Jeremy Budd, Assistant Professor at the University of Birmingham, and Tim Scarfe, CEO of Machine Learning Street Talk, discuss the paper “Why Creativity Cannot Be Interpolated”, which argues that genuine creativity requires respect for constraints that today’s AI lacks.

Building on ideas from François Chollet, Kenneth Stanley, and others, explore why AI slop is the result of novelty unconstrained by understanding and how systems capable of extending their own phylogeny could become creative, regardless of substrate.

In This Episode -

• Creativity vs. interpolation

• Understanding as structured constraint-following

• Picbreeder’s evolutionary image representations

• AlphaZero and creative game play

• Why LLMs remain highly derivative

• Human-AI co-creativity

• Open-ended search vs. optimization

• Evolvable representations and abstraction

• Constraints enable creativity

• Future directions beyond gradient descent

References -

• CBMM10 Panel: Research on Intelligence in the Age of AI - https://www.youtube.com/watch?v=Gg-w_n9NJIE&t=2885

• “Sparks of Artificial General Intelligence: Early experiments with GPT-4” - https://arxiv.org/abs/2303.12712

• Chollet: “On the Measure of Intelligence” - https://arxiv.org/abs/1911.01547

• Stanley: PicBreeder - https://picbreeder.net/6793

• Sakana’s PicBreeder Experiment - https://pub.sakana.ai/picbreeder-vlm/

• ARC-AGI-3 - https://arcprize.org/arc-agi/3

About the Paper -

“Why Creativity Cannot Be Interpolated: And Why Understanding Is the Path to Get There”

Jeremy Budd and Tim Scarfe

The paper argues that novelty alone is insufficient for creativity. Instead, creative systems must develop structured, path-dependent representations that preserve the constraints underlying previous discoveries, allowing them to extend rather than merely recombine existing ideas. Through examples including Picbreeder, AlphaGo, AlphaZero, and modern large language models, the authors propose that human-AI collaboration currently offers the strongest path toward genuinely creative machine intelligence.

https://arxiv.org/abs/1911.01547

About the Guests -

Dr. Jeremy Budd is Assistant Professor of Mathematics at the University of Birmingham. His research focuses on the intersection of applied analysis and data science, specializing in graph-based learning methods for image processing.

https://jeremybudd.com/

Dr. Tim Scarfe is the founder and host of the popular AI podcast Machine Learning Street Talk (MLST). He’s a multi-time startup founder and was previously a Principal Engineer at Microsoft and Chief Data Scientist at bp. He has a Ph.D in machine learning and a first-class degree in computer science.

https://www.mlst.ai/about

https://www.youtube.com/@MachineLearningStreetTalk

Credits -

• Host & Music: Bryan Landers, Technical Staff, Ndea

• Editor: Alejandro Ramirez

• https://x.com/ndea

• https://x.com/bryanlanders

• https://ndea.com

Loris D’Antoni, Professor of Computer Science and Engineering at UC San Diego, discusses his paper “Constrained Adaptive Rejection Sampling,” which introduces a constrained decoding algorithm that preserves the original language model distribution while satisfying formal constraints, enabling higher-quality structured generation for applications including compiler testing, code generation, and scientific discovery.

Explore how the rise of large language models has reshaped research in programming languages, and how formal methods remain essential for producing software that is both useful and trustworthy in the era of AI-generated code.

In This Episode -

• Program synthesis in the age of LLMs

• Why constrained decoding distorts language model distributions

• Adaptive rejection sampling with remembered failures

• Formal methods for trustworthy AI-generated code

• Compiler fuzzing with language models

• Using symbolic methods to improve LLM output

• Automata theory

• Verified code translation and equivalence checking

References -

• UCSD Programming Systems: https://cseweb.ucsd.edu/groups/progsys/

• Nadia Polikarpova: https://cseweb.ucsd.edu/~npolikarpova/

• Rajeev Alur: https://www.cis.upenn.edu/~alur/

• Code Metal: https://www.codemetal.ai/

About the Paper -

“Constrained Adaptive Rejection Sampling”

Loris D’Antoni, Pavel Parys, Sriram Vadia, Taylor Berg-Kirkpatrick

Large language models often rely on constrained decoding to generate outputs that satisfy grammars or structured schemas, but existing methods can substantially distort the model’s probability distribution. This paper introduces Constrained Adaptive Rejection Sampling (CARS), an algorithm that incrementally learns from rejected samples while provably sampling from the correct constrained distribution, producing significantly higher-quality outputs and large improvements in practical tasks such as compiler fuzzing.

https://arxiv.org/pdf/2510.01902

About the Guest -

Loris D’Antoni is Jacobs Faculty Scholar and Professor of Computer Science and Engineering at the University of California, San Diego, where he leads the Programming Systems Group. His research spans program synthesis, programming languages, formal verification, compiler testing, and trustworthy AI systems, with recent work focusing on combining formal methods with LLMs. He also serves as a Scholar at Code Metal, where he works on verified AI-assisted software engineering.

https://cseweb.ucsd.edu/~ldantoni/

Credits -

• Host & Music: Bryan Landers, Technical Staff, Ndea

• Editor: Alejandro Ramirez

• https://x.com/ndea

• https://x.com/bryanlanders

• https://ndea.com

Stephen Muggleton, Emeritus Professor at Imperial College London, discusses his paper “Inductive Logic Programming”, which introduced and named the field. The paper presents a framework that combines logic programming with machine learning, enabling systems to learn interpretable logical rules from examples and background knowledge.

Muggleton reflects on the intellectual origins of ILP, tracing its development through his PhD work under Donald Michie and his interactions with pioneering figures including John McCarthy, Ross Quinlan, and others from the early AI community. He describes how dissatisfaction with purely propositional learning systems motivated a search for richer representations capable of expressing structured knowledge and supporting scientific discovery.

In This Episode -

• Origins of ILP

• Michie, Turing, and AI research bans

• Logic programming meets machine learning

• Learning from positive examples

• Learning from a single example

• Predicate invention & abstraction

• Robot Scientist research program

• Efficient greedy search algorithms

• ILP & modern large language models

References -

• https://www.doc.ic.ac.uk/~shm/Papers/Reduce.pdf

• https://en.wikipedia.org/wiki/Donald_Michie

• https://en.wikipedia.org/wiki/John_McCarthy_(computer_scientist)

• https://en.wikipedia.org/wiki/Ross_Quinlan

• https://en.wikipedia.org/wiki/Karl_Popper

About the Paper -

“Inductive Logic Programming”

Author: Stephen Muggleton

Venue: New Generation Computing (1991)

The paper formally introduced inductive logic programming as a research field at the intersection of machine learning and logic programming. It argues that learning systems should be able to construct logical theories using both observed examples and existing background knowledge, enabling more expressive and interpretable forms of machine learning.

https://www.doc.ic.ac.uk/~shm/Papers/ilp.pdf

About the Guest -

Stephen Muggleton is Emeritus Professor of Machine Learning at Imperial College London. He is the founder of inductive logic programming and has made foundational contributions to machine learning, scientific discovery systems, program synthesis, and neurosymbolic AI. His research focuses on machine learning, logic-based reasoning, scientific discovery, probabilistic inference, and automated knowledge acquisition.

https://www.doc.ic.ac.uk/~shm/

Credits -

• Host & Music: Bryan Landers, Technical Staff, Ndea

• Editor: Alejandro Ramirez

• https://x.com/ndea

• https://x.com/bryanlanders

• https://ndea.com

Aws Albarghouthi, Associate Professor of Computer Science at the University of Wisconsin-Madison, discusses his paper “Recursive Program Synthesis”, which introduced Escher, an inductive synthesis algorithm for learning recursive programs from input-output examples.

The project emerged from Albarghouthi’s early work in program verification and inductive proofs for recursive procedures. After he and fellow graduate student Zachary Kincaid developed initial ideas for synthesizing recursive programs, they cold-emailed Sumit Gulwani at Microsoft Research, whose feedback and collaboration helped shape the direction of the paper.

In This Episode -

• Recursive synthesis from examples

• Escher’s forward and backward search

• Goal graphs for partial programs

• Components as reusable building blocks

• Synthesis benchmarks and comparisons with Sketch

• Quantum compiler synthesis

• Qubit mapping and routing synthesis- Agent correctness and prompt injection

References -

• Microsoft PROSE: https://www.microsoft.com/en-us/research/project/prose/

• SKETCH: https://people.csail.mit.edu/asolar/papers/Solar-Lezama09.pdf

• Generating Compilers for Qubit Mapping and Routing: https://arxiv.org/abs/2508.10781

• Synthesizing Quantum-Circuit Optimizers: https://arxiv.org/abs/2211.09691

• 'Introduction to Neural Network Verification' book: https://verifieddeeplearning.com/

About the Paper -

“Recursive Program Synthesis”

Aws Albarghouthi, Sumit Gulwani, and Zachary Kincaid

Computer Aided Verification, CAV 2013The paper presents Escher, a synthesis algorithm that learns recursive procedures from input-output examples. Escher combines component-based enumeration, interactive example refinement, and a goal graph that helps assemble partial programs into complete recursive solutions.

https://www.microsoft.com/en-us/research/publication/recursive-program-synthesis/

About the Guest -

Aws Albarghouthi is an associate professor of computer science at the University of Wisconsin-Madison. His research focuses on program synthesis, formal verification, quantum computing systems, and the correctness of AI agents.

https://pages.cs.wisc.edu/~aws/

Credits -

• Host & Music: Bryan Landers, Technical Staff, Ndea

• Editor: Alejandro Ramirez

• https://x.com/ndea

• https://x.com/bryanlanders

• https://ndea.com

Kevin Ellis, Assistant Professor at Cornell University, discusses his influential paper “DreamCoder,” which presents a system that jointly learns reusable program abstractions and a neural search strategy through an iterative wake-sleep process.

The work emerged from early efforts in library learning and a broader question about how humans accumulate concepts over time. Ellis reflects on the challenge of searching vast program spaces and how inspiration from cognitive processes, particularly dreaming and replay, led to a system that incrementally builds knowledge by reusing prior solutions.

In This Episode -

• Program synthesis beyond formal specifications

• Natural language as executable programs

• Library learning for compositional reuse

• Wake-sleep cycles for program learning

• Neural-guided search over program space

• E-graph refactoring for abstraction discovery

• Emergence of map and fold primitives

• Probabilistic programs for uncertainty

• World models beyond frame prediction

• Program synthesis benchmarks

References -

• ARC-AGI-3: https://arcprize.org/arc-agi/3

• ExoPredicator: https://arxiv.org/abs/2509.26255

• AutumnBench: https://www.basis.ai/blog/autumn-platform-2025/

About the Paper -

“DreamCoder: bootstrapping inductive program synthesis with wake-sleep library learning”

Kevin Ellis, Catherine Wong, Maxwell Nye, Mathias Sablé-Meyer, Lucas Morales, Luke Hewitt, Luc Cary, Armando Solar-Lezama, Joshua B. Tenenbaum

PLDI 2021 (ACM SIGPLAN Conference on Programming Language Design and Implementation)

DreamCoder is a program synthesis system that learns both a library of reusable program components and a neural search policy by iteratively solving tasks and compressing solutions into abstractions. It alternates between solving problems (wake phase) and improving its internal representations via abstraction and dreaming phases, enabling more efficient search and generalization across domains.

https://dl.acm.org/doi/10.1145/3453483.3454080

About the Guest -

Kevin Ellis is an Assistant Professor at Cornell University working on program synthesis, neurosymbolic AI, and computational models of cognition. His research focuses on learning structured representations such as programs that capture compositional knowledge about the world.

https://www.cs.cornell.edu/~ellisk/

Credits -

• Host & Music: Bryan Landers, Technical Staff, Ndea

• Editor: Alejandro Ramirez

• https://x.com/ndea

• https://x.com/bryanlanders

• https://ndea.com

Gust Verbruggen, Senior AI researcher and member of the PROSE team at Microsoft, discusses his paper "Semantic Programming by Example with Pre-trained Models," which introduces a framework for integrating inductive program synthesis with large language models.

The project emerged from an attempt to extend Flash Fill-style program synthesis beyond purely syntactic string transformations. Motivated by limitations in symbolic systems - especially their inability to access semantic knowledge without manually encoding it - Verbruggen and collaborators explored how GPT-3 could serve as a semantic oracle within the PROSE framework. The result is a neurosymbolic architecture that preserves the efficiency and guarantees of symbolic synthesis while selectively delegating semantic subproblems to a language model.

In This Episode -

• Limitations of both program synthesis and LLMs

• Programming by example

• Syntactic versus semantic

• Integrating GPT-3 as semantic operators

• Semantic map, position, and condition operators

• Deductive backpropagation in PROSE

• Deferred query execution for efficiency

• Greedy clustering to control search explosion

• Ranking programs to minimize semantic calls

References

• https://www.microsoft.com/en-us/research/group/prose/

• https://www.microsoft.com/en-us/research/project/prose-framework/

• https://www.dagstuhl.de/en/seminars/seminar-calendar

• Sumit Gulwani's Flash Fill talk: https://youtu.be/421gU482xFE

About the Paper -

"Semantic Programming by Example with Pre-trained Models"

Gust Verbruggen, Vu Le, Sumit Gulwani

Proceedings of the ACM on Programming Languages (OOPSLA), 2021

This paper presents a framework for augmenting inductive program synthesis with semantic operators powered by large language models. By decomposing tasks into syntactic and semantic subproblems, the system delegates only the irreducibly semantic components to a pre-trained model, while maintaining symbolic guarantees elsewhere. A deferred query execution strategy allows efficient learning without excessive model calls.

https://dl.acm.org/doi/10.1145/3485477

About the Guest -

Gust Verbruggen is a researcher at KU Leuven and a member of Microsoft’s PROSE team. His work focuses on program synthesis, data wrangling, and neurosymbolic integration, particularly in real-world automation settings such as spreadsheets and code refactoring tools.

• https://www.microsoft.com/en-us/research/people/gverbruggen/

• https://scholar.google.com/citations?user=TmU3sKMAAAAJ&hl=en

Credits -

• Host & Music: Bryan Landers, Technical Staff, Ndea

• Editor: Alejandro Ramirez

• https://x.com/ndea

• https://x.com/bryanlanders

• https://ndea.com

Program synthesis is the problem of automatically generating code that satisfies a specification. The real challenge isn’t searching faster, it’s making the right parts of the search space searchable at all.

This week's episode is a short recap of the podcast so far. Across the past 8 conversations - spanning grammar filtering, temporal synthesis, inductive logic programming, vision-language programs, and symbolic world models - we explore 3 emergent themes.

1. Shrinking the search space, without breaking correctness

2. Why "correct" programs still behave badly

3. The real meaning of "neurosymbolic"

At a high level, all of the solutions we've explored are grappling with the problem of search - from problem representation to the optimal divide between neural and symbolic.

Credits -

• Host, Editor, Music: Bryan Landers, Technical Staff, Ndea

• https://x.com/ndea

• https://x.com/bryanlanders

• https://ndea.com

The way a problem is represented can determine whether it is solvable at all.

Céline Hocquette, AI researcher at Ndea and former postdoctoral researcher at the University of Oxford, discusses her paper “Relational Decomposition for Program Synthesis”, which introduces a representation-driven approach to inductive program synthesis based on decomposing examples into relational facts.

The paper emerged from Hocquette’s long-standing engagement with inductive logic programming (ILP), beginning with her doctoral work at Imperial College London under Stephen Muggleton and continuing through her time in Andrew Cropper’s group in Oxford. Motivated by the scalability limits of learning long chains of reasoning, the work reflects a broader intellectual trajectory focused on making symbolic learning systems more efficient by rethinking representation and decomposition rather than adding domain-specific heuristics.

In This Episode -

• Inductive logic programming (ILP)

• Deductive vs. inductive program synthesis

• Relational vs. functional programs

• Decomposing examples into logical facts

• Datasets: ARC-AGI, 1D-ARC, strings, list functions

• Systems & approaches: POPPER, ARGA, METABIAS, BEN, Hacker-Like

References -

• https://github.com/logic-and-learning-lab/Popper

• https://andrewcropper.com/

• ARC-AGI - https://arcprize.org/arc-agi

• 1D-ARC - https://arxiv.org/abs/2305.18354

• ARGA - https://arxiv.org/abs/2210.09880

• METABIAS - https://www.doc.ic.ac.uk/~shm/Papers/ECAI-546.pdf

• BEN - https://arxiv.org/abs/2301.03094

• Hacker-Like - https://www.nature.com/articles/s41467-024-50966-x

About the Paper -

“Relational Decomposition for Program Synthesis”

Céline Hocquette, Andrew Cropper

arXiv, 2024

The paper proposes transforming inductive program synthesis problems into sets of relational input–output facts, allowing systems to learn smaller, reusable logical rules instead of long functional compositions. This decomposition significantly improves scalability and generalization when learning programs from few examples across strings, lists, and ARC-style reasoning tasks.

https://arxiv.org/abs/2408.12212

About the Guest -

Céline Hocquette, Technical Staff at Ndea, works on program synthesis, inductive logic programming, and symbolic reasoning. She completed her PhD at Imperial College London and previously held a research position at the University of Oxford in Andrew Cropper’s lab. Her work focuses on scalable learning of interpretable programs from small data.

https://celinehocquette.github.io/

Credits -

• Host & Music: Bryan Landers, Technical Staff, Ndea

• Editor: Alejandro Ramirez

• https://x.com/ndea

• https://x.com/bryanlanders

• https://ndea.com

Wasu "Top" Piriyakulkij, PhD student at Cornell University advised by Kevin Ellis, discusses his paper "PoE-World: Compositional World Modeling with Products of Programmatic Experts." The episode explores how symbolic, programmatic world models can achieve strong generalization and sample efficiency by composing many small causal programs instead of learning a single monolithic model.

The conversation traces how PoE-World emerged from earlier work on active concept learning and hypothesis testing, and how object-centric Atari environments became a natural testbed for scaling symbolic world models beyond grid worlds. Piriyakulkij reflects on design failures, surprising successes, and the moment the learned world model became interactive enough to serve as a real-time simulator.

In This Episode -

• Symbolic vs. neural world models

• Products of programmatic experts

• Modular causal rules as world models

• Object-centric Atari environments

• Montezuma’s Revenge as exploration benchmark

• Sample-efficient learning from demonstrations

• Weights as expert confidence signals

• World models as executable simulators

• Exploration as program testing

References -

• WorldCoder - https://arxiv.org/abs/2402.12275

• Object-Centric Atari - https://arxiv.org/abs/2306.08649v2

• ARC-AGI-3 - https://arcprize.org

• VisualPredicator - https://arxiv.org/abs/2410.23156

• People: Marvin Minsky, François Chollet, Armando Solar-Lezama

About the Paper -

"PoE-World: Compositional World Modeling with Products of Programmatic Experts"

Authors: Wasu Top Piriyakulkij, Yishou Wang, Hao Tang, Martha Lewis, Kevin Ellis

The paper introduces a symbolic world modeling framework in which many small, interpretable programs - each encoding a simple causal rule - are combined multiplicatively into a probabilistic world model. By learning weights over these programmatic experts from limited demonstrations, the system produces accurate, stochastic simulators that generalize to new environments with minimal data.

https://arxiv.org/abs/2505.10819

About the Guest -

Wasu Top Piriyakulkij is a PhD student at Cornell University advised by Kevin Ellis. His research focuses on symbolic world models, program synthesis, and human-like learning and exploration in artificial agents. He is particularly interested in how compositional structure enables generalization in complex environments.

• https://www.cs.cornell.edu/~wp237/

• https://scholar.google.com/citations?user=nlO1TkkAAAAJ&hl=en

Credits -

• Host & Music: Bryan Landers, Technical Staff, Ndea

• Editor: Alejandro Ramirez

• https://x.com/ndea

• https://x.com/bryanlanders

• https://ndea.com

Antonia Wüst, PhD student at TU Darmstadt, discusses her paper "Synthesizing Visual Concepts as Vision-Language Programs," which introduces a neurosymbolic approach to visual concept induction by combining vision-language models with program synthesis.

The work grew out of Wüst’s early PhD research on visual concept learning with symbolic programs, initially in synthetic domains, and her dissatisfaction with reliance on pre-trained object detectors. As vision-language models matured, the project evolved into a broader attempt to treat these models as perceptual tools embedded within a symbolic reasoning system.

In This Episode -

• Strengths & weaknesses of vision-language models (VLMs)

• Visual concept induction

• Symbol grounding across image sets

• Designing a domain-specific language (DSL) for visual reasoning

• A probabilistic context-free grammar for program search

• Interpretability benefits of synthesized visual programs

• Bongard problems and human-like abstraction

References -

• https://arxiv.org/abs/2511.18964

• https://cs.stanford.edu/people/jcjohns/clevr/

• https://en.wikipedia.org/wiki/Bongard_problem

• https://wolfstam.github.io/

• https://www.hikarushindo.com/

• https://www.ml.informatik.tu-darmstadt.de/people/lhelff/index.html

• https://ojs.aaai.org/index.php/AAAI/article/view/20616

• https://arcprize.org/arc-agi

About the Paper -

“Synthesizing Visual Concepts as Vision-Language Programs”

Antonia Wüst, Wolfgang Stammer, Hikaru Shindo, Lucas Nunes, Christian Kersting

NeurIPS 2025

The paper presents a neurosymbolic framework that combines vision-language models with program synthesis to learn visual concepts from examples. Vision-language models provide grounded symbolic representations, while program synthesis performs explicit reasoning to derive interpretable and reliable visual rules.

https://arxiv.org/abs/2511.18964

About the Guest -

Antonia Wüst is a PhD student at Technische Universität Darmstadt in the AI and Machine Learning Lab, supervised by Christian Kersting. Her research focuses on abstract visual reasoning, visual concept induction, and neurosymbolic AI, with an emphasis on combining perception and symbolic reasoning.

• https://www.ml.informatik.tu-darmstadt.de/people/awuest/index.html

• https://x.com/toniwuest

Credits -

• Host & Music: Bryan Landers, Technical Staff, Ndea

• Editor: Alejandro Ramirez

• https://x.com/ndea

• https://x.com/bryanlanders

• https://ndea.com