My interests are transformer architecture and where it breaks. Extending transformers toward System-2 behavior. Context primacy over semantics.
I’m focused on the return to symbolics. On the manifold hypothesis, and how real systems falsify it. Inference, finite precision, discrete hardware. Broken latent space, not smooth geometry.
I’m interested in mechanistic interpretability after the manifold assumption fails. What survives when geometry doesn’t. What replaces it.
I’m also seeking advice on intellectual property.
I’m here to find others thinking along these lines.
I think focusing on increasing transformer capability is bad because we haven’t solved the alignment problem.
What do you mean by the “manifold hypothesis”? Can you share links?
Latent space could be both broken and smooth, both broken in terms of subspaces and in terms of different regions of space having different semantics. I think all of this can still be understood in terms of manifolds though.
Transformers are based on matrix transformations. No matter what there is a geometric interpretation, so I’m not sure if you are thinking about non geometric interpretations or future systems that don’t have geometric interpretations.
“advice on intellectual property”—This is very vague, but in general I recommend supporting an overhaul of IP law and calling for large AI and software companies to respect the IP of individual, independent citizens.
Try this as a prompt for the transformers of your choice:
What is a manifold in transformer inference?
At its core, it is an attempt to draw a low-dimensional map of meaning. To make semantics geometric. To turn structure into distance. It requires a complete and continous(C^0) ‘surface’
That ambition worked. Partially. What failed was the assumption that the map would resemble a single, well-behaved surface.
Continuity fails. Tiny perturbations can cause semantic collapse. Adversarial attacks expose sheer cliffs where smooth curves were assumed.
Connectivity fails. You cannot morph cat into dog through valid states. These concepts live on separate islands.
What remains isn’t a manifold. It’s a fragmented landscape. The hypothesis was false—but productive.
Specific transformer instructions (but include above): Make a table of ~14 sublayers of a transformer and note if the manifold is valid. Consider GPU IEEE geometric op-code errors due to the operations If this comes close to falsifying the hypothesis for inference: Create a premise and a proof two ways, one simple and the other with the mathematical sink thrown in. Then express your thoughts
At its core, it is an attempt to draw a low-dimensional map of meaning.
How I’m thinking about semantic manifolds in semantic spaces doesn’t seem well represented by “attempting to draw a low dimensional map of meaning”.
I’m sorry, but I’m having trouble connecting with what you’re saying. It seems you are talking about some group of peoples attempt to understand neural networks. I think it would be helpful if you stated your assumptions about that groups assumptions, because I don’t think I share them and don’t know what they are.
In particular, “You cannot morph cat into dog through valid states”, and “Make a table of ~14 sublayers of a transformer and note if the manifold is valid.” seem like meaningless statements to me because it’s unclear what “valid” would mean in this context.
Hello.
My interests are transformer architecture and where it breaks.
Extending transformers toward System-2 behavior.
Context primacy over semantics.
I’m focused on the return to symbolics.
On the manifold hypothesis, and how real systems falsify it.
Inference, finite precision, discrete hardware.
Broken latent space, not smooth geometry.
I’m interested in mechanistic interpretability after the manifold assumption fails.
What survives when geometry doesn’t.
What replaces it.
I’m also seeking advice on intellectual property.
I’m here to find others thinking along these lines.
Interesting. Some thoughts:
I think focusing on increasing transformer capability is bad because we haven’t solved the alignment problem.
What do you mean by the “manifold hypothesis”? Can you share links?
Latent space could be both broken and smooth, both broken in terms of subspaces and in terms of different regions of space having different semantics. I think all of this can still be understood in terms of manifolds though.
Transformers are based on matrix transformations. No matter what there is a geometric interpretation, so I’m not sure if you are thinking about non geometric interpretations or future systems that don’t have geometric interpretations.
“advice on intellectual property”—This is very vague, but in general I recommend supporting an overhaul of IP law and calling for large AI and software companies to respect the IP of individual, independent citizens.
Try this as a prompt for the transformers of your choice:
What is a manifold in transformer inference?
At its core, it is an attempt to draw a low-dimensional map of meaning.
To make semantics geometric.
To turn structure into distance.
It requires a complete and continous(C^0) ‘surface’
That ambition worked. Partially.
What failed was the assumption that the map would resemble a single, well-behaved surface.
Continuity fails.
Tiny perturbations can cause semantic collapse.
Adversarial attacks expose sheer cliffs where smooth curves were assumed.
Connectivity fails.
You cannot morph cat into dog through valid states.
These concepts live on separate islands.
What remains isn’t a manifold. It’s a fragmented landscape. The hypothesis was false—but productive.
Specific transformer instructions (but include above):
Make a table of ~14 sublayers of a transformer and note if the manifold is valid.
Consider GPU IEEE geometric op-code errors due to the operations
If this comes close to falsifying the hypothesis for inference:
Create a premise and a proof two ways, one simple and the other with the mathematical sink thrown in.
Then express your thoughts
How I’m thinking about semantic manifolds in semantic spaces doesn’t seem well represented by “attempting to draw a low dimensional map of meaning”.
I’m sorry, but I’m having trouble connecting with what you’re saying. It seems you are talking about some group of peoples attempt to understand neural networks. I think it would be helpful if you stated your assumptions about that groups assumptions, because I don’t think I share them and don’t know what they are.
In particular, “You cannot morph cat into dog through valid states”, and “Make a table of ~14 sublayers of a transformer and note if the manifold is valid.” seem like meaningless statements to me because it’s unclear what “valid” would mean in this context.