1.
How Fast is AI in Pharo?
Benchmarking Linear Regression
1Arolla, Paris
2Inria, Univ. Lille, CNRS, Centrale Lille, UMR 9189 - CRIStAL
Oleksandr ZAITSEV1,2, Sebastian JORDAN MONTAÑO2, Stéphane DUCASSE 2
IWST22 — International Workshop on Smalltalk Technologies Novi Sad, Serbia
oleksandr.zaitsev@arolla.fr

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2
Fast
Very slow!
Why?
pharo-ai
Scikit-learn
(Python)
Training machine learning models

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Training machine learning models
Can we do the same in Pharo?

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4

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5
LAPACK SciPy scikit-learn
pharo-ai
PolyMath
LAPACK
Pharo
Python
Fast
Algebra
Math
Machine
Learning

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We want to provide a proof of concept that math & AI
algorithms in Pharo can be boosted by delegating time-
consuming operations to highly-optimised external libraries.
To do that, we build a prototype implementation of linear
regression based on the DGELSD routine of LAPACK

7.
Linear regression
and how it is
implemented

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Linear Regression Problem

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Linear Regression Problem

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Linear Regression Problem

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Linear Regression Implementations
Implementation
Gradient Descent Least Squares
- Iterative
- Approximate
- One iteration
- Exact solution

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Implementation 1. Gradient Descent

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Need to minimise the errors
ei = ̂
yi − yi
Cost function
- mean squared errors
J(w) =
1
m
m
∑
i=1
e2
i
Implementation 1. Gradient Descent

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J(w) =
1
m
m
∑
i=1
( ̂
yi − yi)2
Implementation 1. Gradient Descent

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J(w) =
1
m
m
∑
i=1
( ̂
yi − yi)2
Implementation 1. Gradient Descent

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J(w) =
1
m
m
∑
i=1
( ̂
yi − yi)2
θ(new)
= θ(old)
− α
∂
∂θi
J(θ)
Implementation 1. Gradient Descent

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Implementation 2. Least Squares
̂
θ = argmin||y − Xθ||2
Orthogonal projection

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Implementation 2. Least Squares
Implemented as
DGELSD routine
In LAPACK
We can call it
through FFI

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Demo will come in the end
Wait for it!

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Experiment

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Datasets

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Research Questions
- RQ.1 - Measuring LAPACK speedup.
How much time improvement can we achieve by calling
LAPACK from Pharo?
- RQ.2 - Comparing to scikit-learn.
How does Pharo & LAPACK implementation compare to the
one provided by scikit-learn?
- RQ.3 - Comparing pure Pharo with Python.
How does pure Pharo implementation of linear regression
compare to equivalent pure Python implementation?

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RQ.1 - Measuring LAPACK speedup

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Time in seconds (less is better)
Small
Medium
Pure Pharo vs Pharo & LAPACK
1820 times faster
2103 times faster
Pharo Pharo & LAPACK
19min40sec 1h44min
0.6sec 2.9sec
Help
RQ.1 - Measuring LAPACK speedup

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RQ.2 - Comparing to scikit-learn.

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RQ.2 - Comparing to scikit-learn.

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RQ.3 - Comparing pure Pharo with Python

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RQ.3 - Comparing pure Pharo with Python

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Summary
‣ We propose a prototype implementation of Linear Regression based on LAPACK
‣ We show that LAPACK & Pharo is up to 2103 times faster than pure Pharo
‣ We also show that scikit-learn is 8-5 times faster than our prototype, depending on the
size of the data.
‣ Finally, we demonstrate that pure Pharo is up to 15 times faster than the equivalent
implementation in pure Python
‣ Those findings can lay the foundation for the future work in building fast numerical
libraries for Pharo and further using them in higher-level libraries such as pharo-ai.