Neural Information Processing Systems http://nips.cc/

Each specification defines the expected model output for a given input space ( 2.1). The increasing adoption of neural networks in learning-augmented systems highlights the importance Specifically, researchers have relied on their domain knowledge of model safety and robustness, particularly and intuition about individual applications to manually in safety-critical domains. Despite progress in create specifications. For instance, in adaptive video streaming, the formal verification of neural networks, current where a neural network is employed to determine the practices require users to manually define model bitrate for the next video chunk based on recent network specifications--properties that dictate expected conditions, Eliyahu et al. (2021) define a specification as, model behavior in various scenarios. This manual "[if video] chunks were downloaded quickly (more quickly process, however, is prone to human error, limited than it takes to play a chunk), the DNN should eventually in scope, and time-consuming. In this paper, not choose the worst resolution." Similar manual specifications we introduce AutoSpec, the first framework to are devised for other learning-augmented systems, e.g., automatically generate comprehensive and accurate database indexes (Tan et al., 2021), memory allocators (Wei specifications for neural networks in learningaugmented et al., 2023), and job schedulers (Wu et al., 2022).

In the architecture of deep learning models, inspired by biological neurons, activation functions (AFs) play a pivotal role. They significantly influence the performance of artificial neural networks. By modulating the non-linear properties essential for learning complex patterns, AFs are fundamental in both classification and regression tasks. This paper presents a comprehensive review of various types of AFs, including fixed-shape, parametric, adaptive, stochastic/probabilistic, non-standard, and ensemble/combining types. We begin with a systematic taxonomy and detailed classification frameworks that delineates the principal characteristics of AFs and organizes them based on their structural and functional distinctions. Our in-depth analysis covers primary groups such as sigmoid-based, ReLU-based, and ELU-based AFs, discussing their theoretical foundations, mathematical formulations, and specific benefits and limitations in different contexts. We also highlight key attributes of AFs such as output range, monotonicity, and smoothness. Furthermore, we explore miscellaneous AFs that do not conform to these categories but have shown unique advantages in specialized applications. Non-standard AFs are also explored, showcasing cutting-edge variations that challenge traditional paradigms and offer enhanced adaptability and model performance. We examine strategies for combining multiple AFs to leverage complementary properties. The paper concludes with a comparative evaluation of 12 state-of-the-art AFs, using rigorous statistical and experimental methodologies to assess their efficacy. This analysis not only aids practitioners in selecting and designing the most appropriate AFs for their specific deep learning tasks but also encourages continued innovation in AF development within the machine learning community.

We show that hybrid zonotopes offer an equivalent representation of feed-forward fully connected neural networks with ReLU activation functions. Our approach demonstrates that the complexity of binary variables is equal to the total number of neurons in the network and hence grows linearly in the size of the network. We demonstrate the utility of the hybrid zonotope formulation through three case studies including nonlinear function approximation, MPC closed-loop reachability and verification, and robustness of classification on the MNIST dataset.

In the context of a neural network an activation function defines the output of a node/neuron, they could be classified into these categories: Ridge activation functions, Radial activation functions and Folding activation functions. For this article we will be looking at Ridge activation functions. Binary step function is a threshold based activation function meaning that if the input crosses a certain value the neuron is activated and if it goes below that value the neuron is deactivated, this function can be used in tasks of binary classification, This activation function is not suitable at all in the case of non-linearity (most of problem domains). Also, since the network is not differentiable, gradient-based training is not possible. As you can see here our function is directly proportional to the weighted sum of neurons: f(x) x.

We are going to do binary classification, so the value of y (true/target) is going to be either 0 or 1. For example, suppose we have a breast cancer dataset with X being the tumor size and y being whether the lump is malignant(cancerous) or benign(non-cancerous). Whenever a patient visits, your job is to tell him/her whether the lump is malignant(0) or benign(1) given the size of the tumor. There are only two classes in this case. So, y is going to be either 0 or 1. Let's use the following randomly generated data as a motivating example to understand Logistic Regression.

Activation functions shape the outputs of artificial neurons and, therefore, are integral parts of neural networks in general and deep learning in particular. Some activation functions, such as logistic and relu, have been used for many decades. But with deep learning becoming a mainstream research topic, new activation functions have mushroomed, leading to confusion in both theory and practice. This paper provides an analytic yet up-to-date overview of popular activation functions and their properties, which makes it a timely resource for anyone who studies or applies neural networks.

"The Expert in Anything was once a beginner…!!" As a current situation of a covid-19 pandemic, Charotar University of Science and Technology did not stop thinking about the growth of their students. They provide the best chance to improve the skills of the student and provide a many internship opportunities. Nowadays this term is too much popular. Artificial intelligence (AI) is the ability of a computer program or a machine to think and learn. Deep learning (also known as deep structured learning) is part of a broader family of machine learning methods based on artificial neural networks with representation learning. So that's it for the basic information now let's start that how I use my time during this pandemic to get the skill.

Industrial process control systems try to keep an output variable within a given tolerance around a target value. PID control systems have been widely used in industry to control input variables in order to reach this goal. However, this kind of Transfer Function based approach cannot be extended to complex processes where input data might be non-numeric, high dimensional, sparse, etc. In such cases, there is still a need for determining the subspace of input data that produces an output within a given range. This paper presents a non-stochastic heuristic to determine input values for a mathematical function or trained regression model given an output range. The proposed method creates a synthetic training data set of input combinations with a class label that indicates whether the output is within the given target range or not. Then, a decision tree classifier is used to determine the subspace of input data of interest. This method is more general than a traditional controller as the target range for the output does not have to be centered around a reference value and it can be applied given a regression model of the output variable, which may have categorical variables as inputs and may be high dimensional, sparse... The proposed heuristic is validated with a proof of concept on a real use case where the quality of a lamination factory is established to identify the suitable subspace of production variable values.

Neural networks are increasingly deployed in real-world safety-critical domains such as autonomous driving, aircraft collision avoidance, and malware detection. However, these networks have been shown to often mispredict on inputs with minor adversarial or even accidental perturbations. Consequences of such errors can be disastrous and even potentially fatal as shown by the recent Tesla autopilot crash. Thus, there is an urgent need for formal analysis systems that can rigorously check neural networks for violations of different safety properties such as robustness against adversarial perturbations within a certain $L$-norm of a given image. An effective safety analysis system for a neural network must be able to either ensure that a safety property is satisfied by the network or find a counterexample, i.e., an input for which the network will violate the property. Unfortunately, most existing techniques for performing such analysis struggle to scale beyond very small networks and the ones that can scale to larger networks suffer from high false positives and cannot produce concrete counterexamples in case of a property violation. In this paper, we present a new efficient approach for rigorously checking different safety properties of neural networks that significantly outperforms existing approaches by multiple orders of magnitude. Our approach can check different safety properties and find concrete counterexamples for networks that are 10$\times$ larger than the ones supported by existing analysis techniques. We believe that our approach to estimating tight output bounds of a network for a given input range can also help improve the explainability of neural networks and guide the training process of more robust neural networks.