Kolmogorov-Arnold Network (KAN) is a network structure recently proposed by Liu et al. (2024) that offers improved interpretability and a more parsimonious design in many science-oriented tasks compared to multi-layer perceptrons. This work provides a rigorous theoretical analysis of KAN by establishing generalization bounds for KAN equipped with activation functions that are either represented by linear combinations of basis functions or lying in a low-rank Reproducing Kernel Hilbert Space (RKHS). In the first case, the generalization bound accommodates various choices of basis functions in forming the activation functions in each layer of KAN and is adapted to different operator norms at each layer. For a particular choice of operator norms, the bound scales with the $l_1$ norm of the coefficient matrices and the Lipschitz constants for the activation functions, and it has no dependence on combinatorial parameters (e.g., number of nodes) outside of logarithmic factors. Moreover, our result does not require the boundedness assumption on the loss function and, hence, is applicable to a general class of regression-type loss functions. In the low-rank case, the generalization bound scales polynomially with the underlying ranks as well as the Lipschitz constants of the activation functions in each layer. These bounds are empirically investigated for KANs trained with stochastic gradient descent on simulated and real data sets. The numerical results demonstrate the practical relevance of these bounds.

Hand preference and degree of handedness (DoH) are two different aspects of human behavior which are often confused to be one. DoH is a person's inherent capability of the brain; affected by nature and nurture. In this study, we used dominant and non-dominant handwriting traits to assess DoH for the first time, on 43 subjects of three categories- Unidextrous, Partially Unidextrous, and Ambidextrous. Features extracted from the segmented handwriting signals called strokes were used for DoH quantification. Davies Bouldin Index, Multilayer perceptron, and Convolutional Neural Network (CNN) were used for automated grading of DoH. The outcomes of these methods were compared with the widely used DoH assessment questionnaires from Edinburgh Inventory (EI). The CNN based automated grading outperformed other computational methods with an average classification accuracy of 95.06% under stratified 10-fold cross-validation. The leave-one-subject-out strategy on this CNN resulted in a test individual's DoH score which was converted into a 4-point score. Around 90% of the obtained scores from all the implemented computational methods were found to be in accordance with the EI scores under 95% confidence interval. Automated grading of degree of handedness using handwriting signals can provide more resolution to the Edinburgh Inventory scores. This could be used in multiple applications concerned with neuroscience, rehabilitation, physiology, psychometry, behavioral sciences, and forensics.

A Perceptron is a fundamental building block of a neural network. The flexibility and scalability of perceptron make it ubiquitous in building intelligent systems. Studies have shown the efficacy of a single neuron in making intelligent decisions. Here, we examined and compared two perceptrons with distinct mechanisms, and developed a quantum version of one of those perceptrons. As a part of this modeling, we implemented the quantum circuit for an artificial perception, generated a dataset, and simulated the training. Through these experiments, we show that there is an exponential growth advantage and test different qubit versions. Our findings show that this quantum model of an individual perceptron can be used as a pattern classifier. For the second type of model, we provide an understanding to design and simulate a spike-dependent quantum perceptron. Our code is available at \url{https://github.com/ashutosh1919/quantum-perceptron}

Time series forecasting (TSF) plays a crucial role in various domains, including web data analysis, energy consumption prediction, and weather forecasting. While Multi-Layer Perceptrons (MLPs) are lightweight and effective for capturing temporal dependencies, they are prone to overfitting when used to model inter-channel dependencies. In this paper, we investigate the overfitting problem in channel-wise MLPs using Rademacher complexity theory, revealing that extreme values in time series data exacerbate this issue. To mitigate this issue, we introduce a novel Simplex-MLP layer, where the weights are constrained within a standard simplex. This strategy encourages the model to learn simpler patterns and thereby reducing overfitting to extreme values. Based on the Simplex-MLP layer, we propose a novel \textbf{F}requency \textbf{S}implex \textbf{MLP} (FSMLP) framework for time series forecasting, comprising of two kinds of modules: \textbf{S}implex \textbf{C}hannel-\textbf{W}ise MLP (SCWM) and \textbf{F}requency \textbf{T}emporal \textbf{M}LP (FTM). The SCWM effectively leverages the Simplex-MLP to capture inter-channel dependencies, while the FTM is a simple yet efficient temporal MLP designed to extract temporal information from the data. Our theoretical analysis shows that the upper bound of the Rademacher Complexity for Simplex-MLP is lower than that for standard MLPs. Moreover, we validate our proposed method on seven benchmark datasets, demonstrating significant improvements in forecasting accuracy and efficiency, while also showcasing superior scalability. Additionally, we demonstrate that Simplex-MLP can improve other methods that use channel-wise MLP to achieve less overfitting and improved performance. Code are available \href{https://github.com/FMLYD/FSMLP}{\textcolor{red}{here}}.

Tabular data plays a critical role in real-world financial scenarios. Traditionally, tree models have dominated in handling tabular data. However, financial datasets in the industry often encounter some challenges, such as data heterogeneity, the predominance of numerical features and the large scale of the data, which can range from tens of millions to hundreds of millions of records. These challenges can lead to significant memory and computational issues when using tree-based models. Consequently, there is a growing need for neural network-based solutions that can outperform these models. In this paper, we introduce TKGMLP, an hybrid network for tabular data that combines shallow Kolmogorov Arnold Networks with Gated Multilayer Perceptron. This model leverages the strengths of both architectures to improve performance and scalability. We validate TKGMLP on a real-world credit scoring dataset, where it achieves state-of-the-art results and outperforms current benchmarks. Furthermore, our findings demonstrate that the model continues to improve as the dataset size increases, making it highly scalable. Additionally, we propose a novel feature encoding method for numerical data, specifically designed to address the predominance of numerical features in financial datasets. The integration of this feature encoding method within TKGMLP significantly improves prediction accuracy. This research not only advances table prediction technology but also offers a practical and effective solution for handling large-scale numerical tabular data in various industrial applications.

The neural radiance field (NERF) advocates learning the continuous representation of 3D geometry through a multilayer perceptron (MLP). By integrating this into a generative model, the generative neural radiance field (GRAF) is capable of producing images from random noise z without 3D supervision. In practice, the shape and appearance are modeled by z_s and z_a, respectively, to manipulate them separately during inference. However, it is challenging to represent multiple scenes using a solitary MLP and precisely control the generation of 3D geometry in terms of shape and appearance. In this paper, we introduce a controllable generative model (i.e. \textbf{CtrlNeRF}) that uses a single MLP network to represent multiple scenes with shared weights. Consequently, we manipulated the shape and appearance codes to realize the controllable generation of high-fidelity images with 3D consistency. Moreover, the model enables the synthesis of novel views that do not exist in the training sets via camera pose alteration and feature interpolation. Extensive experiments were conducted to demonstrate its superiority in 3D-aware image generation compared to its counterparts.

The autonomous learning of new goals in robotics remains a complex issue to address. Here, we propose a model where curiosity influence learning flexibility. To do so, this paper proposes to root curiosity and attention together by taking inspiration from the Locus Coeruleus-Norepinephrine system along with various cognitive processes such as cognitive persistence and visual habituation. We apply our approach by experimenting with a simulated robotic arm on a set of objects with varying difficulty. The robot first discovers new goals via bottom-up attention through motor babbling with an inhibition of return mechanism, then engage to the learning of goals due to neural activity arising within the curiosity mechanism. The architecture is modelled with dynamic neural fields and the learning of goals such as pushing the objects in diverse directions is supported by the use of forward and inverse models implemented by multi-layer perceptrons. The adoption of dynamic neural fields to model curiosity, habituation and persistence allows the robot to demonstrate various learning trajectories depending on the object. In addition, the approach exhibits interesting properties regarding the learning of similar goals as well as the continuous switch between exploration and exploitation.

The evolving capabilities of large language models are accompanied by growing sizes and deployment costs, necessitating effective inference optimisation techniques. We propose a novel pruning method utilising centrality measures from graph theory, reducing both the computational requirements and the memory footprint of these models. Specifically, we devise a method for creating a weighted directed acyclical graph representation of multilayer perceptrons to which we apply a modified version of the weighted PageRank centrality measure to compute node importance scores. In combination with uniform pruning this leads to structured sparsity. We call this pruning method MLPRank. Furthermore we introduce an extension to decoder-only transformer models and call it LLMRank. For both variants we demonstrate a strong performance. With MLPRank on average leading to 6.09 % higher accuracy retention than three popular baselines and 13.42 % with LLMRank compared to two popular baselines. Code is available at https://github.com/amazon-science/llm-rank-pruning.

Binary Neural Networks (BNNs) hold the potential for significantly reducing computational complexity and memory demand in machine and deep learning. However, most successful training algorithms for BNNs rely on quantization-aware floating-point Stochastic Gradient Descent (SGD), with full-precision hidden weights used during training. The binarized weights are only used at inference time, hindering the full exploitation of binary operations during the training process. In contrast to the existing literature, we introduce, for the first time, a multi-layer training algorithm for BNNs that does not require the computation of back-propagated full-precision gradients. Specifically, the proposed algorithm is based on local binary error signals and binary weight updates, employing integer-valued hidden weights that serve as a synaptic metaplasticity mechanism, thereby establishing it as a neurobiologically plausible algorithm. The binary-native and gradient-free algorithm proposed in this paper is capable of training binary multi-layer perceptrons (BMLPs) with binary inputs, weights, and activations, by using exclusively XNOR, Popcount, and increment/decrement operations, hence effectively paving the way for a new class of operation-optimized training algorithms. Experimental results on BMLPs fully trained in a binary-native and gradient-free manner on multi-class image classification benchmarks demonstrate an accuracy improvement of up to +13.36% compared to the fully binary state-of-the-art solution, showing minimal accuracy degradation compared to the same architecture trained with full-precision SGD and floating-point weights, activations, and inputs. The proposed algorithm is made available to the scientific community as a public repository.

This paper presents an enhanced adaptive random Fourier features (ARFF) training algorithm for shallow neural networks, building upon the work introduced in "Adaptive Random Fourier Features with Metropolis Sampling", Kammonen et al., \emph{Foundations of Data Science}, 2(3):309--332, 2020. This improved method uses a particle filter-type resampling technique to stabilize the training process and reduce the sensitivity to parameter choices. The Metropolis test can also be omitted when resampling is used, reducing the number of hyperparameters by one and reducing the computational cost per iteration compared to the ARFF method. We present comprehensive numerical experiments demonstrating the efficacy of the proposed algorithm in function regression tasks as a stand-alone method and as a pretraining step before gradient-based optimization, using the Adam optimizer. Furthermore, we apply the proposed algorithm to a simple image regression problem, illustrating its utility in sampling frequencies for the random Fourier features (RFF) layer of coordinate-based multilayer perceptrons. In this context, we use the proposed algorithm to sample the parameters of the RFF layer in an automated manner.