Making deep learning perform real algorithms with Category Theory (Andrew Dudzik, Petar Velichkovich, Taco Cohen, Bruno Gavranović, Paul Lessard) - Machine Learning Street Talk (MLST) Recap

Podcast: Machine Learning Street Talk (MLST)

Published: 2025-12-22

Duration: 44 min

Summary

The episode explores the limitations of language models in performing arithmetic and the potential of deep learning architectures to better align with algorithmic processes through concepts from category theory and geometric deep learning.

What Happened

In this episode, the hosts engage in a deep discussion about the capabilities and shortcomings of large language models (LLMs) when it comes to performing basic arithmetic operations. Andrew Dudzik points out that while LLMs can sometimes recognize patterns and trick questions, they ultimately fail at fundamental operations like addition. For instance, he illustrates that if you ask a model about the sum of a series of numbers with a slight modification, it often resorts to incorrect responses. This indicates a significant gap between the training of these models and the reliable execution of computational tasks, which raises concerns for applications requiring precision, such as robotics and scientific reasoning.

The conversation also delves into the notion of internalizing algorithms within deep learning architectures rather than relying solely on external tools. The speakers agree that while integrating calculators as tools can enhance performance, it’s crucial to build models that can inherently perform calculations efficiently. Dudzik emphasizes the need for models to not only absorb vast amounts of knowledge but also to execute reasoning and computation internally, reducing the need for repeated calls to external tools, which can be inefficient and error-prone.

As they explore geometric deep learning, the hosts highlight its foundational principles, including equivariance to symmetry transformation. They discuss the importance of designing neural networks that respond predictably to transformations in input data, using examples like image translations. However, they caution that current approaches may not fully address the complexities of computation, suggesting a need for broader frameworks that can accommodate the intricacies of algorithmic processes. This introspection about the limits and potentials of LLMs and geometric deep learning sets the stage for future research directions aimed at improving model performance in algorithmic contexts.

Key Insights

Key Questions Answered

Why can't language models perform basic arithmetic?

Andrew Dudzik explains that language models, like ChatGPT, can recognize some arithmetic patterns but fail when faced with slight changes in the numbers involved. For example, if a simple addition problem is altered, the model often produces incorrect answers, indicating its inability to truly understand the underlying arithmetic process. This limitation is crucial as it shows a disconnect between the model's training and real computational tasks.

What are the advantages of internalizing algorithms in models?

The episode discusses that integrating the ability to perform computations internally within models can lead to significant efficiency gains. Instead of repeatedly calling external tools for various calculations, a model equipped with internal computation can process information seamlessly, reducing the risk of errors and streamlining complex reasoning tasks.

How does geometric deep learning relate to traditional neural networks?

Geometric deep learning builds on the notion of constructing neural networks that are equivariant to symmetry transformations. This means that if an input is transformed in a certain way, the output should remain consistent. The discussion highlights how this principle can enhance model performance, especially in tasks that involve spatial data, yet acknowledges that it may not fully address the intricacies of algorithmic computation.

What implications does category theory have for deep learning?

The hosts suggest that category theory could provide a framework for better aligning deep learning models with computational tasks. By understanding and structuring models through the lens of category theory, researchers might develop architectures that can more effectively handle algorithmic processes, which are currently a challenge for many existing models.

What are the future directions for deep learning architectures?

The conversation points towards the necessity of evolving deep learning models to better encapsulate algorithmic reasoning and computation. The speakers advocate for research that broadens the scope of geometric deep learning to include more robust mechanisms for computation, which could ultimately lead to models that are not only powerful but also reliable in logical and scientific reasoning contexts.