A feedforward neural network using rectified linear units constructs a mapping from inputs to outputs by partitioning its input space into a set of convex regions where points within a region share a single affine transformation. In order to understand how neural networks work, when and why they fail, and how they compare to biological intelligence, we need to understand the organization and formation of these regions. Step one is to design and implement algorithms for exact region enumeration in networks beyond toy examples. In this work, we present parallel algorithms for exact enumeration in deep (and shallow) neural networks. Our work has three main contributions: (1) we present a novel algorithm framework and parallel algorithms for region enumeration; (2) we implement one of our algorithms on a variety of network architectures and experimentally show how the number of regions dictates runtime; and (3) we show, using our algorithm's output, how the dimension of a region's affine transformation impacts further partitioning of the region by deeper layers. To our knowledge, we run our implemented algorithm on networks larger than all of the networks used in the existing region enumeration literature. Further, we experimentally demonstrate the importance of parallelism for region enumeration of any reasonably sized network.

Manufacturing energy consumption data contains important process signatures required for operational visibility and diagnostics. These signatures may be of different temporal scales, ranging from monthly to sub-second resolutions. We introduce a hierarchical machine learning approach to identify automotive process signatures from paint shop electricity consumption data at varying temporal scales (weekly and daily). A Multi-Layer Perceptron (MLP), a Convolutional Neural Network (CNN), and Principal Component Analysis (PCA) combined with Logistic Regression (LR) are used for the analysis. We validate the utility of the developed algorithms with subject matter experts for (i) better operational visibility, and (ii) identifying energy saving opportunities.

In this paper, we investigate the interplay between attention heads and specialized "next-token" neurons in the Multilayer Perceptron that predict specific tokens. By prompting an LLM like GPT-4 to explain these model internals, we can elucidate attention mechanisms that activate certain next-token neurons. Our analysis identifies attention heads that recognize contexts relevant to predicting a particular token, activating the associated neuron through the residual connection. We focus specifically on heads in earlier layers consistently activating the same next-token neuron across similar prompts. Exploring these differential activation patterns reveals that heads that specialize for distinct linguistic contexts are tied to generating certain tokens. Overall, our method combines neural explanations and probing isolated components to illuminate how attention enables context-dependent, specialized processing in LLMs.

W e study the in-context learning (ICL) ability of a Linear Transformer Block (L TB) that combines a linear attention component and a linear multi-layer perceptron (MLP) component. For ICL of linear regression with a Gaussian prior and a nonzero mean, we show that L TB can achieve nearly Bayes optimal ICL risk. In contrast, using only linear attention must incur an irreducible additive approximation error. Furthermore, we establish a correspondence between L TB and one-step gradient descent estimators with learnable initialization ( GD- β), in the sense that every GD- β estimator can be implemented by an L TB estimator and every optimal L TB estimator that minimizes the in-class ICL risk is effectively a GD- β estimator. Finally, we show that GD- β estimators can be efficiently optimized with gradient flow, despite a non-convex training objective. Our results reveal that L TB achieves ICL by implementing GD- β, and they highlight the role of MLP layers in reducing approximation error.

This paper proposes an Intrusion Detection System (IDS) employing the Harris Hawks Optimization algorithm (HHO) to optimize Multilayer Perceptron learning by optimizing bias and weight parameters. HHO-MLP aims to select optimal parameters in its learning process to minimize intrusion detection errors in networks. HHO-MLP has been implemented using EvoloPy NN framework, an open-source Python tool specialized for training MLPs using evolutionary algorithms. For purposes of comparing the HHO model against other evolutionary methodologies currently available, specificity and sensitivity measures, accuracy measures, and mse and rmse measures have been calculated using KDD datasets. Experiments have demonstrated the HHO MLP method is effective at identifying malicious patterns. HHO-MLP has been tested against evolutionary algorithms like Butterfly Optimization Algorithm (BOA), Grasshopper Optimization Algorithms (GOA), and Black Widow Optimizations (BOW), with validation by Random Forest (RF), XG-Boost. HHO-MLP showed superior performance by attaining top scores with accuracy rate of 93.17%, sensitivity level of 89.25%, and specificity percentage of 95.41%.

In real recommendation scenarios, users often have different types of behaviors, such as clicking and buying. Existing research methods show that it is possible to capture the heterogeneous interests of users through different types of behaviors. However, most multi-behavior approaches have limitations in learning the relationship between different behaviors. In this paper, we propose a novel multilayer perceptron (MLP)-based heterogeneous sequential recommendation method, namely behavior-aware multilayer perceptron (BMLP). Specifically, it has two main modules, including a heterogeneous interest perception (HIP) module, which models behaviors at multiple granularities through behavior types and transition relationships, and a purchase intent perception (PIP) module, which adaptively fuses subsequences of auxiliary behaviors to capture users' purchase intent. Compared with mainstream sequence models, MLP is competitive in terms of accuracy and has unique advantages in simplicity and efficiency. Extensive experiments show that BMLP achieves significant improvement over state-of-the-art algorithms on four public datasets. In addition, its pure MLP architecture leads to a linear time complexity.

Recently, several researchers have reported encouraging experimental re(cid:173) sults when using Gaussian or bump-like activation functions in multilayer perceptrons. Networks of this type usually require fewer hidden layers and units and often learn much faster than typical sigmoidal networks. To explain these results we consider a hyper-ridge network, which is a simple perceptron with no hidden units and a rid e activation function. If we are interested in partitioningp points in d dimensions into two classes then in the limit as d approaches infinity the capacity of a hyper-ridge and a perceptron is identical. However, we show that for p d, which is the usual case in practice, the ratio of hyper-ridge to perceptron dichotomies approaches pl2(d 1).

In the evolving landscape of Environmental, Social, and Corporate Governance (ESG) impact assessment, the ML-ESG-2 shared task proposes identifying ESG impact types. To address this challenge, we present a comprehensive system leveraging ensemble learning techniques, capitalizing on early and late fusion approaches. Our approach employs four distinct models: mBERT, FlauBERT-base, ALBERT-base-v2, and a Multi-Layer Perceptron (MLP) incorporating Latent Semantic Analysis (LSA) and Term Frequency-Inverse Document Frequency (TF-IDF) features. Through extensive experimentation, we find that our early fusion ensemble approach, featuring the integration of LSA, TF-IDF, mBERT, FlauBERT-base, and ALBERT-base-v2, delivers the best performance. Our system offers a comprehensive ESG impact type identification solution, contributing to the responsible and sustainable decision-making processes vital in today's financial and corporate governance landscape.

Graph Neural Networks (GNNs) have demonstrated effectiveness in various graph learning tasks, yet their reliance on message-passing constraints their deployment in latency-sensitive applications such as financial fraud detection. Recent works have explored distilling knowledge from GNNs to Multi-Layer Perceptrons (MLPs) to accelerate inference. However, this task-specific supervised distillation limits generalization to unseen nodes, which are prevalent in latency-sensitive applications. To this end, we present \textbf{\textsc{SimMLP}}, a \textbf{\textsc{Sim}}ple yet effective framework for learning \textbf{\textsc{MLP}}s on graphs without supervision, to enhance generalization. \textsc{SimMLP} employs self-supervised alignment between GNNs and MLPs to capture the fine-grained and generalizable correlation between node features and graph structures, and proposes two strategies to alleviate the risk of trivial solutions. Theoretically, we comprehensively analyze \textsc{SimMLP} to demonstrate its equivalence to GNNs in the optimal case and its generalization capability. Empirically, \textsc{SimMLP} outperforms state-of-the-art baselines, especially in settings with unseen nodes. In particular, it obtains significant performance gains {\bf (7$\sim$26\%)} over MLPs and inference acceleration over GNNs {\bf (90$\sim$126$\times$)} on large-scale graph datasets. Our codes are available at: \url{https://github.com/Zehong-Wang/SimMLP}.

Inner products of neural network feature maps arises in a wide variety of machine learning frameworks as a method of modeling relations between inputs. This work studies the approximation properties of inner products of neural networks. It is shown that the inner product of a multi-layer perceptron with itself is a universal approximator for symmetric positive-definite relation functions. In the case of asymmetric relation functions, it is shown that the inner product of two different multi-layer perceptrons is a universal approximator. In both cases, a bound is obtained on the number of neurons required to achieve a given accuracy of approximation. In the symmetric case, the function class can be identified with kernels of reproducing kernel Hilbert spaces, whereas in the asymmetric case the function class can be identified with kernels of reproducing kernel Banach spaces. Finally, these approximation results are applied to analyzing the attention mechanism underlying Transformers, showing that any retrieval mechanism defined by an abstract preorder can be approximated by attention through its inner product relations. This result uses the Debreu representation theorem in economics to represent preference relations in terms of utility functions.