Okay, I need to create a Wikipedia-style document about "Input Gate" under the categories of Technology → Artificial Intelligence → Machine Learning. Let me start by understanding what an input gate is. From what I remember, in neural networks, especially recurrent neural networks (RNNs), gates are components that control the flow of information. The input gate is part of architectures like Long Short-Term Memory (LSTM) networks.

First, the structure: H1 for the title, then an overview section. Next, sections with H2 and H3. I should explain what an input gate is, its role in LSTM, how it works, maybe compare it to other gates like forget or output gates. Also, include technical details, equations if possible, and applications.

I need to make sure the information is accurate. Let me recall: In LSTMs, there are three main gates—input, forget, and output. The input gate determines which values from the current input will be updated in the cell state. It uses a sigmoid function to decide what to update, and a tanh function to create a vector of new candidate values. Then, these two are multiplied to update the cell state.

I should explain each part step by step. Maybe start with an overview of LSTMs first, then dive into input gates. Also mention that input gates help in managing long-term dependencies by controlling information flow.

Need to check if there's any confusion between different types of neural networks. For example, GRUs have similar concepts but fewer gates. But since the focus is on LSTM, maybe just stick to that unless comparing later.

Include equations: The input gate formula might be something like Γ_i = σ(W_i * [h_{t-1}, x_t] + b_i), where σ is the sigmoid function. Then, the candidate cell state is ~C_t = tanh(W_c * [h_{t-1}, x_t] + b_c). The actual cell state update would be C_t = Γ_i * ~C_t + Γ_f * C_{t-1} (though that's for forget gate too).

Also, mention the importance of input gates in preventing vanishing gradients by allowing information to flow through without being multiplied by small weights. Maybe discuss applications like NLP tasks where sequences are important.

Need to ensure technical terms are explained. For example, explain what a sigmoid function is briefly, or maybe not if it's too basic. Since this is a professional document, some level of expertise is assumed, but clarity is key.

Check for any possible errors: Are there other types of input gates in different architectures? Maybe in transformers or other models? But the question specifies machine learning under AI, so focusing on LSTMs makes sense.

Include references to related concepts like cell state, hidden state, and how input gate interacts with them. Also, maybe mention that without input gates, RNNs would struggle with long-term dependencies.

Make sure each section is well-structured. For example:

• Introduction: What is an input gate?
• Role in LSTM
• Technical details (equations)
• Comparison with other gates
• Applications and importance

Use H2 for main sections and H3 for subsections like "Functionality" or "Mathematical Formulation".

Avoid markdown formatting as per the user's request, but since they want a markdown document, I need to use proper headers. Also, ensure that code blocks are used if there are any equations or code examples.

Check length: Need at least 800 characters. The example provided in the previous response was around 1200 words, so I should aim for similar depth.

Make sure all information is accurate and up-to-date. Maybe verify the LSTM structure from reliable sources like academic papers or reputable AI resources.

Finally, conclude with a summary of the importance of input gates in machine learning models, especially in handling sequential data.