Trijna Labs — Holonomy-Inspired Foundation Model Architecture

01 / Path-Dependent State Engineering

Holonomy-Inspired. Mathematically Grounded.

In differential geometry, holonomy describes how a vector changes when transported along a path to the final state depends on the route taken.

We have borrowed this intuition. Our core state vector $S$ evolves via a linear recurrence in the frequency domain. Because the state accumulates the entire input history, the resulting representation is coherently path-dependent conceptually similar to parallel transport in curved space.

A note on our implementation

We do not compute a connection 1-form or curvature 2-tensor. We use complex linear projections in Fourier space to mix frequency bands together structurally analogous to a gauge transformation, not a literal geometric one. We use the term "holonomy-inspired" to convey the intuition behind the design, not to claim an implementation of physical field theory.

02 / Why This Matters

Three properties of the architecture.

01

Byte-Level Processing

Implemented & Tested

The architecture ingests raw UTF-8 byte sequences directly, without a tokenizer step, tried in one of our model which preserves the full nuance of Indic scripts and other languages without artificial subword splitting into a hard-coded architectural reality and not a roadmap item.

02

Linear-Time Recurrence

( Benchmarking Underway)

Transformers scale quadratically with context length via self-attention. Our recurrence is designed for linear-time scaling with context length.

03

Sparse Ternary Weights

Implemented & Validated · Cache Optimization Ongoing

The architecture uses ternary (2-bit) weights for low-power inference, aimed at efficient deployment on domestic infrastructure. Implemented and validated in hardware trials, with ongoing cache-level optimization.

03 / Our Technical Philosophy

Building With Integrity.

What we've built is a frequency-domain, linear state-space recurrence with path-dependent memory. We welcome technical scrutiny of the underlying linear algebra and complexity claims.

We are building a foundation model architecture that is:

Sovereign AI
Engineered in Bharat, for Bharat's linguistic and computational needs and designed to run on accessible hardware rather than large server farms.

04 / Visual Strategy

How the architecture looks.

Inspiration

Path-Dependent Transport

Curved manifold, vector transported along a loop. The final vector depends on the route the mathematical intuition behind our state recurrence.

Reality

Frequency-Band Mixing

Frequency-domain diagram showing bands mixing via complex projections. This is what the implementation actually computes FFT, gauge weights, IFFT.

Benefit

Accumulated Path-Memory

Side-by-side: Transformer's sliding window versus Trijna's accumulating state vector $S t$ growing with context, enabling longer-horizon reasoning.

AI democratized and research that puts Bharat first.