The Hierarchical Reasoning Model (HRM) introduces a biologically inspired recurrent architecture designed to overcome the reasoning limitations of standard Transformers and Chain-of-Thought (CoT) prompting. Comprising two interdependent modules—a slow, high-level planner and a fast, low-level executor—HRM achieves deep computational reasoning in a single forward pass without pretraining or intermediate supervision. With just 27M parameters and 1,000 training examples, it surpasses much larger models on benchmarks like ARC-AGI, Sudoku-Extreme, and Maze-Hard, demonstrating near-perfect accuracy on tasks that typically require symbolic search and backtracking.

We’ve all heard of recurrent neural networks (RNNs), the workhorse of sequence modeling for decades. RNNs explicitly model sequences by maintaining a hidden state that evolves over time, allowing the network to ‘remember’ information from previous inputs. But recurrence isn’t limited to RNNs. In fact, there are many ways that modern models implement some form of recurrence, often in unexpected ways.

ARC-AGI-3 is the latest challenge in Francois Chollet’s ARC Prize. While currently still under development, the authors released a sample of the challenges and are running a small competition. In this post I’d like to discuss my attempt at ‘hand-writing’ some solutions and what it told me about a real solution. If you’d like to know more about the ARC-AGI-3 challenge, I previously wrote about it here.

When we write code we typically leverage something like Git or Mercurial to track changes we make to files. These systems make it easy to see what has changed at a glance without picking through every line of code. Personally, I use VSCode’s Git integration. But who writes code themselves these days? When producing code with LLMs we still want to be able to track diffs easily.

I’ve been a long-time user of Notion for knowledge management. For reference, I have around 1000 pages covering various topics from physics, to sports, to dreams and aspirations. I manage my to-do lists there, travel plans and goal tracking. It’s a terrific visual tool and readily accessible everywhere. But I want more.

Recently I ran an experiment in which I tried to get LLMs to output explicit world models in the form of Python code which could be used as the core of a MCTS policy for control in basic gymnasium environments. This is different to typical world model learning which would be something like a parameterised neural network. The reason why we would care about something like this is for on-the-fly reasoning, such as in ARC-AGI-3 where agents must act in a completely new environment.