Bogdan Burlacu’s research while affiliated with University of Applied Sciences Upper Austria and other places

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Publications (71)


How to Measure Explainability and Interpretability of Machine Learning Results
  • Chapter

February 2025

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20 Reads

Elisabeth Mayrhuber

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Bogdan Burlacu

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The increasing complexity of machine learning models has motivated the need to ensure that the results are understandable and transparent, enabling trust and accountability. This work provides an extensive overview of methods to measure the explainability and interpretability of machine learning results. This work addresses the challenges posed by closed-box models, which lack transparency in their decision-making processes and evaluates techniques used to make these models more understandable. Through the application of open-box models, like symbolic regression, we demonstrate that it is possible to achieve high interpretability without sacrificing model performance. Additionally, we highlight the necessity for robust and unified evaluation metrics for explainability and interpretability, evaluating complexity and fidelity scores as a comprehensive measure. A variety of closed-box models have been trained and evaluated in terms of performance, and explainability including, artificial neural networks, support vector regression, and random forest regression. Additionally, we trained symbolic regression models with different levels of complexity, which were evaluated regarding their performance and interpretability. Our results underscore the importance of developing methodologies that balance complexity and interpretability, advocating for further research into explainable artificial intelligence frameworks, particularly those incorporating genetic programming. This work aims to contribute to the advancement of responsible and transparent artificial intelligence systems.


Revisiting Gradient-Based Local Search in Symbolic Regression

February 2025

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2 Reads

Gradient descent-based local search can dramatically improve solution performance in symbolic regression tasks, at the cost of significantly higher runtime as well as increased risks of overfitting. In this paper, we investigate exactly what amount of local search is really needed within the GP population. We show that low intensity local search is sufficient to boost the fitness of the entire population, provided that local search information in the form of optimized numerical parameters is written back into the genotype at least some of the time. Our results suggest that spontaneous adaptations (in the Lamarckian sense) act as evolutionary fuel for the Baldwin effect in genetic programming, and that in the absence of the former, the latter does not occur and evolution is hindered. The Lamarckian model works particularly well in symbolic regression, as local search only affects model coefficients and does not affect the inheritance of useful building blocks contained in the model structure.


It’s Time to Revisit the Use of FPGAs for Genetic Programming

February 2025

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4 Reads

In the past, field-programmable gate arrays (FPGAs) have had some notable successes when employed for Boolean and fixed-point genetic programming (GP) systems, but the more common floating-point representations were largely off limits, due to a general lack of efficient device support. However, recent work suggests that for both the training and inference phases of floating-point-based GP, contemporary FPGA technologies may enable significant performance and energy improvements—potentially multiple orders of magnitude—when compared to general-purpose CPU/GPU devices. In this chapter, we highlight the potential advantages and challenges of using FPGAs for GP systems, and we showcase how novel algorithmic considerations likely need to be made in order to extract the most benefits from specialized hardware. Primarily, we consider tree-based GP, although we include suggestions for other program representations. Overall, we conclude that the GP community should earnestly revisit the use of FPGA devices, especially the tailoring of state-of-the-art algorithms to FPGAs, since valuable enhancements may be realized. Most notably, FPGAs may allow for faster and/or less costly GP runs, in which case it may also be possible for better solutions to be found when allowing an FPGA to consume the same amount of runtime/energy as another platform.


An example LUT-based implementation. A LUT-based implementation of a full adder, with carry-in and carry-out. Importantly, the depicted LUT memory could implement not only this circuit, but all 3-input, 2-output digital circuits. Also, note that the schematic in the bottom-right is just for illustration; with a LUT-based implementation, no logic gates are used. For a more thorough example, see [43, Example 5.5]
A portrayal of how our GP accelerator can parallelize the evaluation of different data points and different solutions every clock cycle via a reconfigurable tree pipeline. Each node of the pipeline can perform any function within the GP primitive set, as well as a bypass, which allows for arbitrary program shapes
High-level overview of the accelerator architecture. The accelerator stores programs (e.g., sin(v0)+1.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{sin}(v_0)+1.0$$\end{document}) in aprogram memory, which are dynamically compiled by the bprogram compiler into configuration data for the cprogram evaluator. The program evaluator uses a reconfigurable function tree pipeline to execute a compiled expression for a set of fitness cases, resulting in a set of outputs to which the dfitness evaluator compares a set of desired outputs
Median sample nodes per second (NPS) vs. program bin number and maximum program size, for the nicolau_a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {nicolau\_a}$$\end{document} primitive set. For Operon and TensorGP, NPS values corresponding to the 75th\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$75^\textrm{th}$$\end{document}/25th\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$25^\textrm{th}$$\end{document} percentiles for runtime are also plotted. Note that the legend from a applies to all sub-figures, and note the use of a log scale
Sample median nodes per second (NPS) vs. program bin number and maximum program size, for the nicolau_b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {nicolau\_b}$$\end{document} primitive set. For Operon and TensorGP, NPS values corresponding to the 75th\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$75^\textrm{th}$$\end{document}/25th\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$25^\textrm{th}$$\end{document} percentiles for runtime are also plotted. Note that the legend from a applies to all sub-figures, and note the use of a log scale

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Using FPGA devices to accelerate the evaluation phase of tree-based genetic programming: an extended analysis
  • Article
  • Publisher preview available

January 2025

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33 Reads

Genetic Programming and Evolvable Machines

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Wesley Piard

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Greg Stitt

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[...]

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Wolfgang Banzhaf

This paper establishes the potential of accelerating the evaluation phase of tree-based genetic programming through contemporary field-programmable gate array (FPGA) technology. This exploration stems from the fact that FPGAs can sometimes leverage increased levels of both data and function parallelism, as well as superior power/energy efficiency, when compared to general-purpose CPU/GPU systems. In this investigation, we introduce a fixed-depth, tree-based architecture that can fully parallelize tree evaluation for type-consistent primitives that are unrolled and pipelined. We show that our accelerator on a 14nm FPGA achieves an average speedup of 43×\times when compared to a recent open-source GPU solution, TensorGP, implemented on 8nm process-node technology, and an average speedup of 4,902×\times when compared to a popular baseline GP software tool, DEAP, running parallelized across all cores of a 2-socket, 28-core (56-thread), 14nm CPU server. Despite our single-FPGA accelerator being 2.4×\times slower on average when compared to the recent state-of-the-art Operon tool executing on the same 2-processor, 28-core CPU system, we show that this single-FPGA system is 1.4×\times better than Operon in terms of performance-per-watt. Importantly, we also describe six future extensions that could provide at least a 64–192×\times speedup over our current design. Therefore, our initial results provide considerable motivation for the continued exploration of FPGA-based GP systems. Overall, any success in significantly improving runtime and energy efficiency could potentially enable novel research efforts through faster and/or less costly GP runs, similar to how GPUs unlocked the power of deep learning during the past fifteen years.

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Citations (39)


... ACM ISBN 978-x-xxxx-xxxx-x/YY/MM https://doi.org/10.1145/nnnnnnn.nnnnnnn regression models [17,18] or for scientific discovery [6,8,18,23,31,35]. ...

Reference:

Improving Genetic Programming for Symbolic Regression with Equality Graphs
Multiview Symbolic Regression

... In contrast to classical regression methods, like linear and polynomial regression, an advantage of symbolic regression is that neither the model structure, nor its parameters have to be pre-defined. Additionally highly non-linear relationships can be expressed and the generated models can be easily manipulated and transformed into any expert system [63] . Symbolic regression involves finding the best model structure and its coefficients simultaneously. ...

Evolutionary Computation and Genetic Programming
  • Citing Chapter
  • July 2024

... La Cava et al. [11] advanced this effort even further by incorporating new algorithms into the benchmark, dubbed SRBench, and proposing a collaborative environment facilitating the benchmarking of new algorithms using a common Python interface and a verified installation environment that enabled external peers to replicate the benchmark. This effort spanned multiple competitions, one of which led to a publication highlighting the challenges still faced by the field of SR in general, not only GP [5]. ...

SRBench++: Principled Benchmarking of Symbolic Regression With Domain-Expert Interpretation

IEEE Transactions on Evolutionary Computation

... However, an important disadvantage is that the structure optimization aspect makes of SR an NP-hard problem [81]. While a variety of SR algorithms exist, including deep learning-based ones [21,36,38,46,79,87], those based on genetic programming (GP) [40] often achieve state-of-the-art results [44]. GP is an approach inspired by evolution, where a population of candidate programs (or, in this context, models) adapts by recombination and mutation of their atomic components, and selection of the fittest, over a number of generations. ...

Contemporary Symbolic Regression Methods and their Relative Performance
  • Citing Article
  • December 2021

Advances in Neural Information Processing Systems

... After the first seminal papers on this topic [5][6][7], several emulators have been produced in the literature, emulating the output of Boltzmann solvers such as CAMB [8] or CLASS [9], with applications ranging from the Cosmic Microwave Background (CMB) [10][11][12][13][14], the linear matter power spectrum [11,[15][16][17][18][19], galaxy power spectrum multipoles [17,[19][20][21][22], and the galaxy survey angular power spectrum [23][24][25][26][27][28][29]. ...

A precise symbolic emulator of the linear matter power spectrum

Astronomy and Astrophysics

... Addressing the lack of standardized benchmarking, an open-source platform was introduced to evaluate 14 SR and 7 ML methods across 252 regression problems, demonstrating the effectiveness of genetic algorithms combined with parameter estimation or semantic search drivers in real-world scenarios [Cava et al. 2021]. The Operon framework, utilizing local search optimizations, balances accuracy, and simplicity, achieving high performance in synthetic track experiments [Burlacu et al. 2020, Burlacu 2023. ...

GECCO'2022 Symbolic Regression Competition: Post-Analysis of the Operon Framework
  • Citing Conference Paper
  • July 2023

... We assume that beyond 10% noise, it is difficult to recover the exact equation. The noise levels of 5% and 10% were inspired by [5,15]. For the Rydberg equation, noise levels beyond 3% were too noisy for the exact equation to be recovered, as experiments with 10% noise indicated [4]. ...

Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competition

... This characteristic significantly enhances the efficiency of the GA in identifying the optimal solution, thereby accelerating the overall computational process. The linear ranking selection [21]- [23] is also applied in our algorithm to eliminate some individuals with lower adaptability, leading to a reduction in genetic diversity in the population and, as a result, earlier convergence of the minimal THD. In the process of optimizing adaptability, individuals are systematically organized in an ascending sequence. ...

Population diversity and inheritance in genetic programming for symbolic regression

Natural Computing

... The authors demonstrated in experiments that iEQL learned interpretable and accurate models. Shape-constrained symbolic regression was introduced in [12,20,25]. It allows for the inclusion of vague prior knowledge by measuring properties of the model's shape, such as monotonicity and convexity, using interval arithmetic. ...

Shape-constrained multi-objective genetic programming for symbolic regression
  • Citing Article
  • November 2022

Applied Soft Computing

... These techniques have the advantage of having an extensive set of tools created to find an optimal parameters set. On the other hand, working with a fixed function can limit the possible shapes the regression model can fit, limiting their extrapolation capabilities [4,5]. ...

Comparing optimistic and pessimistic constraint evaluation in shape-constrained symbolic regression
  • Citing Conference Paper
  • July 2022