Latent Space Podcast 8/16/23 [Summary] - The Mathematics of Training LLMs — with Quentin Anthony of Eleuther AI

Explore the math behind training LLMs with Quentin Anthony from Eleuther AI. Dive into the Transformers Math 101 article & master distributed training techniques for peak GPU performance.

Prof. Otto NomosOct 05, 2023 3 min read

Original Link: The Mathematics of Training LLMs — with Quentin Anthony of Eleuther AI

The Mathematics Behind Training Large Language Models [Summary]

In the recent episode of the Latent Space podcast, hosts Alessio and Swyx are joined by Quentin Anthony, an integral figure from They begin by appreciating Eleuther's Transformers Math 101 article, regarded by many as a highly authoritative source for understanding AI's underlying math and the intricacies of training large language models. Quentin elaborates on his journey, from being a PhD student at Ohio State University to joining Eleuther and diving deep into the challenges of distributed AI model training.

Quentin also sheds light on the primary motivation behind writing the article. Despite many in the Deep Learning (DL) space being familiar with the theory of AI, few delve into the practical intricacies—such as understanding how AI inference runs correctly across multiple GPUs. With the article, Eleuther aimed to bridge this gap and share knowledge that would benefit engineers beyond the institution's walls.

Further, Quentin emphasizes the importance of considering not just the dataset but also the computational requirements. This involves taking into account the total computational time and the cost associated with it, making the equation they discuss central to understanding compute requirements. The conversation steers towards the strategies for efficient GPU usage, pointing out the common pitfalls and challenges faced during high-scale deployments.

Throughout, the underlying theme is the need for practical intuition, with Quentin stressing the "good enough" approach over chasing perfection. The talk offers a blend of theoretical understanding and pragmatic insights into the world of AI and large model training.


Deep Dive into Computational Efficiencies and Memory Requirements in AI Systems

In a detailed discussion:

  • Forward and Backward Passes: Alessio questioned why computers have a 2:1 ratio for forward and backward passes (2PD for forward and 4PD for backward). Quentin explained that the forward pass involves simple propagation of inputs through a layer, whereas the backward pass is more complicated, entailing backpropagation.

  • Deep Learning Math: Swyx mentioned the efficiency of deep learning mathematics, particularly backpropagation, compared to traditional numerical methods.

  • Complexities Behind Simple Numbers: Alessio pointed out that while some math equations appear simple and elegant, the logic behind them can be complex. This sentiment is seen in the public's perception of optimal ratios on platforms like Twitter.

  • Theoretical vs. Actual FLOPs: Swyx brought up the distinction between theoretical and actual FLOPs, noting discrepancies in reported values. Quentin explained that theoretical FLOPs are based on hardware expectations, but full utilization doesn't always occur due to synchronization waits, data movement between CPU and GPU, and other delays. He suggests benchmarking expected FLOPs against known GPU capabilities.

  • GPU Considerations: The discussion touched on the differences between Nvidia and AMD GPUs. While AMD may offer better theoretical performance, Nvidia's CUDA software and vast open-source support offer practical advantages. Quentin highlighted that the choice often boils down to the efficiency of the software stack and the momentum in the open-source domain.

  • Memory Requirements and Precision: Alessio and Swyx delved into memory requirements for training models, particularly focusing on precision and quantization. Quentin explained that transitioning from FP32 to mixed precision, like FP16 and FP32, or BF16 and FP32, often results in more memory usage due to storing both versions of weights. He also emphasized the evolution of precision types in response to hardware advancements, hinting at the future potential of using even smaller representations like INT4.


Deep Learning Memory Dilemmas: The Adam Optimizer's Challenge

In a discussion about deep learning and optimization methods, Quentin highlighted the RWKV paper as an exploration into achieving Transformer quality without the quadratic attention overhead. The essence of the dialogue revolves around the challenges and intricacies of handling the computational memory requirements of the Adam optimizer. Notably, Quentin points out that while Adam is efficient, it consumes more memory than SGD, particularly three times as much. As a result, distributing memory, especially when dealing with model parallelism and optimizer states, becomes crucial in deep learning operations. Alessio then underlines the memory implications of vanilla Adam, emphasizing that it uses 12 bytes per parameter, which balloons when considering other components like quantization levels. The overarching theme is the quest for efficiency and understanding in the realm of deep learning optimization and memory management.


Optimizing Memory and Training Models in Deep Learning

Quentin, Swyx, and Alessio discuss memory challenges and optimizations in training large models.

Key Points:

  1. Model vs. Optimizer Memory: While most attention is on the model's memory, the optimizer (e.g., Adam) typically requires more memory. It stores momentum, variance, and other parameters. Optimizing the optimizer can yield better memory efficiency than solely focusing on the model.

  2. Memory Components in Training: When training a model, the main memory components are model parameters, optimizer states, gradients, and activation memory. Activation memory dynamically changes, which can cause unexpected out-of-memory issues.

  3. Activation Recomputation: To handle memory concerns, some strategies involve recomputing activations rather than storing them. Strategies vary from recomputing everything, selective recomputation based on tensor sizes, or setting a static size threshold for which tensors are stored.

  4. Distributed Training with Zero: The Zero algorithm optimizes distributed training. It scatters parameters, gradients, and optimizer states across multiple GPUs, then gathers them back during each training step. The aim is to shard the states across GPUs, but this increases communication overhead.

  5. Fine-tuning vs. Training: While there are established methods and knowledge about training models, fine-tuning presents its challenges. Aspects like learning rate adjustments and transferring datasets are still areas of exploration.

  6. Considerations for Scaling: The ideal number of GPUs for distributed training varies based on the interconnect speed and the total parameters. Too much sharding can introduce inefficiencies due to synchronization overheads.

The discussion underscores the intricacies of memory management and the importance of optimizing not just model parameters but also other components, like the optimizer, for efficient deep learning.


Deciphering 3D Parallelism: A Deep Dive into Advanced AI Model Techniques

In a conversation between Alessio, Quentin, and Swyx, the concept of 3D parallelism in AI models is explored.

  • 3D Parallelism:

    1. Data Parallelism: Described as having a copy of the model on each GPU. If two GPUs are present, each has a copy of the model that performs a forward and backward pass, after which they synchronize and average the gradients.

    2. Tensor Parallelism: This involves splitting the model. If two GPUs are present, the model is split in the middle, with each GPU operating on its specific tensor. Synchronization between GPUs happens only when necessary.

    3. Pipeline Parallelism: Illustratively, if there are four layers in the model and four GPUs, each GPU holds one layer. As each GPU finishes its forward pass, it sends its output to the next GPU in line. The process is reminiscent of a pipeline, hence the name.

  • Issues & Considerations:

    1. A potential issue raised is the need for all GPUs to be uniform in their capabilities. Disparity in VRAM between GPUs can lead to bottlenecks. Similarly, having GPUs of varying speeds will lead to synchronization issues, making the system only as fast as the slowest GPU.

    2. Quentin cites a real-world example where nodes had varying network switches, resulting in operations moving at the pace of the slowest switch.

    3. When asked about the widespread adoption of the techniques discussed, Quentin mentions that while many GPT-based models use this scheme, a pure sharded system seems to be more prevalent as it offers simplicity.

  • Future Challenges:

    1. Adapting the 3D parallel scheme to new model features, especially with the rise of multimodal models which combine different data types like text and vision.

    2. Communication becoming a bottleneck, especially when transferring data across nodes.

By the end, Quentin offers to answer further questions on the topic offline and mentions his swift response time on Discord. The talk concludes with Alessio and Swyx thanking Quentin for his insights.

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