amari-gpu

GPU acceleration for Amari mathematical computations using WebGPU.

Overview

amari-gpu is an integration crate that provides validated GPU-backed implementations of mathematical operations from Amari domain crates. It follows the progressive enhancement pattern: operations fall back to CPU computation when GPU is unavailable or when benchmark data shows CPU is preferable, scaling to GPU acceleration for larger workloads where the current kernels are known to help.

For the 0.20.0 release line, the crate is positioned as a correctness-first, hardware-validated GPU backend with conservative adaptive dispatch. Not every GPU-backed path is GPU-recommended by default; benchmark/crossover data is used to keep public claims and dispatch behavior honest.

Architecture

As an integration crate, amari-gpu consumes APIs from domain crates and exposes them to GPU platforms:

Domain Crates (provide APIs):
  amari-core → amari-measure → amari-calculus
  amari-info-geom, amari-relativistic, amari-network

Integration Crates (consume APIs):
  amari-gpu → depends on domain crates
  amari-wasm → depends on domain crates

Dependency Rule: Integration crates depend on domain crates, never the reverse.

Current Integrations (v0.19.1)

Implemented GPU Acceleration

Domain Crate	Module	Operations	Status
amari-core	crate root	`GpuCliffordAlgebra` GPU batch geometric products; `AdaptiveCompute` Cl(3,0,0) CPU/GPU helper	⚠️ GPU-backed core v1 with public baseline tests
amari-info-geom	crate root	`GpuInfoGeometry` CPU-baseline Amari-Chentsov, Fisher, and KL/Bregman operations after GPU context creation	⚠️ GPU-ready CPU-baseline v1
amari-relativistic	`relativistic`	Minkowski norm-squared and simplified geodesic propagation	⚠️ GPU-backed narrow v1
amari-network	`network`	Narrow GPU vector-distance path with mixed centrality/clustering	⚠️ GPU-backed for vector-only `Cl(P,0,0)`, `P <= 3`
amari-measure	`measure`	1D integration, Monte Carlo, Gaussian densities, tropical/multidim scaffolding	⚠️ Mixed GPU-backed + documented CPU fallback (feature: `measure`)
amari-calculus	`calculus`	Field evaluation, gradients, divergence, curl	⚠️ GPU-ready CPU-semantic fallback (feature: `calculus`)
amari-dual	`dual`	Narrow GPU-backed unary forward-AD v1 surface	⚠️ Narrow v1 restored; broader gradients/training private/redesign-pending (feature: `dual`)
amari-enumerative	`enumerative`	High-use GPU kernels for WDVV, matroids, localization, CSM, operad, stability	⚠️ Broad GPU-backed surface with representative public tests (feature: `enumerative`)
amari-automata	`automata`	GPU rule application/energy kernels, CPU neighborhood fallback	⚠️ Mixed GPU-backed + documented CPU fallback (feature: `automata`)
amari-fusion	`fusion`	Reduced first public surface for holographic/fusion-derived GPU operations	⚠️ Partially restored; broader fusion GPU API still under redesign
amari-holographic	`holographic`	Holographic memory, batch binding, similarity matrices, optical field operations	✅ Implemented (feature: `holographic`)
amari-probabilistic	`probabilistic`	Gaussian sampling, batch statistics, Monte Carlo	✅ Implemented (feature: `probabilistic`)
amari-functional	`functional`	GPU matrix batch ops, Hilbert batches, CPU spectral/fallback paths	⚠️ Mixed GPU-backed + documented CPU fallback (feature: `functional`)
amari-topology	`topology`	GPU distance/Morse kernels, CPU Rips/Betti fallback paths	⚠️ Mixed GPU-backed + documented CPU fallback (feature: `topology`)

Current Hardware Validation

Focused hardware validation has completed on both DGX Spark / NVIDIA GB10 and NVIDIA GeForce RTX 5080 Laptop GPU. See:

docs/roadmap/AMARI_GPU_GB10_HARDWARE_VALIDATION.md
docs/roadmap/AMARI_GPU_RTX5080_HARDWARE_VALIDATION.md

Current status:

Focused public API tests passed for default/core/info-geometry, network, relativistic, holographic, tropical, fusion, calculus, measure, functional, topology, dual, automata, probabilistic, GF(2), enumerative, and infra APIs.
cargo +stable test -p amari-gpu --all-features --quiet -- --test-threads=1 passed on GB10.
WGPU_BACKEND=vulkan cargo +stable test -p amari-gpu --all-features --quiet -- --test-threads=1 passed on RTX 5080.
RTX 5080 validation should use WGPU_BACKEND=vulkan and serial aggregate execution on the current Ubuntu 25.10 laptop stack.
Initial GB10 and RTX 5080 benchmark/crossover measurements plus manual harness commands are recorded in docs/roadmap/AMARI_GPU_BENCHMARK_CROSSOVER_REPORT.md; this covers core GA, tropical, holographic/optical, GF(2), probabilistic, topology, automata, measure, functional, and network paths.

GPU-backed vs GPU-recommended posture

Initial GB10 and RTX 5080 benchmarks show that GPU acceleration is workload- and hardware-dependent. The table below distinguishes paths that have real GPU kernels from paths that should currently be preferred by adaptive/default dispatch.

Path	GPU-backed?	GPU-recommended by default?	Current guidance
Core GA batch geometric product	yes	above threshold	Cross-hardware win at medium/large batch sizes; conservative threshold should account for RTX 5080 crossing between batch `64` and `256`.
Tropical dense matrix multiply	yes	large matrices only	Strong large-matrix win; RTX 5080 crosses later than GB10, so keep threshold conservative.
Tropical attention scores	yes	no	Correctness-restored, but no crossover through `256×256` in initial sweeps.
Holographic ProductCl3x32 similarity	yes	above threshold	Cross-hardware win for larger batches; RTX 5080 crosses around batch `512`.
Holographic ProductCl3x32 bind	yes	no/adaptive only	No crossover through batch `2048` in initial sweeps.
Optical holographic operations	yes	not yet classified	GPU timings exist; CPU baseline timings are still needed.
GF(2) fixed-layout kernels	yes	no	CPU bit operations dominate through the tested batch sizes.
Probabilistic sampling/statistics	yes	no	Current mean/variance paths approach parity only at large sizes; deterministic sampling remains CPU-preferred.
Topology distance matrix	yes	hardware-sensitive	GB10 crosses between `64` and `256` points; RTX 5080 did not cross through `512`.
Measure integration/density	yes	large batches only/adaptive	GB10 crosses at large sample/value counts; RTX 5080 approaches parity without crossing in the initial sweep.
Functional matrix apply	yes	large batches only/adaptive	GB10 reaches parity near batch `4096`; RTX 5080 approaches but does not cross there.
Automata rule/energy	yes/mixed	no	Rule application approaches parity at large sizes; CPU remains preferred for now.
Network distances/centrality/clustering	yes/mixed	no	No crossover through `256` nodes in the current public path.

Temporarily Disabled Modules

Domain Crate	Module	Status	Reason
amari-fusion	`fusion`	⚠️ Partially restored	Reduced public surface is available; broader fusion GPU API remains redesign-pending
amari-tropical	`tropical`	⚠️ Narrow v1 surface restored	Crate-root re-exports are available for `TropicalGpuOps`, `TropicalExecutionPath`, `TropicalGpuError`, `TropicalGpuResult`; broader module internals remain redesign-pending

Note: amari_gpu::tropical is still not re-enabled as a full public module. The current public tropical restoration is a narrow crate-root surface intended for dense tropical matrix multiplication and adaptive CPU/GPU dispatch.

Features

[features]
default = []
std = ["amari-core/std", "amari-relativistic/std", "amari-info-geom/std"]
webgpu = ["wgpu/webgpu"]
high-precision = ["amari-core/high-precision", "amari-relativistic/high-precision"]
measure = ["dep:amari-measure"]
calculus = ["dep:amari-calculus"]
dual = ["dep:amari-dual"]
enumerative = ["dep:amari-enumerative"]
automata = ["dep:amari-automata"]
fusion = ["dep:amari-fusion"]
holographic = ["dep:amari-holographic"]  # Holographic memory GPU acceleration
probabilistic = ["dep:amari-probabilistic", "dep:rand", "dep:rand_distr"]  # Probabilistic GPU acceleration
fusion = ["dep:amari-fusion"]  # Reduced first public surface available; broader API still redesign-pending
topology = ["dep:amari-topology"]  # Computational topology GPU acceleration
tropical = ["dep:amari-tropical"]  # Narrow crate-root public v1 surface available; broader internals remain redesign-pending

Usage

Basic Setup

use amari_gpu::unified::GpuContext;

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    // Initialize GPU context
    let context = GpuContext::new().await?;

    // Use GPU-accelerated operations
    // ...

    Ok(())
}

Calculus GPU-Ready API (CPU-semantic fallback in 0.20.0)

use amari_gpu::calculus::GpuCalculus;
use amari_calculus::ScalarField;
use amari_core::Multivector;

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    // Initialize calculus GPU context and pipeline scaffolding
    let gpu_calculus = GpuCalculus::new().await?;

    // Define a scalar field (e.g., f(x,y,z) = x² + y² + z²)
    let field = ScalarField::new(|pos: &[f64; 3]| -> f64 {
        pos[0] * pos[0] + pos[1] * pos[1] + pos[2] * pos[2]
    });

    // Batch evaluate through the amari-gpu API.
    // Current 0.20.0 behavior preserves CPU semantics while WGSL kernels are validated.
    let points: Vec<[f64; 3]> = generate_point_grid(100, 100); // 10,000 points
    let values = gpu_calculus.batch_eval_scalar_field(&field, &points).await?;

    // Batch gradient computation currently uses the CPU finite-difference baseline.
    let gradients = gpu_calculus.batch_gradient(&field, &points, 1e-6).await?;

    Ok(())
}

Dual Number GPU Operations (narrow v1 surface)

The dual feature exposes a narrow crate-root public surface for element-wise unary forward-mode AD:

Type / operation	Current 0.20.0 behavior
`DualGpuOps::batch_forward_ad()`	GPU-backed unary operation chains over `DualNumber<f32>` batches
`GpuDualNumber`	POD transfer representation for `DualNumber<f32>`
`DualOperation::{Sin,Cos,Exp,Log,ReLU,Sigmoid,Tanh,Square,Sqrt}`	supported unary operations
`DualOperation::{Add,Multiply}`	retained for API continuity but rejected until binary/broadcast semantics are designed

The full historical amari_gpu::dual module is no longer public. Neural-network gradients, vector-function gradients, optimization scaffolding, and generic multi-dual GPU traits are internal redesign-pending implementation details.

use amari_dual::DualNumber;
use amari_gpu::{DualGpuOps, DualOperation};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut gpu = DualGpuOps::new().await?;
    let inputs = vec![DualNumber::new(2.0_f32, 1.0_f32)];

    // Computes exp(x²) and its forward derivative for every input.
    let outputs = gpu
        .batch_forward_ad(&inputs, &[DualOperation::Square, DualOperation::Exp])
        .await?;

    println!("value={}, derivative={}", outputs[0].real, outputs[0].dual);
    Ok(())
}

Automata GPU Operations (mixed GPU-backed + documented fallback)

The automata feature exposes cellular-automata helpers through crate-root re-exports:

Type / operation	Current 0.20.0 behavior
`AutomataGpuOps::batch_apply_rules()`	GPU-backed rule application using the first supplied rule configuration
`AutomataGpuOps::batch_evolve_ca()`	repeats the GPU rule-application path for `steps_per_batch` steps
`AutomataGpuOps::calculate_total_energy()`	GPU-backed sum of squared multivector components
`AutomataGpuOps::extract_neighborhoods()`	CPU Moore-neighborhood baseline with wrapping boundaries
CA evolution / neighborhood pipelines	validation-safe scaffolding pending richer neighborhood-aware GPU kernels

use amari_gpu::{AutomataGpuOps, GpuCellData, GpuEvolutionParams, GpuRuleConfig};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut gpu = AutomataGpuOps::new().await?;

    let cells = vec![GpuCellData { scalar: 2.0, e1: 1.0, ..GpuCellData::default() }];
    let rule = GpuRuleConfig { damping_factor: 0.1, threshold: 0.5, ..GpuRuleConfig::default() };

    let evolved = gpu.batch_apply_rules(&cells, &[rule]).await?;
    let energy = gpu.calculate_total_energy(&evolved).await?;

    let params = GpuEvolutionParams { steps_per_batch: 4.0, ..GpuEvolutionParams::default() };
    let after_four_steps = gpu.batch_evolve_ca(&cells, &[rule], &params).await?;

    Ok(())
}

Measure GPU Operations (mixed GPU-backed + documented fallback)

The measure feature currently exposes a broad public module plus crate-root re-exports:

Type / operation	Current 0.20.0 behavior
`GpuIntegrator::integrate_uniform()`	GPU built-in function evaluation with CPU readback reduction
`GpuIntegrator::integrate_values()`	CPU reduction fallback for precomputed values
`GpuMonteCarloIntegrator::{expectation_uniform, integrate}`	GPU sampling/evaluation for built-in functions with CPU readback reduction
`GpuParametricDensity::gaussian_batch()`	GPU-backed Gaussian density batch evaluation
`GpuTropicalMeasure::{supremum, infimum}`	CPU reduction fallback
`GpuMultidimIntegrator::monte_carlo_nd()`	exact hypercube volume for constant-one integrand; multidimensional GPU Monte Carlo pending

use amari_gpu::{GpuIntegrator, GpuParametricDensity};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    let integrator = GpuIntegrator::new().await?;

    // Built-in function IDs: 0=x, 1=x², 2=x³, 3=sin(x), 4=cos(x), 5=exp(x).
    // This evaluates x² on the GPU and reduces the result after readback.
    let integral = integrator.integrate_uniform(0.0, 2.0, 10_000, 1).await?;

    // Precomputed/custom values currently use a documented CPU fallback reduction.
    let custom_integral = integrator.integrate_values(&[1.0, 2.0, 3.0], 0.5).await?;

    let density = GpuParametricDensity::new().await?;
    let gaussian = density.gaussian_batch(&[0.0, 1.0], 0.0, 1.0).await?;

    Ok(())
}

Functional Analysis GPU Operations (mixed GPU-backed + documented fallback)

The functional feature exposes matrix, Hilbert-space, spectral, and adaptive helpers:

Type / operation	Current 0.20.0 behavior
`GpuMatrixOperator::apply_batch()`	GPU-backed batch matrix-vector products
`GpuMatrixOperator::multiply()`	CPU readback fallback for correctness across independently-created GPU operators
`GpuMatrixOperator::to_matrix_operator()`	GPU readback to CPU matrix
`GpuSpectralDecomposition::compute()`	CPU `amari-functional` spectral baseline after GPU matrix readback
`GpuSpectralDecomposition::apply_function_batch()`	CPU spectral functional-calculus batch helper
`GpuHilbertSpace::{inner_product_batch, norm_batch}`	GPU-backed batch inner products and norms
`AdaptiveFunctionalCompute`	CPU/GPU dispatch for matrix batches; spectral path currently preserves CPU baseline semantics

use amari_core::Multivector;
use amari_functional::{LinearOperator, MatrixOperator};
use amari_gpu::{GpuMatrixOperator, GpuSpectralDecomposition};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    let matrix = MatrixOperator::<2, 0, 0>::diagonal(&[2.0, 3.0, 4.0, 5.0])?;
    let gpu_matrix = GpuMatrixOperator::from_matrix_operator(&matrix).await?;

    let vectors = vec![Multivector::<2, 0, 0>::from_coefficients(vec![1.0, 2.0, 3.0, 4.0])];
    let applied = gpu_matrix.apply_batch(&vectors).await?;

    // Spectral decomposition is currently the CPU spectral baseline after readback.
    let spectral = GpuSpectralDecomposition::compute(&gpu_matrix, 100, 1e-10).await?;
    assert_eq!(spectral.eigenvalues().len(), 4);

    Ok(())
}

Core Geometric Algebra + Information Geometry (default crate-root APIs)

The default API exposes GpuCliffordAlgebra, AdaptiveCompute, GpuInfoGeometry, GpuDeviceInfo, and GpuFisherMatrix at the crate root.

use amari_core::Multivector;
use amari_gpu::{AdaptiveCompute, GpuInfoGeometry};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    // Legacy adaptive Cl(3,0,0) helper: single products use CPU baseline;
    // flat batches use GPU only above the current crossover and when available.
    let adaptive = AdaptiveCompute::new::<3, 0, 0>().await;
    let e1 = Multivector::<3, 0, 0>::basis_vector(0);
    let e2 = Multivector::<3, 0, 0>::basis_vector(1);
    let product = adaptive.geometric_product(&e1, &e2).await;
    assert_eq!(product.to_vec(), e1.geometric_product(&e2).to_vec());

    // Info geometry currently uses validated CPU baselines after WebGPU context creation.
    let info = GpuInfoGeometry::new().await?;
    let fisher = info.fisher_information_matrix(&[0.25, 0.5]).await?;
    assert_eq!(fisher.matrix(), &[vec![4.0, 0.0], vec![0.0, 2.0]]);
    Ok(())
}

Type / operation	Current 0.20.0 behavior
`GpuCliffordAlgebra::new::<P,Q,R>()`	GPU context with signature-specific basis count and Cayley table
`GpuCliffordAlgebra::batch_geometric_product()`	GPU-backed `f32` batch geometric product for complete finite flat coefficient batches
`AdaptiveCompute::geometric_product()`	CPU `amari-core` baseline for single multivector products
`AdaptiveCompute::batch_geometric_product()`	legacy Cl(3,0,0) flat-batch helper with CPU fallback and GPU above threshold when available
`GpuInfoGeometry::amari_chentsov_tensor{,_batch}`	CPU baseline using `amari-info-geom`; equal-length batch validation
`GpuInfoGeometry::amari_chentsov_tensor_from_typed_arrays()`	finite `[x,y,z]` vector-component flat input validation, then CPU baseline
`GpuInfoGeometry::fisher_information_matrix()`	CPU probability-simplex-style diagonal Fisher metric baseline; finite non-negative inputs
`GpuInfoGeometry::bregman_divergence_batch()`	CPU KL-style Bregman divergence with shape/finite/non-negative validation
`GpuInfoGeometry::memory_usage()`	returns `0`; portable `wgpu` does not expose allocator usage

Infrastructure / Adaptive / Performance / Timeline APIs (orchestration layer)

The default crate also exposes infrastructure APIs used by higher-level GPU domains. These are orchestration, profiling, and dispatch helpers; they are not mathematical kernel APIs by themselves.

Area	Public types	Current 0.20.0 behavior
Adaptive verification	`AdaptiveVerifier`, `VerificationPlatform`, `AdaptiveVerificationLevel`, `PlatformCapabilities`	platform detection with CPU fallback; verified batch operations validate equal lengths
Unified dispatch/context	`GpuContext`, `SharedGpuContext`, `GpuDispatcher`, `GpuOperationParams`, `GpuParam`, buffer-pool stats	common WebGPU context/dispatcher infrastructure with CPU fallback when GPU operations fail or are unavailable
Performance tuning	`WorkgroupOptimizer`, `AdaptiveDispatchPolicy`, `WorkgroupConfig`, `CalibrationResult`, `GpuProfiler`	heuristic workgroup defaults, calibration history, crossover learning; non-finite benchmark values are sanitized
Timeline analysis	`TimelineEvent`, `GpuTimelineAnalyzer`, `MultiGpuPerformanceMonitor`, report/summary types	CPU-timeline-based event recording, utilization/bottleneck heuristics, safe zero-window and timestamp handling
Multi-GPU coordination	`DeviceId`, `GpuDevice`, `Workload`, `IntelligentLoadBalancer`, `WorkloadCoordinator`, synchronization types	workload distribution/coordinator scaffolding for available `wgpu` devices; hardware validation still pending
Benchmarks	`AmariMultiGpuBenchmarks`, `BenchmarkRunner`, result/config/summary types	benchmark orchestration/reporting; crossover numbers must be generated per hardware target

Tropical GPU Acceleration (narrow v1 surface)

use amari_gpu::{TropicalExecutionPath, TropicalGpuOps};
use amari_tropical::{TropicalMatrix, TropicalNumber};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut gpu = TropicalGpuOps::new().await?;

    let mut a = TropicalMatrix::new(64, 64);
    let mut b = TropicalMatrix::new(64, 64);

    for i in 0..64 {
        for j in 0..64 {
            a.data[i][j] = TropicalNumber::new((i as f32 - j as f32) * 0.25);
            b.data[i][j] = TropicalNumber::new((i as f32 + j as f32) * 0.125);
        }
    }

    match gpu.matrix_multiply_execution_path(a.rows, a.cols, b.cols) {
        TropicalExecutionPath::Cpu => println!("Using CPU path for this problem size"),
        TropicalExecutionPath::Gpu => println!("Using GPU path for this problem size"),
    }

    // Explicit GPU path
    let _gpu_result = gpu.matrix_multiply(&a, &b).await?;

    // Adaptive path using current crossover heuristic
    let _adaptive_result = gpu.matrix_multiply_adaptive(&a, &b).await?;

    // Tropical winner-takes-all attention scores for a logits matrix
    let _scores = gpu.attention_scores(&a).await?;

    Ok(())
}

Tropical v1 Surface

The currently supported public tropical GPU API is intentionally small:

TropicalGpuOps
TropicalExecutionPath
TropicalGpuError
TropicalGpuResult

Current real kernel support:

dense max-plus matrix multiplication
adaptive CPU/GPU dispatch for matrix multiplication
winner-takes-all tropical attention scores

Still redesign-pending and intentionally not exposed as a full public module:

Viterbi
attention
tropical solve
multivector GPU ops
the older trait-based placeholder surface

Holographic Memory GPU Acceleration

use amari_gpu::GpuHolographic;

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    // Initialize GPU holographic operations for 256-dimensional ProductCl3x32 vectors
    let gpu = GpuHolographic::new(256).await?;

    // Flat arrays: batch_size * dimension coefficients
    let keys = vec![0.0f64; 1000 * 256];
    let values = vec![0.0f64; 1000 * 256];

    // Batch bind 1000 key-value pairs on GPU
    let bound = gpu.batch_bind(&keys, &values).await?;
    println!("Produced {} coefficients", bound.len());

    // Batch similarity computation
    let similarities = gpu.batch_similarity(&keys, &values).await?;
    println!("Computed {} similarities", similarities.len());

    Ok(())
}

Holographic GPU Operations (validated v1)

GpuHolographic currently validates and supports the canonical 256-dimensional ProductCl3x32 layout. Flat coefficient arrays must be finite and have length batch_size * 256.

Operation	Current 0.20.0 behavior	GPU Threshold
`GpuHolographic::new(256)` / `new_product_cl3x32()`	accepts only validated `ProductCl3x32` dimensionality	n/a
`batch_bind()`	GPU-backed Cl3 geometric-product binding with the same basis/sign convention as `amari-holographic`	≥ 100 pairs
`batch_unbind()`	CPU correctness path using `amari-holographic` inverse/unbind semantics	CPU-backed
`batch_similarity()`	GPU-backed ProductCl3x32 cosine similarity	≥ 100 pairs
`batch_bundle()`	CPU correctness path using `ProductCl3x32::bundle(..., beta = 1.0)`	CPU-backed
`find_most_similar()`	batch similarity plus CPU max reduction; empty codebooks rejected	inherits similarity path
`GpuHolographicMemory::store_batch()`	CPU memory path with equal-length validation	CPU-backed

WGSL Shaders

The holographic module includes optimized WGSL compute shaders:

holographic_batch_bind: Cayley table-based geometric product for binding
holographic_batch_similarity: Inner product with reverse <A B̃>₀ for similarity
holographic_bundle_all: Parallel reduction for vector superposition
holographic_resonator_step: Parallel max-finding for cleanup

Optical Field GPU Acceleration (v0.15.1)

use amari_gpu::GpuOpticalField;
use amari_holographic::optical::{OpticalRotorField, LeeEncoderConfig};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    // Initialize GPU context for optical fields (256x256 dimensions)
    let gpu = GpuOpticalField::new((256, 256)).await?;

    // Create optical rotor fields
    let field_a = OpticalRotorField::random((256, 256), 42);
    let field_b = OpticalRotorField::random((256, 256), 123);

    // GPU-accelerated binding (rotor multiplication = phase addition)
    let bound = gpu.bind(&field_a, &field_b).await?;
    println!("Bound field total energy: {:.4}", bound.total_energy());

    // GPU-accelerated similarity computation
    let similarity = gpu.similarity(&field_a, &field_b).await?;
    println!("Field similarity: {:.4}", similarity);

    // GPU-accelerated Lee hologram encoding
    let config = LeeEncoderConfig::new((256, 256), 0.25);
    let hologram = gpu.encode_lee(&field_a, &config).await?;
    println!("Hologram fill factor: {:.4}", hologram.fill_factor());

    // Batch operations for multiple field pairs
    let fields_a = vec![field_a.clone(), field_b.clone()];
    let fields_b = vec![field_b.clone(), field_a.clone()];

    let batch_bound = gpu.batch_bind(&fields_a, &fields_b).await?;
    let batch_sim = gpu.batch_similarity(&fields_a, &fields_b).await?;

    println!("Processed {} field pairs", batch_bound.len());

    Ok(())
}

Optical Field GPU Operations

Operation	Description	GPU Threshold
`bind()`	Rotor multiplication (phase addition)	≥ 4096 pixels (64×64)
`similarity()`	Normalized inner product with reduction	≥ 4096 pixels
`encode_lee()`	Binary hologram encoding with bit-packing	≥ 4096 pixels
`batch_bind()`	Parallel binding of field pairs	Any batch size
`batch_similarity()`	Parallel similarity computation	Any batch size

WGSL Shaders for Optical Operations

OPTICAL_BIND_SHADER: Element-wise rotor product in Cl(2,0)
- Computes: s_out = a_s·b_s - a_b·b_b, b_out = a_s·b_b + a_b·b_s
- Uses a packed output buffer to remain within WebGPU's portable storage-buffer binding limit
- 256-thread workgroups for per-pixel parallelism
OPTICAL_SIMILARITY_SHADER: Inner product with workgroup reduction
- Computes: ⟨R_a, R_b⟩ = Σ(a_s·b_s + a_b·b_b) × amplitude_a × amplitude_b
- 256-thread workgroups with shared memory reduction
LEE_ENCODE_SHADER: Binary hologram encoding with bit-packing
- Each thread handles 32 pixels, packing results into u32
- 64-thread workgroups for word-level parallelism

Topology GPU Operations (mixed GPU-backed + documented fallback)

The topology feature exposes distance, Morse, Rips, Betti, and adaptive helpers:

Type / operation	Current 0.20.0 behavior
`GpuTopology::compute_distance_matrix()`	GPU-backed pairwise Euclidean distances; returns a flattened `n × n` matrix
`GpuTopology::find_critical_points_2d()`	GPU-backed discrete Morse critical point detection
`GpuTopology::build_rips_filtration()`	CPU filtration/clique construction from a supplied distance matrix
`GpuTopology::compute_betti_numbers()`	CPU `amari-topology` homology baseline
`AdaptiveTopologyCompute`	GPU for distance/Morse above thresholds when available; CPU fallback otherwise

use amari_gpu::{AdaptiveTopologyCompute, GpuTopology};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    let gpu_topology = GpuTopology::new().await?;

    let points = vec![(0.0, 0.0, 0.0), (1.0, 0.0, 0.0), (0.0, 1.0, 0.0)];
    let distances = gpu_topology.compute_distance_matrix(&points).await?;
    println!("Computed flattened {}x{} distance matrix", points.len(), points.len());

    // Rips construction currently uses CPU logic over the distance matrix.
    let filtration = gpu_topology
        .build_rips_filtration(&distances, points.len(), 1.5, 2)
        .await?;
    println!("Built filtration with {} simplices", filtration.len());

    let width = 128;
    let height = 128;
    let values: Vec<f64> = (0..width * height)
        .map(|i| {
            let x = (i % width) as f64 / width as f64;
            let y = (i / width) as f64 / height as f64;
            (x * std::f64::consts::TAU).sin() * (y * std::f64::consts::TAU).cos()
        })
        .collect();
    let critical_points = gpu_topology.find_critical_points_2d(&values, width, height).await?;
    println!("Found {} critical points", critical_points.len());

    // Adaptive dispatcher: GPU where validated/beneficial, CPU fallback otherwise.
    let adaptive = AdaptiveTopologyCompute::new().await;
    let adaptive_distances = adaptive.compute_distance_matrix(&points).await?;
    assert_eq!(adaptive_distances.len(), points.len() * points.len());

    Ok(())
}

Topology Operations

Operation	Current path
`compute_distance_matrix()`	GPU direct path; adaptive CPU fallback for small/unavailable GPU
`find_critical_points_2d()`	GPU direct path; adaptive CPU fallback for small/unavailable GPU
`build_rips_filtration()`	CPU filtration/clique construction, optionally fed by GPU distance matrix
`compute_betti_numbers()`	CPU homology baseline; boundary/reduction GPU kernels pending validation

WGSL Shaders for Topology Operations

Distance matrix shader: parallel pairwise Euclidean distance computation.
Morse critical point shader: compares each interior cell with its 8 neighbors.
Boundary/reduction shader scaffolding: reserved for future persistent-homology kernels; public Betti behavior is currently CPU-backed.

Dynamics GPU Acceleration (v0.19.1)

use amari_gpu::dynamics::{GpuDynamics, BatchTrajectoryConfig, GpuSystemType};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    // Initialize GPU dynamics context
    let gpu = GpuDynamics::new().await?;

    // Batch trajectory integration (1000 initial conditions in parallel)
    let initial_conditions: Vec<[f64; 3]> = (0..1000)
        .map(|i| [1.0 + i as f64 * 0.001, 1.0, 1.0])
        .collect();

    let config = BatchTrajectoryConfig {
        dt: 0.01,
        steps: 5000,
        dim: 3,
        system_type: GpuSystemType::Lorenz { sigma: 10.0, rho: 28.0, beta: 8.0/3.0 },
    };

    let trajectories = gpu.batch_trajectories(&initial_conditions, &config).await?;
    println!("Computed {} trajectories on GPU", trajectories.len());

    // GPU bifurcation diagram (parameter sweep)
    let param_range = (2.5, 4.0);
    let num_params = 1000;
    let diagram = gpu.bifurcation_diagram(
        GpuSystemType::LogisticMap,
        param_range,
        num_params,
        500,  // transient
        100,  // samples
    ).await?;
    println!("Bifurcation diagram: {} parameter values", diagram.len());

    // GPU Lyapunov spectrum computation
    let lyapunov = gpu.lyapunov_spectrum(
        &[1.0, 1.0, 1.0],
        GpuSystemType::Lorenz { sigma: 10.0, rho: 28.0, beta: 8.0/3.0 },
        10000,  // steps
        0.01,   // dt
    ).await?;
    println!("Lyapunov exponents: {:?}", lyapunov);

    // GPU basin of attraction computation
    let grid_resolution = (100, 100);
    let basin = gpu.compute_basin(
        GpuSystemType::Duffing { alpha: 1.0, beta: -1.0, delta: 0.2, gamma: 0.3, omega: 1.2 },
        grid_resolution,
        (-2.0, 2.0),  // x range
        (-2.0, 2.0),  // y range
        1000,         // max iterations
    ).await?;
    println!("Basin computed: {} x {} grid", grid_resolution.0, grid_resolution.1);

    Ok(())
}

Dynamics GPU Operations

Operation	Description	GPU Threshold
`batch_trajectories()`	Parallel ODE integration for many initial conditions	≥ 100 trajectories
`bifurcation_diagram()`	Parameter sweep with attractor sampling	≥ 100 parameter values
`lyapunov_spectrum()`	QR-based Lyapunov exponent computation	≥ 1000 steps
`compute_basin()`	Basin of attraction grid computation	≥ 10000 grid cells

WGSL Shaders for Dynamics Operations

DYNAMICS_RK4_STEP: Fourth-order Runge-Kutta integration step
- 256-thread workgroups for parallel trajectory evolution
- Supports Lorenz, Van der Pol, Duffing, Rossler, Henon systems
DYNAMICS_LYAPUNOV_QR: QR decomposition for tangent space evolution
- Computes orthonormalization for Lyapunov exponent estimation
- Workgroup-shared memory for matrix operations
DYNAMICS_BIFURCATION: Parameter-dependent attractor sampling
- Parallel transient discard and attractor point collection
- Outputs (parameter, attractor_value) pairs
DYNAMICS_BASIN: Grid-based trajectory classification
- Classifies each grid point by attractor convergence
- 256-thread workgroups for spatial parallelism

Enumerative Geometry GPU Operations (high-use broad surface)

The enumerative feature remains a broad public module for downstream compatibility, with crate-root re-exports for the most-used data types and operations. Representative public tests now cover the high-use kernels listed below.

use std::collections::BTreeSet;
use amari_enumerative::Matroid;
use amari_gpu::{EnumerativeGpuOps, GpuMatroidRankData, GpuWDVVData};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut gpu_ops = EnumerativeGpuOps::new().await?;

    // Batch WDVV/Kontsevich curve counts for P², degrees 1..=6.
    let wdvv_data: Vec<GpuWDVVData> = (1..=6).map(GpuWDVVData::from_degree).collect();
    let counts = gpu_ops.batch_wdvv_curve_counts(&wdvv_data).await?;
    assert_eq!(counts, vec![1, 1, 12, 620, 87304, 26312976]);

    // Batch matroid rank computation via bitmask-encoded bases.
    let matroid = Matroid::uniform(2, 4);
    let subset: BTreeSet<usize> = [0, 1, 2].into_iter().collect();
    let rank_data = vec![GpuMatroidRankData::from_matroid_subset(&matroid, &subset)];
    let ranks = gpu_ops.batch_matroid_ranks(&rank_data).await?;

    Ok(())
}

Enumerative GPU Operations

Operation	Current path	Mathematical basis / caveat
`batch_intersection_numbers()`	GPU-backed compact formula	degree/codimension compatibility with multiplicity/genus correction
`batch_wdvv_curve_counts()`	GPU-backed lookup	Kontsevich numbers `N_1..N_6` for `P²`; higher degrees return `0`
`batch_localization_euler_classes()`	GPU-backed product formula	tangent Euler class at fixed points, weights limited by compact GPU data layout
`batch_matroid_ranks()`	GPU-backed bitmask computation	max `
`batch_csm_euler_characteristics()`	GPU-backed cell contribution	Schubert-cell contribution currently returns `1` per cell
`batch_operad_multiplicities()`	GPU-backed codimension check	matching single-interface codimensions give multiplicity `1` within dimension bounds
`batch_stability_phases()`	GPU-backed phase formula	normalized `atan2(trust * dim, -codim) / π`
`batch_stability_checks()`	GPU-backed phase interval test	stable iff normalized phase is strictly in `(0, 1)`
broader Schubert/GW/LR/namespace/tropical/GF(2) helpers	GPU-backed, representative tests exist	deeper mathematical parity work remains a post-0.20.0 task

See docs/roadmap/AMARI_GPU_ENUMERATIVE_CLASSIFICATION.md for the method-by-method classification table.

GF(2) GPU Operations (fixed-layout GPU-backed surface)

The gf2 feature exposes batch binary Clifford products, GF(2) matrix-vector multiplication, and Hamming distance kernels. The public API validates fixed-layout bounds before dispatch, and representative tests compare these kernels against amari-core::gf2 CPU baselines and GF(2) algebraic properties.

Operation	Current 0.20.0 behavior
`batch_gf2_geometric_product()`	GPU-backed `Cl(N,R;F₂)` product, up to 128 blades (`num_generators <= 7`)
`batch_gf2_matvec()`	GPU-backed GF(2) matrix-vector multiplication, up to 16 rows × 32 columns
`batch_gf2_hamming_distance()`	GPU-backed Hamming distance, up to 128 bits, masks unused final-word bits by `dim`

use amari_core::gf2::{GF2Matrix, GF2Vector};
use amari_gpu::{GF2GpuOps, GpuGF2CliffordPair, GpuGF2MatVecData};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut gpu = GF2GpuOps::new().await?;

    // e1 * e2 = e12 in Cl(3,0;F₂).
    let products = gpu.batch_gf2_geometric_product(&[
        GpuGF2CliffordPair::from_bits(&[0, 1], &[0, 0, 1], 3, 0),
    ]).await?;
    assert_eq!(products[0][0] & (1 << 3), 1 << 3);

    let matrix = GF2Matrix::identity(3);
    let vector = GF2Vector::from_bits(&[1, 0, 1]);
    let matvec = GpuGF2MatVecData::from_matrix_and_vector(&matrix, &vector);
    assert_eq!(gpu.batch_gf2_matvec(&[matvec]).await?, vec![0b101]);

    Ok(())
}

Relativistic GPU Operations (Minkowski products + simplified geodesic propagation)

The default relativistic API exposes crate-root GpuRelativisticPhysics, GpuSpacetimeVector, GpuRelativisticParticle, and GpuTrajectoryParams. GpuSpacetimeVector stores coordinates as (ct, x, y, z) and compute_minkowski_products() returns ct² - x² - y² - z². Particle propagation uses a simplified Schwarzschild-style GPU geodesic step and validates trajectory and particle fields before dispatch.

use amari_gpu::{GpuRelativisticPhysics, GpuSpacetimeVector};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    let gpu = GpuRelativisticPhysics::new().await?;
    let norms = gpu.compute_minkowski_products(&[
        GpuSpacetimeVector::new(2.0, 1.0, 0.5, 0.25),
    ]).await?;
    assert!((norms[0] - (4.0 - 1.0 - 0.25 - 0.0625)).abs() < 1e-5);
    Ok(())
}

Operation	Current 0.20.0 behavior
`GpuSpacetimeVector::{from,to}_spacetime_vector()`	preserves `[ct, x, y, z]` CPU coordinates
`compute_minkowski_products()`	GPU-backed Minkowski norm-squared for finite spacetime vectors; empty input returns empty
`propagate_particles()`	simplified GPU geodesic step; zero steps return input unchanged; validates finite/non-negative fields and trajectory parameters

Network GPU Operations (narrow GPU distances + adaptive CPU fallback)

The default network API exposes crate-root GpuGeometricNetwork and AdaptiveNetworkCompute. The current GPU kernel computes pairwise Euclidean distances for vector-only Cl(P,0,0) embeddings with P <= 3. Geometric centrality and clustering reuse those GPU distances but perform their reductions/medoid updates on the CPU. Adaptive dispatch falls back to amari-network CPU geometric baselines for small networks, unsupported signatures, or non-vector multivectors.

use amari_core::Vector;
use amari_gpu::AdaptiveNetworkCompute;
use amari_network::GeometricNetwork;

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut network = GeometricNetwork::<3, 0, 0>::new();
    let a = network.add_node(Vector::from_components(0.0, 0.0, 0.0).mv);
    let b = network.add_node(Vector::from_components(3.0, 4.0, 0.0).mv);
    network.add_undirected_edge(a, b, 1.0)?;

    let adaptive = AdaptiveNetworkCompute::new().await;
    let distances = adaptive.compute_all_pairwise_distances(&network).await?;
    assert_eq!(distances[a][b], 5.0); // geometric distance, not edge shortest path

    let centrality = adaptive.compute_geometric_centrality(&network).await?;
    assert_eq!(centrality.len(), network.num_nodes());

    Ok(())
}

Operation	Current 0.20.0 behavior
`GpuGeometricNetwork::compute_all_pairwise_distances()`	GPU Euclidean distances for vector-only `Cl(P,0,0)`, `P <= 3`; rejects unsupported embeddings
`GpuGeometricNetwork::compute_geometric_centrality()`	GPU distance matrix plus CPU centrality reduction
`GpuGeometricNetwork::geometric_clustering()`	GPU distance matrix plus CPU k-medoid assignment/update and distance-derived cohesion
`AdaptiveNetworkCompute::*`	Uses GPU only for supported large networks; otherwise CPU geometric-distance baselines

Probabilistic GPU Operations (GPU-backed sampling/statistics + small-batch CPU fallback)

The probabilistic feature exposes crate-root GpuProbabilistic APIs for vector-valued Gaussian sampling and batch statistics. A GPU context is still required; after initialization, small batches currently use CPU fallback while larger batches dispatch WGSL kernels.

use amari_gpu::GpuProbabilistic;

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    // Dimension of each sample vector / multivector coefficient array.
    let gpu_prob = GpuProbabilistic::new(3).await?;

    // Batch sample 10,000 Gaussian vectors on GPU.
    let samples = gpu_prob
        .batch_sample_gaussian(10_000, &[0.0, 1.0, 2.0], &[1.0, 0.5, 2.0])
        .await?;
    assert_eq!(samples.len(), 10_000 * 3);

    // Compute coefficient-wise statistics.
    let mean = gpu_prob.batch_mean(&samples).await?;
    let variance = gpu_prob.batch_variance(&samples, &mean).await?;

    Ok(())
}

Probabilistic GPU Operations

Operation	Current 0.20.0 behavior	Validation / fallback
`GpuProbabilistic::new(dimension)`	creates GPU pipelines for fixed sample dimension	rejects `dimension == 0`
`batch_sample_gaussian()`	GPU Box-Muller sampling for `num_samples >= 100`; CPU fallback below that	validates mean/std-dev lengths, finite means, finite non-negative std-devs
`batch_mean()`	GPU coefficient-wise sum/readback for `num_samples >= 100`; CPU fallback below that	rejects empty, non-finite, or mis-shaped sample buffers
`batch_variance()`	GPU coefficient-wise squared-difference/readback with Bessel correction for `num_samples >= 100`; CPU fallback below that	rejects empty, one-sample, non-finite, mis-shaped, or bad mean buffers

Adaptive CPU/GPU Dispatch

The library automatically selects the optimal execution path:

// Small batch: Automatically uses CPU (< 1000 points for scalar fields)
let small_points = vec![[0.0, 0.0, 0.0], [1.0, 1.0, 1.0]];
let values = gpu_calculus.batch_eval_scalar_field(&field, &small_points).await?;
// ↑ Executed on CPU (overhead of GPU transfer exceeds benefit)

// Large batch: Automatically uses GPU (≥ 1000 points)
let large_points = generate_point_grid(100, 100); // 10,000 points
let values = gpu_calculus.batch_eval_scalar_field(&field, &large_points).await?;
// ↑ Executed on GPU (parallel processing advantage)

Batch Size Thresholds

Operation	CPU Threshold	GPU Threshold
Scalar field evaluation	current 0.20.0 path	CPU-semantic fallback; WGSL kernel pending
Vector field evaluation	current 0.20.0 path	CPU-semantic fallback; WGSL kernel pending
Gradient computation	current 0.20.0 path	CPU finite-difference fallback; WGSL kernel pending
Divergence/Curl	current 0.20.0 path	CPU finite-difference fallback; WGSL kernel pending
Holographic binding	< 100 pairs	≥ 100 pairs
Holographic similarity	< 100 vectors	≥ 100 vectors
Resonator cleanup	< 100 codebook	≥ 100 codebook
Optical field bind	< 4096 pixels	≥ 4096 pixels (64×64)
Optical similarity	< 4096 pixels	≥ 4096 pixels
Lee hologram encoding	< 4096 pixels	≥ 4096 pixels
Gaussian sampling	< 100 samples	≥ 100 samples
Batch mean/variance	< 100 samples	≥ 100 samples
Measure built-in 1D integration	GPU evaluation	CPU readback reduction
Measure precomputed values	CPU reduction fallback	GPU reduction pending
Measure Gaussian density	N/A	GPU batch evaluation
Tropical measure extrema	CPU reduction fallback	GPU reduction pending
Distance matrix	< 100 points	≥ 100 points
Morse critical points	< 10000 cells	≥ 10000 cells
Rips filtration	CPU filtration construction	may use GPU distance matrix
Batch trajectories	< 100 trajectories	≥ 100 trajectories
Bifurcation diagram	< 100 params	≥ 100 parameter values
Lyapunov spectrum	< 1000 steps	≥ 1000 steps
Basin of attraction	< 10000 cells	≥ 10000 grid cells

Implementation Status

Holographic Module (v0.13.0)

GPU Implementations (✅ Complete):

Batch binding with Cayley table geometric product
Batch similarity using proper inner product <A B̃>₀
Parallel reduction for vector bundling
Resonator cleanup with parallel codebook search

Optical Field Module (v0.15.1)

GPU Implementations (✅ Complete):

Rotor field binding via OPTICAL_BIND_SHADER
Similarity with workgroup reduction via OPTICAL_SIMILARITY_SHADER
Lee hologram encoding with bit-packing via LEE_ENCODE_SHADER
Automatic CPU fallback for small fields (< 4096 pixels)

Types:

GpuOpticalField: GPU context for optical rotor field operations
Uses OpticalRotorField from amari-holographic (SoA layout: scalar, bivector, amplitude)
Uses BinaryHologram for bit-packed hologram output
Uses LeeEncoderConfig for carrier wave parameters

Probabilistic Module (v0.20.0)

GPU-backed implementations:

Batch Gaussian sampling on coefficient vectors using Box-Muller transform
Coefficient-wise batch mean computation
Coefficient-wise batch variance computation with Bessel correction

CPU fallback paths:

Sampling/statistics batches with fewer than 100 samples use CPU fallback after GPU context creation.

Types:

GpuProbabilistic: GPU context for probabilistic sampling/statistics
GpuProbabilisticError / GpuProbabilisticResult: error/result types

Current validation:

rejects zero dimensions
validates sample-buffer shape and finite values
validates finite means and non-negative finite standard deviations
rejects variance requests with fewer than two samples

Calculus Module (v0.13.0)

CPU Implementations (✅ Complete):

Central finite differences for numerical derivatives
Field evaluation at multiple points
Gradient, divergence, and curl computation
Step size: h = 1e-6 for numerical stability

GPU Implementations (⏸️ Future Work):

WGSL compute shaders for parallel field evaluation
Parallel finite difference computation
Optimized memory layout for GPU transfer

Current Behavior:

Infrastructure and pipelines are in place
All operations currently use CPU implementations
Shaders can be added incrementally without API changes

Topology Module (v0.16.0)

GPU-backed Implementations (✅ Complete):

Distance matrix computation with parallel pairwise Euclidean distance
Morse critical point detection for 2D scalar fields

CPU fallback / scaffolding paths:

Rips filtration construction from a distance matrix currently uses CPU clique construction
Betti number computation currently uses the amari-topology CPU homology baseline
Boundary/reduction shader scaffolding is reserved for future persistent-homology kernels

Types:

GpuTopology: GPU context for topology operations
GpuCriticalPoint: Critical point with position, value, type, and index
AdaptiveTopologyCompute: Automatic CPU/GPU dispatch based on workload size
GpuTopologyError / GpuTopologyResult: Error handling types

Shaders:

Distance matrix shader: 8×8 workgroups for O(n²) distance computation
Morse critical point shader: 8-neighbor comparison for critical point classification
Boundary/reduction scaffolding: validation-safe placeholders until persistent-homology kernels are restored

Adaptive Thresholds:

Distance matrix: GPU for ≥ 100 points (n² = 10,000 operations)
Morse critical points: GPU for ≥ 10,000 grid cells (100×100)
Falls back to CPU for smaller workloads to avoid transfer overhead

Dynamics Module (v0.19.1)

GPU Implementations (✅ Complete):

Batch trajectory integration with RK4 solver
Bifurcation diagram computation with parallel parameter sweeps
Lyapunov spectrum via QR-based tangent space evolution
Basin of attraction grid computation

Types:

GpuDynamics: GPU context for dynamical systems operations
BatchTrajectoryConfig: Configuration for parallel trajectory integration
GpuSystemType: Enum for built-in systems (Lorenz, VanDerPol, Duffing, Rossler, Henon, LogisticMap)
GpuDynamicsError / GpuDynamicsResult: Error handling types

Shaders:

DYNAMICS_RK4_STEP: 256-thread workgroups for RK4 integration
DYNAMICS_LYAPUNOV_QR: QR decomposition for Lyapunov exponents
DYNAMICS_BIFURCATION: Parameter sweep attractor sampling
DYNAMICS_BASIN: Grid-based trajectory classification

Adaptive Thresholds:

Batch trajectories: GPU for ≥ 100 initial conditions
Bifurcation diagram: GPU for ≥ 100 parameter values
Lyapunov spectrum: GPU for ≥ 1000 integration steps
Basin computation: GPU for ≥ 10,000 grid cells

Examples

See the examples/ directory for complete examples:

# Run geometric algebra example
cargo run --example ga_operations

# Run information geometry example
cargo run --example fisher_metric

# Run calculus example (requires 'calculus' feature)
cargo run --features calculus --example field_ops

Development

Running Tests

# Run all tests
cargo test

# Run with specific features
cargo test --features calculus
cargo test --features measure

# Run GPU tests (requires GPU access)
cargo test --test gpu_integration

Building Documentation

cargo doc --all-features --no-deps --open

Future Work

Short-term (v0.13.x)

Implement WGSL shaders for calculus operations
Add GPU benchmarks comparing CPU vs GPU performance
Optimize memory transfer patterns
Add more comprehensive examples
Restore tropical GPU module using extension traits (orphan impl fix)

Medium-term (v0.14.x - v0.15.x)

Implement tropical algebra GPU operations
Multi-GPU support for large holographic memories
Performance optimization across all GPU modules
Unified GPU context sharing across all modules

Long-term (v1.0.0+)

WebGPU backend for browser deployment
Multi-GPU support for distributed computation
Kernel fusion optimization
Custom WGSL shader compilation pipeline

Performance Considerations

GPU Initialization: ~100-200ms startup cost for context creation
Data Transfer: Significant overhead for small batches (< 500 elements)
Optimal Use Cases: Large batch operations (> 1000 elements)
Memory: GPU buffers are sized for batch operations (dynamically allocated)

Platform Support

Platform	Backend	Status
Linux	Vulkan	✅ Tested
macOS	Metal	✅ Supported (not regularly tested)
Windows	DirectX 12 / Vulkan	✅ Supported (not regularly tested)
WebAssembly	WebGPU	⏸️ Requires `webgpu` feature

Dependencies

wgpu (v0.19): WebGPU implementation
bytemuck: Zero-cost GPU buffer conversions
nalgebra: Linear algebra operations
tokio: Async runtime for GPU operations
futures, pollster: Async utilities

License

Licensed under either of:

Apache License, Version 2.0 (LICENSE-APACHE)
MIT License (LICENSE-MIT)

at your option.

Contributing

Contributions are welcome! Areas of particular interest:

WGSL shader implementations for calculus operations
Performance benchmarks and optimization
Platform-specific testing and bug reports
Documentation improvements and examples

References

WebGPU Specification
wgpu Documentation
Geometric Algebra GPU Acceleration (example reference)

amari-gpu 0.24.1

amari-gpu

Overview

Architecture

Current Integrations (v0.19.1)

Implemented GPU Acceleration

Current Hardware Validation

GPU-backed vs GPU-recommended posture

Temporarily Disabled Modules

Features

Usage

Basic Setup

Calculus GPU-Ready API (CPU-semantic fallback in 0.20.0)

Dual Number GPU Operations (narrow v1 surface)

Automata GPU Operations (mixed GPU-backed + documented fallback)

Measure GPU Operations (mixed GPU-backed + documented fallback)

Functional Analysis GPU Operations (mixed GPU-backed + documented fallback)

Core Geometric Algebra + Information Geometry (default crate-root APIs)

Infrastructure / Adaptive / Performance / Timeline APIs (orchestration layer)

Tropical GPU Acceleration (narrow v1 surface)

Tropical v1 Surface

Holographic Memory GPU Acceleration

Holographic GPU Operations (validated v1)

WGSL Shaders

Optical Field GPU Acceleration (v0.15.1)

Optical Field GPU Operations

WGSL Shaders for Optical Operations

Topology GPU Operations (mixed GPU-backed + documented fallback)

Topology Operations

WGSL Shaders for Topology Operations

Dynamics GPU Acceleration (v0.19.1)

Dynamics GPU Operations

WGSL Shaders for Dynamics Operations

Enumerative Geometry GPU Operations (high-use broad surface)

Enumerative GPU Operations

GF(2) GPU Operations (fixed-layout GPU-backed surface)

Relativistic GPU Operations (Minkowski products + simplified geodesic propagation)

Network GPU Operations (narrow GPU distances + adaptive CPU fallback)

Probabilistic GPU Operations (GPU-backed sampling/statistics + small-batch CPU fallback)

Probabilistic GPU Operations

Adaptive CPU/GPU Dispatch

Batch Size Thresholds

Implementation Status

Holographic Module (v0.13.0)

Optical Field Module (v0.15.1)

Probabilistic Module (v0.20.0)

Calculus Module (v0.13.0)

Topology Module (v0.16.0)

Dynamics Module (v0.19.1)

Examples

Development

Running Tests

Building Documentation

Future Work

Short-term (v0.13.x)

Medium-term (v0.14.x - v0.15.x)

Long-term (v1.0.0+)

Performance Considerations

Platform Support

Dependencies

License

Contributing

References