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arxiv: 2606.10237 · v1 · pith:KUIUOL7Fnew · submitted 2026-06-08 · 💻 cs.AI · cs.LG

Minimalist Genetic Programming

Leonardo Trujillo This is my paper

Pith reviewed 2026-06-27 16:05 UTC · model grok-4.3

classification 💻 cs.AI cs.LG
keywords minimalist genetic programmingsymbolic regressionprogram inductionMERGE operatorsyntactic derivationgenetic programming
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The pith

When given the right atomic building blocks, Minimalist Genetic Programming recovers exact ground truth models on symbolic regression tasks where standard GP fails.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes Minimalist Genetic Programming as a new approach to program induction. It replaces the evolutionary search of standard genetic programming with a syntactic derivation process inspired by the Minimalist Program in linguistics. The core process is the MERGE operator, which incrementally combines atomic syntactic objects into complex expressions using a simple Markovian process. On symbolic regression benchmarks known to cause bloat in GP, MGP consistently produces the exact target model when a suitable lexicon is provided. This reframes program induction as a derivation task rather than a search problem.

Core claim

MGP is able to discover the core building blocks of the symbolic expressions, and to incrementally combine them using MERGE. When a proper lexicon of atomic syntactic objects is chosen, MGP consistently produces the exact ground truth model on symbolic regression tasks where standard GP struggles.

What carries the argument

The MERGE operator, a binary set formation process that constructs complex syntactic structures incrementally from a lexicon of atomic objects.

If this is right

  • MGP avoids bloat by using incremental derivation instead of evolutionary growth.
  • It can recover exact models without the search overhead of GP when the lexicon is appropriate.
  • The minimalist approach shows that program induction can be solved through syntactic merging rather than optimization.
  • Insights from human language syntax are relevant to constructing symbolic models in AI.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the lexicon must be chosen by hand, the method shifts the problem from search to lexicon design for new tasks.
  • Automating lexicon selection could combine MGP with other methods to handle a wider range of problems.
  • This derivation view might apply to other program induction domains beyond symbolic regression.
  • Testing on problems where the ground truth is not known could reveal if the method generalizes without oracle knowledge of the target.

Load-bearing premise

A proper lexicon of atomic syntactic objects can be chosen in advance for the target problem.

What would settle it

Running MGP on one of the benchmark symbolic regression tasks with the stated proper lexicon and observing that it does not recover the exact ground truth model.

Figures

Figures reproduced from arXiv: 2606.10237 by Leonardo Trujillo.

Figure 1
Figure 1. Figure 1: General overview of the main elements in MP syntax considered for this [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Trees generated by MERGE. (a) A generic tree generated by MERGE, [LABEL ′SOa SO′ b ]. (b) Example using a mathematical Lexicon [semantic ′x1 + x ′ 2 ]. (C) The same expression using a typical GP tree. that the derivation has converged; if not, then the derivation is said to have crashed and the workspace is discarded. This process is depicted clearly in [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: First, consider MERGE of an operator and a semantic atomic object. For binary operators the new object is labeled as incomplete, such as [incomplete ′x1+′ ] or [incomplete ′x1×′ ], because they are not computable. If the operator is unary (such as sin() or √) MERGE does trigger a Phase Transition and the object is evalu￾ated, computing its output semantics and labeling it as a semantic object, such as [sem… view at source ↗
Figure 3
Figure 3. Figure 3: Examples of First-Order MERGE: (a) a binary operator and an atomic termi￾nal [incomplete ′x1+′ ]; (b) a unary operator and an atomic terminal [semantic ′ sin(x1) ′ ]; (c) two atomic terminals x1 and x2, labeled as xu ∈ x1, x2 depending on the interface con￾dition; (d) two operators with the same arity creates a list of operators [operator ′+, ×′ ]; and (e) an unary operator sin() and a binary operator +, l… view at source ↗
Figure 4
Figure 4. Figure 4: Examples of Higher-Order MERGE with operator objects: (a) non￾symmetric merge between [operator ′+′ ] and [operator ′÷′ , ′ ×′ ] to generate [operator ′+′ ]; (b) an operator object [operator ′+, ÷′ ] and a semantic object [semantic ′x ′ 1 ] to generate [incomplete ′x1 +, ÷′ ]; and (c) an operator object [operator ′+, ×′ ] and an incomplete object [incomplete ′x1−′ ] to generate [incomplete ′x1 + ×′ ]. • In… view at source ↗
Figure 5
Figure 5. Figure 5: Examples of Higher-Order MERGE with semantic and incomplete objects: (a) an incomplete object [incomplete ′x2+′ ] and a semantic object [semantic ′x1 + x ′ 1 ] to generate [semantic ′x2 + x1 + x ′ 1 ]; (b) two incomplete objects [incomplete ′x1+′ ] and [incomplete ′x2×′ ] to generate [semantic ′x1 op x′ 2 ] where op ∈ {+, ×} that is selected based on the interface condition; and (c) two incomplete objects … view at source ↗
Figure 6
Figure 6. Figure 6: High-level view of Minimalist Genetic Programming. [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Convergence plots of MGP on each of the Solvable benchmark problems, [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Workspace composition during the final main derivation for Solvable bench [PITH_FULL_IMAGE:figures/full_fig_p026_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Convergence plots of MGP on each of the unsolvable benchmark problems, [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Workspace composition during the final main derivation for Unsolvable [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Polynomial approximations for the Unsolvable benchmark problems. [PITH_FULL_IMAGE:figures/full_fig_p028_11.png] view at source ↗
read the original abstract

Genetic programming (GP) is based on two important insights. First, that any learning task can fundamentally be posed as a program induction problem, where the goal is to construct a symbolic hierarchical model that is expressed as a syntax tree. Second, to pose this task as a search problem, and use evolution to locate the desired model. Since it was proposed, GP has produced notable results in a wide range of tasks and problem domains. This work presents an alternative view by modifying the second core insight of GP, posing the problem as a syntactic derivation task instead. In particular, this paper presents Minimalist Genetic Programming (MGP), an algorithm that like GP is biologically inspired, but instead of evolution it takes inspiration from the Minimalist Program to human language, in which syntax is understood as an optimal solution to the problem of linking two other mental systems. In minimalism, the core computational process is a binary set formation operator called $MERGE$, than can be used to incrementally construct complex syntactic structures using a simple Markovian process. MGP is able to discover the core building blocks of the symbolic expressions, and to incrementally combined them using $MERGE$. The proposed system is benchmarked on symbolic regression tasks that are known to be difficult to solve with standard GP systems because of the propensity for bloat. Results show that when a proper lexicon of atomic syntactic objects are chosen, MGP is able to consistently produce the exact ground truth model on a set of symbolic regression where standard GP struggles to do the same. The insights provided by minimalism are shown to be relevant to the problem of program induction, and should be explored further based on the potential exhibited by MGP in this work.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper proposes Minimalist Genetic Programming (MGP), which reframes program induction as a syntactic derivation task using the binary MERGE operator from the Minimalist Program in linguistics rather than evolutionary search. It claims that, when a proper lexicon of atomic syntactic objects is chosen in advance, MGP consistently recovers exact ground-truth models on bloat-prone symbolic regression tasks where standard GP fails to do so.

Significance. If the central claim holds with a general, target-independent lexicon procedure, the work would establish a non-evolutionary, Markovian derivation method capable of exact recovery in symbolic regression, offering a potential alternative to GP that avoids bloat while drawing on linguistic syntax insights.

major comments (2)
  1. [Abstract] Abstract: the claim that 'MGP is able to consistently produce the exact ground truth model on a set of symbolic regression' is presented without any experimental details, data sets, lexicon selection procedure, quantitative metrics, or comparison protocol, rendering the central empirical result unverifiable from the manuscript.
  2. [Abstract] Abstract: the performance difference versus standard GP is conditioned on pre-selecting a 'proper lexicon of atomic syntactic objects' chosen in advance by the experimenter; no procedure is given for constructing this lexicon without knowledge of the target expression's operators and terminals, making the assumption load-bearing for any claim of a general advantage over evolutionary search.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their comments. We address each major point below regarding the abstract. We will revise the abstract to include more experimental context while preserving its brevity.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'MGP is able to consistently produce the exact ground truth model on a set of symbolic regression' is presented without any experimental details, data sets, lexicon selection procedure, quantitative metrics, or comparison protocol, rendering the central empirical result unverifiable from the manuscript.

    Authors: The abstract provides a high-level summary of the contribution. The full manuscript details the symbolic regression benchmarks, the lexicons employed for each task, the exact-recovery metric, and comparisons against standard GP. To improve verifiability from the abstract itself, we will add a brief clause referencing the evaluation protocol and the conditional nature of the results. revision: yes

  2. Referee: [Abstract] Abstract: the performance difference versus standard GP is conditioned on pre-selecting a 'proper lexicon of atomic syntactic objects' chosen in advance by the experimenter; no procedure is given for constructing this lexicon without knowledge of the target expression's operators and terminals, making the assumption load-bearing for any claim of a general advantage over evolutionary search.

    Authors: The manuscript already qualifies its empirical claim with the phrase 'when a proper lexicon of atomic syntactic objects are chosen.' No general, target-independent lexicon-construction procedure is presented because the work focuses on the MERGE-based Markovian derivation process once suitable atomic objects are supplied. The paper does not assert an unconditional advantage over GP; the lexicon requirement is explicit and load-bearing by design. Future extensions could address automated lexicon discovery, but that lies beyond the current scope. revision: no

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper presents MGP as an alternative to evolutionary search by reframing program induction as incremental syntactic derivation via the MERGE operator drawn from linguistic theory. The central mechanism (binary set formation to build syntax trees from a lexicon) is described independently of any fitted parameters or self-referential definitions. Results are reported under the explicit condition of a pre-chosen lexicon, which parallels the standard practice of specifying function/terminal sets in GP rather than constituting a fitted input renamed as a prediction. No equations, uniqueness theorems, or self-citations are invoked to force the outcome by construction, and the derivation remains self-contained against the stated syntactic process.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that linguistic minimalism provides a suitable computational model for program induction and on the free parameter of a pre-chosen lexicon whose selection process is unspecified.

free parameters (1)
  • lexicon of atomic syntactic objects
    The paper states success depends on choosing a proper lexicon but provides no method or criteria for its construction or selection.
axioms (1)
  • domain assumption Syntax is an optimal solution to linking mental systems via a binary set formation operator MERGE that constructs structures through a simple Markovian process.
    Invoked directly from the Minimalist Program in linguistics and applied to symbolic expression building.

pith-pipeline@v0.9.1-grok · 5822 in / 1354 out tokens · 29545 ms · 2026-06-27T16:05:25.817702+00:00 · methodology

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Reference graph

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