Binary neural networks leverage $\mathrm{Sign}$ function to binarize weights and activations, which require gradient estimators to overcome its non-differentiability and will inevitably bring gradient errors during backpropagation. Although many hand-designed soft functions have been proposed as gradient estimators to better approximate gradients, their mechanism is not clear and there are still huge performance gaps between binary models and their full-precision counterparts. To address these issues and reduce gradient error, we propose to tackle network binarization as a binary classification problem and use a multi-layer perceptron (MLP) as the classifier in the forward pass and gradient estimator in the backward pass. Benefiting from the MLP's theoretical capability to fit any continuous function, it can be adaptively learned to binarize networks and backpropagate gradients without any prior knowledge of soft functions. From this perspective, we further empirically justify that even a simple linear function can outperform previous complex soft functions. Extensive experiments demonstrate that the proposed method yields surprising performance both in image classification and human pose estimation tasks. Specifically, we achieve $65.7\%$ top-1 accuracy of ResNet-34 on ImageNet dataset, with an absolute improvement of $2.6\%$. Moreover, we take binarization as a lightweighting approach for pose estimation models and propose well-designed binary pose estimation networks SBPN and BHRNet. When evaluating on the challenging Microsoft COCO keypoint dataset, the proposed method enables binary networks to achieve a mAP of up to $60.6$ for the first time. Experiments conducted on real platforms demonstrate that BNN achieves a better balance between performance and computational complexity, especially when computational resources are extremely low.

Deep neural networks (DNN) with a huge number of adjustable parameters remain largely black boxes. To shed light on the hidden layers of DNN, we study supervised learning by a DNN of width $N$ and depth $L$ consisting of $NL$ perceptrons with $c$ inputs by a statistical mechanics approach called the teacher-student setting. We consider an ensemble of student machines that exactly reproduce $M$ sets of $N$ dimensional input/output relations provided by a teacher machine. We show that the problem becomes exactly solvable in what we call as 'dense limit': $N \gg c \gg 1$ and $M \gg 1$ with fixed $\alpha=M/c$ using the replica method developed in (H. Yoshino, (2020)). We also study the model numerically performing simple greedy MC simulations. Simulations reveal that learning by the DNN is quite heterogeneous in the network space: configurations of the teacher and the student machines are more correlated within the layers closer to the input/output boundaries while the central region remains much less correlated due to the over-parametrization in qualitative agreement with the theoretical prediction. We evaluate the generalization-error of the DNN with various depth $L$ both theoretically and numerically. Remarkably both the theory and simulation suggest generalization-ability of the student machines, which are only weakly correlated with the teacher in the center, does not vanish even in the deep limit $L \gg 1$ where the system becomes heavily over-parametrized. We also consider the impact of effective dimension $D(\leq N)$ of data by incorporating the hidden manifold model (S. Goldt et. al., (2020)) into our model. The theory implies that the loop corrections to the dense limit become enhanced by either decreasing the width $N$ or decreasing the effective dimension $D$ of the data. Simulation suggests both lead to significant improvements in generalization-ability.

Toeplitz Neural Networks (TNNs) (Qin et. al. 2023) are a recent sequence model with impressive results. They require O(n log n) computational complexity and O(n) relative positional encoder (RPE) multi-layer perceptron (MLP) and decay bias calls. We aim to reduce both. We first note that the RPE is a non-SPD (symmetric positive definite) kernel and the Toeplitz matrices are pseudo-Gram matrices. Further 1) the learned kernels display spiky behavior near the main diagonals with otherwise smooth behavior; 2) the RPE MLP is slow. For bidirectional models, this motivates a sparse plus low-rank Toeplitz matrix decomposition. For the sparse component's action, we do a small 1D convolution. For the low rank component, we replace the RPE MLP with linear interpolation and use asymmetric Structured Kernel Interpolation (SKI) (Wilson et. al. 2015) for O(n) complexity: we provide rigorous error analysis. For causal models, "fast" causal masking (Katharopoulos et. al. 2020) negates SKI's benefits. Working in the frequency domain, we avoid an explicit decay bias. To enforce causality, we represent the kernel via the real part of its frequency response using the RPE and compute the imaginary part via a Hilbert transform. This maintains O(n log n) complexity but achieves an absolute speedup. Modeling the frequency response directly is also competitive for bidirectional training, using one fewer FFT. We set a speed state of the art on Long Range Arena (Tay et. al. 2020) with minimal score degradation.

Hyperspectral images have significant applications in various domains, since they register numerous semantic and spatial information in the spectral band with spatial variability of spectral signatures. Two critical challenges in identifying pixels of the hyperspectral image are respectively representing the correlated information among the local and global, as well as the abundant parameters of the model. To tackle this challenge, we propose a Multi-Scale U-shape Multi-Layer Perceptron (MUMLP) a model consisting of the designed MSC (Multi-Scale Channel) block and the UMLP (U-shape Multi-Layer Perceptron) structure. MSC transforms the channel dimension and mixes spectral band feature to embed the deep-level representation adequately. UMLP is designed by the encoder-decoder structure with multi-layer perceptron layers, which is capable of compressing the large-scale parameters. Extensive experiments are conducted to demonstrate our model can outperform state-of-the-art methods across-the-board on three wide-adopted public datasets, namely Pavia University, Houston 2013 and Houston 2018

Regionalization (MPR) method, combining descriptors upscaling Regardless of the improvements made in hydrological and pre-regionalization function in form of multilinear forward models and available data, hydrological calibration regressions, implemented within a spatially distributed remains a challenging ill-posed inverse problem faced with multiscale hydrological model (mHm), has been proposed the equifinality (Beven, 2001) of feasible solutions. Most by Samaniego et al. (2010), and later applied to other gridded calibration approaches aim to estimate spatially uniform model hydrological models in several applicative studies (e.g., parameters for a single gauged catchment, resulting in piecewise Mizukami et al. (2017); Beck et al. (2020)). In all the constant discontinuous parameters fields for adjacent above studies, state of the art optimization algorithms are catchments. Moreover, these calibrated parameter are not used, especially Shuffle Complex Evolution algorithm (SCE) transferable to ungauged locations, which represents the majority (Duan et al., 1992) in Mizukami et al. (2017) or Distributed of the global land surface (Fekete & Vörösmarty, 2007; Evolutionary Algorithms (DEAP) (Fortin et al., 2012) in Beck Hannah et al., 2011).

Exploring the climate impacts of various anthropogenic emissions scenarios is key to making informed decisions for climate change mitigation and adaptation. State-of-the-art Earth system models can provide detailed insight into these impacts, but have a large associated computational cost on a per-scenario basis. This large computational burden has driven recent interest in developing cheap machine learning models for the task of climate model emulation. In this manuscript, we explore the efficacy of randomly wired neural networks for this task. We describe how they can be constructed and compare them to their standard feedforward counterparts using the ClimateBench dataset. Specifically, we replace the serially connected dense layers in multilayer perceptrons, convolutional neural networks, and convolutional long short-term memory networks with randomly wired dense layers and assess the impact on model performance for models with 1 million and 10 million parameters. We find that models with less complex architectures see the greatest performance improvement with the addition of random wiring (up to 30.4% for multilayer perceptrons). Furthermore, out of 24 different model architecture, parameter count, and prediction task combinations, only one saw a statistically significant performance deficit in randomly wired networks compared to their standard counterparts, with 14 cases showing statistically significant improvement. We also find no significant difference in prediction speed between networks with standard feedforward dense layers and those with randomly wired layers. These findings indicate that randomly wired neural networks may be suitable direct replacements for traditional dense layers in many standard models.

Knowledge graphs (KGs) facilitate a wide variety of applications. Despite great efforts in creation and maintenance, even the largest KGs are far from complete. Hence, KG completion (KGC) has become one of the most crucial tasks for KG research. Recently, considerable literature in this space has centered around the use of Message Passing (Graph) Neural Networks (MPNNs), to learn powerful embeddings. The success of these methods is naturally attributed to the use of MPNNs over simpler multi-layer perceptron (MLP) models, given their additional message passing (MP) component. In this work, we find that surprisingly, simple MLP models are able to achieve comparable performance to MPNNs, suggesting that MP may not be as crucial as previously believed. With further exploration, we show careful scoring function and loss function design has a much stronger influence on KGC model performance. This suggests a conflation of scoring function design, loss function design, and MP in prior work, with promising insights regarding the scalability of state-of-the-art KGC methods today, as well as careful attention to more suitable MP designs for KGC tasks tomorrow. Our codes are publicly available at: https://github.com/Juanhui28/Are_MPNNs_helpful.

In the negative perceptron problem we are given $n$ data points $({\boldsymbol x}_i,y_i)$, where ${\boldsymbol x}_i$ is a $d$-dimensional vector and $y_i\in\{+1,-1\}$ is a binary label. The data are not linearly separable and hence we content ourselves to find a linear classifier with the largest possible \emph{negative} margin. In other words, we want to find a unit norm vector ${\boldsymbol \theta}$ that maximizes $\min_{i\le n}y_i\langle {\boldsymbol \theta},{\boldsymbol x}_i\rangle$. This is a non-convex optimization problem (it is equivalent to finding a maximum norm vector in a polytope), and we study its typical properties under two random models for the data. We consider the proportional asymptotics in which $n,d\to \infty$ with $n/d\to\delta$, and prove upper and lower bounds on the maximum margin $\kappa_{\text{s}}(\delta)$ or -- equivalently -- on its inverse function $\delta_{\text{s}}(\kappa)$. In other words, $\delta_{\text{s}}(\kappa)$ is the overparametrization threshold: for $n/d\le \delta_{\text{s}}(\kappa)-\varepsilon$ a classifier achieving vanishing training error exists with high probability, while for $n/d\ge \delta_{\text{s}}(\kappa)+\varepsilon$ it does not. Our bounds on $\delta_{\text{s}}(\kappa)$ match to the leading order as $\kappa\to -\infty$. We then analyze a linear programming algorithm to find a solution, and characterize the corresponding threshold $\delta_{\text{lin}}(\kappa)$. We observe a gap between the interpolation threshold $\delta_{\text{s}}(\kappa)$ and the linear programming threshold $\delta_{\text{lin}}(\kappa)$, raising the question of the behavior of other algorithms.

Recent progress in long sequence time-series forecasting (LSTF) has been led by either transformers with sparse attention ([16] and references therein) or attention in combination with signal preprocessing such as seasonal-trend decomposition [17] or adopting auto-correlation to account for periodicity in the data [13]. On the other hand, Fourier transform has been proposed as an alternative mixing tool in lieu of standard attention [12] to speed up prediction in natural language processing (NLP) tasks (FNet, [2]). Though Fourier transform is meant to mimic the mixing functions of multilayer perceptron(MLP,[11]), it is not well-understood why it works and when assistance from attention layers remain necessary to maintain performance. In computer vision (CV), Fourier transform is also used as a filtering step in early stages of transformer (GFNet,[8]) to enhance a fully attention-based architecture. A recent advance in CV is to adopt window attention to reduce quadratic complexity of full attention [12].

In the context of Industry 4.0, the use of artificial intelligence (AI) and machine learning for anomaly detection is being hampered by high computational requirements and associated environmental effects. This study seeks to address the demands of high-performance machine learning models with environmental sustainability, contributing to the emerging discourse on 'Green AI.' An extensive variety of machine learning algorithms, coupled with various Multilayer Perceptron (MLP) configurations, were meticulously evaluated. Our investigation encapsulated a comprehensive suite of evaluation metrics, comprising Accuracy, Area Under the Curve (AUC), Recall, Precision, F1 Score, Kappa Statistic, Matthews Correlation Coefficient (MCC), and F1 Macro. Simultaneously, the environmental footprint of these models was gauged through considerations of time duration, CO2 equivalent, and energy consumption during the training, cross-validation, and inference phases. Traditional machine learning algorithms, such as Decision Trees and Random Forests, demonstrate robust efficiency and performance. However, superior outcomes were obtained with optimised MLP configurations, albeit with a commensurate increase in resource consumption. The study incorporated a multi-objective optimisation approach, invoking Pareto optimality principles, to highlight the trade-offs between a model's performance and its environmental impact. The insights derived underscore the imperative of striking a balance between model performance, complexity, and environmental implications, thus offering valuable directions for future work in the development of environmentally conscious machine learning models for industrial applications.