In the field of continual learning, models are designed to learn tasks one after the other. While most research has centered on supervised continual learning, recent studies have highlighted the strengths of self-supervised continual representation learning. The improved transferability of representations built with self-supervised methods is often associated with the role played by the multi-layer perceptron projector. In this work, we depart from this observation and reexamine the role of supervision in continual representation learning. We reckon that additional information, such as human annotations, should not deteriorate the quality of representations. Our findings show that supervised models when enhanced with a multi-layer perceptron head, can outperform self-supervised models in continual representation learning.

Classical neural networks achieve only limited convergence in hard problems such as XOR or parity when the number of hidden neurons is small. With the motivation to improve the success rate of neural networks in these problems, we propose a new neural network model inspired by existing neural network models with so called product neurons and a learning rule derived from classical error backpropagation, which elegantly solves the problem of mutually exclusive situations. Unlike existing product neurons, which have weights that are preset and not adaptable, our product layers of neurons also do learn. We tested the model and compared its success rate to a classical multilayer perceptron in the aforementioned problems as well as in other hard problems such as the two spirals. Our results indicate that our model is clearly more successful than the classical MLP and has the potential to be used in many tasks and applications.

Graph pooling has been increasingly recognized as crucial for Graph Neural Networks (GNNs) to facilitate hierarchical graph representation learning. Existing graph pooling methods commonly consist of two stages: selecting top-ranked nodes and discarding the remaining to construct coarsened graph representations. However, this paper highlights two key issues with these methods: 1) The process of selecting nodes to discard frequently employs additional Graph Convolutional Networks or Multilayer Perceptrons, lacking a thorough evaluation of each node's impact on the final graph representation and subsequent prediction tasks. 2) Current graph pooling methods tend to directly discard the noise segment (dropped) of the graph without accounting for the latent information contained within these elements. To address the first issue, we introduce a novel Graph Explicit Pooling (GrePool) method, which selects nodes by explicitly leveraging the relationships between the nodes and final representation vectors crucial for classification. The second issue is addressed using an extended version of GrePool (i.e., GrePool+), which applies a uniform loss on the discarded nodes. This addition is designed to augment the training process and improve classification accuracy. Furthermore, we conduct comprehensive experiments across 12 widely used datasets to validate our proposed method's effectiveness, including the Open Graph Benchmark datasets. Our experimental results uniformly demonstrate that GrePool outperforms 14 baseline methods for most datasets. Likewise, implementing GrePool+ enhances GrePool's performance without incurring additional computational costs.

Recent studies attempted to utilize multilayer perceptrons (MLPs) to solve semi-supervised node classification on graphs, by training a student MLP by knowledge distillation (KD) from a teacher graph neural network (GNN). While previous studies have focused mostly on training the student MLP by matching the output probability distributions between the teacher and student models during KD, it has not been systematically studied how to inject the structural information in an explicit and interpretable manner. Inspired by GNNs that separate feature transformation $T$ and propagation $\Pi$, we re-frame the KD process as enabling the student MLP to explicitly learn both $T$ and $\Pi$. Although this can be achieved by applying the inverse propagation $\Pi^{-1}$ before distillation from the teacher GNN, it still comes with a high computational cost from large matrix multiplications during training. To solve this problem, we propose Propagate & Distill (P&D), which propagates the output of the teacher GNN before KD and can be interpreted as an approximate process of the inverse propagation $\Pi^{-1}$. Through comprehensive evaluations using real-world benchmark datasets, we demonstrate the effectiveness of P&D by showing further performance boost of the student MLP.

Artificial Intelligence(AI) widely applies in Image Classification and Recognition, Text Understanding and Natural Language Processing, which makes great progress. In this paper, we introduced AI into the fruit quality detection field. We designed a fruit sugar degree regression model using an Artificial Neural Network based on spectra of fruits within the visible/near-infrared(V/NIR)range. After analysis of fruit spectra, we innovatively proposed a new neural network structure: low layers consist of a Multilayer Perceptron(MLP), a middle layer is a 2-dimensional correlation matrix layer, and high layers consist of several Convolutional Neural Network(CNN) layers. In this study, we used fruit sugar value as a detection target, collecting two fruits called Gan Nan Navel and Tian Shan Pear as samples, doing experiments respectively, and comparing their results. We used Analysis of Variance(ANOVA) to evaluate the reliability of the dataset we collected. Then, we tried multiple strategies to process spectrum data, evaluating their effects. In this paper, we tried to add Wavelet Decomposition(WD) to reduce feature dimensions and a Genetic Algorithm(GA) to find excellent features. Then, we compared Neural Network models with traditional Partial Least Squares(PLS) based models. We also compared the neural network structure we designed(MLP-CNN) with other traditional neural network structures. In this paper, we proposed a new evaluation standard derived from dataset standard deviation(STD) for evaluating detection performance, validating the viability of using an artificial neural network model to do fruit sugar degree nondestructive detection.

Convolutional Neural Networks (CNNs) have revolutionized image classification by extracting spatial features and enabling state-of-the-art accuracy in vision-based tasks. The squeeze and excitation network proposed module gathers channelwise representations of the input. Multilayer perceptrons (MLP) learn global representation from the data and in most image classification models used to learn extracted features of the image. In this paper, we introduce a novel aggregated multilayer perceptron, a multi-branch dense layer, within the Squeeze excitation residual module designed to surpass the performance of existing architectures. Our approach leverages a combination of squeeze excitation network module with dense layers. This fusion enhances the network's ability to capture channel-wise patterns and have global knowledge, leading to a better feature representation. This proposed model has a negligible increase in parameters when compared to SENet. We conduct extensive experiments on benchmark datasets to validate the model and compare them with established architectures. Experimental results demonstrate a remarkable increase in the classification accuracy of the proposed model.

Time series forecasting has played the key role in different industrial, including finance, traffic, energy, and healthcare domains. While existing literatures have designed many sophisticated architectures based on RNNs, GNNs, or Transformers, another kind of approaches based on multi-layer perceptrons (MLPs) are proposed with simple structure, low complexity, and {superior performance}. However, most MLP-based forecasting methods suffer from the point-wise mappings and information bottleneck, which largely hinders the forecasting performance. To overcome this problem, we explore a novel direction of applying MLPs in the frequency domain for time series forecasting. We investigate the learned patterns of frequency-domain MLPs and discover their two inherent characteristic benefiting forecasting, (i) global view: frequency spectrum makes MLPs own a complete view for signals and learn global dependencies more easily, and (ii) energy compaction: frequency-domain MLPs concentrate on smaller key part of frequency components with compact signal energy. Then, we propose FreTS, a simple yet effective architecture built upon Frequency-domain MLPs for Time Series forecasting. FreTS mainly involves two stages, (i) Domain Conversion, that transforms time-domain signals into complex numbers of frequency domain; (ii) Frequency Learning, that performs our redesigned MLPs for the learning of real and imaginary part of frequency components. The above stages operated on both inter-series and intra-series scales further contribute to channel-wise and time-wise dependency learning. Extensive experiments on 13 real-world benchmarks (including 7 benchmarks for short-term forecasting and 6 benchmarks for long-term forecasting) demonstrate our consistent superiority over state-of-the-art methods.

Realistic graphs contain both rich self-features of nodes and informative structures of neighborhoods, jointly handled by a GNN in the typical setup. We propose to decouple the two modalities by mixture of weak and strong experts (Mowst), where the weak expert is a light-weight Multi-layer Perceptron (MLP), and the strong expert is an off-the-shelf Graph Neural Network (GNN). To adapt the experts' collaboration to different target nodes, we propose a "confidence" mechanism based on the dispersion of the weak expert's prediction logits. The strong expert is conditionally activated when either the node's classification relies on neighborhood information, or the weak expert has low model quality. We reveal interesting training dynamics by analyzing the influence of the confidence function on loss: our training algorithm encourages the specialization of each expert by effectively generating soft splitting of the graph. In addition, our "confidence" design imposes a desirable bias toward the strong expert to benefit from GNN's better generalization capability. Mowst is easy to optimize and achieves strong expressive power, with a computation cost comparable to a single GNN. Empirically, Mowst shows significant accuracy improvement on 6 standard node classification benchmarks (including both homophilous and heterophilous graphs).

Chain-of-thought (CoT) is a method that enables language models to handle complex reasoning tasks by decomposing them into simpler steps. Despite its success, the underlying mechanics of CoT are not yet fully understood. In an attempt to shed light on this, our study investigates the impact of CoT on the ability of transformers to in-context learn a simple to study, yet general family of compositional functions: multi-layer perceptrons (MLPs). In this setting, we find that the success of CoT can be attributed to breaking down in-context learning of a compositional function into two distinct phases: focusing on and filtering data related to each step of the composition and in-context learning the single-step composition function. Through both experimental and theoretical evidence, we demonstrate how CoT significantly reduces the sample complexity of in-context learning (ICL) and facilitates the learning of complex functions that non-CoT methods struggle with. Furthermore, we illustrate how transformers can transition from vanilla in-context learning to mastering a compositional function with CoT by simply incorporating additional layers that perform the necessary data-filtering for CoT via the attention mechanism. In addition to these test-time benefits, we show CoT helps accelerate pretraining by learning shortcuts to represent complex functions and filtering plays an important role in this process. These findings collectively provide insights into the mechanics of CoT, inviting further investigation of its role in complex reasoning tasks.

Recently, there has been a growing focus on determining the minimum width requirements for achieving the universal approximation property in deep, narrow Multi-Layer Perceptrons (MLPs). Among these challenges, one particularly challenging task is approximating a continuous function under the uniform norm, as indicated by the significant disparity between its lower and upper bounds. To address this problem, we propose a framework that simplifies finding the minimum width for deep, narrow MLPs into determining a purely geometrical function denoted as $w(d_x, d_y)$. This function relies solely on the input and output dimensions, represented as $d_x$ and $d_y$, respectively. Two key steps support this framework. First, we demonstrate that deep, narrow MLPs, when provided with a small additional width, can approximate a $C^2$-diffeomorphism. Subsequently, using this result, we prove that $w(d_x, d_y)$ equates to the optimal minimum width required for deep, narrow MLPs to achieve universality. By employing the aforementioned framework and the Whitney embedding theorem, we provide an upper bound for the minimum width, given by $\operatorname{max}(2d_x+1, d_y) + \alpha(\sigma)$, where $0 \leq \alpha(\sigma) \leq 2$ represents a constant depending on the activation function. Furthermore, we provide a lower bound of $4$ for the minimum width in cases where the input and output dimensions are both equal to two.