What if spacetime itself - the fabric of our reality - could be formulated as a neural network?

In 2021, physicist Lee Smolin, Jaron Lanier, and others published a paper, The Autodidactic Universe, with a claim: write Einstein's general relativity in a specific form (the Plebanski equation), and the equations governing spacetime curvature correspond to the equations of a Restricted Boltzmann Machine (RBM).

I had to read that sentence three times.

The trick is to bridge the gap using a common language - matrices. In physics, N×N matrices are used to describe gauge fields and matter fields, and when N→∞, can be used to describe continuous spacetime and quantum fields. In machine learning, matrices represent the weights in the neural network, determining how information flows between the layers.

Here's the correspondence:

PLEBANSKI GRAVITY                  RESTRICTED BOLTZMANN MACHINE
───────────────────────────────────────────────────────
Quantum matter fields           ↔   Network layers
Quantum gauge, gravity fields   ↔   Network weights  
Evolution of the law over time  ↔   Learning (updating weights)

The implication: the very structure of spacetime itself might have been learned over time, and is fundamentally learnable. Taking this further, the authors of the paper argue that the nature of our universe is one in which physical laws (like gravity) are learnable.

Note: I am not a physicist, so I recommend reading the original paper and/or talking to my NotebookLM notebook to query the paper to gain a deeper understanding.

The Caveat

This isn't an equivalence - the paper clearly states so.

The correspondence only works when you reduce continuous spacetime to finite matrices. Physical gravity requires taking those matrices to infinity (N→∞). The neural network at N→∞ is a different beast.

Despite this, harmony between two domains that have no business rhyming is still remarkable.

How the Universe Learns

But what does it even mean for a universe to "learn"?

Think of a river carving a canyon. The water molecules are fast variables - they rush and swirl, their paths dictated by the riverbed. The canyon walls are slow variables - to the water, they appear as fixed "laws" governing where it can flow. But in truth, the canyon wall is anything but fixed. Zoom out to geological timescales, and we see that it evolves over time, and this evolution is dictated by the movement of the water molecules.

The canyon is what the authors call a consequencer - a structure that allows the past to impact the future by accumulating information over time. As they put it: "The consequencer is no more and no less than the information that must change when learning occurs".

In neural networks, we can see weights serving as the consequencer. While training, billions/trillions of data points flow through the system (fast variables), while the weights (slow variables) change over time to cement patterns. In each individual run, to the data, the weights appear to be (and are!) fixed constructs governing how information flows. Zoom out to the epoch level though, it becomes clear that the "laws" (weights) are learning over time, and encoding information into its structure.

The authors of the paper suggest that the structure of the universe works similarly, with geometry itself as the consequencer.

            creates
    MATTER ─────────► GEOMETRY
       ▲                  │
       │                  │
       │    tells how     │
       └───── to move ────┘

Matter shapes geometry; geometry constrains matter; the cycle repeats. Each loop encodes information from the past into the structure of spacetime itself.

An Autodidactic View of the Universe

If our universe truly is autodidactic (self learning), it may help answer a crucial question in physics: why do we have the laws that we do?

For those with an Anthropic viewpoint, an argument may be: the fact that we're here to observe the laws is sufficient reason alone - if they were different, we wouldn't exist to even ask the question.

Alternatively, the Autodidactic Universe answers that laws exist because the universe learned them over time as an answer to a cost function - one that prioritizes stability or variety.

The "over time" part is crucial. In Smolin's Time Reborn, he argues, against modern physics, for the reality of time. If instead, as Einstein proposed in Special Relativity, time is unreal, then the concept of learning over time fundamentally doesn't make sense.

What this can tell us about AI

If learning is a fundamental to reality itself - if the universe has been doing "gradient descent" for the past 13 billion years - then perhaps the tools we're building might not be as artificial as the name suggests.

AI certainly isn't (and can never truly be) human - no matter how much tech executives would like you to believe otherwise.

But just because it isn't human, doesn't mean it isn't natural.

The tools (like Claude), which helped me research this topic and proofread this post - that we're collectively spending trillions to build - may be yet another case of humanity "rediscovering" systems that Nature has honed over eons, morphing them for our economic and societal gain.

This raises questions we're not yet asking: What can physics' unsolved problems (e.g. quantum gravity) teach us about scaling AI? Should AI architecture evolve to mirror cosmological principles?

Might the next big leap in the AI arms race come from cosmological physics instead of computer science? Time will tell.

— Ben

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References

• The Autodidactic Universe and associated NotebookLM
• Smolin's Time Reborn (2013) for general readers on evolving laws. Fascinating read to challenge our assumptions about time and the universe as a whole
• Kurzgesagt video about JWST discoveries causing a "crisis" in cosmological physics that inspired this rabbit hole