This paper explores the possibility of determining the weights and thresholds of a neural network using the potential -- a parameter of an electrostatic field -- without analytical calculations and without applying training algorithms. The work is based on neural network architectures employing metric recognition methods. The electrostatic field is simulated in the Builder C++ environment. In the same environment, a neural network based on metric recognition methods is constructed, with the weights of the first-layer neurons determined by the values of the potentials of the simulated electrostatic field. The effectiveness of the resulting neural network within the simulated system is evaluated using the MNIST test dataset under various initial conditions of the simulated system. The results demonstrated functional viability. The implementation of this approach shows that a neural network can obtain weight values almost instantaneously from the electrostatic field, without the need for analytical computations, lengthy training procedures, or massive training datasets.

Neural networks based on metric recognition methods have a strictly determined architecture. Number of neurons, connections, as well as weights and thresholds values are calculated analytically, based on the initial conditions of tasks: number of recognizable classes, number of samples, metric expressions used. This paper discusses the possibility of transforming these networks in order to apply classical learning algorithms to them without using analytical expressions that calculate weight values. In the received network, training is carried out by recognizing images in pairs. This approach simplifies the learning process and easily allows to expand the neural network by adding new images to the recognition task. The advantages of these networks, including such as: 1) network architecture simplicity and transparency; 2) training simplicity and reliability; 3) the possibility of using a large number of images in the recognition problem using a neural network; 4) a consistent increase in the number of recognizable classes without changing the previous values of weights and thresholds.

Understanding the function of individual units in a neural network is an important building block for mechanistic interpretability. This is often done by generating a simple text explanation of the behavior of individual neurons or units. For these explanations to be useful, we must understand how reliable and truthful they are. In this work we unify many existing explanation evaluation methods under one mathematical framework. This allows us to compare existing evaluation metrics, understand the evaluation pipeline with increased clarity and apply existing statistical methods on the evaluation. In addition, we propose two simple sanity checks on the evaluation metrics and show that many commonly used metrics fail these tests and do not change their score after massive changes to the concept labels. Based on our experimental and theoretical results, we propose guidelines that future evaluations should follow and identify a set of reliable evaluation metrics.

The paper discusses the capabilities of multilayer perceptron neural networks implementing metric recognition methods, for which the values of the weights are calculated analytically by formulas. Comparative experiments in training a neural network with pre-calculated weights and with random initialization of weights on different sizes of the MNIST training dataset are carried out. The results of the experiments show that a multilayer perceptron with pre-calculated weights can be trained much faster and is much more robust to the reduction of the training dataset.

Despite considerable theoretical progress in the training of neural networks viewed as a multi-agent system of neurons, particularly concerning biological plausibility and decentralized training, their applicability to real-world problems remains limited due to scalability issues. In contrast, error-backpropagation has demonstrated its effectiveness for training deep networks in practice. In this study, we propose a local objective for neurons that, when pursued by neurons individually, align them to exhibit similarities to error-backpropagation in terms of efficiency and scalability during training. For this purpose, we examine a neural network comprising decentralized, self-interested neurons seeking to maximize their local objective -- attention from subsequent layer neurons -- and identify the optimal strategy for neurons. We also analyze the relationship between this strategy and backpropagation, establishing conditions under which the derived strategy is equivalent to error-backpropagation. Lastly, we demonstrate the learning capacity of these multi-agent neural networks through experiments on three datasets and showcase their superior performance relative to error-backpropagation in a catastrophic forgetting benchmark.

With the advent of the big data era, the data quality problem is becoming more critical. Among many factors, data with missing values is one primary issue, and thus developing effective imputation models is a key topic in the research community. Recently, a major research direction is to employ neural network models such as self-organizing mappings or automatic encoders for filling missing values. However, these classical methods can hardly discover interrelated features and common features simultaneously among data attributes. Especially, it is a very typical problem for classical autoencoders that they often learn invalid constant mappings, which dramatically hurts the filling performance. To solve the above-mentioned problems, we propose a missing-value-filling model based on a feature-fusion-enhanced autoencoder. We first incorporate into an autoencoder a hidden layer that consists of de-tracking neurons and radial basis function neurons, which can enhance the ability of learning interrelated features and common features. Besides, we develop a missing value filling strategy based on dynamic clustering that is incorporated into an iterative optimization process. This design can enhance the multi-dimensional feature fusion ability and thus improves the dynamic collaborative missing-value-filling performance. The effectiveness of the proposed model is validated by extensive experiments compared to a variety of baseline methods on thirteen data sets.

In this paper, we propose CLIP-Dissect, a new technique to automatically describe the function of individual hidden neurons inside vision networks. CLIP-Dissect leverages recent advances in multimodal vision/language models to label internal neurons with open-ended concepts without the need for any labeled data or human examples. We show that CLIP-Dissect provides more accurate descriptions than existing methods for last layer neurons where the ground-truth is available as well as qualitatively good descriptions for hidden layer neurons. In addition, our method is very flexible: it is model agnostic, can easily handle new concepts and can be extended to take advantage of better multimodal models in the future. Finally CLIP-Dissect is computationally efficient and can label all neurons from five layers of ResNet-50 in just 4 minutes, which is more than 10 times faster than existing methods. Our code is available at https://github.com/Trustworthy-ML-Lab/CLIP-dissect. Finally, crowdsourced user study results are available at Appendix B to further support the effectiveness of our method.

Depth separation--why a deeper network is more powerful than a shallower one-- has been a major problem in deep learning theory. Previous results often focus on representation power. For example, Safran et al. (2019) constructed a function that is easy to approximate using a 3-layer network but not approximable by any 2-layer network. In this paper, we show that this separation is in fact algorithmic: one can learn the function constructed by Safran et al. (2019) using an overparameterized network with polynomially many neurons efficiently. Our result relies on a new way of extending the mean-field limit to multilayer networks, and a decomposition of loss that factors out the error introduced by the discretization of infinite-width mean-field networks. One of the mysteries in deep learning theory is why we need deeper networks. In particular, seminal works of Eldan & Shamir (2016); Safran et al. (2019) constructed a simple function (f However, these results are only about the representation power of neural networks and do not guarantee that training a deep neural network from reasonable initialization can indeed learn such functions. To analyze the training dynamics, we develop a new framework to generalize mean-field analysis of neural networks (Chizat & Bach, 2018; Mei et al., 2018) to multiple layers. As a result, all the layer weights can change significantly during the training process (unlike many previous works on neural tangent kernel or fixing lower-layer representations). Our analysis also gives a decomposition of loss that allows us to decouple the training of multiple layers. In the remainder of the paper, we first introduce our new framework for multilayer mean-field analysis, then give our main result and techniques. We discuss several related works in the algorithmic aspect for depth separation in Section 1.3. Similar to standard mean-field analysis, we first consider the infinite-width dynamics in Section 3, then we discuss our new ideas in discretizing the result to a polynomial-size network (see Section 4). We propose a new way to extend the mean-field analysis to multiple layers.

We consider the natural problem of learning a ReLU network from queries, which was recently remotivated by model extraction attacks. In this work, we present a polynomial-time algorithm that can learn a depth-two ReLU network from queries under mild general position assumptions. We also present a polynomial-time algorithm that, under mild general position assumptions, can learn a rich class of depth-three ReLU networks from queries. For instance, it can learn most networks where the number of first layer neurons is smaller than the dimension and the number of second layer neurons. These two results substantially improve state-of-the-art: Until our work, polynomial-time algorithms were only shown to learn from queries depth-two networks under the assumption that either the underlying distribution is Gaussian (Chen et al. (2021)) or that the weights matrix rows are linearly independent (Milli et al. (2019)). For depth three or more, there were no known poly-time results. With the growth of neural-network-based applications, many commercial companies offer machine learning services, allowing public use of trained networks as a black-box. Those networks allow the user to query the model and, in some cases, return the exact output of the network to allow the users to reason about the model's output.

Survival risk prediction using gene expression data is important in making treatment decisions in cancer. Standard neural network (NN) survival analysis models are black boxes with lack of interpretability. More interpretable visible neural network (VNN) architectures are designed using biological pathway knowledge. But they do not model how pathway structures can change for particular cancer types. We propose a novel Mutated Pathway VNN or MPVNN architecture, designed using prior signaling pathway knowledge and gene mutation data-based edge randomization simulating signal flow disruption. As a case study, we use the PI3K-Akt pathway and demonstrate overall improved cancer-specific survival risk prediction results of MPVNN over standard non-NN and other similar sized NN survival analysis methods. We show that trained MPVNN architecture interpretation, which points to smaller sets of genes connected by signal flow within the PI3K-Akt pathway that are important in risk prediction for particular cancer types, is reliable.