Can large language models truly grasp algorithms, or are they just faking it? A new research paper proposes a fascinating approach: equipping LLMs with a built-in library of fundamental operations, like a differentiable computer they can tap into. Imagine giving an LLM the ability to access not just data, but pre-compiled building blocks for common algorithms. This allows them to bypass learning complex processes from scratch, potentially unlocking genuine algorithmic reasoning. This approach involves adding memory, registers, and adaptive recurrence to a transformer architecture, similar to enhancing a basic computer. Researchers compiled algorithms directly into this differentiable library, allowing the LLM to leverage these pre-built functions for various tasks. Initial tests explored how well the model could adapt and combine library modules for novel challenges. Preliminary results suggest that while differentiability helps with fine-tuning, there are practical limits, especially when dealing with more complex, deep computations. However, even within these limits, the researchers had some interesting wins, like effectively teaching a small language model how to use a calculator. This research opens exciting doors to bridging the gap between symbolic programming and neural networks. Imagine LLMs not just generating text but genuinely reasoning, with verifiable, robust capabilities. It hints at a future where AI could grasp complex algorithms with far greater efficiency, potentially transforming fields like automated planning and complex problem-solving.