Tensors in Machine Learning

Machine learning has transformed a variety of industries, offering innovative solutions to complex problems. Key applications include neural networks, computer vision, and natural language processing (NLP). This chapter explores these core areas, examining the structures and data flow that power each.

1. Neural Networks

Neural networks are foundational to many machine learning applications, enabling systems to identify patterns and make predictions based on large datasets. A neural network is composed of multiple layers, each containing neurons that perform computations on input data.

In this context:

  • Input tensors hold batches of data and are typically formatted as (batch_size, feature_dim). This structure allows the network to process multiple data points in parallel.

  • Weight tensors represent the learnable parameters of the network, connecting neurons across layers. Each weight tensor's dimensions depend on the layer structure, often appearing as (input_dim, output_dim).

  • Activation tensors store the outputs of each layer. After applying an activation function, such as ReLU or sigmoid, the activations are passed forward in the network, contributing to the model's final prediction.

Through iterative training, neural networks learn patterns from data, updating weight tensors to minimize error.

2. Computer Vision

Computer vision leverages machine learning to interpret visual data, finding applications in facial recognition, object detection, and image classification. Key elements in computer vision models include:

  • Image tensors represent the input images and typically take the shape (batch_size, height, width, channels). Each image has dimensions for height and width, and a channel dimension (often 3 for RGB color images).

  • Convolutional kernels are small matrices with dimensions (kernel_height, kernel_width, in_channels, out_channels) that slide over the input image to capture spatial hierarchies. Each kernel is responsible for detecting specific patterns, like edges or textures.

  • Feature maps are the outputs of convolutional layers. They highlight critical features detected by the convolutional kernels, which the network can use to identify objects or patterns within images.

Through layered convolutional and pooling operations, computer vision models excel at recognizing patterns in visual data.

3. Natural Language Processing (NLP)

Natural language processing focuses on analyzing and understanding human language, with applications ranging from machine translation to sentiment analysis. NLP relies heavily on sequential data, processed using embeddings and attention mechanisms.

In NLP:

  • Word embeddings represent words in a dense vector space, allowing models to capture semantic relationships. Typically formatted as (vocabulary_size, embedding_dim), these embeddings provide context, enabling the model to understand nuances in language.

  • Sequence data is the structured format for sentences or phrases, taking the shape (batch_size, sequence_length, feature_dim). The sequence length captures the number of words, while feature dimensions often represent embedding values or encoded features.

  • Attention matrices are used in models like Transformers to capture relationships between words, with a shape of (batch_size, num_heads, sequence_length, sequence_length). Each value reflects the importance of a word to other words, improving context and coherence in predictions.

Attention mechanisms have driven major advancements in NLP, especially in tasks like machine translation and text generation.

In these domains, machine learning’s ability to process vast quantities of structured data has unlocked powerful capabilities.

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