mlxGPT: Rewrite of Karpathy's NanoGPT in mlx

Currently it isn't perfect but it sort of? learns when I run it; albeit a bit slowly. I'm taking a break from this project to level up so I can write better code.

To do:

• Find/gather a dataset to train
  • Tokenizer
  • Getting GPUs ready and initializing device deets
  • Getting dataset in a format ready to be trained
  • Format to download and extract the data
• Save and load model weights (GPT-2?)
  • Getting the model weights; loading them

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Notes of the rewrite

Components of NanoGPT:

• LayerNorm
• Causal Self-Attention
• Multi-Layer Perceptron (MLP)
• GPT

(12, 1024, 50247) -> (12, 1024, 50247) (12, 1024, 50247) (12, 1024, 50247) ->

LayerNorm

• https://arxiv.org/pdf/1607.06450.pdf
• Counters the highly-correlated nature of batch norm
• Batch norm has to estimate because it’s impractical to go through all the weights (Eq. 2)
• µ and σ are calculated using the empirical samples from the current mini-batch, which constraints the size of the batch and is hard to apply to RNNs.

Specifically, for the $i^{th}$ summed input in the $l^{th}$ layer, the batch normalization method rescales the summed inputs according to their variances under the distribution of the data:

Where $a^{-l}_i$ is normalized summed inputs to the $i^{th}$ hidden unit in the $l^{th}$ layer and $g_i$ is a gain parameter scaling the normalized activation before the non-linear activation function. }

$a^l$: the vector representation of the summed inputs to the neurons in that layer

$g_i$: gain parameter, used to scale the weights, helps control the variance of the outputs of neurons

$σ_i^{'}$: the standard deviation of activations $a_i^{'}$ over the batch of data

$µ_i^{'}$: mean of activations of $a_i^{'}$ over the batch of data

Layer normalization

• Reduces highly correlated changes in the summed inputs to the next layer (especially ReLU)
• "Covariate shift" problem can be reduced by fixing the mean and variance of summed input (µ and σ)
• The layer normalization statistics over all hidden units in the layer are computed with the following equations:

Where H denotes the no. hidden units in the layer. Unlike BatchNorm, LayerNorm does not impose any constraint on the size of a mini-batch and can be used in the pure online regime (?) with batch size 1.

Note that the normalization terms only depend on the summed inputs to a layer in the current time step. It also has only one set of gain and bias parameters shared over all time steps.

In RNN

The summed inputs in the recurrent layer are computed from the current input $x^t$ and previous vector of hidden states $h^{t-1}$, which are computed as $a^t$ = $W_{hh} h^{t-1} + W_{xh} x^t$.

The LayerNorm-ed recurrent layer recenters and rescales the activations using extra terms:

Where $W_{hh}$ is the recurrent hidden to hidden weights and $W_{xh}$ are the bottom up input to hidden weights.

The O. thing is the elem-wise multiplication between 2 vectors b & g are the bias and gain params, same dimension as $h^t$

In a layer normalized RNN, the normalization terms make it invariant to re-scaling all of the summed inputs to a layer, which results in much more stable hidden-to-hidden dynamics.

Causal Self Attention

Self attention:

• Self attention is the ability to piece different positions of a single sequence to create a representation of the whole sequence.
• Attention scores are computed and used to amplify/quieten signals

Causality:

• Prevents the model looking into the future
• Achieved by masking
• This is what I tried to do for three whole days

How it works:

1. A mask is applied to the upper triangular portion of the score matrix and sets them to very negative number (so when softmax is applied, they're irrelevant)
2. The model processes sequence token by token and predicts the next token based on the shown tokens.

Scaled Dot Product Attention: The image is split into 3 tensors: Q, K, and V

The equation is just this: