# R18: Compact: Approximating Complex Activation Functions for Secure Computation

Compact builds input-density-aware piecewise polynomial approximations for complex activations. PLLM status: tracked.

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Document ID: `pllm.docs.research.papers.r18-compact`  
Release: `0.1.0`

**Status:** `tracked`
**Year:** 2024
**Authors:** Mazharul Islam, Sunpreet S. Arora, Rahul Chatterjee, Peter Rindal, Maliheh Shirvanian
**External source:** [Compact: Approximating Complex Activation Functions for Secure Computation](https://arxiv.org/abs/2309.04664)

## Source contribution

Compact builds input-density-aware piecewise polynomial approximations for complex activations.

## PLLM perspective

Implement its fitting objective and published approximation profile separately from protected evaluation. Freeze coefficient/interval hashes and add explicit tail policy.

Our Fourier/boundary-matched fits are distinct hypotheses, not Compact reproductions.

This paper remains tracked. Named modules below are implementation targets, not finished PLLM components; no reproduction, integration, assurance, or matched benchmark is claimed.

The source's boundary remains binding: Calibration is not a proof of a worst-case range. Model quality and exact agreement with the chosen approximation are distinct.

## PLLM modules and documentation

Target module identifiers: `numeric.piecewise_fit`, `compiler.approximation_profile`. These identifiers describe scoped work unless this page explicitly links an implementation source. Dependencies: None.

- [Research backlog](/research/backlog/)
- [Reimplementation backlog](/research/backlog/)
- [Clean-room workflow](/research/clean-room/)

## Backlog

This source is assigned to reimplementation priority 2, **Activation approximation**. Its source-registry order is 18. Follow current gates and unfinished work in the [research backlog](/research/backlog/).