuitive spatial relationships, pair-t offers a rotation-disentangled alternative. The two representations contribute to enhanced adaptability across diverse application scenarios, further improving our module's robustness. Extensive experiments on two state-of-the-art methods (RelPose++ and Forge) using public datasets (C03D and IMC PhotoTourism) validate both the effectiveness and generalizability of T-Graph. The results demonstrate consistent improvements across various metrics, notably camera center accuracy, which improves by 1% to 6% from 2 to 8 viewpoints
Tensor Product Neural Networks for Functional ANOVA Model
Get PDFInterpretability for machine learning models is becoming more and more important as machine learning models become more complex. The functional ANOVA model, which decomposes a high-dimensional function into a sum of lower dimensional functions (commonly referred to as components), is one of the most popular tools for interpretable AI, and recently, various neural networks have been developed for estimating each component in the functional ANOVA model. However, such neural networks are highly unstable when estimating each component since the components themselves are not uniquely defined. That is, there are multiple functional ANOVA decompositions for a given function. In this paper, we propose a novel neural network which guarantees a unique functional ANOVA decomposition and thus is able to estimate each component stably and accurately. We call our proposed neural network ANOVA Tensor Product Neural Network (ANOVA-TPNN) since it is motivated by the tensor product basis expansion. Theoretically, we prove that ANOVA-TPNN can approximate any smooth function well. Empirically, we show that ANOVA-TPNN provide much more stable estimation of each component and thus much more stable interpretation when training data and initial values of the model parameters vary than existing neural networks do
A Generalisation of Ville's Inequality to Monotonic Lower Bounds and Thresholds
Get PDFEssentially all anytime-valid methods hinge on Ville's inequality to gain validity across time without incurring a union bound. Ville's inequality is a proper generalisation of Markov's inequality. It states that a non-negative supermartingale will only ever reach a multiple of its initial value with small probability. In the classic rendering both the lower bound (of zero) and the threshold are constant in time. We generalise both to monotonic curves. That is, we bound the probability that a supermartingale which remains above a given decreasing curve exceeds a given increasing threshold curve. We show our bound is tight by exhibiting a supermartingale for which the bound is an equality. Using our generalisation, we derive a clean finite-time version of the law of the iterated logarithm
Multi-scale optimal control for Einstein Telescope active seismic isolation
Get PDFWe present a multi-scale optimal control framework for active seismic isolation in the Einstein Telescope, a third-generation gravitational-wave observatory. Our approach jointly optimizes feedback and blending filters in a cross-coupled opto-mechanical system using a unified cost function based on the "acausal optimum," which quantifies sensor signal-to-noise ratios across frequencies. This method enables efficient re-optimization under varying sensor configurations and environmental conditions. We apply the framework to two candidate sensing systems: OmniSens-a six-degree-of-freedom inertial isolation system-and BRS-T360, which combines Beam Rotation Sensor (BRS) as an inertial tilt sensor with T360 as a horizontal seismometer. We demonstrate superior low-frequency isolation with OmniSens, reducing platform motion by up to two orders of magnitude near the microseism. The framework allows for ready optimization and projection of sensor noise to metrics relevant to the performance of the instrument, aiding the design of the Einstein Telescope
Combinatorial Designs and Cellular Automata:A Survey
Get PDFCellular Automata (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebraic systems, focusing on the combinatorial designs induced by their short-term behavior. Specifically, we review the main results published in the literature concerning the construction of mutually orthogonal Latin squares via bipermutive CA, considering both the linear and nonlinear cases. We then survey some significant applications of these results to cryptography, and conclude with a discussion of open problems to be addressed in future research on CA-based combinatorial designs
Self-Orthogonal Cellular Automata
Get PDFIt is known that no-boundary Cellular Automata (CA) defined by bipermutive local rules give rise to Latin squares. In this paper, we study under which conditions the Latin square generated by a bipermutive CA is self-orthogonal, i.e. orthogonal to its transpose. We first enumerate all bipermutive CA over the binary alphabet up to diameter , remarking that only some linear rules give rise to self-orthogonal Latin squares. We then give a full theoretical characterization of self-orthogonal linear CA, by considering the square matrix obtained by stacking the transition matrices of the CA and of its transpose, and determining when it is invertible. Interestingly, the stacked matrix turns out to have a circulant structure, for which there exists an extensive body of results to characterize its invertibility. Further, for the case of the binary alphabet we prove that irreducibility is a sufficient condition for self-orthogonality, and we derive a simpler characterization which boils down to computing the parity of the central coefficients of the local rule
Addressing the Collaboration Dilemma in Low-Data Federated Learning via Transient Sparsity
Get PDFFederated learning (FL) enables collaborative model training across decentralized clients while preserving data privacy, leveraging aggregated updates to build robust global models. However, this training paradigm faces significant challenges due to data heterogeneity and limited local datasets, which often impede effective collaboration. In such scenarios, we identify the Layer-wise Inertia Phenomenon in FL, wherein the middle layers of global model undergo minimal updates after early communication rounds, ultimately limiting the effectiveness of global aggregation. We demonstrate the presence of this phenomenon across a wide range of federated settings, spanning diverse datasets and architectures. To address this issue, we propose LIPS (Layer-wise Inertia Phenomenon with Sparsity), a simple yet effective method that periodically introduces transient sparsity to stimulate meaningful updates and empower global aggregation. Experiments demonstrate that LIPS effectively mitigates layer-wise inertia, enhances aggregation effectiveness, and improves overall performance in various FL scenarios. This work not only deepens the understanding of layer-wise learning dynamics in FL but also paves the way for more effective collaboration strategies in resource-constrained environments. Our code is publicly available at: https://github.com/QiaoXiao7282/LIPS
