Deep Learning

LoRA stands for Low-Rank Adaptation. It is one of the most useful ideas in modern LLM fine-tuning because it changes the question from: How do we update all of the model's weights? to: How do we learn a small update that is still expressive enough for the new task? That is the whole trick. Instead of fine-tuning every entry of a large weight matrix, LoRA keeps the original pretrained weight frozen and learns a low-rank correction on top of it. This makes training much cheaper in parameters, optimizer state, checkpoint size, and often VRAM. ...

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. ...