Uploaded September 2024 | Updated September 2026, 1 week ago
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David Spivak, a mathematician at MIT's Topos Institute known for his work in applied category theory, talks with Tim Scarfe about the nature of intelligence, creativity, and knowledge itself.
Spivak explains category theory in surprisingly concrete terms. Categories are about systems of relationships -- not just collections of things, but how those things relate to each other. Functors map one system of relationships to another, like how "counting" connects the world of sets to the world of numbers. He argues category theory's value lies in making the obvious things mathematically precise, which sounds trivial until you realize how much of mathematics depends on shared but unspoken assumptions.
The conversation moves to collective intelligence and sense-making. Drawing on Mike Levin's claim that all intelligence is collective intelligence, Spivak describes sense-making as a process of "accounting" -- like balancing a checkbook, where different perspectives contribute until the books settle and understanding stabilizes. This applies at every scale, from neurons communicating in a shared language to two people trying to agree on what category theory means for machine learning.
Where things get genuinely interesting is Spivak's take on creativity and open-endedness. He pushes back on the idea that Karl Friston's prediction error minimization framework captures everything interesting about intelligence. His counterexample: a kid shoveling sand in a sandbox who cries when pulled away. There's something about care and engagement that doesn't obviously reduce to prediction error. Questions, he argues, are more important than answers -- the act of questioning creates a spaciousness where real insight can arise.
On AI, Spivak is measured but candid. He thinks current approaches are "kicking the ball really hard" without thinking about where the ball needs to go. He worries about optimization without understanding what we're optimizing for. The discussion covers embodiment and how physical experience shapes abstract thought, the role of written language in transmitting knowledge across generations, and whether the intelligence explosion is an extension of evolutionary processes or something genuinely new.
---
TIMESTAMPS:
00:00:00 Introduction to Category Theory
00:04:40 Collective Intelligence and Sense-Making
00:09:54 Embodiment and Physical Concepts in Knowledge
00:16:23 Creativity, Open-Endedness, and Care
00:25:46 Modeling Creativity and the Role of Questioning
00:36:04 Evolution, Optimization, and AI
00:44:14 Written Language and Knowledge Transmission
---
REFERENCES:
person:
[00:00:00] David Spivak - Personal Page
dspivak.net
[00:04:40] Mike Levin - Google Scholar
scholar.google.com/citations?user=luouyakAAAAJ&hl=en
reference:
[00:00:00] MIT Category Theory Lectures by David Spivak
youtube.com/watch?v=UusLtx9fIjs
[00:00:00] Spotify Podcast Version
podcasters.spotify.com/pod/show/machinelearningstreettalk/episodes/The-Fabric-of-Knowledge---David-Spivak-e2o220h
[00:25:46] Herbert Simon - Satisficing and Bounded Rationality
https://plato.stanford.edu/entries/bounded-rationality/
[00:36:04] Eric Smith - Complexity and Early Life
youtube.com/watch?v=SpJZw-68QyE
book:
[00:09:54] Karl Friston - Active Inference
https://direct.mit.edu/books/oa-monograph/5299/Active-InferenceThe-Free-Energy-Principle-in-Mind
[00:36:04] Richard Dawkins - The Selfish Gene
amzn.to/3X73X8w
[00:36:04] Carl Sagan - The Cosmos Knowing Itself
amzn.to/3XhPruK
paper:
[00:36:04] DeepMind - Open-Ended Systems Paper
arxiv.org/abs/2406.04268
---
LINKS:
Full Transcript: app.rescript.info/share/3e4986b488817a53549bf134e2a5695a
Download PDF transcript: app.rescript.info/api/public/sessions/069a33878cbdd032/pdf
MLST is sponsored by Brave:
The Brave Search API covers over 20 billion webpages, built from scratch without Big Tech biases or the recent extortionate price hikes on search API access. Perfect for AI model training and retrieval augmentated generation. Try it now - get 2,000 free queries monthly at brave.com/api.
David Spivak, a mathematician at MIT's Topos Institute known for his work in applied category theory, talks with Tim Scarfe about the nature of intelligence, creativity, and knowledge itself.
Spivak explains category theory in surprisingly concrete terms. Categories are about systems of relationships -- not just collections of things, but how those things relate to each other. Functors map one system of relationships to another, like how "counting" connects the world of sets to the world of numbers. He argues category theory's value lies in making the obvious things mathematically precise, which sounds trivial until you realize how much of mathematics depends on shared but unspoken assumptions.
The conversation moves to collective intelligence and sense-making. Drawing on Mike Levin's claim that all intelligence is collective intelligence, Spivak describes sense-making as a process of "accounting" -- like balancing a checkbook, where different perspectives contribute until the books settle and understanding stabilizes. This applies at every scale, from neurons communicating in a shared language to two people trying to agree on what category theory means for machine learning.
Where things get genuinely interesting is Spivak's take on creativity and open-endedness. He pushes back on the idea that Karl Friston's prediction error minimization framework captures everything interesting about intelligence. His counterexample: a kid shoveling sand in a sandbox who cries when pulled away. There's something about care and engagement that doesn't obviously reduce to prediction error. Questions, he argues, are more important than answers -- the act of questioning creates a spaciousness where real insight can arise.
On AI, Spivak is measured but candid. He thinks current approaches are "kicking the ball really hard" without thinking about where the ball needs to go. He worries about optimization without understanding what we're optimizing for. The discussion covers embodiment and how physical experience shapes abstract thought, the role of written language in transmitting knowledge across generations, and whether the intelligence explosion is an extension of evolutionary processes or something genuinely new.
---
TIMESTAMPS:
00:00:00 Introduction to Category Theory
00:04:40 Collective Intelligence and Sense-Making
00:09:54 Embodiment and Physical Concepts in Knowledge
00:16:23 Creativity, Open-Endedness, and Care
00:25:46 Modeling Creativity and the Role of Questioning
00:36:04 Evolution, Optimization, and AI
00:44:14 Written Language and Knowledge Transmission
---
REFERENCES:
person:
[00:00:00] David Spivak - Personal Page
dspivak.net
[00:04:40] Mike Levin - Google Scholar
scholar.google.com/citations?user=luouyakAAAAJ&hl=en
reference:
[00:00:00] MIT Category Theory Lectures by David Spivak
youtube.com/watch?v=UusLtx9fIjs
[00:00:00] Spotify Podcast Version
podcasters.spotify.com/pod/show/machinelearningstreettalk/episodes/The-Fabric-of-Knowledge---David-Spivak-e2o220h
[00:25:46] Herbert Simon - Satisficing and Bounded Rationality
https://plato.stanford.edu/entries/bounded-rationality/
[00:36:04] Eric Smith - Complexity and Early Life
youtube.com/watch?v=SpJZw-68QyE
book:
[00:09:54] Karl Friston - Active Inference
https://direct.mit.edu/books/oa-monograph/5299/Active-InferenceThe-Free-Energy-Principle-in-Mind
[00:36:04] Richard Dawkins - The Selfish Gene
amzn.to/3X73X8w
[00:36:04] Carl Sagan - The Cosmos Knowing Itself
amzn.to/3XhPruK
paper:
[00:36:04] DeepMind - Open-Ended Systems Paper
arxiv.org/abs/2406.04268
---
LINKS:
Full Transcript: app.rescript.info/share/3e4986b488817a53549bf134e2a5695a
Download PDF transcript: app.rescript.info/api/public/sessions/069a33878cbdd032/pdf
![Neural Networks Are Elastic Origami! [Prof. Randall Balestriero]](https://i.ytimg.com/vi/l3O2J3LMxqI/mqdefault.jpg "Neural Networks Are Elastic Origami! [Prof. Randall Balestriero]
Professor Randall Balestriero joins us to discuss neural network geometry, spline theory, and emerging phenomena in deep learning, based on research presented at ICML. Topics include the delayed emergence of adversarial robustness in neural networks (grokking), geometric interpretations of neural networks via spline theory, and challenges in reconstruction learning. We also cover geometric analysis of Large Language Models (LLMs) for toxicity detection and the relationship between intrinsic dimensionality and model control in RLHF.
SPONSOR MESSAGES:
***
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Tufa AI Labs is a brand new research lab in Zurich started by Benjamin Crouzier focussed on o-series style reasoning and AGI. Are you interested in working on reasoning, or getting involved in their events?
Goto https://tufalabs.ai/
***
Show notes and transcript: https://www.dropbox.com/scl/fi/3lufge4upq5gy0ug75j4a/RANDALLSHOW.pdf?rlkey=nbemgpa0jhawt1e86rx7372e4&dl=0
TOC:
[00:00:00] Introduction
1. Neural Network Geometry and Spline Theory
[00:01:41] 1.1 Neural Network Geometry and Spline Theory
[00:07:41] 1.2 Deep Networks Always Grok
[00:11:39] 1.3 Grokking and Adversarial Robustness
[00:16:09] 1.4 Double Descent and Catastrophic Forgetting
2. Reconstruction Learning
[00:18:49] 2.1 Reconstruction Learning
[00:24:15] 2.2 Frequency Bias in Neural Networks
3. Geometric Analysis of Neural Networks
[00:29:02] 3.1 Geometric Analysis of Neural Networks
[00:34:41] 3.2 Adversarial Examples and Region Concentration
4. LLM Safety and Geometric Analysis
[00:40:05] 4.1 LLM Safety and Geometric Analysis
[00:46:11] 4.2 Toxicity Detection in LLMs
[00:52:24] 4.3 Intrinsic Dimensionality and Model Control
[00:58:07] 4.4 RLHF and High-Dimensional Spaces
5. Conclusion
[01:02:13] 5.1 Neural Tangent Kernel
[01:08:07] 5.2 Conclusion
REFS:
[00:01:35] Balestriero/Humayun – Deep network geometry & input space partitioning
https://arxiv.org/html/2408.04809v1
[00:03:55] Balestriero & Paris – Linking deep networks to adaptive spline operators
https://proceedings.mlr.press/v80/balestriero18b/balestriero18b.pdf
[00:13:55] Song et al. – Gradient-based white-box adversarial attacks
https://arxiv.org/abs/2012.14965
[00:16:05] Humayun, Balestriero & Baraniuk – Grokking phenomenon & emergent robustness
https://arxiv.org/abs/2402.15555
[00:18:25] Humayun – Training dynamics & double descent via linear region evolution
https://arxiv.org/abs/2310.12977
[00:20:15] Balestriero – Power diagram partitions in DNN decision boundaries
https://arxiv.org/abs/1905.08443
[00:23:00] Frankle & Carbin – Lottery Ticket Hypothesis for network pruning
https://arxiv.org/abs/1803.03635
[00:24:00] Belkin et al. – Double descent phenomenon in modern ML
https://arxiv.org/abs/1812.11118
[00:25:55] Balestriero et al. – Batch normalization’s regularization effects
https://arxiv.org/pdf/2209.14778
[00:29:35] EU – EU AI Act 2024 with compute restrictions
https://www.lw.com/admin/upload/SiteAttachments/EU-AI-Act-Navigating-a-Brave-New-World.pdf
[00:39:30] Humayun, Balestriero & Baraniuk – SplineCam: Visualizing deep network geometry
https://openaccess.thecvf.com/content/CVPR2023/papers/Humayun_SplineCam_Exact_Visualization_and_Characterization_of_Deep_Network_Geometry_and_CVPR_2023_paper.pdf
[00:40:40] Carlini – Trade-offs between adversarial robustness and accuracy
https://arxiv.org/abs/1902.06705
[00:44:55] Balestriero & LeCun – Limitations of reconstruction-based learning methods
https://raw.githubusercontent.com/mlresearch/v235/main/assets/balestriero24b/balestriero24b.pdf
[00:47:20] Balestriero & LeCun – Spectral analysis of neural network learning
https://proceedings.neurips.cc/paper_files/paper/2022/file/aa56c74513a5e35768a11f4e82dd7ffb-Paper-Conference.pdf
[00:49:45] He et al. – MAE: Masked Autoencoders for self-supervised learning
https://arxiv.org/abs/2111.06377
[00:54:50] Balestriero et al. – Geometric analysis of LLM layers for toxicity detection
https://arxiv.org/abs/2309.12312
[00:59:35] Balestriero et al. – Superior toxicity detection via geometric features
https://arxiv.org/html/2312.01648v2
[01:04:45] UofT ML – Self-attention control & context length effects
https://arxiv.org/abs/2310.04444
[01:11:55] Roberts – Foundations of deep learning theory
https://arxiv.org/abs/2106.10165
[01:15:40] Balestriero & Cha – Kolmogorov GAM Networks via spline partition theory
https://arxiv.org/pdf/2501.00704
[01:16:40] Various – Graph Kolmogorov-Arnold Networks (GKAN) extension
https://www.nature.com/articles/s41598-024-85083-8")
![The ARC Prize 2024 Winning Algorithm [Daniel Franzen and Jan Disselhoff]](https://i.ytimg.com/vi/mTX_sAq--zY/mqdefault.jpg "The ARC Prize 2024 Winning Algorithm [Daniel Franzen and Jan Disselhoff]
SPONSOR MESSAGES:
***
CentML offers competitive pricing for GenAI model deployment, with flexible options to suit a wide range of models, from small to large-scale deployments. Check out their super fast DeepSeek R1 hosting!
https://centml.ai/pricing/
Daniel Franzen and Jan Disselhoff the ARChitects won the ARC Prize 2024 with co-researcher David Hartmann, achieving a remarkable 53.5% accuracy on the ARC challenge using a 12-billion parameter language model. Filmed at Tufa Labs in Zurich, they walk through their solution architecture in detail: how they tokenized grid-based visual puzzles as text and fed them directly into an LLM, why test-time training on evaluation examples gave a major score boost, and how depth-first search over token probabilities outperformed greedy and beam search for solution generation.
The conversation gets into the surprising computational capabilities of language models on spatial reasoning tasks. The team found that LLMs could handle 2D grid reasoning without explicit positional encodings, that symmetry augmentations served as a powerful validation mechanism rather than a training aid, and that the models second-best solutions were often conceptually correct just wrong in a specific detail like rotation direction. They also discuss why their fine-tuned 12B model outperformed much larger foundation models, the role of LoRA in preventing catastrophic forgetting during test-time training, and what the entropy distribution of their search trees reveals about how the model represents uncertainty across different task types.
REFERENCES:
Paper:
[00:01:00] The ARChitects: Winning ARC Prize 2024 Solution
https://github.com/da-fr/arc-prize-2024/blob/main/the_architects.pdf
[00:03:38] Robustness of Analogical Reasoning in LLMs
https://arxiv.org/html/2411.14215
[00:14:58] Search Methods in Language Models
https://arxiv.org/html/2408.00724v2
[00:22:28] GPT-4 Code Solutions for ARC (50% SOTA)
https://redwoodresearch.substack.com/p/getting-50-sota-on-arc-agi-with-gpt
[00:53:08] Overcoming Catastrophic Forgetting
https://www.pnas.org/doi/10.1073/pnas.1611835114
[00:53:58] LoRA: Low-Rank Adaptation of Large Language Models
https://arxiv.org/abs/2106.09685
Tool:
[00:07:48] Re-ARC Dataset Generator
https://github.com/michaelhodel/re-arc
LINKS:
Full Transcript: https://app.rescript.info/share/57e5d773f2d0b195cbce7eee1f53aef2
Download PDF transcript: https://app.rescript.info/api/public/sessions/7772acbf1f11f44b/pdf
Daniel Franzen
https://github.com/da-fr
REFS
[00:01:05] Winning ARC 2024 solution using 12B param model, Franzen, Disselhoff, Hartmann
https://github.com/da-fr/arc-prize-2024/blob/main/the_architects.pdf
[00:07:50] Re-ARC dataset generator for ARC task variations, Michael Hodel
https://github.com/michaelhodel/re-arc
[00:22:30] GPT-4 guided code solutions for ARC tasks, Ryan Greenblatt
https://redwoodresearch.substack.com/p/getting-50-sota-on-arc-agi-with-gpt")
