How Hologram
Works
High-performance compute acceleration via geometric canonicalization. Built on a two-torus lattice (48 × 256 cells) and MoonshineHRM algebraic framework for \(O(1)\) modular arithmetic routing.
The Mathematical Core
The Monster Group's immense symmetry combined with a 96-class geometric system enables pattern-based canonicalization. The MoonshineHRM algebraic framework (⊕, ⊗, ⊙) provides the foundation for \(O(1)\) lookup operations.
Monster Group
The largest sporadic simple group with order ≈ 8×10⁵³ provides the mathematical foundation.
Griess Algebra
A 196,884-dimensional algebra where group operations live, enabling constant-time computations.
Component Breakdown
The four pillars of the Hologram 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.
Computation Workflow
From circuit compilation to multi-backend execution. The Hologram 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 Hologram's $O(1)$ architecture compares to traditional approaches.
Traditional \(O(n^2)\)
Latency increases exponentially with context size. Processing time grows quadratically.
Hologram \(O(1)\)
Latency remains constant regardless of data load. ~35ns execution time.
Key Benefits
Unit Groups & Hash Structures
Group theory hash structures enable instant multiplicative inverse retrieval. The mathematical elegance of unit groups provides the foundation for \(O(1)\) division operations.
“Complexity is in the mathematics, not the hardware. The same circuit runs on CUDA, Metal, WebGPU, or CPU with \(O(1)\) performance.”
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 hologram import Tensor
# Create Hologram 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 Hologram from your preferred language. UniFFI generates type-safe bindings automatically from the Rust core.
Crate Architecture
Python
from hologram 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 'hologram';
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 for training ML models.
Quantization
INT8/INT16 quantized operations for efficient inference. Reduce memory footprint and increase throughput.
Distributed Execution
Multi-GPU and multi-node execution with data, model, and pipeline parallelism strategies.
Lazy Evaluation
Operation fusion engine defers execution to optimize the computation graph before running.
Extended Precision
Types from I256 to I4096 for arbitrary precision arithmetic in cryptographic and scientific applications.
Atlas ISA
50+ instruction set with transcendentals, reductions, and Atlas-specific operations for \(O(1)\) execution.