Q -you are expert llm training engineering working at large scale production grade multli node large cluster training org, also you are great teacher to simplyfy things, teach by hands on , top down approach

https://github.com/SDcodehub/assignment1-basics, my repository, get all the files and structure in the file.

till tokeniser everything is done, refer to the files names from the repo.

now I want to move to the transformer language coding.

move step by step, do not give me full code, move as per the outline of the pdf.

I think linear module implentation seems to be good starting point, correct if I am wrong.

lets start with this model, help me understad basics and move to final code of linear module, I have basic understanding of pytorch

Of course! You’re absolutely on the right track. Starting with the Linear module is the perfect first step. It’s the fundamental building block for almost every part of the Transformer, from the feed-forward networks to the attention mechanism itself.

Let’s break it down, top-down, just like you asked.

## 1. The Big Picture: What is a Linear Layer?

At its core, a linear layer (or “fully connected” layer) is one of the simplest and most important components in any neural network. Its job is to perform a linear transformation on the input data.

Think of it like a function $y = Wx$. It takes an input vector $x$ and multiplies it by a weight matrix $W$ to produce an output vector $y$.

  • Input (x): A vector representing some data. In our Transformer, this will be a vector representing a token at a specific position in the sequence, with dimension d_model.
  • Weights (W): This is a matrix of learnable parameters. This is the “brain” of the layer. During training, the optimizer will tweak the values in this matrix to help the model make better predictions.
  • Output (y): The transformed vector. The layer “projects” the input from its original dimensional space to a new one. For example, it might take a vector of size 512 and project it into a space of size 2048.

[cite_start]The PDF also mentions that we’ll be implementing it without a bias term ($y = Wx$ instead of $y = Wx + b$)[cite: 523]. This is a common practice in modern large language models (LLMs) like LLaMA, as other layers (like normalization layers) can handle shifting the activations, making the explicit bias term redundant.

## 2. The Blueprint: Coding a Linear Module in PyTorch

To implement this in PyTorch, we’ll create a class that inherits from torch.nn.Module. This is the standard way to build any custom layer. Inheriting from torch.nn.Module gives us a ton of useful functionality for free, like tracking parameters, moving them between CPU/GPU, and saving/loading the model state.

Our class will need two key methods:

  1. __init__(self, ...): The constructor. This is where we’ll define and initialize our weight matrix W.
  2. forward(self, x): This is where the action happens. We’ll take an input tensor x and perform the actual matrix multiplication using our weight matrix W.

## 3. The Details: __init__ and Parameter Initialization

Let’s look at the constructor first. It needs to create our learnable weight matrix W.

  • Shape: If the input vector has size in_features and we want the output vector to have size out_features, our weight matrix W needs to have the shape (out_features, in_features).
  • torch.nn.Parameter: We can’t just use a regular torch.Tensor for our weights. We need to wrap it in torch.nn.Parameter. [cite_start]This is a special wrapper that tells PyTorch, “Hey, this tensor is a learnable parameter. When it’s time to train, make sure the optimizer updates this!“[cite: 541].
  • Initialization: How we set the initial values of W is surprisingly important. Bad initial values can cause the model to fail to train. [cite_start]The assignment gives us a specific recipe: a truncated normal distribution[cite: 515, 543]. This helps ensure that the signals flowing through our network at the beginning of training are in a healthy range (not too big, not too small). We’ll use torch.nn.init.trunc_normal_ for this.

## 4. The Details: forward and Matrix Multiplication

The forward method is where we implement the equation $y=Wx$.

In PyTorch, a standard matrix multiplication is done with the @ operator or torch.matmul. Our input x will have a shape like (batch_size, sequence_length, in_features). Our weight matrix W has the shape (out_features, in_features).

To make the dimensions line up for multiplication, we need to multiply x by the transpose of W. The operation will be x @ self.W.T.

[cite_start]The PDF also strongly encourages using torch.einsum[cite: 401]. It’s a very powerful and self-documenting way to perform tensor operations. For our linear layer, it would look like this:

y = torch.einsum("... d_in, d_out d_in -> ... d_out", x, self.W)

This notation says:

  • Take the input x, which has some leading batch dimensions (...) and a final dimension d_in.
  • Take the weight matrix W, with dimensions d_out and d_in.
  • Multiply them by contracting (summing over) the common d_in dimension.
  • The output y will have the same leading batch dimensions (...) and a final dimension of d_out.

It’s a great habit to get into, as it makes your code clearer and less prone to dimension-shuffling bugs.

## 5. The Final Code

Okay, let’s put all of that together. Based on your repository structure, a good place for this would be a new file: cs336_basics/model.py.

Here is the complete, commented code for the Linear module.

# In cs336_basics/model.py

import torch
import torch.nn as nn
from torch.nn.init import trunc_normal_

class Linear(nn.Module):
    """
    Implementation of a Linear layer from scratch, as required by the assignment.
    This module performs a linear transformation on the input data: y = xW^T.
    It does not include a bias term, following modern LLM practices.
    """
    def __init__(self, in_features: int, out_features: int, device=None, dtype=None):
        """
        Initializes the Linear module.

        Args:
            in_features (int): Size of each input sample.
            out_features (int): Size of each output sample.
            device (torch.device, optional): The device to store parameters on. Defaults to None.
            dtype (torch.dtype, optional): The data type of the parameters. Defaults to None.
        """
        super().__init__()
        self.in_features = in_features
        self.out_features = out_features

        # 1. Create the weight matrix as a torch.nn.Parameter.
        # This tells PyTorch that it's a learnable parameter.
        # The shape is (out_features, in_features) which is the standard PyTorch convention.
        self.W = nn.Parameter(torch.empty((out_features, in_features), device=device, dtype=dtype))

        # 2. Initialize the weights according to the assignment's specification.
        self.reset_parameters()

    def reset_parameters(self):
        """
        Initializes the weight matrix using a truncated normal distribution.
        This specific initialization is crucial for stable training in pre-norm Transformers.
        Ref: Section 3.4.1 in the assignment PDF.
        """
        # The formula for standard deviation is sqrt(2 / (d_in + d_out))
        std = (2 / (self.in_features + self.out_features))**0.5
        # Truncate at 3 standard deviations.
        trunc_normal_(self.W, mean=0.0, std=std, a=-3*std, b=3*std)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        """
        Applies the linear transformation to the input tensor.

        Args:
            x (torch.Tensor): Input tensor of shape (..., in_features).

        Returns:
            torch.Tensor: Output tensor of shape (..., out_features).
        """
        # The assignment recommends using einsum for clarity and robustness.
        # "... d_in" means the input tensor can have any number of leading (batch) dimensions.
        # "d_out d_in" is the shape of our weight matrix.
        # "-> ... d_out" specifies the output shape, preserving batch dimensions.
        return torch.einsum("... d_in, d_out d_in -> ... d_out", x, self.W)

    def extra_repr(self) -> str:
        """
        Provides a string representation of the module's configuration,
        similar to PyTorch's built-in layers.
        """
        return f'in_features={self.in_features}, out_features={self.out_features}, bias=False'

## Next Steps

  1. Add the code to your cs336_basics/model.py file.
  2. [cite_start]Implement the test adapter in adapters.py to hook up your new Linear class to the test suite, as described in section 3.4.2 of the PDF[cite: 544].
  3. Run the tests using uv run pytest -k test_linear.

[cite_start]Once you’ve passed the tests for the Linear module, the next logical step is implementing the Embedding module[cite: 552]. It’s very similar in spirit—it’s a simple lookup table, also implemented as a torch.nn.Module.

Let me know when you’re ready to move on to that!