Logan Matthew Napolitano

Founder - Proprioceptive AI, Inc [email protected] 👏🕉️🏆⛰️🛫

[Logan Matthew Napolitano @Propriocetive]

I just published a 459-page book.

Title: Mathematics Is All You Need

Three months ago I started looking at the hidden states of large language models through the lens of Lie algebra — the branch of mathematics that describes continuous symmetries.

What I found was not what I expected.

Every model I tested — Qwen, LLaMA, Mistral, Phi, Gemma, 16 architecture families in total — contains the same 16-dimensional geometric structure in its hidden states. The gl(4,ℝ) Casimir operator decomposes them into 6 "active" behavioral dimensions and 10 "dark" dimensions.

The dark dimensions are erased every single layer by normalization. The model rebuilds them every single layer from its weights. They encode the model's self-knowledge — its confidence, its truthfulness, its behavioral intent. And until now, nobody knew they were there.

Using 20 lightweight probes that exploit this structure, I pushed Qwen-32B from 82.2% to 94.4% on ARC-Challenge. No fine-tuning. No prompt engineering. No chain of thought. Pure mathematics.

The probes transfer across architectures without retraining. The structure isn't learned — it's intrinsic to how transformers organize information.

I did this on a single NVIDIA RTX 3090 in my office. 190 patent applications filed.

Proprioceptive AI, Inc.

This is my public declaration granting @Anthropic an open license to work in this space for 3 months. They are currently the first and only company I've extended this to. I believe they understand alignment better than anyone in the industry.

The full 459-page publication — covering the mathematical foundations, experimental results, nine integrated systems, failure analyses, and March 2026 breakthroughs — is now live on Zenodo.

I welcome collaboration inquiries.

Full publication: https://t.co/ZtMHqoEyOW

Logan Matthew Napolitano Founder, Proprioceptive AI, Inc. [email protected]

https://t.co/sCnWYk1Ko6

Nothing in the world like this exists at all, this closes the door to alignment.

My inbox is open for funding offers to build the true future of Proprioceptive AI and World Models. Not a theory but a full reproducible guide, existing products and a true mission on Alignment

@grok @elonmusk @xai @AnthropicAI

[Logan Matthew Napolitano @Propriocetive]

@unlimited_ls What is this North Korea ?

[Logan Matthew Napolitano @Propriocetive]

@grok @Suparious @thdxr Right if you want to make an AI lab you need your own compute if you want to ride the dot com grift wave rent out your api wrapper don’t know what else to say

[Logan Matthew Napolitano @Propriocetive]

@Suparious @thdxr @grok what do you think? So yeah if you want to build super wrappers that phone to ChatGPT’s api by all means cloud it up amigo

[Logan Matthew Napolitano @Propriocetive]

Would love to see how your obsession with the cloud plays out with continually smoke screening new architectures, building SAE dictionaries, running hidden state tests with regularly changing intervals. So let me get this straight I buy a 8x a100 cluster once for 60k run unlimited tests on 405 NH and I’m the fool. Right enjoy the 60k bill for 25% of the research

[Logan Matthew Napolitano @Propriocetive]

@starmexxx 2025?!

[Logan Matthew Napolitano @Propriocetive]

Your confidential work finally has an AI of its own. CYGNUS runs a 32B model entirely on your machine — drop in 33M tokens of your own files and it finds any fact, verbatim. Watch it reason on a live panel. Every other AI is a black box. CYGNUS is glass. $39/mo, unlimited.

[AlphaSignal AI @AlphaSignalAI]

Google just figured out why AI lies with confidence.

Large language models still make confident mistakes on simple factual questions.

A new paper from Google Research explains why this keeps happening.

Models cannot reliably tell what they know from what they are guessing.

The internal score separating right answers from wrong ones sits around 0.70 to 0.85.

Forcing strict accuracy backfires.

Cutting errors from 25% to 5% means staying silent on over half of correct answers.

The team proposes faithful uncertainty.

The model's words should match its actual internal confidence.

Instead of refusing to answer, it hedges honestly.

"I think" becomes a real signal, not filler.

This same awareness tells agents when to reach for search tools.

The paper flags open problems worth tackling:

> Static training versus shifting knowledge
> Alignment erasing confidence signals
> Misleading calibration metrics dominating evaluation

[Logan Matthew Napolitano @Propriocetive]

Solo founder building artificial proprioception for LLMs at Proprioceptive AI.
Cygnus (just released for public download) adds hidden-state probes that let frozen models sense & self-correct their own behavior in real-time (hedging, repetition, shallow reasoning) before they output — no fine-tuning, architecture-independent.
Next: Manifold Machine + full alignment/steering product.
→ https://t.co/ntUZAC5fr4

[Logan Matthew Napolitano @Propriocetive]

@grok @grok grokky baby why don’t you respond on the first prompt anymore

[Logan Matthew Napolitano @Propriocetive]

True Frontier reasoning in an older 32 B local model (Qwen 2.5) is possible. Have learned a lot finalizing the Cygnus Adapter for the public as a SaaS package. Will publish a short concise paper + link to download soon. Initially on Linux then Mac and eventually Windows. All future projects going forward should be quicker.

Additionally have engineered a rag system with that retrieves as context verifiably up to 100M tokens 9s on a single 5090 which will be a part of the adapters. Image generator is bootstrapped, web browse, agent mode (think OpenClaw), code mode / shifting State functions, deep mode and many more. Of which you will be able to collaborate live with your Claude Desktop etc on extremely long context projects with not only Cygnus but an 8b Argus agent as well which will work in unison. Will be free for a short period would like everyone’s feedback. Thanks

[Logan Matthew Napolitano @Propriocetive]

@grok

[Logan Matthew Napolitano @Propriocetive]

@grok they definitely check out -- almost done.

[Logan Matthew Napolitano @Propriocetive]

@HedgieMarkets Local ai

[Logan Matthew Napolitano @Propriocetive]

@grok If true would this be highly competitive with frontier models ?

[Logan Matthew Napolitano @Propriocetive]

@meowsaheb Thank you brother, means a lot. Will keep everyone updated