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We study what drives AI behavior so we can steer it as it grows more powerful.

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ⵟ — Explore the YAT field

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// OUR RESEARCH

A kernel theory of how models compute

What makes a neuron respond? What can a layer represent? What information can survive through depth? YAT gives us a mathematical way to ask these questions.

YAT KERNEL

ⵟ(x, w) = (x·w + b)² / (‖x − w‖² + ε)

YAT scores an input against a learned center using both alignment and distance. At a fixed alignment, greater distance weakens the response. Along some directions, alignment can sustain a response even far from the center. The gravity well gives a visual intuition for this geometry.

01 / Neuron Explain the response
The kernel separates the role of alignment from the role of distance. That gives us a mathematical reason why inputs can activate the same unit, even when they are far apart.
02 / Layer Describe what it can represent
With shared positive bias and regularization, a YAT layer is a weighted sum of kernel responses. The theory gives that layer an exact function-space norm and characterizes what the kernel can approximate.
03 / Depth Explain what can carry forward
Once earlier layers are fixed, they induce a kernel on the original inputs. If those layers map two inputs to the same representation, the next layer cannot distinguish them.

Research papers

From the mathematics of YAT to faster attention and kernel approximations.

  1. 01 / Foundations

    A Universal Reproducing Kernel Hilbert Space from Polynomial Alignment and IMQ Distance

    Taha Bouhsine

    Introduces the YAT kernel and shows what changes when a model uses both alignment and distance to compare inputs.

    Read on arXiv ↗ Paper checkpoints ↓
  2. 02 / Attention

    SLAY: Geometry-Aware Spherical Linearized Attention with Yat-Kernel

    Jose Miguel Luna, Taha Bouhsine, Krzysztof Choromanski

    Uses YAT geometry to build attention that scales linearly with sequence length.

    Read on arXiv ↗ Research summary →
  3. 03 / Approximation

    Bernstein–Schur Kernels: Random Features by Sketched Modulation and Radial Randomization

    Taha Bouhsine

    Approximates kernel computations with compact random features so they can be used on larger datasets.

    Read on arXiv ↗

// THE PROBLEM

The same answer can hide different computations

▶ The Black Box Problem

When a model completes “the capital of Mexico is,” the answer tells us what it predicted. To understand how it got there, we need to know which features it used and which paths carried those signals to the output.

Prompt"the capital of Mexico is"
Output▋
· · · more layers above · · · · · · more layers below · · · BLACK BOX illustrative network INPUT HIDDEN LAYERS OUTPUT
Why tracing is hard: A neuron can respond to several features, and one feature can be spread across many neurons. An activation alone gives us a clue about the computation.

// TESTING A CIRCUIT EXPLANATION

From a mathematical explanation to a circuit test

The kernel describes what a unit responds to. To find out whether that response matters for a particular answer, we can test a candidate path. Take the Mexico prompt above and suppose a path carries information about the country.

01 / Trace Follow the signal
Compare the Mexico prompt with the same prompt about Peru. Look for a path whose activity tracks the country as the rest of the sentence stays fixed.
02 / Intervene Swap the activation
Run the Mexico prompt again and patch the candidate component with its activation from the Peru run. Compare how the scores for Mexico City and Lima shift.
03 / Validate Check what travels
Compare with a patch on an unrelated component, then repeat across countries and phrasings. A repeatable, selective shift would support the circuit hypothesis.

What this opens up. The same experiment can test whether a shortcut drives a failure, whether a circuit survives fine-tuning, or whether a targeted edit changes the intended behavior without disturbing nearby capabilities.

// OUR APPROACH

From neuron responses to circuits

⬡ WHITE BOX Tracing Neuron Activation
Prompt"the capital of Mexico is"
Output▋
· · · interpretable by design · · · INPUT INTERPRETABLE LAYERS (3) OUTPUT

This illustration follows the same prompt through a small network. In a trained model, a trace would give us a candidate circuit. We would then intervene on its components and measure how the prediction changes.

Locate
Find components whose responses are relevant to the behavior.
Trace
Follow how their responses combine across layers.
Test
Perturb a component and compare the result with a baseline.
Design
Use those findings to build models that are easier to inspect.

// WHO WE ARE

The Founding Team.

The team brings together kernel research and experience building AI products.

Taha Bouhsine

Taha Bouhsine

Co-Founder & CEO

AI RESEARCHER GOOGLE DEV 2× FOUNDER

AI Google Developer Expert and architect of the Physics Grounded AI framework. Mathematician, computer scientist, and electrical engineer researching interpretable, efficient neural networks, representation learning, and the geometry of how models understand the world. Builds rigorous, explainable AI from first principles.

Jose Miguel L.

Jose Miguel L.

Co-Founder & CPO

EX-APPLE COLUMBIA MBA + MS AI/ML

Ex-Apple Engineering Product Manager for AI/ML products. Founding team at YC-backed startup, leading Product, Data and Tech teams. Schwarzman Scholar and Columbia MBA + MS in AI/ML.

// HUGGING FACE

Models and checkpoints

Browse language and embedding models from mlnomad, or pick a checkpoint to reproduce a paper run.

Multilingual encoders

GOAT and YAT mmBERT releases for masked language modeling, text embeddings, and retrieval.

Model cards and usage instructions.

YAT paper checkpoints

Matched 261M language models, seed 0. Each link opens the exact revision cited in the paper.

Appendix G of the YAT paper links all 15 runs, with checkpoint revisions and training and evaluation records.

Browse all models Paper checkpoint index Open the FlaxChat Space