How Homgram
Works
High-performance compute acceleration via geometric canonicalization. Built on a two-torus lattice (48 × 256 cells) for O(1) modular arithmetic routing.
System Architecture
Data is mapped from linear memory arrays onto a two-torus lattice structure, enabling O(1) coordinate lookup through geometric canonicalization.
The Mathematical Core
A 96-class geometric system enables pattern-based canonicalization. The algebraic framework (⊕, ⊗, ⊙) provides the foundation for O(1) lookup operations.
96-Class System
Incoming data is phase-shifted into 96 disjoint resonance classes for efficient routing.
Character Table
A 194×194 matrix enables constant-time lookups, replacing traditional matrix multiplication.
Component Breakdown
The four pillars of the Homgram architecture that enable O(1) computation.
Resonance Filter
Incoming data is phase-shifted into 96 disjoint resonance classes to prevent collision.
Orbit Splitter
The prism effect. Data is routed into 32 parallel orbit tracks for efficient processing.
Character Table
The O(1) Core. A 194-dimensional lookup replaces traditional matrix multiplication.
Unit Group Hash
Instant multiplicative inverses are retrieved via group theory hash structures.
Compilation Pipeline
From circuit compilation to multi-backend execution. The Homgram Compiler canonicalizes operations while the runtime leverages CUDA, Metal, WebGPU, or CPU backends with O(1) runtime cost.
Computation Workflow
From circuit compilation to multi-backend execution. The Homgram Compiler canonicalizes operations, while the runtime leverages CUDA, Metal, WebGPU, or CPU backends with O(1) runtime cost and zero-copy efficiency.
Pre-computation
Outcomes are computed across 96 resonance classes
Runtime Lookup
~35ns execution: Hashing (~10ns) + Lookup (~25ns)
Multi-Backend Execution
Same circuit runs on CUDA, Metal, WebGPU, or CPU with O(1) performance
Performance Comparison
See how Homgram's O(1) architecture compares to traditional approaches.
Traditional O(n²)
Latency increases exponentially with context size. Processing time grows quadratically.
Homgram O(1)
Latency remains constant regardless of data load. ~35ns execution time.
Key Benefits
Framework Interoperability
Zero-copy data exchange with the ML and analytics ecosystem.
DLPack
Industry-standard tensor exchange protocol for zero-copy interoperability with ML frameworks.
Apache Arrow
Columnar memory format for efficient analytics and data processing integration.
# Zero-copy exchange with PyTorch
import torch
from Homgram import Tensor
# Create Homgram tensor
holo_tensor = Tensor.from_data([1.0, 2.0, 3.0])
# Export to PyTorch (zero-copy via DLPack)
torch_tensor = torch.from_dlpack(holo_tensor)
# Import from PyTorch
holo_back = Tensor.from_dlpack(torch_tensor)Language Bindings
Use Homgram from your preferred language. UniFFI generates type-safe bindings automatically from the Rust core.
Python
from Homgram import Executor, BackendType
exec = Executor.new(BackendType.CUDA)
buf = exec.allocate_f32(1024)
buf.copy_from([1.0] * 1024)
exec.run(circuit)TypeScript
import { Executor, BackendType } from 'Homgram';
const exec = new Executor(BackendType.WebGPU);
const buf = exec.allocateF32(1024);
await exec.run(circuit);Advanced Features
Production-ready capabilities for demanding workloads.
Automatic Differentiation
Built-in gradient tracking and backpropagation. Define forward pass, get gradients automatically.
Quantization
INT8/INT16 quantized operations for efficient inference. Reduce memory footprint.
Distributed Execution
Multi-GPU and multi-node execution with data, model, and pipeline parallelism.
Lazy Evaluation
Operation fusion engine defers execution to optimize the computation graph.
Extended Precision
Types from I256 to I4096 for arbitrary precision arithmetic.
Atlas ISA
50+ instruction set with transcendentals, reductions, and Atlas-specific operations.