---
layout: '@/layouts/Doc.astro'
title: 'Scientific AI at Scale: Distributed Training'
date: '2025-09-02'
---

Sam Foreman
2025-09-02

- [👀 Overview](#eyes-overview)
- [📑 Outline](#bookmark_tabs-outline)
- [🚀 Scaling: Overview](#rocket-scaling-overview)
- [🐢 Training on a Single Device](#turtle-training-on-a-single-device)
- [🐢 Training on a Single
  Device](#turtle-training-on-a-single-device-1)
- [🐢 Training on a Single
  Device](#turtle-training-on-a-single-device-2)
- [Training on Multiple GPUs: Data
  Parallelism](#training-on-multiple-gpus-data-parallelism)
- [Data Parallel: Forward Pass](#data-parallel-forward-pass)
- [Data Parallel: Backward Pass](#data-parallel-backward-pass)
- [Data Parallel: Training](#data-parallel-training)
- [🗣️ Communication](#speaking_head-communication)
- [AllReduce](#allreduce)
- [Reduce](#reduce)
- [Broadcast](#broadcast)
- [AllGather](#allgather)
- [Scatter](#scatter)
- [Why Distributed Training?](#why-distributed-training)
- [Why Distributed Training?
  Speedup!](#why-distributed-training-speedup)
- [Dealing with Data](#dealing-with-data)
- [Broadcast Initial State](#broadcast-initial-state)
- [Best Practices](#best-practices)
- [Going Beyond Data Parallelism](#going-beyond-data-parallelism)
- [Going beyond Data Parallelism: DeepSpeed +
  `ZeRO`](#going-beyond-data-parallelism-b58fc729-690b-4000-b19f-365a4093b2ff7b7b3c2069636f6e696679206c6f676f73206d6963726f736f66742d69636f6e203e7d7d-deepspeed--zero)
- [Fully Sharded Data Parallel: 🔥 PyTorch +
  `FSDP`](#fully-sharded-data-parallel-fire-pytorch--fsdp)
- [🕸️ Additional Parallelism
  Strategies](#spider_web-additional-parallelism-strategies)
- [Pipeline Parallelism (PP)](#pipeline-parallelism-pp)
- [Tensor Parallel (TP)](#tensor-parallel-tp)
- [Tensor Parallel (TP)](#tensor-parallel-tp-1)
- [Tensor (/ Model) Parallel Training:
  Example](#tensor--model-parallel-training-example)
- [Tensor (Model)
  Parallelism](#tensor-model-parallelismefficient-large-scale)
- [Tensor Parallelism](#tensor-parallelism)
- [3D Parallelism](#3d-parallelism)
- [Deciding on a Parallelism
  Strategy](#deciding-on-a-parallelism-strategy)
- [🦙 Large Language Models](#llama-large-language-models)
- [🔮 Emergent Abilities](#crystal_ball-emergent-abilities)
- [🚂 Training LLMs](#steam_locomotive-training-llms)
- [♻️ Life-Cycle of the LLM](#recycle-life-cycle-of-the-llm)
- [🎀 Life-Cycle of the LLM](#ribbon-life-cycle-of-the-llm)
- [⏩ Forward Pass](#fast_forward-forward-pass)
- [💬 Generating Text](#speech_balloon-generating-text)
- [👋 Hands On](#wave-hands-on)
- [🧑‍💻 Hands On: Getting Started](#technologist-hands-on-getting-started)
- [📦 Install {`ezpz`, `wordplay`}](#package-install-ezpz-wordplay)
- [ `ezpz`: Example
  \[video\]](#b58fc729-690b-4000-b19f-365a4093b2ff7b7b3c206661206272616e647320676974687562203e7d7d-ezpz-example-video)
- [Install `wordplay` 🎮💬](#install-wordplay-video_gamespeech_balloon)
- [Prepare Data](#prepare-data)
- [Launch Training (DDP)](#launch-training-ddp)
- [Training: Example Output](#training-example-output)
- [ `wordplay`: Example
  \[video\]](#b58fc729-690b-4000-b19f-365a4093b2ff7b7b3c206661206272616e647320676974687562203e7d7d-wordplay-example-video)
- [❤️ Thank you!](#heart-thank-you)
- [📓 References](#notebook-references)

## 👀 Overview

- 📊 Slides @
  [samforeman.me/talks/openskai25/training/slides](https://samforeman.me/talks/openskai25/training/slides)
    - 📄 HTML version:
      [samforeman.me/talks/openskai25/training](https://samforeman.me/talks/openskai25/training)

## 📑 Outline

1.  [Scaling: Overview](#scaling-overview)
2.  [Data Parallel Training](#data-parallel-training)
    1.  [Communication](#communication)
    2.  [Why Distributed Training?](#why-distributed-training)
3.  [Beyond Data Parallelism](#going-beyond-data-parallelism)
    1.  [Additional Parallelism
        Strategies](#additional-parallelism-strategies)
4.  [Large Language Models](#large-language-models)
5.  [Hands On](#hands-on)

## 🚀 Scaling: Overview

- ✅ **Goal**:
    - Minimize: <span class="highlight-red">Cost</span> (i.e. amount of
      time spent training)
    - Maximize: <span class="highlight-blue">Performance</span>

    > [!NOTE] 📑 Note
    >
    > See [🤗 Performance and
    > Scalability](https://huggingface.co/docs/transformers/v4.46.0/performance)
    > for more details

## 🐢 Training on a Single Device

- See [🤗 Methods and tools for efficient training on a single
  GPU](https://huggingface.co/docs/transformers/v4.46.0/perf_train_gpu_one)

<div id="fig-single-gpu-1">

```mermaid
flowchart LR
    subgraph G0["`GPU0`"]
        subgraph N0["`Network`"]
        end
        L0("`Loss`")
    end
    subgraph D["`Data`"]
        x("`x0`")
        x1("`x1`")
        x2("`x2`")
    end
    x --> N0
    N0 --> L0
    L0 --> N0
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,color:#838383
classDef red fill:#ff8181,stroke:#333,stroke-width:1px,color:#000
classDef green fill:#98E6A5,stroke:#333,stroke-width:1px,color:#000
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef grey fill:#cccccc,stroke:#333,stroke-width:1px,color:#000
class x,L0 red
class x1 green
class x2 blue
class x3 grey
class N0,D,G0,n0 block
```

Figure 1: **SLOW** !! model size limited by GPU memory

</div>

## 🐢 Training on a Single Device

- See [🤗 Methods and tools for efficient training on a single
  GPU](https://huggingface.co/docs/transformers/v4.46.0/perf_train_gpu_one)

<div id="fig-single-gpu-2">

```mermaid
flowchart LR
    subgraph G0["`GPU0`"]
        subgraph N0["`Network`"]
        end
        L0("`Loss`")
    end
    subgraph D["`Data`"]
        x("`x1`")
        x1("`x2`")
        x2("`x3`")
    end
    x --> N0
    N0 --> L0
    L0 --> N0
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,color:#838383
classDef red fill:#ff8181,stroke:#333,stroke-width:1px,color:#000
classDef grey fill:#cccccc,stroke:#333,stroke-width:1px,color:#000
classDef orange fill:#FFC47F,stroke:#333,stroke-width:1px,color:#000
classDef yellow fill:#FFFF7F,stroke:#333,stroke-width:1px,color:#000
classDef green fill:#98E6A5,stroke:#333,stroke-width:1px,color:#000
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef purple fill:#FFCBE6,stroke:#333,stroke-width:1px,color:#000
classDef text fill:#CCCCCC02,stroke:#838383,stroke-width:0px,color:#838383
class x,L0 green
class x1 blue
class x2 yellow
class x3 grey
class N0,D,G0,n0 block
```

Figure 2: **SLOW** !! model size limited by GPU memory

</div>

## 🐢 Training on a Single Device

- See [🤗 Methods and tools for efficient training on a single
  GPU](https://huggingface.co/docs/transformers/v4.46.0/perf_train_gpu_one)

<div id="fig-single-gpu-3">

```mermaid
flowchart LR
    subgraph G0["`GPU0`"]
        subgraph N0["`Network`"]
        end
        L0("`Loss`")
    end
    subgraph D["`Data`"]
        x("`x2`")
        x1("`x3`")
        x2("`x4`")
    end
    x --> N0
    N0 --> L0
    L0 --> N0
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,color:#838383
classDef red fill:#ff8181,stroke:#333,stroke-width:1px,color:#000
classDef grey fill:#cccccc,stroke:#333,stroke-width:1px,color:#000
classDef orange fill:#FFC47F,stroke:#333,stroke-width:1px,color:#000
classDef yellow fill:#FFFF7F,stroke:#333,stroke-width:1px,color:#000
classDef green fill:#98E6A5,stroke:#333,stroke-width:1px,color:#000
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef purple fill:#FFCBE6,stroke:#333,stroke-width:1px,color:#000
classDef text fill:#CCCCCC02,stroke:#838383,stroke-width:0px,color:#838383
class x,L0 blue
class x1 yellow
class x2 purple
class x3 grey
class N0,D,G0,n0 block
```

Figure 3: **SLOW** !! model size limited by GPU memory

</div>

## Training on Multiple GPUs: Data Parallelism

<div id="fig-ddp-training-mermaid">

```mermaid
flowchart LR
    subgraph D["`Data`"]
        direction TB
        x("`x₀`")
        x1("`x₁`")
        x2("`x₂`")
    end
    direction LR
    subgraph G0["`GPU0`"]
        direction LR
        subgraph N0["`NN`"]
        end
        %%y0("`y₀`")
        L0["`Loss`"]
    end
    subgraph G1["`GPU1`"]
        direction LR
        subgraph N1["`NN`"]
        end
        L1["`Loss`"]
    end
    subgraph G2["`GPU2`"]
        direction LR
        subgraph N2["`NN`"]
        end
        L2["`Loss`"]
    end
    x --> G0
    x1 --> G1
    x2 --> G2
    N0 --> L0
    N1 --> L1
    N2 --> L2
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,color:#838383
classDef text fill:#CCCCCC02,stroke:#838383,stroke-width:0px,color:#838383
classDef grey fill:#cccccc,stroke:#333,stroke-width:1px,color:#000
classDef red fill:#ff8181,stroke:#333,stroke-width:1px,color:#000
classDef orange fill:#FFC47F,stroke:#333,stroke-width:1px,color:#000
classDef yellow fill:#FFFF7F,stroke:#333,stroke-width:1px,color:#000
classDef green fill:#98E6A5,stroke:#333,stroke-width:1px,color:#000
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef purple fill:#FFCBE6,stroke:#333,stroke-width:1px,color:#000
class x,y0,L0 red
class x1,L1 green
class x2,L2 blue
class x3,ar grey
class D,N0,N1,N2,G0,G1,G2,GU block
class AR block
class bc text
```

Figure 4: Each GPU receives **unique** data at each step

</div>

## Data Parallel: Forward Pass

<div id="fig-ddp-training-mermaid-allreduce">

```mermaid
flowchart LR
    subgraph D["`Data`"]
        direction TB
        x("`x₀`")
        x1("`x₁`")
        x2("`x₂`")
    end
    direction LR
    subgraph G0["`GPU0`"]
        direction LR
        subgraph N0["`NN`"]
        end
        L0["`Loss`"]
    end
    subgraph G1["`GPU1`"]
        direction LR
        subgraph N1["`NN`"]
        end
        L1["`Loss`"]
    end
    subgraph G2["`GPU2`"]
        direction LR
        subgraph N2["`NN`"]
        end
        L2["`Loss`"]
    end
    ar("`Avg. Grads<br>(∑ₙgₙ)/N`")
    x --> G0
    x1 --> G1
    x2 --> G2
    N0 --> L0
    N1 --> L1
    N2 --> L2
    L0 -.-> ar
    L1 -.-> ar
    L2 -.-> ar
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,color:#838383
classDef grey fill:#cccccc,stroke:#333,stroke-width:1px,color:#000
classDef red fill:#ff8181,stroke:#333,stroke-width:1px,color:#000
classDef orange fill:#FFC47F,stroke:#333,stroke-width:1px,color:#000
classDef yellow fill:#FFFF7F,stroke:#333,stroke-width:1px,color:#000
classDef green fill:#98E6A5,stroke:#333,stroke-width:1px,color:#000
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef purple fill:#FFCBE6,stroke:#333,stroke-width:1px,color:#000
classDef text fill:#CCCCCC02,stroke:#838383,stroke-width:0px,color:#838383
class x,y0,L0 red
class x1,L1 green
class x2,L2 blue
class x3,ar grey
class D,N0,N1,N2,G0,G1,G2,GU block
class AR block
class bc text
```

Figure 5: Average gradients across all GPUs

</div>

## Data Parallel: Backward Pass

<div id="fig-ddp-backward-mermaid">

```mermaid
flowchart RL
    subgraph D["`Data`"]
        direction TB
        x("`x₀`")
        x1("`x₁`")
        x2("`x₂`")
    end
    subgraph G0["`GPU0`"]
        direction RL
        subgraph N0["`NN`"]
        end
        L0["`Loss`"]
    end
    subgraph G1["`GPU1`"]
        direction RL
        subgraph N1["`NN`"]
        end
        L1["`Loss`"]
    end
    subgraph G2["`GPU2`"]
        direction RL
        subgraph N2["`NN`"]
        end
        L2["`Loss`"]
    end
    subgraph BC["`Send Updates`"]
        direction TB
    end
    BC -.-> G0
    BC -.-> G1
    BC -.-> G2
    L0 ~~~ N0
    L1 ~~~ N1
    L2 ~~~ N2
    G0 ~~~ x
    G1 ~~~ x1
    G2 ~~~ x2
classDef grey fill:#cccccc,stroke:#333,stroke-width:1px,color:#000
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,color:#838383
classDef red fill:#ff8181,stroke:#333,stroke-width:1px,color:#000
classDef orange fill:#FFC47F,stroke:#333,stroke-width:1px,color:#000
classDef yellow fill:#FFFF7F,stroke:#333,stroke-width:1px,color:#000
classDef green fill:#98E6A5,stroke:#333,stroke-width:1px,color:#000
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef purple fill:#FFCBE6,stroke:#333,stroke-width:1px,color:#000
classDef text fill:#CCCCCC02,stroke:#838383,stroke-width:0px,color:#838383
class x,y0,L0 red
class x1,L1 green
class x2,L2 blue
class x3,ar grey
class D,N0,N1,N2,G0,G1,G2,GU block
class BC block
class bc text
```

Figure 6: Send global updates back to each GPU. See: [PyTorch /
Distributed Data
Parallel](https://pytorch.org/tutorials/intermediate/ddp_tutorial.html)

</div>

## Data Parallel: Training

- Each GPU:
    - has **identical copy** of model
    - works on a **unique** subset of data
- Easy to get started (minor modifications to code):
    - [saforem2/`ezpz`](https://github.com/saforem2/ezpz)
    - 🔥 [PyTorch / `DDP`](https://pytorch.org/docs/stable/notes/ddp.html)
    - 🤗 [HF /
      `Accelerate`](https://huggingface.co/docs/transformers/accelerate)
    - [Microsoft / `DeepSpeed`](https://www.deepspeed.ai/)
- Requires **global** communication
    - every rank _must participate_ (collective communication) !!

## 🗣️ Communication

- Need mechanism(s) for communicating across GPUs:
    - [`mpi4py`](https://mpi4py.readthedocs.io/en/stable/tutorial.html)
    - [`torch.distributed`](https://pytorch.org/docs/stable/distributed.html)
- Collective Communication:
    - [Nvidia Collective Communications Library
      (NCCL)](https://developer.nvidia.com/nccl)

    - [Intel oneAPI Collective Communications Library
      (oneCCL)](https://www.intel.com/content/www/us/en/developer/tools/oneapi/oneccl.html#gs.gouznn)

        > [!WARNING] ⌛ Timeouts
        >
        > - Collective operations have to be called for each `rank` to form
        >   a complete collective operation.
        >     - Failure to do so will result in other ranks waiting
        >       **indefinitely**

## AllReduce

Perform _reductions_ on data (e.g. `sum`, `min`, `max`) across ranks,
send result back to everyone.

<div id="fig-all-reduce-mermaid">

```mermaid
flowchart TD
  subgraph R0["`0`"]
    x0("`x0`")
  end
  subgraph R1["`1`"]
    x1("`x1`")
  end
  subgraph R2["`2`"]
    x2("`x2`")
  end
  subgraph R3["`3`"]
    x3("`x3`")
  end
  subgraph AR["`Allreduce`"]
    xp["`x' = ∑ xₙ `"]
  end
  subgraph AR3["`3`"]
    xp3("`x'`")
  end
  subgraph AR2["`2`"]
    xp2("`x'`")
  end
  subgraph AR1["`1`"]
    xp1("`x'`")
  end
  subgraph AR0["`0`"]
    xp0("`x'`")
  end
  x0 --> AR
  x1 --> AR
  x2 --> AR
  x3 --> AR
  AR --> xp0
  AR --> xp1
  AR --> xp2
  AR --> xp3
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,color:#838383
classDef red fill:#ff8181,stroke:#333,stroke-width:1px,color:#000
classDef orange fill:#FFC47F,stroke:#333,stroke-width:1px,color:#000
classDef yellow fill:#FFFF7F,stroke:#333,stroke-width:1px,color:#000
classDef green fill:#98E6A5,stroke:#333,stroke-width:1px,color:#000
classDef pink fill:#E599F7,stroke:#333,stroke-width:1px,color:#000
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef purple fill:#FFCBE6,stroke:#333,stroke-width:1px,color:#000
class R0,R1,R2,R3,AR,AR0,AR1,AR2,AR3 block
class xp,xp0,xp1,xp2,xp3 purple
class x0 red
class x1 green
class x2 blue
class x3 yellow
```

Figure 7: All-Reduce operation: each rank receives the reduction of
input values across ranks.

</div>

## Reduce

- Perform a _reduction_ on data across ranks, send to individual

<div id="fig-reduce-mermaid">

```mermaid
flowchart TD
  subgraph R0["`0`"]
    x0("`x0`")
  end
  subgraph R1["`1`"]
    x1("`x1`")
  end
  subgraph R2["`2`"]
    x2("`x2`")
  end
  subgraph R3["`3`"]
    x3("`x3`")
  end
  subgraph AR["`Reduce`"]
    xp["`x'=reduce(x, 2, SUM)`"]
  end
  subgraph AR3["`3`"]
  end
  subgraph AR2["`2`"]
    xp2("`x'`")
  end
  subgraph AR1["`1`"]
  end
  subgraph AR0["`0`"]
  end
  x0 --> AR
  x1 --> AR
  x2 --> AR
  x3 --> AR
  AR --> AR3
  AR --> xp2
  AR --> AR1
  AR --> AR0
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,color:#838383
classDef red fill:#ff8181,stroke:#333,stroke-width:1px,color:#000
classDef orange fill:#FFC47F,stroke:#333,stroke-width:1px,color:#000
classDef green fill:#98E6A5,stroke:#333,stroke-width:1px,color:#000
classDef yellow fill:#FFFF7F,stroke:#333,stroke-width:1px,color:#000
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef purple fill:#FFCBE6,stroke:#333,stroke-width:1px,color:#000
classDef pink fill:#E599F7,stroke:#333,stroke-width:1px,color:#000
class R0,R1,R2,R3,AR,AR0,AR1,AR2,AR3 block
class xp,xp2 purple
class x0 red
class x1 green
class x2 blue
class x3 yellow
```

Figure 8: Reduce operation: one rank receives the reduction of input
values across ranks

</div>

## Broadcast

<div id="fig-broadcast-mermaid">

```mermaid
flowchart TD
  subgraph R3["`3`"]
  end
  subgraph R2["`2`"]
    x2("`x2`")
  end
  subgraph R1["`1`"]
  end
  subgraph R0["`0`"]
  end
  subgraph AR["` `"]
    xp["`broadcast(x2, 2)`"]
  end
  subgraph AR0["`0`"]
    xp0("`x2`")
  end
  subgraph AR1["`1`"]
    xp1("`x2`")
  end
  subgraph AR2["`2`"]
    xp2("`x2`")
  end
  subgraph AR3["`3`"]
    xp3("`x2`")
  end
  x2 --> AR
  AR --> AR0
  AR --> AR1
  AR --> AR2
  AR --> AR3
classDef text fill:#CCCCCC02,stroke:#838383,stroke-width:0px,color:#838383,font-weight:500
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,font-weight:500,color:#838383
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef yellow fill:#FFFF7F,stroke:#333,stroke-width:1px,color:#000
class R0,R1,R2,R3,AR0,AR1,AR2,AR3,AR block
class x2,xp0,xp1,xp2,xp3 blue
class xp text
```

Figure 9: `broadcast` (send) a tensor <code>$x$</code> from one rank to
all ranks

</div>

## AllGather

<div id="fig-allgather-mermaid">

```mermaid
flowchart LR
  subgraph R0["`0`"]
    x0("`x0`")
  end
  subgraph R1["`1`"]
    x1("`x1`")
  end
  subgraph R2["`2`"]
    x2("`x2`")
  end
  subgraph AG["`Allgather`"]
    %%xp0["`z=[empty_like(x) for _ in range(4)]`"]
    %%xp1["`dist.all_gather(z, x)`"]
  end
  subgraph AG2["`2`"]
    direction TB
    xp02("`x0`")
    xp12("`x1`")
    xp22("`x2`")
  end
  subgraph AG1["`1`"]
    direction TB
    xp01("`x0`")
    xp11("`x1`")
    xp21("`x2`")
  end
  subgraph AG0["`0`"]
    direction TB
    xp00("`x0`")
    xp10("`x1`")
    xp20("`x2`")
  end
  x0 --> AG
  x1 --> AG
  x2 --> AG
  AG --> AG0
  AG --> AG1
  AG --> AG2
classDef red fill:#ff8181,stroke:#333,stroke-width:1px,color:#000
classDef orange fill:#FFC47F,stroke:#333,stroke-width:1px,color:#000
classDef yellow fill:#FFFF7F,stroke:#333,stroke-width:1px,color:#000
classDef green fill:#98E6A5,stroke:#333,stroke-width:1px,color:#000
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef purple fill:#FFCBE6,stroke:#333,stroke-width:1px,color:#000
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,font-weight:500,color:#838383
classDef text fill:#CCCCCC02,stroke:#838383,stroke-width:0px,color:#838383
class xp0,xp1 text
class AG0,AG1,AG2,AG3,AG,R0,R1,R2,R3 block
class xp00,xp01,xp02,xp03 red
class xp10,xp11,xp12,xp13 green
class xp20,xp21,xp22,xp23 blue
class xp30,xp31,xp32,xp33 yellow
class x0 red
class x1 green
class x2 blue
class x3 yellow
```

Figure 10: Gathers tensors from the whole group in a list.

</div>

## Scatter

<div id="fig-scatter-mermaid">

```mermaid
flowchart TD
  subgraph R3["`3`"]
  end
  subgraph R2["`2`"]
  end
  subgraph R1["`1`"]
    direction TB
    xp0("`x0`")
    xp1("`x1`")
    xp2("`x2`")
    xp3("`x3`")
  end
  subgraph R0["`0`"]
  end
  subgraph S["`Scatter`"]
  end
  subgraph S3["`3`"]
    x3("`x3`")
  end
  subgraph S2["`2`"]
    x2("`x2`")
  end
  subgraph S1["`1`"]
    x1("`x1`")
  end
  subgraph S0["`0`"]
    x0("`x0`")
  end
  R1 --> S
  S --> S0
  S --> S1
  S --> S2
  S --> S3
classDef red fill:#ff8181,stroke:#333,stroke-width:1px,color:#000
classDef orange fill:#FFC47F,stroke:#333,stroke-width:1px,color:#000
classDef yellow fill:#FFFF7F,stroke:#333,stroke-width:1px,color:#000
classDef green fill:#98E6A5,stroke:#333,stroke-width:1px,color:#000
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef purple fill:#FFCBE6,stroke:#333,stroke-width:1px,color:#000
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,font-weight:500,color:#838383
class AG0,AG1,AG2,AG3,S,R0,R1,R2,R3,S0,S1,S2,S3 block
class x0,xp0 red
class x1,xp1 green
class x2,xp2 blue
class x3,xp3 yellow
```

Figure 11: Scatters a list of tensors to the whole group

</div>

## Why Distributed Training?

- `N` workers each processing unique batch[^1] of data:
    - \[`micro_batch_size = 1`\] $\times$ \[`N` GPUs\] $\rightarrow$
      \[<b><code>global_batch_size = N</code></b>\]
- Improved gradient estimators
    - Smooth loss landscape
    - Less iterations needed for same number of epochs
        - common to scale learning rate `lr *= sqrt(N)`
- See: [Large Batch Training of Convolutional
  Networks](https://arxiv.org/abs/1708.03888)

## Why Distributed Training? Speedup!

<div id="tbl-recent-progress">

Table 1: Recent progress

| Year |  Author  | GPU  | Batch Size |              \# GPU               |              TIME (s)               |  ACC   |
| :--: | :------: | :--: | :--------: | :-------------------------------: | :---------------------------------: | :----: |
| 2016 |    He    | P100 |    256     |   <span class="red-bg">8</span>   | <span class="red-bg">104,400</span> | 75.30% |
| 2019 | Yamazaki | V100 |   81,920   | <span class="blue-bg">2048</span> |   <span class="blue-bg">72</span>   | 75.08% |

</div>

## Dealing with Data

- At each training step, we want to ensure that **each worker receives
  unique data**
- This can be done in one of two ways:
    1.  Manually partition data (ahead of time)
        - Assign **unique subsets** to each worker
        - Each worker can only see their local portion of the data
        - Most common approach
    2.  From each worker, randomly select a mini-batch
        - Each worker can see the full dataset
        - ⚠️ When randomly selecting, it is important that each worker
          uses different seeds to ensure they receive unique data

## Broadcast Initial State

- At the start of training (or when loading from a checkpoint), we want
  all of our workers to be initialized consistently
    - **Broadcast** the model and optimizer states from `rank() == 0`
      worker

<div id="fig-broadcast">

```mermaid
flowchart TD
  0["GPU0"] --> 1["GPU 1"]
  CKPT --> 0
  0 --> 2["GPU 2"]
  0 --Model + Optim. State-->3["GPU 3"]
  0 --> X["`...`"]
  0 --> N["GPU N"]
classDef text fill:#CCCCCC02,stroke:#838383,stroke-width:0px,color:#838383,font-weight:500
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,font-weight:500,color:#838383
class 0,1,2,3,N,X,CKPT block
```

Figure 12: To ensure all workers have the same copies, we load on
`RANK==0` and `broadcast`

</div>

## Best Practices

> [!IMPORTANT] ⏰ Keeping things in Sync
>
> **Computation stalls during communication !!**
>
> Keeping the communication to computation ratio small is important for
> effective scaling.

<div class="flex-container">

<column style="width:50%;">

- Use parallel IO whenever possible
    - Feed each rank from different files
    - Use MPI IO to have each rank read its own batch from a file
    - Use several ranks to read data, MPI to scatter to remaining ranks
        - Most practical in big _at-scale_ training

</column>

<column style="width:50%;">

- Take advantage of data storage
    - Use [striping on
      lustre](https://wiki.lustre.org/Configuring_Lustre_File_Striping)
- Use the right optimizations for Aurora, Polaris, etc.
- Preload data when possible
    - Offloading to a GPU frees CPU cycles for loading the next batch of
      data
        - **minimize IO latency this way**

</column>

</div>

## Going Beyond Data Parallelism

- ✅ Useful when model fits on single GPU:
    - ultimately **limited by GPU memory**
    - model performance limited by size
- ⚠️ When model does not fit on a single GPU:
    - Offloading (can only get you so far…):
        - [DeepSpeed + `ZeRO`](https://www.deepspeed.ai/tutorials/zero/)
        - 🔥 [PyTorch +
          `FSDP`](https://pytorch.org/blog/introducing-pytorch-fully-sharded-data-parallel-api/)
    - Otherwise, resort to [model parallelism
      strategies](#additional-parallelism-strategies)

## Going beyond Data Parallelism: DeepSpeed + `ZeRO`

- Depending on the `ZeRO` stage (1, 2, 3), we can offload:
    1.  **Stage 1**: optimizer states $\left(P_{\mathrm{os}}\right)$
    2.  **Stage 2**: gradients + opt. states
        $\left(P_{\mathrm{os}+\mathrm{g}}\right)$
    3.  **Stage 3**: model params + grads + opt. states
        $\left(P_{\mathrm{os}+\mathrm{g}+\mathrm{p}}\right)$

<div id="fig-zero">

<img src="/assets/zero.png" class="r-stretch" />

Figure 13: [DeepSpeed](deepspeed.ai) +
[`ZeRO`](https://www.deepspeed.ai/tutorials/zero-offload/)

</div>

## Fully Sharded Data Parallel: 🔥 PyTorch + `FSDP`

- Instead of maintaining per-GPU copy of `{params, grads, opt_states}`,
  FSDP shards (distributes) these across data-parallel workers
    - can optionally offload the sharded model params to CPU
- [Introducing PyTorch Fully Sharded Data Parallel (FSDP) API \|
  PyTorch](https://pytorch.org/blog/introducing-pytorch-fully-sharded-data-parallel-api/)

<div id="fig-fsdp">

<img src="/assets/fsdp.png" />

Figure 14: FSDP Workflow.
[Source](https://pytorch.org/blog/introducing-pytorch-fully-sharded-data-parallel-api/)

</div>

## 🕸️ Additional Parallelism Strategies

- **Tensor (/ Model) Parallelism** (`TP`):
    - 🤗 [Tensor
      Parallelism](https://huggingface.co/docs/text-generation-inference/en/conceptual/tensor_parallelism)
    - 🔥 [Large Scale Transformer model training with Tensor Parallel
      (TP)](https://pytorch.org/tutorials/intermediate/TP_tutorial.html)
- **Pipeline Parallelism** (`PP`):
    - 🔥
      [PyTorch](https://pytorch.org/docs/main/distributed.pipelining.html),
      [DeepSpeed](https://deepspeed.readthedocs.io/en/latest/pipeline.html)
- **Sequence Parallelism** (`SP`):
    - [DeepSpeed
      Ulysses](https://github.com/microsoft/DeepSpeed/blob/master/blogs/deepspeed-ulysses/README.md)
    - [Megatron / Context
      Parallelism](https://docs.nvidia.com/megatron-core/developer-guide/latest/api-guide/context_parallel.html)
    - [Unified Sequence Parallel
      (USP)](https://arxiv.org/abs/2405.07719v3)
        - [feifeibear/`long-context-attention`](https://github.com/feifeibear/long-context-attention)
- [x]
  [argonne-lcf/`Megatron-DeepSpeed`](https://github.com/argonne-lcf/Megatron-DeepSpeed)
    - Supports 4D Parallelism (`DP` + `TP` + `PP` + `SP`)

## Pipeline Parallelism (PP)

<div class="flex-container" style="place-content: end space-evenly;">

<column style="width:60%;">

- Model is split up **vertically** (layer-level) across multiple GPUs
- Each GPU:
    - has a portion of the full model
    - processes _in parallel_ different stages of the pipeline (on a small
      chunk of the batch)
- See:
    - 🔥 [PyTorch / Pipeline
      Parallelism](https://pytorch.org/docs/main/distributed.pipelining.html)
    - [DeepSpeed / Pipeline
      Parallelism](https://deepspeed.readthedocs.io/en/latest/pipeline.html)

</column>

<column style="width:40%;">

<div id="fig-pipeline-parallelism">

```mermaid
flowchart TB
    subgraph G0["`GPU 0`"]
        direction LR
        a0("`Layer 0`")
        b0("`Layer 1`")
    end
    subgraph G1["`GPU 1`"]
        direction LR
        a1("`Layer 2`")
        b1("`Layer 3`")
    end
    a0 -.-> b0
    b0 --> a1
    a1 -.-> b1
classDef block fill:#CCCCCC02,stroke:#838383,stroke-width:1px,color:#838383
classDef red fill:#ff8181,stroke:#333,stroke-width:1px,color:#000
classDef orange fill:#FFC47F,stroke:#333,stroke-width:1px,color:#000
classDef yellow fill:#FFFF7F,stroke:#333,stroke-width:1px,color:#000
classDef green fill:#98E6A5,stroke:#333,stroke-width:1px,color:#000
classDef blue fill:#7DCAFF,stroke:#333,stroke-width:1px,color:#000
classDef purple fill:#FFCBE6,stroke:#333,stroke-width:1px,color:#000
class G0,G1 block
class a0 red
class b0 green
class a1 blue
class b1 yellow
```

Figure 15: Pipeline Parallelism

</div>

</column>

</div>

## Tensor Parallel (TP)

<div>

</div>

## Tensor Parallel (TP)

<div>

</div>

<div class="notes">

- Split up network over multiple workers
- Each receives disjoint subset
- All communication associated with subsets are distributed
- Communication whenever dataflow between two subsets
- Typically **more complicated** to implement than data parallel
  training
- Suitable when the model is too large to fit onto a single device (CPU
  / GPU)

</div>

## Tensor (/ Model) Parallel Training: Example

Want to compute:
$y = \sum_{i} x_{i} W_{i} = x_0 * W_0 + x_1 * W_1 + x_2 * W_2$  
where each GPU only has only its portion of the full weights as shown
below

1.  Compute: $y_{0} = x_{0} * W_{0}\rightarrow$ `GPU1`
2.  Compute: $y_{1} = y_{0} + x_{1} * W_{1}\rightarrow$ `GPU2`
3.  Compute: $y = y_{1} + x_{2} * W_{2} = \sum_{i} x_{i} W_{i}$ ✅

<div id="fig-tensor-parallel-example">

```mermaid
flowchart LR
    subgraph X0["`GPU0`"]
        direction LR
        a("`W0`")
    end
    subgraph X1["`GPU1`"]
        direction LR
        b("`W1`")
    end
    subgraph X2["`GPU2`"]
        direction LR
        c("`W2`")
    end
  t0("`x₀`")-->X0
  X0 -->|"`x₀ W₀`"|X1
  X1 -->|"`x₀ W₀ <br>+ x₁ W₁`"|X2
  t1("`x₁`") --> X1
  t2("`x₂`") --> X2
```

Figure 18

</div>

## Tensor (Model) Parallelism[^2]

- In **Tensor Paralleism** each GPU processes only a slice of a tensor
  and only aggregates the full tensor for operations that require the
  whole thing.
    - The main building block of any transformer is a fully connected
      `nn.Linear` followed by a nonlinear activation GeLU.
        - `Y = GeLU(XA)`, where X and Y are the input and output vectors,
          and A is the weight matrix.
    - If we look at the computation in matrix form, it’s easy to see how
      the matrix multiplication can be split between multiple GPUs:

## Tensor Parallelism

<div id="fig-parallel-gemm">

<img src="/assets/parallelism-tp-parallel_gemm.png" />

Figure 19: Tensor Parallel GEMM. This information is based on (the much
more in-depth) [TP
Overview](https://github.com/huggingface/transformers/issues/10321#issuecomment-783543530)
by [@anton-l](https://github.com/anton-l)

</div>

## 3D Parallelism

- `DP` + `TP` + `PP` (3D) Parallelism

<div id="fig-3dparallel">

<img src="/assets/parallelism-deepspeed-3d.png" />

Figure 20: Figure taken from [3D parallelism: Scaling to
trillion-parameter
models](https://www.microsoft.com/en-us/research/blog/deepspeed-extreme-scale-model-training-for-everyone/)

</div>

## Deciding on a Parallelism Strategy

<div class="panel-tabset">

### Single GPU

- Model fits onto a single GPU:
    - Normal use
- Model **DOES NOT** fit on a single GPU:
    - `ZeRO` + Offload CPU (or, optionally, `NVMe`)
- Largest layer **DOES NOT** fit on a single GPU:
    - `ZeRO` + Enable [Memory Centric Tiling
      (MCT)](https://deepspeed.readthedocs.io/en/latest/zero3.html#memory-centric-tiling)
        - MCT Allows running of arbitrarily large layers by automatically
          splitting them and executing them sequentially.

### Single Node / Multi-GPU

<div class="flex-container">

<column>

- Model fits onto a single GPU
    - [`DDP`](https://pytorch.org/docs/stable/notes/ddp.html)
    - [`ZeRO`](https://deepspeed.readthedocs.io/en/latest/zero3.html)

</column>

<column>

- Model **DOES NOT** fit onto a single GPU
    1.  [Pipeline Parallelism
        (`PP`)](https://www.deepspeed.ai/tutorials/pipeline/)
    2.  [`ZeRO`](https://deepspeed.readthedocs.io/en/latest/zero3.html)
    3.  [Tensor Parallelism
        (`TP`)](https://pytorch.org/docs/stable/distributed.tensor.parallel.html)

</column>

</div>

- With sufficiently fast connectivity between nodes, these three
  strategies should be comparable.
    - Otherwise, `PP` \> `ZeRO` $\simeq$ `TP`.

### Multi-Node / Multi-GPU

- When you have fast inter-node connectivity:
    - `ZeRO` (virtually **NO** modifications)
    - `PP` + `ZeRO` + `TP` + `DP` (less communication, at the cost of
      **MAJOR** modifications)
        - when you have slow inter-node connectivity and still low on GPU
          memory:

            ```bash
            DP + PP + TP + ZeRO-1
            ```

    - **NOTE**: `TP` is almost _always_ used within a single node, e.g.  
      `TP <= GPUS_PER_NODE`

</div>

## 🦙 Large Language Models

<div id="fig-llms">

![](https://github.com/Hannibal046/Awesome-LLM/raw/main/resources/image8.gif)

Figure 21: Large Language Models have (LLM)s have taken the ~~NLP
community~~ **world** by storm[^3].

</div>

## 🔮 Emergent Abilities

<div id="fig-emergent-abilities">

<img src="/assets/emergent-abilities.gif" />

Figure 22: See Wei et al. (2022), Yao et al. (2023)

</div>

## 🚂 Training LLMs

<div>

</div>

## ♻️ Life-Cycle of the LLM

<div class="flex-container">

<column style="width: 40%;">

1.  Data collection + preprocessing
2.  **Pre-training**
    - Architecture decisions, model size, etc.
3.  Supervised Fine-Tuning
    - Instruction Tuning
    - Alignment
4.  Deploy (+ monitor, re-evaluate, etc.)

</column>

<column style="width:50%;">

<div id="fig-pretrain-two">

<img src="/assets/gpt3-training-step-back-prop.gif" />

Figure 23: **Pre-training**: Virtually _all of the compute_ used during
pre-training[^4].

</div>

</column>

</div>

## 🎀 Life-Cycle of the LLM

<div class="flex-container">

<column style="width: 50%;">

1.  Data collection + preprocessing
2.  Pre-training
    - Architecture decisions, model size, etc.
3.  **Supervised Fine-Tuning**
    - Instruction Tuning
    - Alignment
4.  Deploy (+ monitor, re-evaluate, etc.)

</column>

<column style="width:50%;">

<div id="fig-finetune-lifecycle">

<img src="/assets/gpt3-fine-tuning.gif" />

Figure 24: **Fine-tuning**: Fine-tuning actually updates the model’s
weights to make the model better at a certain task[^5].

</div>

</column>

</div>

## ⏩ Forward Pass

<div id="fig-hf-assisted-generation">

<video
    src="/assets/hf_assisted_generation.mov"
    controls
    preload="metadata"></video>

Figure 25: Language Model trained for causal language modeling[^6].

</div>

## 💬 Generating Text

<div id="fig-generating-text">

<video
    src="/assets/hf_assisted_generation2.mov"
    controls
    preload="metadata"></video>

Figure 26: Language Model trained for causal language modeling[^7].

</div>

## 👋 Hands On

[ShakespeareGPT](https://colab.research.google.com/github/saforem2/intro-hpc-bootcamp-2025/blob/main/docs/02-llms/08-shakespeare-example-colab/index.out.ipynb)

[ai-science-training-series /
06_parallel_training](https://github.com/argonne-lcf/ai-science-training-series/tree/main/06_parallel_training#hands-on)

## 🧑‍💻 Hands On: Getting Started

1.  🌱 Clone Repo(s):
    - [saforem2/`wordplay`](https://github.com/saforem2/wordplay)

    ```bash
    git clone https://github.com/saforem2/wordplay
    cd wordplay
    ```

    - [saforem2/`ezpz`](https://github.com/saforem2/ezpz)

    ```bash
    git clone https://github.com/saforem2/ezpz deps/ezpz
    ```

2.  🐍 Setup Python:

    ```bash
    export PBS_O_WORKDIR=$(pwd) && source deps/ezpz/src/ezpz/bin/utils.sh
    ezpz_setup_python
    ezpz_setup_job
    ```

## 📦 Install {`ezpz`, `wordplay`}

1.  Install Python packages:
    1.  [saforem2/`ezpz`](https://github.com/saforem2/ezpz):

        ```bash
        python3 -m pip install -e "./deps/ezpz" --require-virtualenv
        ```

    2.  [saforem2/`wordplay`](https://github.com/saforem2/ezpz):

        ```bash
        # from inside `wordplay/`
        python3 -m pip install -e . --require-virtualenv
        ```

2.  Test distributed setup:

    ```bash
    mpirun -n "${NGPUS}" python3 -m ezpz.test_dist
    ```

    See: 🍋
    [`ezpz/test_dist.py`](https://github.com/saforem2/ezpz/blob/main/src/ezpz/test_dist.py)

## [`ezpz`](https://github.com/saforem2/ezpz): Example \[[video](https://asciinema.org/a/668460)\]

<div id="fig-ezpz-asciinema">

<script
    src="https://asciinema.org/a/668460.js"
    id="asciicast-668460"
    async="true"></script>

Figure 27: Example: using [🍋
`ezpz.test_dist`](https://github.com/saforem2/ezpz/blob/main/src/ezpz/test_dist.py)
to train a small model using DDP

</div>

## Install [`wordplay` 🎮💬](https://github.com/saforem2/wordplay)

<div id="fig-nanoGPT">

<img src="/assets/nanogpt.jpg" />

Figure 28: The simplest, fastest repository for training / finetuning
GPT based models. Figure from
[karpathy/`nanoGPT`](https://github.com/karpathy/nanoGPT)

</div>

## Prepare Data

```bash
$ python3 wordplay/data/shakespeare_char/prepare.py
Using HF_DATASETS_CACHE=/home/foremans/tmp/polaris-talk/2024-07-17-073327/wordplay/data/shakespeare_char/.cache/huggingface
length of dataset in characters: 1,115,394
all the unique characters:
 !$&\',-.3:;?ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
vocab size: 65
train has 1,003,854 tokens
val has 111,540 tokens
```

## Launch Training (DDP)

```bash
launch python3 -m wordplay \
    train.backend=DDP \
    train.eval_interval=100 \
    data=shakespeare \
    train.dtype=bf16 \
    model.batch_size=64 \
    model.block_size=1024 \
    train.max_iters=1000 \
    train.log_interval=10 \
    train.compile=false \
    | tee wordplay-gpt2-DDP.log
```

## Training: Example Output

```bash
$ launch python3 -m wordplay \
    train.backend=DDP \
    train.eval_interval=100 \
    data=shakespeare \
    train.dtype=bf16 \
    model.batch_size=64 \
    model.block_size=1024 \
    train.max_iters=1000 \
    train.log_interval=10 \
    train.compile=false \
    | tee wordplay-gpt2-DDP.log
[2024-07-17 07:42:11.746540][INFO][__init__:156] - Setting logging level to 'INFO' on 'RANK == 0'
[2024-07-17 07:42:11.748763][INFO][__init__:157] - Setting logging level to 'CRITICAL' on all others 'RANK != 0'
[2024-07-17 07:42:11.749453][INFO][__init__:160] - To disable this behavior, and log from ALL ranks (not recommended), set: 'export LOG_FROM_ALL_RANKS=1'  in your environment, and re-run.
[2024-07-17 07:42:11.772718][INFO][configs:81] - Setting HF_DATASETS_CACHE to /home/foremans/tmp/polaris-talk/2024-07-17-073327/wordplay/.cache/huggingface/datasets
[2024-07-17 07:42:15.341532][INFO][dist:358] - [device='cuda'][rank=2/3][local_rank=2/3][node=0/0]
[2024-07-17 07:42:15.342381][INFO][dist:358] - [device='cuda'][rank=1/3][local_rank=1/3][node=0/0]
[2024-07-17 07:42:15.342430][INFO][dist:358] - [device='cuda'][rank=3/3][local_rank=3/3][node=0/0]
[2024-07-17 07:42:15.348657][INFO][dist:95] -

[dist_info]:
  • DEVICE=cuda
  • DEVICE_ID=cuda:0
  • DISTRIBUTED_BACKEND=nccl
  • GPUS_PER_NODE=4
  • HOSTS=['x3101c0s13b0n0.hsn.cm.polaris.alcf.anl.gov']
  • HOSTFILE=/var/spool/pbs/aux/2024084.polaris-pbs-01.hsn.cm.polaris.alcf.anl.gov
  • HOSTNAME=x3101c0s13b0n0.hsn.cm.polaris.alcf.anl.gov
  • LOCAL_RANK=0
  • MACHINE=Polaris
  • NUM_NODES=1
  • NGPUS=4
  • NGPUS_AVAILABLE=4
  • NODE_ID=0
  • RANK=0
  • SCHEDULER=PBS
  • WORLD_SIZE_TOTAL=4
  • WORLD_SIZE_IN_USE=4
  • LAUNCH_CMD=mpiexec --verbose --envall -n 4 -ppn 4 --hostfile /var/spool/pbs/aux/2024084.polaris-pbs-01.hsn.cm.polaris.alcf.anl.gov --cpu-bind depth -d 16

[2024-07-17 07:42:15.351446][INFO][dist:725] - [0/4] Using device='cuda' with backend='DDP' + 'nccl' for distributed training.
[2024-07-17 07:42:15.356169][INFO][dist:358] - [device='cuda'][rank=0/3][local_rank=0/3][node=0/0]
[2024-07-17 07:42:15.356692][WARNING][dist:364] - Using [4 / 4] available "cuda" devices !!
[2024-07-17 07:42:15.359571][INFO][configs:317] - Loading val from /home/foremans/tmp/polaris-talk/2024-07-17-073327/wordplay/data/shakespeare_char/val.bin
[2024-07-17 07:42:15.360138][INFO][configs:317] - Loading train from /home/foremans/tmp/polaris-talk/2024-07-17-073327/wordplay/data/shakespeare_char/train.bin
[2024-07-17 07:42:15.361154][INFO][configs:442] - Tokens per iteration: 262,144
[2024-07-17 07:42:15.361574][INFO][configs:465] - Using self.ptdtype=torch.float16 on self.device_type='cuda'
[2024-07-17 07:42:15.362002][INFO][configs:471] - Initializing a new model from scratch
[2024-07-17 07:42:15.362529][INFO][dist:874] - Setting up wandb from rank: 0
[2024-07-17 07:42:15.362896][INFO][dist:875] - Using: WB PROJECT: WordPlay
[2024-07-17 07:42:16.451786][INFO][dist:905] - W&B RUN: [still-frog-17](https://wandb.ai/aurora_gpt/WordPlay/runs/6by9vpcj)
[2024-07-17 07:42:16.464106][INFO][dist:312] - Updating wandb.run: still-frog-17 config with "DIST_INFO"
[2024-07-17 07:42:16.469424][INFO][dist:938] - Running on machine='Polaris'
[2024-07-17 07:42:16.471151][WARNING][__main__:89] - {
    "train": {
        "framework": "pytorch",
        "backend": "DDP",
        "device": null,
        "seed": null,
        "port": null,
        "ds_config_path": null,
        "precision": null,
        "ngpus": null,
        "use_wandb": true,
        "eval_interval": 100,
        "log_interval": 10,
        "eval_iters": 200,
        "eval_only": false,
        "always_save_checkpoint": false,
        "init_from": "scratch",
        "wandb_project": "WordPlay",
        "max_iters": 1000,
        "warmup_iters": 100,
        "dtype": "bf16",
        "compile": false
    },
    "model": {
        "n_layer": 12,
        "n_head": 12,
        "n_embd": 768,
        "batch_size": 64,
        "block_size": 1024,
        "activation": "gelu",
        "dropout": 0.0,
        "bias": false,
        "vocab_size": 65
    },
    "data": {
        "dataset": "shakespeare_char",
        "out_dir": "out-shakespeare-char",
        "root_path": null
    },
    "optimizer": {
        "gas": 1,
        "name": "AdamW",
        "learning_rate": 0.0006,
        "weight_decay": 0.1,
        "beta1": 0.9,
        "beta2": 0.95,
        "grad_clip": 1.0,
        "decay_lr": true,
        "lr_decay_iters": 600000,
        "min_lr": 6e-05
    }
}
[2024-07-17 07:42:16.474305][WARNING][__main__:90] - Output dir: /home/foremans/tmp/polaris-talk/outputs/runs/pytorch/DDP/2024-07-17/07-42-13
[2024-07-17 07:42:16.474922][INFO][trainer:246] - Initializing a new model from scratch
[2024-07-17 07:42:17.258904][INFO][model:255] - number of parameters: 85.00M
[2024-07-17 07:42:17.290004][INFO][trainer:264] - Model size: num_params=85003776
[2024-07-17 07:42:17.292626][INFO][model:445] - num decayed parameter tensors: 50, with 85,771,008 parameters
[2024-07-17 07:42:17.293296][INFO][model:449] - num non-decayed parameter tensors: 25, with 19,200 parameters
[2024-07-17 07:42:17.515324][CRITICAL][trainer:316] - "devid='cuda:1'"
[2024-07-17 07:42:17.515340][CRITICAL][trainer:316] - "devid='cuda:2'"
[2024-07-17 07:42:17.515465][CRITICAL][trainer:316] - "devid='cuda:3'"
[2024-07-17 07:42:18.431814][INFO][model:465] - using fused AdamW: True
[2024-07-17 07:42:18.432620][CRITICAL][trainer:316] - "devid='cuda:0'"
[2024-07-17 07:42:19.951020][INFO][trainer:356] - • self.model=GPT(
  (transformer): ModuleDict(
    (wte): Embedding(65, 768)
    (wpe): Embedding(1024, 768)
    (drop): Dropout(p=0.0, inplace=False)
    (h): ModuleList(
      (0-11): 12 x Block(
        (ln_1): LayerNorm()
        (attn): CausalSelfAttention(
          (c_attn): Linear(in_features=768, out_features=2304, bias=False)
          (c_proj): Linear(in_features=768, out_features=768, bias=False)
          (attn_dropout): Dropout(p=0.0, inplace=False)
          (resid_dropout): Dropout(p=0.0, inplace=False)
        )
        (ln_2): LayerNorm()
        (mlp): MLP(
          (c_fc): Linear(in_features=768, out_features=3072, bias=False)
          (act_fn): GELU(approximate='none')
          (c_proj): Linear(in_features=3072, out_features=768, bias=False)
          (dropout): Dropout(p=0.0, inplace=False)
        )
      )
    )
    (ln_f): LayerNorm()
  )
  (lm_head): Linear(in_features=768, out_features=65, bias=False)
)
[2024-07-17 07:42:19.955340][INFO][trainer:357] - • self.grad_scaler=<torch.cuda.amp.grad_scaler.GradScaler object at 0x145a38f0f090>
[2024-07-17 07:42:19.956897][INFO][trainer:358] - • self.model_engine=DistributedDataParallel(
  (module): GPT(
    (transformer): ModuleDict(
      (wte): Embedding(65, 768)
      (wpe): Embedding(1024, 768)
      (drop): Dropout(p=0.0, inplace=False)
      (h): ModuleList(
        (0-11): 12 x Block(
          (ln_1): LayerNorm()
          (attn): CausalSelfAttention(
            (c_attn): Linear(in_features=768, out_features=2304, bias=False)
            (c_proj): Linear(in_features=768, out_features=768, bias=False)
            (attn_dropout): Dropout(p=0.0, inplace=False)
            (resid_dropout): Dropout(p=0.0, inplace=False)
          )
          (ln_2): LayerNorm()
          (mlp): MLP(
            (c_fc): Linear(in_features=768, out_features=3072, bias=False)
            (act_fn): GELU(approximate='none')
            (c_proj): Linear(in_features=3072, out_features=768, bias=False)
            (dropout): Dropout(p=0.0, inplace=False)
          )
        )
      )
      (ln_f): LayerNorm()
    )
    (lm_head): Linear(in_features=768, out_features=65, bias=False)
  )
)
[2024-07-17 07:42:19.961066][INFO][trainer:359] - • self.optimizer=AdamW (
Parameter Group 0
    amsgrad: False
    betas: (0.9, 0.95)
    capturable: False
    differentiable: False
    eps: 1e-08
    foreach: None
    fused: True
    lr: 0.0006
    maximize: False
    weight_decay: 0.1

Parameter Group 1
    amsgrad: False
    betas: (0.9, 0.95)
    capturable: False
    differentiable: False
    eps: 1e-08
    foreach: None
    fused: True
    lr: 0.0006
    maximize: False
    weight_decay: 0.0
)
[2024-07-17 07:42:19.988827][INFO][trainer:802] - Startup time: 6.7125
                Training Legend
┏━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃    abbr     ┃ desc                           ┃
┡━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩
│    step     │ Current training iteration     │
│    loss     │ Loss value                     │
│     dt      │ Elapsed time per training step │
│     dtf     │ Elapsed time per forward step  │
│     dtb     │ Elapsed time per backward step │
│     sps     │ Samples per second             │
│ sps_per_gpu │ Samples per second (per GPU)   │
│     tps     │ Tokens per second              │
│ tps_per_gpu │ Tokens per second (per GPU)    │
│     mfu     │ Model flops utilization        │
│ train_loss  │ Training loss value            │
│  val_loss   │ Validation loss value          │
└─────────────┴────────────────────────────────┘
[2024-07-17 07:42:21.451865][INFO][trainer:820] - ['prompt']: 'What is an LLM?'
[2024-07-17 07:42:21.452667][INFO][trainer:824] - ['response']:
What is an LLM?eelEl\'$nltPwBSWal,;PWw bbu\'HiyP\'FWwF &AhW:ygrn kk-\'\'KFlMwnlEfflkc,elpWaWtgml$Pgglhllw lglhFllzczPAFHpeAAPPSltgkrWPPhlEMgcrN ggPWt-WPSSzHSkkrzzk.FFrtSSkgMll&gFXr,hghaueaVPW-pHFF-gg,,,FF,,kbApgg gg\'aWWzzkk\'a\'CggHl$bGeA,FFk,,SF;UF,,aZ ;gglee$,k.US&kg:S,,zVzzc
[2024-07-17 07:43:01.573073][INFO][trainer:885] - step=10 loss=3.154310 dt=0.282833 dtf=0.005247 dtb=0.011417 sps=14.142633 sps_per_gpu=3.535658 tps=926851.609409 tps_per_gpu=231712.902352 mfu=46.288281 train_loss=4.125778 val_loss=4.128809
[2024-07-17 07:43:04.402750][INFO][trainer:885] - step=20 loss=2.660851 dt=0.306263 dtf=0.005233 dtb=0.011419 sps=13.060678 sps_per_gpu=3.265170 tps=855944.613638 tps_per_gpu=213986.153409 mfu=45.934162 train_loss=4.125778 val_loss=4.128809
[2024-07-17 07:43:07.237507][INFO][trainer:885] - step=30 loss=2.543283 dt=0.283021 dtf=0.005238 dtb=0.011245 sps=14.133211 sps_per_gpu=3.533303 tps=926234.088226 tps_per_gpu=231558.522057 mfu=45.966490 train_loss=4.125778 val_loss=4.128809
[2024-07-17 07:43:10.077248][INFO][trainer:885] - step=40 loss=2.503963 dt=0.285001 dtf=0.005213 dtb=0.011471 sps=14.035061 sps_per_gpu=3.508765 tps=919801.749941 tps_per_gpu=229950.437485 mfu=45.963461 train_loss=4.125778 val_loss=4.128809
[2024-07-17 07:43:12.917039][INFO][trainer:885] - step=50 loss=2.477469 dt=0.283532 dtf=0.005166 dtb=0.011294 sps=14.107763 sps_per_gpu=3.526941 tps=924566.380009 tps_per_gpu=231141.595002 mfu=45.984530 train_loss=4.125778 val_loss=4.128809
[2024-07-17 07:43:15.760749][INFO][trainer:885] - step=60 loss=2.471083 dt=0.284630 dtf=0.005140 dtb=0.011224 sps=14.053326 sps_per_gpu=3.513332 tps=920998.786204 tps_per_gpu=230249.696551 mfu=45.985675 train_loss=4.125778 val_loss=4.128809
[2024-07-17 07:43:18.602785][INFO][trainer:885] - step=70 loss=2.458894 dt=0.283926 dtf=0.005219 dtb=0.010383 sps=14.088155 sps_per_gpu=3.522039 tps=923281.352698 tps_per_gpu=230820.338174 mfu=45.998106 train_loss=4.125778 val_loss=4.128809
[2024-07-17 07:43:21.451433][INFO][trainer:885] - step=80 loss=2.489088 dt=0.285537 dtf=0.005183 dtb=0.011373 sps=14.008683 sps_per_gpu=3.502171 tps=918073.060430 tps_per_gpu=229518.265108 mfu=45.983282 train_loss=4.125778 val_loss=4.128809
[2024-07-17 07:43:24.302241][INFO][trainer:885] - step=90 loss=2.471990 dt=0.300767 dtf=0.005445 dtb=0.010290 sps=13.299337 sps_per_gpu=3.324834 tps=871585.359388 tps_per_gpu=217896.339847 mfu=45.737774 train_loss=4.125778 val_loss=4.128809
[2024-07-17 07:43:27.153275][INFO][trainer:885] - step=100 loss=2.445556 dt=0.285869 dtf=0.005182 dtb=0.011251 sps=13.992403 sps_per_gpu=3.498101 tps=917006.151328 tps_per_gpu=229251.537832 mfu=45.743655 train_loss=4.125778 val_loss=4.128809
[2024-07-17 07:43:28.182553][INFO][trainer:820] - ['prompt']: 'What is an LLM?'
[2024-07-17 07:43:28.183179][INFO][trainer:824] - ['response']:

What is an LLM?

Goupay my winghimithell bls ger t bon sinthard ht omind be,
And lereind h py balithand frd oforondof wimon me hageas thinero mand,
Thacanes,
An frift ghik med d herthecke ntore thack couthen ale, t thit ang d m t h chy me fache ag, wit my hathan glat ng
[2024-07-17 07:44:06.025837][INFO][trainer:760] - Saving checkpoint to: /home/foremans/tmp/polaris-talk/outputs/runs/pytorch/DDP/2024-07-17/07-42-13
[2024-07-17 07:44:06.026607][INFO][trainer:761] - Saving model to: /home/foremans/tmp/polaris-talk/outputs/runs/pytorch/DDP/2024-07-17/07-42-13/model.pth
[2024-07-17 07:44:07.682968][INFO][configs:141] - Appending /home/foremans/tmp/polaris-talk/outputs/runs/pytorch/DDP/2024-07-17/07-42-13 to /home/foremans/tmp/polaris-talk/2024-07-17-073327/wordplay/src/ckpts/checkpoints.log
[2024-07-17 07:44:10.519506][INFO][trainer:885] - step=110 loss=2.433923 dt=0.285038 dtf=0.005757 dtb=0.011762 sps=14.033209 sps_per_gpu=3.508302 tps=919680.367894 tps_per_gpu=229920.091974 mfu=45.762304 train_loss=2.439494 val_loss=2.478951
[2024-07-17 07:44:13.362148][INFO][trainer:885] - step=120 loss=2.429014 dt=0.284445 dtf=0.005222 dtb=0.011486 sps=14.062460 sps_per_gpu=3.515615 tps=921597.361532 tps_per_gpu=230399.340383 mfu=45.788661 train_loss=2.439494 val_loss=2.478951
[2024-07-17 07:44:16.210694][INFO][trainer:885] - step=130 loss=2.402059 dt=0.285559 dtf=0.005199 dtb=0.011765 sps=14.007633 sps_per_gpu=3.501908 tps=918004.211586 tps_per_gpu=229501.052897 mfu=45.794438 train_loss=2.439494 val_loss=2.478951
[2024-07-17 07:44:19.061546][INFO][trainer:885] - step=140 loss=2.374062 dt=0.285476 dtf=0.005239 dtb=0.011453 sps=14.011662 sps_per_gpu=3.502916 tps=918268.297093 tps_per_gpu=229567.074273 mfu=45.800956 train_loss=2.439494 val_loss=2.478951
[2024-07-17 07:44:21.917283][INFO][trainer:885] - step=150 loss=2.365385 dt=0.285846 dtf=0.005125 dtb=0.011320 sps=13.993568 sps_per_gpu=3.498392 tps=917082.475791 tps_per_gpu=229270.618948 mfu=45.800900 train_loss=2.439494 val_loss=2.478951
[2024-07-17 07:44:24.771924][INFO][trainer:885] - step=160 loss=2.317337 dt=0.280788 dtf=0.005173 dtb=0.011249 sps=14.245602 sps_per_gpu=3.561401 tps=933599.792506 tps_per_gpu=233399.948127 mfu=45.883340 train_loss=2.439494 val_loss=2.478951
[2024-07-17 07:44:27.626812][INFO][trainer:885] - step=170 loss=2.256231 dt=0.284973 dtf=0.005141 dtb=0.011299 sps=14.036416 sps_per_gpu=3.509104 tps=919890.544506 tps_per_gpu=229972.636126 mfu=45.889069 train_loss=2.439494 val_loss=2.478951
[2024-07-17 07:44:30.480952][INFO][trainer:885] - step=180 loss=2.216419 dt=0.286555 dtf=0.005180 dtb=0.011402 sps=13.958906 sps_per_gpu=3.489726 tps=914810.852170 tps_per_gpu=228702.713043 mfu=45.868857 train_loss=2.439494 val_loss=2.478951
[2024-07-17 07:44:33.337342][INFO][trainer:885] - step=190 loss=2.145123 dt=0.291456 dtf=0.005409 dtb=0.019347 sps=13.724205 sps_per_gpu=3.431051 tps=899429.467247 tps_per_gpu=224857.366812 mfu=45.773849 train_loss=2.439494 val_loss=2.478951
[2024-07-17 07:44:36.194584][INFO][trainer:885] - step=200 loss=2.068149 dt=0.285703 dtf=0.005153 dtb=0.011286 sps=14.000555 sps_per_gpu=3.500139 tps=917540.393411 tps_per_gpu=229385.098353 mfu=45.778791 train_loss=2.439494 val_loss=2.478951
[2024-07-17 07:44:37.224149][INFO][trainer:820] - ['prompt']: 'What is an LLM?'
[2024-07-17 07:44:37.224745][INFO][trainer:824] - ['response']:

What is an LLM?

LORTESS LA:
No, sighappat selace? don downd sourciceans note cancen up sof liond
This and my man, werame, of re thee
Thise not will I on land brond sul me a fingore?

FLER:
Tisint your not nare lame o igen,-to brorst.

SamERS:
Sin:
I\'l hell she lor hen w
[2024-07-17 07:45:14.409129][INFO][trainer:760] - Saving checkpoint to: /home/foremans/tmp/polaris-talk/outputs/runs/pytorch/DDP/2024-07-17/07-42-13
[2024-07-17 07:45:14.409820][INFO][trainer:761] - Saving model to: /home/foremans/tmp/polaris-talk/outputs/runs/pytorch/DDP/2024-07-17/07-42-13/model.pth
[2024-07-17 07:45:16.366935][INFO][configs:141] - Appending /home/foremans/tmp/polaris-talk/outputs/runs/pytorch/DDP/2024-07-17/07-42-13 to /home/foremans/tmp/polaris-talk/2024-07-17-073327/wordplay/src/ckpts/checkpoints.log
[2024-07-17 07:45:19.245061][INFO][trainer:885] - step=210 loss=1.982169 dt=0.283305 dtf=0.005223 dtb=0.011284 sps=14.119042 sps_per_gpu=3.529760 tps=925305.515083 tps_per_gpu=231326.378771 mfu=45.822019 train_loss=2.045786 val_loss=2.148510
[2024-07-17 07:45:22.092430][INFO][trainer:885] - step=220 loss=1.897731 dt=0.284759 dtf=0.005217 dtb=0.011187 sps=14.046945 sps_per_gpu=3.511736 tps=920580.608106 tps_per_gpu=230145.152026 mfu=45.837327 train_loss=2.045786 val_loss=2.148510
[2024-07-17 07:45:24.942639][INFO][trainer:885] - step=230 loss=1.817213 dt=0.285266 dtf=0.005208 dtb=0.011446 sps=14.022003 sps_per_gpu=3.505501 tps=918945.985503 tps_per_gpu=229736.496376 mfu=45.842940 train_loss=2.045786 val_loss=2.148510
[2024-07-17 07:45:27.797910][INFO][trainer:885] - step=240 loss=1.779287 dt=0.285465 dtf=0.005189 dtb=0.011220 sps=14.012250 sps_per_gpu=3.503062 tps=918306.793546 tps_per_gpu=229576.698387 mfu=45.844800 train_loss=2.045786 val_loss=2.148510
[2024-07-17 07:45:30.653597][INFO][trainer:885] - step=250 loss=1.704220 dt=0.289284 dtf=0.005471 dtb=0.010346 sps=13.827253 sps_per_gpu=3.456813 tps=906182.836379 tps_per_gpu=226545.709095 mfu=45.785926 train_loss=2.045786 val_loss=2.148510
[2024-07-17 07:45:33.512769][INFO][trainer:885] - step=260 loss=1.671318 dt=0.287679 dtf=0.005125 dtb=0.011250 sps=13.904380 sps_per_gpu=3.476095 tps=911237.442617 tps_per_gpu=227809.360654 mfu=45.758182 train_loss=2.045786 val_loss=2.148510
[2024-07-17 07:45:36.373461][INFO][trainer:885] - step=270 loss=1.650952 dt=0.298661 dtf=0.005118 dtb=0.011520 sps=13.393107 sps_per_gpu=3.348277 tps=877730.651421 tps_per_gpu=219432.662855 mfu=45.565875 train_loss=2.045786 val_loss=2.148510
[2024-07-17 07:45:39.236930][INFO][trainer:885] - step=280 loss=1.573242 dt=0.285970 dtf=0.005171 dtb=0.011290 sps=13.987477 sps_per_gpu=3.496869 tps=916683.279847 tps_per_gpu=229170.819962 mfu=45.587333 train_loss=2.045786 val_loss=2.148510
[2024-07-17 07:45:42.100605][INFO][trainer:885] - step=290 loss=1.533265 dt=0.286487 dtf=0.005432 dtb=0.011288 sps=13.962259 sps_per_gpu=3.490565 tps=915030.617828 tps_per_gpu=228757.654457 mfu=45.598392 train_loss=2.045786 val_loss=2.148510
[2024-07-17 07:45:44.964424][INFO][trainer:885] - step=300 loss=1.492064 dt=0.288480 dtf=0.005355 dtb=0.011480 sps=13.865774 sps_per_gpu=3.466443 tps=908707.340870 tps_per_gpu=227176.835218 mfu=45.576766 train_loss=2.045786 val_loss=2.148510
[2024-07-17 07:45:45.995833][INFO][trainer:820] - ['prompt']: 'What is an LLM?'
[2024-07-17 07:45:45.996497][INFO][trainer:824] - ['response']:

What is an LLM?

RICHMORD:
Char stire? how in those are name the range hone.

GLOUCESTER:
Nay, in lond's time the palt are worder more
That wilt in the purpose be a pey
And thou thine onter hands, and the which broth.

ELBOWINCA:
At lie my lord with the me an arms be a s
[2024-07-17 07:46:23.549987][INFO][trainer:760] - Saving checkpoint to: /home/foremans/tmp/polaris-talk/outputs/runs/pytorch/DDP/2024-07-17/07-42-13
[2024-07-17 07:46:23.550696][INFO][trainer:761] - Saving model to: /home/foremans/tmp/polaris-talk/outputs/runs/pytorch/DDP/2024-07-17/07-42-13/model.pth
[2024-07-17 07:46:25.496559][INFO][configs:141] - Appending /home/foremans/tmp/polaris-talk/outputs/runs/pytorch/DDP/2024-07-17/07-42-13 to /home/foremans/tmp/polaris-talk/2024-07-17-073327/wordplay/src/ckpts/checkpoints.log
[2024-07-17 07:46:28.374854][INFO][trainer:885] - step=310 loss=1.444200 dt=0.299907 dtf=0.005333 dtb=0.010637 sps=13.337481 sps_per_gpu=3.334370 tps=874085.133345 tps_per_gpu=218521.283336 mfu=45.384395 train_loss=1.495372 val_loss=1.713714
[2024-07-17 07:46:31.223079][INFO][trainer:885] - step=320 loss=1.429350 dt=0.285238 dtf=0.005245 dtb=0.011485 sps=14.023353 sps_per_gpu=3.505838 tps=919034.479880 tps_per_gpu=229758.619970 mfu=45.435743 train_loss=1.495372 val_loss=1.713714
[2024-07-17 07:46:34.074957][INFO][trainer:885] - step=330 loss=1.362220 dt=0.285027 dtf=0.005165 dtb=0.011407 sps=14.033736 sps_per_gpu=3.508434 tps=919714.904826 tps_per_gpu=229928.726207 mfu=45.485355 train_loss=1.495372 val_loss=1.713714
[2024-07-17 07:46:36.929464][INFO][trainer:885] - step=340 loss=1.350888 dt=0.284436 dtf=0.005199 dtb=0.011287 sps=14.062893 sps_per_gpu=3.515723 tps=921625.744709 tps_per_gpu=230406.436177 mfu=45.539549 train_loss=1.495372 val_loss=1.713714
```

## [`wordplay`](https://github.com/saforem2/wordplay): Example \[[video](https://asciinema.org/a/668462)\]

<div id="fig-wordplay-asciinema">

<script
    src="https://asciinema.org/a/668462.js"
    id="asciicast-668462"
    async="true"></script>

Figure 29: Training a LLM to talk like Shakespeare using
[saforem2/`wordplay` 🎮💬](https://github.com/saforem2/wordplay)

</div>

## ❤️ Thank you!

- Organizers

- Feel free to reach out!

            <split even>

    [<i class="fas fa-home"></i>](https://samforeman.me)
    [<i class="far fa-paper-plane"></i>](mailto:foremans@anl.gov)
    [<i class="fab fa-twitter"></i>](https://www.twitter.com/saforem2)

            </split>

> [!NOTE] Acknowledgements
>
> This research used resources of the Argonne Leadership Computing
> Facility, which is a DOE Office of Science User Facility supported
> under Contract DE-AC02-06CH11357

## 📓 References

- Title slide (Tetris animation) from:
  [emilhvitfeldt/quarto-iframe-examples](https://github.com/emilhvitfeldt/quarto-iframe-examples)

<div id="refs" class="references csl-bib-body hanging-indent">

<div id="ref-wei2022emergentabilitieslargelanguage" class="csl-entry">

Wei, Jason, Yi Tay, Rishi Bommasani, et al. 2022. _Emergent Abilities of
Large Language Models_. [https://arxiv.org/abs/2206.07682](https://arxiv.org/abs/2206.07682).

</div>

<div id="ref-yao2023tree" class="csl-entry">

Yao, Shunyu, Dian Yu, Jeffrey Zhao, et al. 2023. _Tree of Thoughts:
Deliberate Problem Solving with Large Language Models_.
[https://arxiv.org/abs/2305.10601](https://arxiv.org/abs/2305.10601).

</div>

</div>

[^1]: `micro_batch_size` = batch_size **per** GPU

[^2]:
    [Efficient Large-Scale Language Model Training on GPU
    Clusters](https://arxiv.org/abs/2104.04473)

[^3]:
    Source: [
    `Hannibal046/Awesome-LLM`](https://github.com/Hannibal046/Awesome-LLM)

[^4]:
    Figure from [The Illustrated
    Transformer](http://jalammar.github.io/illustrated-transformer/)

[^5]:
    Figure from [The Illustrated
    Transformer](http://jalammar.github.io/illustrated-transformer/)

[^6]:
    Video from: [🤗 Generation with
    LLMs](https://huggingface.co/docs/transformers/main/en/llm_tutorial)

[^7]:
    Video from: [🤗 Generation with
    LLMs](https://huggingface.co/docs/transformers/main/en/llm_tutorial)
