Yes, inductive biases are indeed necessary in Neural Networks. An inductive bias in machine learning is the set of assumptions that the learner uses to predict outputs given inputs that it has not encountered. In case of Neural Networks, these biases are necessary to process effectively. Neural networks have two primary types of inductive biases: 1. **Architectural Inductive Bias**: It involves the decisions related to the architecture of the network such as number of layers, number of neurons per layer, etc. These decisions can control how complex functions your network can represent. 2. **Algorithmic Inductive Bias**: It pertains to the learning algorithm being used like Backpropagation in the neural network to tune its weights and biases. This affects the specific function within the representational capacity of the architecture that will be learned for a given dataset. For more of the mathematical underpinnings and deeper understanding, you could start by referring to the book "Understanding Machine Learning: From Theory to Algorithms" by Shai Shalev-Shwartz and Shai Ben-David. You may also want to explore papers like "Inductive Bias of Neural Networks" by Francois Chollet, "The Implicit Bias of Gradient Descent on Separable Data" by Daniel Soudry et al, to gain more insights. Don't forget that choosing the right inductive biases in neural networks is more of an art rather than science and it usually requires plenty of machine learning experience or trial and error.

Yes, inductive biases are indeed necessary in neural networks and machine learning models in general to improve their learning effectiveness. An "inductive bias" in machine learning refers to a set of assumptions that a learning algorithm uses to predict outputs given inputs it has not encountered, and it guides the learning algorithm by making some hypotheses more likely than others. Without an inductive bias, a model has no preferences and could make highly unreasonable predictions, thereby reducing its performance. Here's why inductive biases are necessary: 1. **Prevents Overfitting:** Biases can help to prevent overfitting by simplifying the model. This reduces the model’s problem-solving capacity to avoid fitting to noise and, instead, capture more significant patterns in the data. 2. **Solves Under-determined Problems:** Many learning problems are under-determined, where the number of possible hypotheses that explain the data accurately is infinite. In such cases, inductive biases help chooses between these equally good solutions. 3. **Reduces Learning Time:** By providing prior knowledge about which types of solutions should be searched, biases can speed up the learning time. Here are some relevant sources that thoroughly cover the topic of inductive bias: 1. Mitchell, T. M. (1980). “The Need for Biases in Learning Generalizations”. Department of Computer Science, Laboratory for Computer Science Research. 2. Geman, Stuart, Elie Bienenstock, and René Doursat. (1992). "Neural networks and the bias/variance dilemma." Neural computation 4.1: 1-58. 3. Haussler, David. (1988) "Quantifying inductive bias: AI learning algorithms and Valiant's learning framework." Artificial Intelligence 36.2: 177-221. By looking into these sources, you will get detailed insights into the necessity and advantages of incorporating inductive biases in neural networks and general machine learning models.