Recently, I started working on my own inference API as a side project and found myself grappling with torch_dtype , which determines the data type of a Tensor. Each dtype is a floating point and values are usually defined in a model's config.json, but I wanted to dig deeper into how they work. I figured it was worth learning more and sharing my findings with others.
When we talk about FP64, FP32, and FP16-double, single, and half precision etc, we're essentially concerned with the different types, as ways of representing numbers in computer memory. Each format offers up a balance between precision and computational efficiency, making them suitable for different stages of the machine learning pipeline, with there being a trade off (as with everything in life). Hopefully I leave you with an understanding of how those choices are made and why.
What is Floating-Point Precision?
At its core, floating-point precision is a method for representing real numbers in computer systems. Think of it as a digital version of scientific notation, where numbers are represented as a significand (it seems to be more commonly referred to as a "mantissa" from what I have read) multiplied by a base raised to an exponent. For instance, just as we might write 299,792,458 as 2.99792458 × 10⁸ in scientific notation, computers use a similar system but with base-2.
For anyone who did their CS degree a long old time ago and needs a reminder, the term "floating-point" comes from the fact that the decimal point can "float" to different positions in the number, allowing it to represent both very large and very small numbers efficiently. This flexibility comes at the cost of having to store three distinct components for each number:
The sign bit, which determines whether the number is positive or negative.
The exponent, that indicates the number's order of magnitude.
The mantissa (significand), that contains the number's significant digits.
The IEEE 754 standard, developed in 1985 and revised in 2019, provides the framework for how these components are organized in memory. This standardization ensures consistent behavior across different hardware and software platforms, making it possible to develop reliable and portable numerical algorithms.
For an example, if we take simple number like 0.15625 that is stored in memory. In binary, this becomes 0.00101, which can be represented as 1.01 × 2⁻³. The sign bit would be 0 (positive), the exponent would store -3 (with an offset), and the mantissa would store 1.01. This standardized representation allows for consistent mathematical operations across different computing systems.
| Sign Bit | Exponent (8 bits) | Mantissa (23 bits) |
|---|---|---|
| 0 | 01111100 (-3 + 127) | 01000000000000000000000 |
Convert to Binary
-
Decimal:
0.15625 -
Binary:
0.00101 -
Normalized:
1.01 × 2⁻³
Breakdown:
-
Sign Bit:
0(Positive) -
Exponent:
01111100(Stored as -3 with a bias of 127: -3 + 127 =124) -
Mantissa:
01000000000000000000000(Remaining fractional part after the leading 1)
Explanation:
- The sign bit determines whether the number is positive (
0) or negative (1). - The exponent is stored with a bias of 127 (in single precision). Here, -3 + 127 =
124(which is01111100in binary). - The mantissa stores the fractional part of the normalized binary representation (
1.01), omitting the leading1(implicit in IEEE 754).
This standardized floating-point representation then allows for accurate storage and computation across different computing architectures.
Understanding FP64, FP32, and FP16
FP64 (Double Precision)
Double precision floating-point numbers represent the gold standard in numerical computing. With 64 bits at their disposal, these numbers allocate 1 bit for the sign, 11 bits for the exponent, and 52 bits for the mantissa. This generous allocation of bits allows FP64 to represent numbers with approximately 16 decimal digits of precision.
The extensive precision of FP64 makes it particularly valuable during the initial training phases of large language models, where small numerical errors can compound over millions of iterations. Consider the backpropagation process in neural networks: when calculating gradients, small rounding errors in less precise formats could lead to significantly different weight updates, potentially affecting the model's final performance.
However, this precision comes at a cost. FP64 operations require more memory bandwidth and computational resources than their lower-precision counterparts. On modern GPUs, FP64 operations often run at a fraction of the speed of FP32 operations, making them impractical for many real-world applications.
FP32 (Single Precision)
Single precision floating-point numbers strike a balance between accuracy and efficiency. With 32 bits total—1 for sign, 8 for exponent, and 23 for mantissa—FP32 provides approximately 7 decimal digits of precision. This precision level proves sufficient for many machine learning applications, including most phases of LLM training and inference.
FP32 has become the default precision for many deep learning frameworks because it offers a sweet spot between numerical stability and computational efficiency. Training in FP32 typically provides enough precision to capture the subtle patterns necessary for model learning while maintaining reasonable memory requirements and computation speeds.
The practical benefits of FP32 become apparent when we consider real-world deployments. Most consumer-grade GPUs are optimized for FP32 operations, making this precision level ideal for researchers and developers working with limited computational resources. Additionally, the reduced memory footprint compared to FP64 allows for larger batch sizes during training, potentially improving model convergence rates.
FP16 (Half Precision)
Half precision floating-point numbers represent the most compact of the three formats, using just 16 bits—1 for sign, 5 for exponent, and 10 for mantissa. While this format sacrifices numerical precision, maintaining only about 3 decimal digits of precision, it offers significant advantages in terms of memory usage and computational speed.
The reduced precision of FP16 makes it particularly attractive for inference tasks, where the model's weights have already been determined and slight numerical imprecisions are less likely to impact output quality. This format has gained popularity with the advent of specialized AI hardware accelerators, which often include dedicated FP16 computation units that can process operations much faster than their FP32 or FP64 counterparts.
Implications of Floating-Point Precision in LLMs
Training with Different Precisions
The choice of floating-point precision during training represents an important decision that can significantly impact the model's final performance and the training process efficiency. While traditional wisdom would suggest using the highest precision possible during training (turn it up max!), modern approaches appear to have demonstrated the viability of mixed-precision training strategies.
Mixed-precision training, which typically combines FP16 computations with FP32 master weights, has emerged as a key technique for accelerating training while maintaining model quality (cost vs quality). This approach stores most operations in FP16 for efficiency but keeps a master copy of the weights in FP32 to maintain stability. The process from what I can understand involves:
Computing forward and backward passes in FP16 to save memory and increase speed Storing gradients in FP32 to maintain numerical stability
Updating master weights in FP32 before converting back to FP16 for the next iteration
This hybrid approach has enabled researchers to train increasingly large models while making efficient use of available computational resources. For instance, many modern transformer-based models employ mixed-precision training to achieve training times that would be impractical with pure FP32 or FP64 implementations.
Inference with Different Precisions
The inference stage presents different challenges and opportunities regarding precision selection. During inference, we're primarily concerned with forward pass computations, which tend to be more numerically stable than training operations. This stability opens the door to using lower precision formats without significantly impacting model performance.
FP16 has become increasingly popular for inference, particularly in production environments where latency and throughput are critical concerns. The reduced memory bandwidth requirements and faster computation times can lead to substantial performance improvements, often without noticeable degradation in output quality.
Modern hardware architectures have embraced this trend, with many AI accelerators optimized for FP16 operations. For example, NVIDIA's Tensor Cores provide specialized hardware support for FP16 matrix operations, enabling significant speedups compared to traditional FP32 computations.
Tuning for Optimal Precision
Finding the right precision configuration then requires experimentation and consideration it seems, of various factors:
The Model Architecture
Different model architectures apparently exhibit varying sensitivity to reduced precision. Attention mechanisms, for instance, require higher precision to maintain stability.
Hardware Constraints
Available memory, computational capabilities, and power constraints often dictate the practical limits of precision selection which is why we only see the tech giants able to produce the incredible large LLMs, hopefully the tide is changing though with smaller GPU pools turning up with big wins (aka deepseek-r1).
Application Requirements
Real-time applications might prioritize lower latency over maximum precision, while critical applications might require the stability of higher precision formats. The same is also playing out with parameter counts, smaller equals faster.
Rounding it all up
So it seems the choice of floating-point precision in large language models is pretty critical a decision to make to make as it impacts every aspect of model development (training, fine tuning) and deployment too (inference, as I found out the hard way!). While FP64 provides the highest numerical precision, the practical benefits of FP32 and FP16 formats have made them increasingly popular in modern AI systems.
The trend now from what I can tell, is a move towards more efficient precision formats seems likely to continue. Emerging techniques like quantization and neural architecture search are touted to further optimize the balance between precision and performance. However, understanding the fundamental trade-offs between different precision formats will remain essential for anyone attempting to strike a balance between energy used and quality of output.
So the key lies in selecting the right precision for each stage of the machine learning pipeline, considering both technical requirements and practical constraints.
Hope that helps, I am still learning so if I misunderstood anything , comment below and I will be sure to correct!
Top comments (2)
Great article!
In addition to FP32 and FP16, bfloat16 (brain float 16) is extensively used in AI workloads. BF16 is less prone to numerical underflow/overflow compared to FP16. It has larger dynamic range but lower precision. [FP16 uses 5 exponent bits and 10 mantissa bits, whereas BF16 uses 8 exponent bits (same as FP32) and 7 mantissa bits.]
Ah yes, ofc. I should add bfloat16 as its the main one I am seeing. I will edit this in.