7B? 13B? 175B? Interpret parameters of large models

Large models are also large and small, and their size is measured by the number of parameters. GPT-3 has 17.5 billion parameters, and Grok-1 is even more impressive, with 31.4 billion parameters. Of course, there are also slimmer ones like Llama, whose number of parameters is only between 7 billion and 70 billion.

The 70B mentioned here may not refer to the amount of training data, but to the densely packed parameters in the model. These parameters are like small "brain cells". The more they are, the smarter the model can be and the better it can understand the intricate relationships in the data. With these "brain cells," models may perform better at tasks. However, many times these parameters, especially in large-scale models, can cause problems. These "brain cells" may interact with each other when processing tasks, making it difficult for the model to understand the complex relationships in the data. With these "brain cells," models may perform better at tasks. Therefore, we need to find a way to manage the relationship between these parameters when working on the task. A common method is through regularization. The parameters of these large models are like the "architects" inside the model. Through complex algorithms and training processes, this huge language is built bit by bit. world. Each parameter has its role, and they work together to allow the model to more accurately understand our language and give more appropriate answers.

So, how are the parameters in the large model composed?

1. Parameters in the large model

The parameters of the large model are its "internal parts". Each of these parts has its own purpose, usually including but not limited to the following categories:

Weights: Weights are like "wires" in a neural network, connecting each neuron. They are responsible for adjusting the "volume" of signal transmission, allowing important information to be transmitted farther and less important information to be quieter. For example, in the fully connected layer, the weight matrix W is a "map" that tells us which input features are most closely related to the output features.

• Biases: Biases are like the "little assistants" of neurons, responsible for setting a baseline for the response of neurons. With it, neurons know at what level they should be active.
• Parameters of the attention mechanism (Attention Parameters): In the Transformer-based model, these parameters are like a "compass", telling the model which information is most worthy of attention. They include query matrices, key matrices, value matrices, etc., which are like finding the most critical "clues" in a large amount of information.
• Embedding Matrices: When processing text data, the embedding matrix is ​​the "dictionary" of the model. Each column represents a word, and a number is used to represent the word. In this way, the model can understand the meaning of the text.
• Hidden State Initialization Parameters (Initial Hidden State Parameters): These parameters are used to set the initial hidden state of the model, just like setting a tone for the model so that it knows where to start "thinking".
• ......
• These parameters generally use 4 expression and storage formats:

Float: 32-bit floating point number , that is, 4 bytes

1. Half/BF16: 16-bit floating point number, that is, 2 bytes
2. Int8: 8-bit integer, that is, 1 byte
3. Int4: 4-bit integer, that is, 0.5 bytes
4. Generally speaking, the number of parameters is the main factor affecting the performance of large models. For example, the 13B-int8 model is generally better than the 7B-BF16 model of the same architecture.

2. Memory requirements for large model parameters

For engineers, what they are faced with is how much memory resources will be used during large model training or inference. Even though the V100 (with 32GB of GPU memory) or the A100 (with 40GB of GPU memory) are very powerful, large models still cannot be trained on a single GPU, such as with Tensorflow or PyTorch.

2.1 Memory requirements during the training phase

During model training, it is mainly reflected in the memory storage requirements for model status and activity processes. The model state consists of tensors consisting of optimizer state, gradients, and parameters. Included in the active process are any tensors created in the forward channel that are required for gradient calculations in the backward channel. In order to optimize memory usage, you can consider the following aspects: 1. Reduce the number of model parameters: You can reduce the number of parameters and reduce memory usage by reducing the model size or using techniques such as sparse matrices. 2. Storage of optimizer state: You can choose to store only the necessary optimizer state instead of saving all states. Optimizer state can be selectively updated and stored as needed. 3. Modify the data type of the tensor:

At any time during training, for each model parameter, there always needs to be enough GPU memory to store:

• The number of bytes copied by model parameters x
• The number of bytes copied by gradient y
• The optimizer status is generally 12 bytes, mainly the copy of parameters, variance, etc. , all optimizer states will be saved in FP32 to maintain stable training and avoid numerical anomalies.

This means that the following memory is required to store all model status and process data during training: (x+y+12) * model_size

2.2 Memory requirements in the inference phase

The inference phase uses pre-trained LLM to complete tasks such as text generation or translation. Here, memory requirements are typically lower, with the main influencing factors being:

• Limited context: Inference typically handles shorter input sequences, requiring less memory to store associated with smaller chunks of text of activation.
• No backpropagation: During inference, LLM does not need to preserve the intermediate values ​​of backpropagation, a technique used for training to adjust parameters. This eliminates a lot of memory overhead.

The inference phase requires no more memory than a quarter of the memory required by the training phase for the same parameter count and type. For example, for a 7B model, in general, using floating point precision requires 28GB of memory, using BF16 precision requires 14GB of memory, and using int8 precision requires 7GB of memory. This rough estimation method can be applied to other versions of the model accordingly.

Also, when tuning LLM for a specific task, fine-tuning requires a higher memory footprint. Fine-tuning typically involves longer training sequences to capture the nuances of the target task. This will lead to larger activations as the LLM processes more text data. The backpropagation process requires the storage of intermediate values ​​for gradient calculations, which are used to update the model's weights during training. This adds a significant memory load compared to inference.

2.3 Memory estimation of large models based on Transformer

Specifically, corresponding to the large model based on Transformer, try to calculate the memory required for training, where set:

• l: Number of layers of transformer
• a: Head number of attention
• b: Batch size
• s: Sequence length
• h : Dimension size of the hidden layer
• p: Accuracy

Here, bshp = b * s * h * p represents the size of the input data. In the linear layer part of the transformer, approximately 9bshp+bsh of space is needed for subsequent activations. In the attention part, self-attention can be expressed as: softmax((XQ)(XK)^T)XV

Then, XQ, XK, and XV all require bshp-sized space. In standard self-attention, the result of multiplying (XQ) * (XK) ^ T is just a b * s * s matrix containing logit. However, in practice, due to the use of a multi-head attention mechanism, a separate s * s storage space needs to be established for each head. This means that abssp bytes of space are required, and storing the output of the softmax also requires abssp bytes. After softmax, additional abss bytes are generally needed to store the mask, so the attention part requires 2abssp+abss storage space.

In addition, there are two Norm layers in the transformer, each of which still requires bshp storage space, for a total of 2 bshp.

So, the memory required for large model training based on Transformer is approximately: L(9bshp+bsh+2abssp+abss +2bshp) = Lbshp[16+2/p+(as/h)(2+1/ p)]

Explain that the memory required to train a large model based on Transformer is approximately: the number of layers of the model x the size of the training batch x sequence length x the dimension of the hidden layer x accuracy x an integer greater than 16

This may be a theoretical lower bound for the memory requirements of large model parameters based on Transfromer during training.

3. GPU requirements for large model parameters

With the memory requirements for large model parameters, we can further estimate the number of GPUs required for training and inference of large models. However, since the estimation of the number of GPUs relies on slightly more parameters, someone (Dr. Walid Soula, https://medium.com/u/e41a20d646a8) gave a simple formula for rough estimation, which also has certain reference significance in engineering.

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Among them,

• Model's parameters in billions is the number of model parameters in B;
• 18 is the memory usage factor of different components during training;
• 1.25 represents the memory quantity factor required for the activation process. Activation is a dynamic data structure that changes as the model processes input data.
• GPU Size in GB is the total amount of available GPU memory

As a practical example, assuming that an NVIDIA RTX 4090 GPU is used, which has 24GB of VRAM, calculate the training The number of GPUs required by the 'Llama3 7B' model is approximately:

The total number of GPUs≈(7 * 18 * 1.25)/24, which is approximately equal to 7

For inference, it can be simplified to 1/8~1/9 of the training stage. Of course, these are only rough estimates in a general sense.

4. From large model parameters to distributed training

Understanding the composition of large model parameters and their requirements for memory and GPU will help to deeply understand the role of distributed training in engineering practice. challenges faced.

The implementation process of distributed training strategies can be significantly simplified by adopting frameworks designed for distributed training, such as TensorFlow or PyTorch, which provide rich tools and APIs. By using techniques such as gradient accumulation before updating the model, or using techniques such as gradient compression to reduce the amount of data exchange between nodes, communication costs can be effectively reduced. It is crucial to determine the optimal batch size for distributed training (the parameter b mentioned above); a b value that is too small may increase communication overhead, while a value that is too large may result in insufficient memory.

The importance of LLMOps has become increasingly prominent. Regularly monitoring the performance indicators configured for distributed training and adjusting hyperparameters, partitioning strategies, and communication settings to optimize performance are key to improving training efficiency. Implementing a checkpointing mechanism for the model and efficient recovery in the event of failure ensures that the training process continues without having to start from scratch.

In other words, the training/inference of large models is essentially a complex distributed system architecture engineering challenge, such as:

• Communication overhead: when performing gradient calculations and data updates The time required for communication may affect the overall acceleration effect.
• Synchronization complexity: When multiple machines are trained in parallel, the complexity of synchronization needs to be carefully designed.
• Fault tolerance and resource management: The impact of single point failure on model training and inference, as well as resource allocation and scheduling strategies for CPU and GPU.
• ......

However, in fact, most engineers may not be directly involved in specific training work, but focus on how to leverage large models when building applications parameters.

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5. Parameters used in large model applications

The main focus here is on how to configure the parameters when using a large model to output text. Three parameters: Temperature, Top-K and Top-P.

The Temperature parameter is often misunderstood as a switch that only controls the creativity of the model, but in fact its deeper role is to adjust the "softness" of the probability distribution. When the Temperature value is set higher, the probability distribution becomes softer and more uniform, which encourages the model to generate more diverse and creative output. Conversely, lower Temperature values ​​will make the distribution sharper and have more obvious peaks, thus tending to produce output similar to the training data.

The Top-K parameter is used to limit the model to output the most likely Top-K tokens at each step. In this way, incoherent or meaningless content in the output can be reduced. This strategy creates a balance between maintaining the best possible consistency of output while allowing a certain degree of creative sampling.

Top-P is another decoding method that selects a minimum set of words whose cumulative probability exceeds the P value as output based on the set P value (0≤P≤1). This method allows the number of selected words to be dynamically increased or decreased based on the probability distribution of the next word. In particular, when the P value is 1, Top-P will select all words, which is equivalent to sampling from the entire distribution, thereby producing a more diverse output; while when the P value is 0, Top-P only selects the words with the highest probability , similar to greedy decoding, makes the output more focused and consistent.

These three parameters work together to affect the behavior of the model. For example, when setting Temperature=0.8, Top-K=36, and Top-P=0.7, the model first calculates the complete unnormalized log probability distribution of the entire vocabulary based on context. Temperature=0.8 means that each log probability is divided by 0.8, which effectively increases the model's confidence in its predictions before normalization. Top-K=36 means selecting the 36 markers with the highest frequency proportional logarithmic probability. Then, Top-P=0.7 applies filtering in this Top-K=36 set, keeping sorting from high to low probability until the cumulative probability reaches 0.7. Finally, this filtered set is renormalized and used in the subsequent sampling process.

6. Summary

In engineering practice, it is meaningful to understand the parameters of large models. Parameters play a decisive role in large models. They define the behavior, performance, implementation costs, and resource requirements of large models. Understanding the parameters of a large model in engineering means grasping the relationship between the complexity, performance, and capabilities of the model. Properly configuring and optimizing these parameters from the perspective of storage and computing can better select and optimize models in practical applications to adapt to different task requirements and resource constraints.

【Reference Materials】

• ZeRO: Memory Optimizations Toward Training Trillion Parameter Models ，https://arxiv.org/pdf/1910.02054v3.pdf
• Reducing Activation Recomputation in Large Transformer Models，https://arxiv.org/pdf/2205.05198.pdf
• https://timdettmers.com/2023/01/30/which-gpu-for-deep-learning/
• https://blog.eleuther.ai/transformer-math/

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