Data & Analytics

Restrictive conditions for solving LTI systems by Ordinary Differential Equations - clarifying smoothness assumptions and applicability limits of standard solution methods. Activation: LTI systems, ODE solutions, system theory, control theory foundations.

**arXiv ID:** 2207.04889 **Authors:** Sijia Lu, Feng Xu **Published:** 2022-05-31T17:02:26Z **Abstract:** Spiking neural networks (SNNs) are brain-inspired machine learning algorithms with merits such as biological plausibility and unsupervised learning capability. Previous works have shown that converting Artificial Neural Networks (ANNs) into SNNs is a practical and efficient approach for implementing an SNN. However, the basic principle and theoretical groundwork are lacking for training a...

Theoretical framework demonstrating that mean-field chaos in random recurrent networks is predictable from continuous past history

Geometric analysis of attractor boundaries and storage capacity limits in kernel Hopfield networks trained with Kernel Logistic Regression (KLR). Covers attractor basin geometry, Ridge of Optimization, morphing analysis, SNR vs Cover's theorem, and dynamical stability. Activation: kernel Hopfield, KLR associative memory, attractor basin geometry, Ridge of Optimization, morphing analysis Hopfield, storage capacity Hopfield, SNR analysis Hopfield, Cover's theorem associative memory, crosstalk n...

Kernel Hopfield networks: geometric analysis of attractor boundaries and storage capacity limits. KLR-trained associative memories with P/N ~16 for random sequences and ~20 for structured data. Trigger words: kernel Hopfield, associative memory, KLR, attractor basin, storage capacity, kernel logistic regression.

Tensor-based framework for higher-order Markov chains with memory on hypergraphs. Use when modeling complex systems with group interactions, memory effects, non-pairwise connections, or analyzing higher-order networks. Keywords: hypergraph, Markov chains, memory, tensor, higher-order networks, complex systems, random walks.

Geometric origin of exact mean-field reductions using Möbius symmetry and the Lorentzian Ansatz — proving the Cauchy-Lorentz family uniquely emerges as invariant under projective transport, unifying Ott-Antonsen and Montbrió-Pazó-Roxin reductions.

Geometric origin of exact mean-field reductions using Möbius symmetry and the Lorentzian Ansatz — proving the Cauchy-Lorentz family uniquely emerges as invariant under projective transport, unifying Ott-Antonsen and Montbrió-Pazó-Roxin reductions.

Dynamical Hamiltonian Encoding (DHE) methodology for quantum machine learning and quantum finance data encoding. Addresses the Inverse Born Rule Fallacy — the limitation of standard amplitude encoding (psi = sqrt(P)) that renders quantum states 'phase-deaf' by restricting to the positive real orthant. DHE uses data to generate non-commutative Hamiltonian evolution (based on QIFT) rather than static phase-locked vectors. Use when: designing quantum data encoding for ML/finance, implementing am...

Gaussian-equivalent process methodology for analyzing nonlinear noise in recurrent neural circuits using Ornstein-Uhlenbeck noise matching and lognormal moment closure. Activation: mean field, nonlinear noise, recurrent networks, OU process.

Cross-modal convergence analysis methodology using Generalized Procrustes Algorithm to measure intra-modal representational convergence at single-stimulus level. Reveals how low intra-modal dispersion (high agreement among vision models) elicits significantly higher cross-modal alignment between vision and language models. Activation: cross-modal convergence, representational alignment, Procrustes analysis, vision-language alignment, neural representation, single-stimulus analysis

Measuring cross-modal neural network convergence using single-stimulus intra-modal dispersion. Generalized Procrustes Algorithm for quantifying how stimuli with low intra-modal dispersion elicit higher cross-modal alignment. Activation triggers: cross-modal convergence, neural network alignment, vision-language alignment, representational similarity.

Calibrated measurement framework using the Brody exponent β as a quantitative measure of short-range exclusion in 2D spatial point processes. Originally from quantum chaos level-spacing statistics, now calibrated for spatial analysis with corrected CSR baseline, empirical β-r_excl calibration (Spearman ρ=0.988), and control protocols. Use for quantum chaos analysis, spatial statistics, prime number embeddings, and manufactured surface characterization.

Graph Neural Network methods for brain connectivity analysis. Use when analyzing fMRI/EEG brain network data, modeling brain structure-function relationships, predicting cognitive outcomes from connectome data, or applying GNN to neuroscience problems. Keywords: brain graph, connectome GNN, neural network brain, fMRI GNN, brain connectivity analysis, 脑网络图神经网络, 脑连接性分析, 认知预测.

Bayesian decision-making framework for membership inference attacks on statistical releases using Bayesian network population models. Reframes membership inference with respect to populations represented as Bayesian networks, enabling more effective specialized attacks by incorporating prior information about attribute dependency structures. Use when analyzing statistical disclosure risk, designing membership inference attacks, or evaluating privacy of released statistics.

**arXiv ID:** 2207.03577 **Authors:** Roland Olsson, Chau Tran, Lars Magnusson **Published:** 2022-06-29T06:35:06Z **Abstract:** We present a new class of neurons, ARNs, which give a cross entropy on test data that is up to three times lower than the one achieved by carefully optimized LSTM neurons. The explanations for the huge improvements that often are achieved are elaborate skip connections through time, up to four internal memory states per neuron and a number of novel activation functi...

ARFIMA decomposition of stride-to-stride fluctuations in human walking for sensorimotor control analysis. Activation triggers: stride fluctuations, human gait, DFA, ARFIMA, fractal analysis, sensorimotor control

**arXiv ID:** 2209.06119 **Authors:** Ravin Kumar **Published:** 2022-09-10T14:26:04Z **Abstract:** Activation Functions introduce non-linearity in the deep neural networks. This nonlinearity helps the neural networks learn faster and efficiently from the dataset. In deep learning, many activation functions are developed and used based on the type of problem statement. ReLU's variants, SWISH, and MISH are goto activation functions. MISH function is considered having similar or even better per...

Algorithmic Bohmian Mechanics (aBM) methodology using algorithmic randomness to formulate the distribution postulate as an objective constraining law. Guarantees standard Born statistics for canonical quantum experiments in the limit. Use for quantum foundations, interpretation of quantum mechanics, and algorithmic randomness in physical theories.

Artificial Intelligence applications in complex network science - network analysis, topology learning, dynamics prediction, and emergent behavior detection. Comprehensive survey covering AI potential, methodology, and applications. Use when analyzing complex networks, network topology learning, dynamics prediction, emergent behavior, social networks, biological networks, or transportation networks. Keywords: complex networks, network science, AI networks, topology dynamics, emergent behavior,...

**arXiv ID:** 2303.05516 **Authors:** Min Zeng, Haimiao Mo, Zhiming Liang, Hua Wang **Published:** 2023-03-09T01:52:54Z **Abstract:** As the use of robotics becomes more widespread, the huge amount of vision data leads to a dramatic increase in data dimensionality. Although deep learning methods can effectively process these high-dimensional vision data. Due to the limitation of computational resources, some special scenarios still rely on traditional machine learning methods. However, these ...

Physics-guided neural network design and training methods. Embed physical laws, constraints, and symmetries into neural network architecture for improved modeling of physical systems (quantum mechanics, statistical physics, fluid dynamics, materials science). Activation: physics guided neural network, 物理学指导神经网络, physics-informed neural network, PINN, physics-constrained learning, quantum neural network, physics-aware training.

Framework for measuring causal emergence (ΦID) in active inference agents with perspective latents architecture, analyzing how architectural separation between fast perception and slow global latents affects information-theoretic signatures of integration. Use when studying causal emergence, active inference, or hierarchical agent architectures.

PEM-UDE methodology for discovering governing equations from chaotic neural systems. Combines prediction-error method with universal differential equations to extract interpretable mathematical expressions from chaotic dynamical systems, applied to neural population dynamics. Activation: pem-ude, governing equations neural, chaotic system discovery, universal differential equations neural, symbolic regression neural, neural population dynamics discovery.