Deep-Learning

The Universal Approximation Theorem (UAT) gets quoted constantly, but it is usually described in a fuzzier way than it deserves. It does not say neural networks are magically good at every task. It does not say a shallow network is the most practical architecture. It does not say gradient descent will easily find the right weights. What it does say is still important: With a suitable nonlinear activation and enough hidden units, a feedforward network can approximate any continuous function on a bounded domain as closely as we want. ...

Once you understand neurons, activations, loss functions, and backpropagation, the next thing to understand is the training loop. This is the repetitive engine of deep learning. At a high level, training is boring in the best possible way. It is the same four steps repeated over and over: make a prediction measure the error compute gradients update the weights The interesting part is not the loop itself. The interesting part is how concepts like batch size, epoch, iteration, and convergence affect the behavior of that loop in practice. ...

Loss functions answer one basic question: How wrong is the model right now? Without a loss function, a neural network has no way to measure its own mistakes, and without that measurement, gradient-based training has nothing to optimize. Two of the most important losses in machine learning are: Mean Squared Error (MSE) Cross-Entropy They are both common. They are both differentiable. But they solve different kinds of problems, and using the wrong one makes training harder than it needs to be. ...

A multi-layer perceptron (MLP) is one of the simplest and most important neural network architectures. It is not flashy. It is not state of the art for language or vision by itself. But if you do not understand MLPs, a lot of modern deep learning stays blurry. MLPs teach the core structure of neural networks: inputs become vectors layers apply learned linear transforms activations add nonlinearity deeper layers build more useful internal representations They also still matter in practice. Even transformers contain MLP blocks. Recommendation systems, tabular models, and many small classifiers still use dense networks directly. ...

The forward pass is the part of a neural network that actually produces a prediction. You feed inputs into the model, the model applies a sequence of mathematical operations, and an output comes out the other side. That sounds trivial, but it is one of the most important ideas in deep learning because everything else depends on it: the loss compares the forward-pass output to the target backpropagation differentiates through the forward pass training is just repeating the forward pass and improving it The easiest way to understand the forward pass is to start with a single neuron and then scale it up into a full layer written in matrix form. ...

Backpropagation is the core algorithm that makes neural networks trainable. The forward pass tells the model what prediction it currently makes. Backpropagation tells the model how each weight contributed to the error so the optimizer can update those weights in the right direction. People often hear that backpropagation is “just the chain rule,” which is true but not especially helpful. The useful mental model is this: the forward pass computes values the backward pass computes sensitivities each node only needs its own local derivative the full gradient is built by multiplying those local derivatives along the path If that sounds abstract, it becomes much clearer once you look at one neuron first and then scale up. ...

Large Language Models (LLMs) such as GPT-2, GPT-3, LLaMA, and BERT are built on top of the Transformer architecture. That architecture changed natural language processing by replacing recurrence with attention, which lets models process sequences more efficiently and capture long-range relationships more directly. If you are trying to understand what terms like layer, transformer block, and attention head actually mean, the easiest way is to follow the path a sentence takes through a GPT-style model. ...

Introduction When training large language models (LLMs) the most important question is simple: how do we measure whether the model is doing well? For regression you use mean squared error, for classification you might use cross-entropy or hinge loss. But for LLMs — which predict sequences of discrete tokens — the right way to turn “this output feels wrong” into a number you can optimize is a specific kind of probability loss: categorical cross-entropy / negative log likelihood, and the closely related, more interpretable metric perplexity. ...

Introduction ComfyUI is a powerful, open-source, node-based interface for generative AI workflows, majorly for image and video workflows. While it’s primarily known for its visual interface, ComfyUI also offers robust API capabilities, enabling developers to integrate and automate workflows programmatically. This guide will walk you through using ComfyUI in API mode. ComfyUI offers a suite of RESTful and WebSocket API endpoints that enable developers to programmatically interact with its workflow engine. These endpoints facilitate tasks such as queuing prompts, retrieving results, uploading images, and monitoring system status. ...

This sound is generated with Kokoro tts The world of text-to-speech (TTS) has seen incredible advancements, but often these powerful models require hefty hardware like GPUs. But what if you could run a top-tier TTS model locally on your CPU? Enter **Kokoro**, a game-changing TTS model that delivers impressive results even on resource-constrained devices. Kokoro: Small but Mighty Kokoro stands out for its remarkable efficiency. With just 82 million parameters, it outperforms models several times its size, including XTTS (467M parameters) and MetaVoice (1.2B parameters). This proves that cutting-edge TTS is achievable without relying on massive models and powerful GPUs. ...