Quadra

Quadra is an experimental mixed-effects inference framework focused on:

• reverse-mode automatic differentiation
• Laplace approximation
• sparse Hessian methods
• implicit differentiation
• scalable scientific inference workflows

The project is oriented toward computational statistics, state-space models, and large-scale scientific modeling applications such as fisheries stock assessment.

Current development emphasizes:

• transparent numerical workflows
• reproducible benchmarking
• sparse linear algebra performance
• modular inference architecture
• computational profiling and scaling analysis

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Core Capabilities

Current implemented capabilities include:

• reverse-mode automatic differentiation
• exact and approximate gradients
• Laplace approximation
• random effects optimization
• sparse Hessian construction
• sparse factorization reuse
• implicit derivative calculations
• profiled derived quantity uncertainty
• delta-method utilities
• benchmark and scaling infrastructure
• benchmark normalization and plotting
• CI benchmark workflows

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Repository Structure

core/
    autodiff/
    laplace/
    inference/
    model/
    optimizer/

examples/
    simple/
    big/

benchmarks/
    analysis/
    comparisons/
    outputs/
    normalized/

tests/

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Building

Requirements

Recommended:

• C++17 compiler
• Eigen
• LBFGSpp
• GNU Make

Optional:

• R
• TMB

Build benchmarks and examples

make

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Running Tests

Run all tests:

make test

Run selected tests:

make test-laplace-implicit-workspace
make test-laplace-profiled-derived-report
make test-random-intercept

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Running Examples

Simple random intercept example

./examples/simple/random_intercept_model

Catch-at-age Laplace example

./examples/big/catch_at_age_laplace

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Benchmarking

Random intercept scaling

make benchmark-random-intercept

State-space scaling

make benchmark-state-space

Quadra vs TMB comparison scaffold

Quadra benchmark:

make benchmark-quadra-tmb-random-intercept-quadra

TMB benchmark:

make benchmark-quadra-tmb-random-intercept-tmb

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Benchmark Analysis

Normalize benchmark outputs:

make benchmark-normalize-all

Generate scaling plots:

make benchmark-plot-random-intercept

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Continuous Integration

GitHub Actions workflows currently provide:

• contract compilation checks
• benchmark execution
• RSS logging
• benchmark normalization
• benchmark artifact uploads
• scaling plot generation

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Current V1 Focus

The current V1 effort is focused on:

• stable mixed-effects workflows
• reusable sparse factorization infrastructure
• implicit differentiation utilities
• scalable state-space inference
• reproducible benchmark infrastructure
• comparative inference benchmarking

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Project Status

Quadra is currently experimental and under active development.

Interfaces, APIs, benchmark structure, and numerical methods may evolve rapidly during the V1 development cycle.