Independent AI research lab

New methods for how networks are built and trained.

Mathalyse develops optimisers and architectures, and the mathematics that explains why they work. Each method starts from a mechanism, and each claim is sized to its evidence.

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Gradient descentloss

Momentumloss

Adamloss

Three optimisers released from the same point on one non-convex loss surface. The deepest well sits to the right of centre. The update rule decides which well each run reaches. Click the surface to release all three from a new point.

Research areas

Three lines of work that share one habit: derive the method from a mechanism, then test it against strong baselines.

Optimisers

Update rules built from an explicit account of what gradient noise, curvature and step size do to training. Every optimiser is evaluated against the strongest published competitors, including our own earlier ones.

Released: ThermoLion.

Architectures

Attention and sequence models analysed with tools from signal processing and quantum physics. The aim is to say what an architecture can represent before training it.

Theory of learning

Statistical mechanics and gauge theory applied to deep learning. Results are stated as theorems with proofs, with experiments kept to what the argument needs.

Released work

Papers that are publicly available. New releases are added here.

Preprint

Unifying Sign and Magnitude for Optimizing Deep Vision Networks via ThermoLion

Ahmed Nebli. arXiv:2512.01881, December 2025.

Read on arXiv

People

A small lab, open to collaborators.

Ahmed Nebli

Founder

Computer scientist working on optimisation, sequence models and the theory of deep learning.

Mathalyse welcomes collaborators in optimisation theory and sequence modelling, and students looking for a well-posed problem to work on. Send a message and a CV.