Large Language Models (LLMs) have transformed natural language processing, powering applications ranging from chatbots to creative writing assistants. However, practitioners often find that running the same model on different machines can yield subtly different outputs. This variability arises from a complex interplay of hardware, software, and computational factors. Understanding these influences is essential for those seeking reproducibility and reliability in their AI workflows.

Hardware Variations #

Large Language Models (LLMs) are intricate mathematical systems whose outputs depend heavily on the precise sequence of numerical computations they perform. While it’s natural to assume that running the same model on different hardware produces identical results, this assumption often falls short in practice.

This difference arises because GPUs vary in their underlying architecture, memory bandwidth, and parallel processing capabilities. For example, the RTX and Tesla GPUs are optimized for distinct workloads and possess different floating-point arithmetic implementations, which affect numerical precision and operation ordering. These subtle architectural differences can cause divergence in the way floating-point calculations accumulate rounding errors or handle intermediate values.

Moreover, GPUs execute thousands of threads in parallel, but how these threads synchronize and schedule computations is hardware-dependent. Small variations in timing and ordering of operations can cascade in non-deterministic ways within deep learning models, leading to variability in token probabilities and final outputs.

It’s not just GPUs, CPUs and TPUs also exhibit their unique characteristics, such as instruction set architectures, cache hierarchies, and precision optimizations. These distinctions further contribute to variations in model inference behavior when switching between hardware platforms.

So, the hardware substrate on which an LLM runs is not a mere performance detail but an integral part of the model’s computational fabric. Changing the GPU or computational platform introduces differences in numerical processing that can alter the model’s behavior.

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Quantization Effects #

Quantization has become an essential technique in deploying large language models (LLMs) efficiently. By reducing numerical precision, commonly from 32-bit floating point (FP32) to 16-bit (FP16) or even 8-bit integers (INT8)—quantization dramatically speeds up inference and decreases memory and energy consumption. This efficiency gain is crucial for making large models practical to run on diverse hardware, from cloud GPUs to edge devices.

However, quantization is a double-edged sword. While it enables scalability and cost reduction, it inherently introduces numerical approximations due to lower precision. These rounding and truncation errors may seem insignificant at the individual operation level, but when propagated through the many layers of a transformer-based LLM, they can accumulate and amplify, causing noticeable differences in the model’s final outputs.

Numerical Precision and Floating-Point Arithmetic #

At the heart of every large language model (LLM) lies an immense volume of numerical computations, predominantly performed using floating-point arithmetic. While floating-point math enables efficient representation and manipulation of real numbers, it inherently comes with limitations in precision and accuracy that subtly influence model behavior and output.

Floating-point numbers approximate real numbers within a fixed number of bits (commonly 32-bit or 16-bit formats). This representation limits the precision with which values can be stored and manipulated, leading to rounding and truncation errors during basic operations such as addition, subtraction, multiplication, and division.

In LLMs, these operations are chained across billions of parameters and tens to hundreds of transformer layers, causing tiny numerical errors to propagate and accumulate. Over many layers, this accumulation can cause measurable divergences in final token probabilities and generated outputs.

Software Frameworks, Libraries and Runtime #

Software frameworks like TensorFlow, PyTorch, and MXNet are the foundation for running large language models, but differences in how they implement operations and manage computations can cause small variations in results. Even different versions of the same framework can change behavior due to updates or optimizations. Additionally, these frameworks rely on hardware acceleration libraries, which can also vary in numerical precision and execution order, further contributing to output differences.

On top of that, compiler and software-level optimizations designed to improve speed often reorder operations or use alternative algorithms, which can introduce tiny rounding errors because floating-point math isn’t perfectly associative. These optimizations may differ across hardware and runs, making exact output replication difficult. While these software and compiler factors help maximize performance, they also mean that outputs can vary subtly.

Sensitivity to Input: How Small Changes Amplify Through Autoregressive Language Models #

Large language models (LLMs) are fundamentally sensitive to their input tokens, where even a single token difference can lead to notably different outputs. This sensitivity arises from the model’s complex, nonlinear transformations across multiple layers, which interpret each token in the context of the entire input sequence. Because LLMs are typically autoregressive — predicting each token based on all previously generated tokens. Any small change early in the input propagates and compounds throughout the generation process.

This autoregressive dependency means that a minor perturbation or substitution in the input doesn’t just affect the immediate next token; it cascades through the entire output sequence, amplifying variations and potentially producing very different results. While this property enables LLMs to generate highly coherent, contextually rich, and flexible text, it also makes them inherently sensitive and somewhat unstable in the face of small input changes, posing challenges for reproducibility, robustness, and controlled generation.

A Parallel with Traditional Software Systems #

In traditional software systems, behavior is largely deterministic and controllable. Given the same inputs, software reliably produces the same outputs. This predictability stems from explicit logic, strict execution order, and mature tooling for testing, debugging, versioning, and deployment. Engineers can trace faults, reproduce bugs, and validate systems with confidence - hallmarks of robust software engineering.

AI systems outputs depend not only on inputs but also on randomness, hardware nuances, floating-point precision, and software stack idiosyncrasies. These factors make even basic principles like reproducibility and debuggability far more elusive.

This naturally raises a critical question: How can we design and build intelligent agents that are predictable, reliable, debuggable and scalable, capable of seamlessly operating across diverse models, hardware architectures, and heterogeneous cloud platforms?