Uploaded April 2024 | Updated September 2026, 1 week ago
Dr. Paul Lessard and his collaborators have written a paper on "Categorical Deep Learning and Algebraic Theory of Architectures". They aim to make neural networks more interpretable, composable and amenable to formal reasoning. The key is mathematical abstraction, as exemplified by category theory - using monads to develop a more principled, algebraic approach to structuring neural networks.
We also discussed the limitations of current neural network architectures in terms of their ability to generalise and reason in a human-like way. In particular, the inability of neural networks to do unbounded computation equivalent to a Turing machine. Paul expressed optimism that this is not a fundamental limitation, but an artefact of current architectures and training procedures.
The power of abstraction - allowing us to focus on the essential structure while ignoring extraneous details. This can make certain problems more tractable to reason about. Paul sees category theory as providing a powerful "Lego set" for productively thinking about many practical problems.
Towards the end, Paul gave an accessible introduction to some core concepts in category theory like categories, morphisms, functors, monads etc. We explained how these abstract constructs can capture essential patterns that arise across different domains of mathematics.
Paul is optimistic about the potential of category theory and related mathematical abstractions to put AI and neural networks on a more robust conceptual foundation to enable interpretability and reasoning. However, significant theoretical and engineering challenges remain in realising this vision.
Please support us on Patreon. We are entirely funded from Patreon donations right now.
patreon.com/mlst
If you would like to sponsor us, so we can tell your story - reach out on mlstreettalk at gmail
Links:
Categorical Deep Learning: An Algebraic Theory of Architectures
Bruno Gavranović, Paul Lessard, Andrew Dudzik,
Tamara von Glehn, João G. M. Araújo, Petar Veličković
Paper: categoricaldeeplearning.com
Symbolica:
twitter.com/symbolica
symbolica.ai
Dr. Paul Lessard (Principal Scientist - Symbolica)
linkedin.com/in/paul-roy-lessard
Neural Networks and the Chomsky Hierarchy (Grégoire Delétang et al)
arxiv.org/abs/2207.02098
Interviewer: Dr. Tim Scarfe
Pod: podcasters.spotify.com/pod/show/machinelearningstreettalk/episodes/Dr--Paul-Lessard---CategoricalStructured-Deep-Learning-e2hqqlq
Transcript:
docs.google.com/document/d/1NiHJKTkeqYdpcgr6lGCTwqMKl6YA9tS5R1jCgi987gA/edit?usp=sharing
More info about NNs not being recursive/TMs:
youtube.com/watch?v=4KIQH1VEwBI
Geometric Deep Learning blueprint:
youtube.com/watch?v=bIZB1hIJ4u8
TOC:
00:00:00 - Intro
00:05:07 - What is the category paper all about
00:07:19 - Composition
00:10:42 - Abstract Algebra
00:23:01 - DSLs for machine learning
00:24:10 - Inscrutability
00:29:04 - Limitations with current NNs
00:30:41 - Generative code / NNs don't recurse
00:34:34 - NNs are not Turing machines (special edition)
00:53:09 - Abstraction
00:55:11 - Category theory objects
00:58:06 - Cat theory vs number theory
00:59:43 - Data and Code are one and the same
01:08:05 - Syntax and semantics
01:14:32 - Category DL elevator pitch
01:17:05 - Abstraction again
01:20:25 - Lego set for the universe
01:23:04 - Reasoning
01:28:05 - Category theory 101
01:37:42 - Monads
01:45:59 - Where to learn more cat theory
Dr. Paul Lessard and his collaborators have written a paper on "Categorical Deep Learning and Algebraic Theory of Architectures". They aim to make neural networks more interpretable, composable and amenable to formal reasoning. The key is mathematical abstraction, as exemplified by category theory - using monads to develop a more principled, algebraic approach to structuring neural networks.
We also discussed the limitations of current neural network architectures in terms of their ability to generalise and reason in a human-like way. In particular, the inability of neural networks to do unbounded computation equivalent to a Turing machine. Paul expressed optimism that this is not a fundamental limitation, but an artefact of current architectures and training procedures.
The power of abstraction - allowing us to focus on the essential structure while ignoring extraneous details. This can make certain problems more tractable to reason about. Paul sees category theory as providing a powerful "Lego set" for productively thinking about many practical problems.
Towards the end, Paul gave an accessible introduction to some core concepts in category theory like categories, morphisms, functors, monads etc. We explained how these abstract constructs can capture essential patterns that arise across different domains of mathematics.
Paul is optimistic about the potential of category theory and related mathematical abstractions to put AI and neural networks on a more robust conceptual foundation to enable interpretability and reasoning. However, significant theoretical and engineering challenges remain in realising this vision.
Please support us on Patreon. We are entirely funded from Patreon donations right now.
patreon.com/mlst
If you would like to sponsor us, so we can tell your story - reach out on mlstreettalk at gmail
Links:
Categorical Deep Learning: An Algebraic Theory of Architectures
Bruno Gavranović, Paul Lessard, Andrew Dudzik,
Tamara von Glehn, João G. M. Araújo, Petar Veličković
Paper: categoricaldeeplearning.com
Symbolica:
twitter.com/symbolica
symbolica.ai
Dr. Paul Lessard (Principal Scientist - Symbolica)
linkedin.com/in/paul-roy-lessard
Neural Networks and the Chomsky Hierarchy (Grégoire Delétang et al)
arxiv.org/abs/2207.02098
Interviewer: Dr. Tim Scarfe
Pod: podcasters.spotify.com/pod/show/machinelearningstreettalk/episodes/Dr--Paul-Lessard---CategoricalStructured-Deep-Learning-e2hqqlq
Transcript:
docs.google.com/document/d/1NiHJKTkeqYdpcgr6lGCTwqMKl6YA9tS5R1jCgi987gA/edit?usp=sharing
More info about NNs not being recursive/TMs:
youtube.com/watch?v=4KIQH1VEwBI
Geometric Deep Learning blueprint:
youtube.com/watch?v=bIZB1hIJ4u8
TOC:
00:00:00 - Intro
00:05:07 - What is the category paper all about
00:07:19 - Composition
00:10:42 - Abstract Algebra
00:23:01 - DSLs for machine learning
00:24:10 - Inscrutability
00:29:04 - Limitations with current NNs
00:30:41 - Generative code / NNs don't recurse
00:34:34 - NNs are not Turing machines (special edition)
00:53:09 - Abstraction
00:55:11 - Category theory objects
00:58:06 - Cat theory vs number theory
00:59:43 - Data and Code are one and the same
01:08:05 - Syntax and semantics
01:14:32 - Category DL elevator pitch
01:17:05 - Abstraction again
01:20:25 - Lego set for the universe
01:23:04 - Reasoning
01:28:05 - Category theory 101
01:37:42 - Monads
01:45:59 - Where to learn more cat theory
![Why High Benchmark Scores Don’t Mean Better AI [SPONSORED]](https://i.ytimg.com/vi/rqiC9a2z8Io/mqdefault.jpg "Why High Benchmark Scores Don’t Mean Better AI [SPONSORED]
Is a car that wins a Formula 1 race the best choice for your morning commute? Probably not. In this sponsored deep dive with Prolific, we explore why the same logic applies to Artificial Intelligence. While models are currently shattering records on technical exams, they often fail the most important test of all: *the human experience.*
Why High Benchmark Scores Don’t Mean Better AI
Joining us are *Andrew Gordon* (Staff Researcher in Behavioral Science) and *Nora Petrova* (AI Researcher) from *Prolific* . They reveal the hidden flaws in how we currently rank AI and introduce a more rigorous, humane way to measure whether these models are actually helpful, safe, and relatable for real people.
Key Insights in This Episode:
* *The F1 Car Analogy:* Andrew explains why a model that excels at the Humanities Last Exam might be a nightmare for daily use. Technical benchmarks often ignore the nuances of human communication and adaptability.
* *The Wild West of AI Safety:* As users turn to AI for sensitive topics like mental health, Nora highlights the alarming lack of oversight and the thin veneer of safety training—citing recent controversial incidents like Grok-3’s Mecha Hitler.
* *Fixing the Leaderboard Illusion:* The team critiques current popular rankings like Chatbot Arena, discussing how anonymous, unstratified voting can lead to biased results and how companies can game the system.
* *The Xbox Secret to AI Ranking:* Discover how Prolific uses *TrueSkill* —the same algorithm Microsoft developed for Xbox Live matchmaking—to create a fairer, more statistically sound leaderboard for LLMs.
* *The Personality Gap:* Early data from the *Humane Leaderboard* suggests that while AI is getting smarter, it is actually performing *worse* on metrics like personality, culture, and sycophancy (the tendency for models to become annoying people-pleasers).
About the HUMAINE Leaderboard
Moving beyond simple A vs. B testing, the researchers discuss their new framework that samples participants based on *census data* (Age, Ethnicity, Political Alignment). By using a representative sample of the general public rather than just tech enthusiasts, they are building a standard that reflects the values of the real world.
*Are we building models for benchmarks, or are we building them for humans? It’s time to change the scoreboard.*
Rescript link:
https://app.rescript.info/public/share/IDqwjY9Q43S22qSgL5EkWGFymJwZ3SVxvrfpgHZLXQc
TIMESTAMPS:
00:00:00 Introduction & The Benchmarking Problem
00:01:58 The Fractured State of AI Evaluation
00:03:54 AI Safety & Interpretability
00:05:45 Bias in Chatbot Arena
00:06:45 Prolifics Three Pillars Approach
00:09:01 TrueSkill Ranking & Efficient Sampling
00:12:04 Census-Based Representative Sampling
00:13:00 Key Findings: Culture, Personality & Sycophancy
REFERENCES:
Paper:
[00:00:15] MMLU
https://arxiv.org/abs/2009.03300
[00:05:10] Constitutional AI
https://arxiv.org/abs/2212.08073
[00:06:45] The Leaderboard Illusion
https://arxiv.org/abs/2504.20879
[00:09:41] HUMAINE Framework Paper
https://huggingface.co/blog/ProlificAI/humaine-framework
Company:
[00:00:30] Prolific
https://www.prolific.com
[00:01:45] Chatbot Arena
https://lmarena.ai/
Person:
[00:00:35] Andrew Gordon
https://www.linkedin.com/in/andrew-gordon-03879919a/
[00:00:45] Nora Petrova
https://www.linkedin.com/in/nora-petrova/
Event:
Algorithm:
[00:09:01] Microsoft TrueSkill
https://www.microsoft.com/en-us/research/project/trueskill-ranking-system/
Leaderboard:
[00:09:21] Prolific HUMAINE Leaderboard
https://www.prolific.com/humaine
[00:09:31] HUMAINE HuggingFace Space
https://huggingface.co/spaces/ProlificAI/humaine-leaderboard
[00:10:21] Prolific AI Leaderboard Portal
https://www.prolific.com/leaderboard
Dataset:
[00:09:51] Prolific Social Reasoning RLHF Dataset
https://huggingface.co/datasets/ProlificAI/social-reasoning-rlhf
Organization:
[00:10:31] MLCommons
https://mlcommons.org/")
![Wild breakthrough on Math after 56 years... [Exclusive]](https://i.ytimg.com/vi/vC9nAosXrJw/mqdefault.jpg "Wild breakthrough on Math after 56 years... [Exclusive]
Google DeepMind just dropped AlphaEvolve, a Gemini-powered evolutionary coding agent that designs advanced algorithms by pairing LLM creativity with automated evaluation. The headline result: it beat Volker Strassens 56-year-old record for 4x4 matrix multiplication, finding a method that uses 48 scalar multiplications instead of 49. No human or AI had managed that in over half a century.
Tim sits down with two of the researchers behind the work Matej Balog and Alexander Novikov to walk through the system, the results, and what it means.
In this episode:
- How AlphaEvolve works: an evolutionary pipeline that pairs LLM-generated code proposals with rigorous automated evaluators, iteratively improving solutions rather than relying on one-shot generation. The gap between single-shot LLM sampling and scaled evolutionary search turns out to be enormous.
- The matrix multiplication breakthrough: AlphaTensor tried for years with reinforcement learning and only cracked the Boolean case. AlphaEvolve found a 48-multiplication algorithm for general 4x4 matrices almost by accident, running for completeness. The result generalises from complex to real matrices, which is counterintuitive solving the harder problem actually made the search easier.
- Three ways to represent the search target: direct solution, constructor function, or search algorithm. For matrix multiplication, AlphaEvolve designed a gradient-based search algorithm that finds matrix multiplication algorithms a meta-level approach that produced loss functions and update rules no human would have tried.
- Real-world impact at Google scale: AlphaEvolve recovered 0.7% of fleet-wide compute resources in the Borg data center scheduling system and sped up Gemini training by 1%. These are already-heavily-optimized production systems.
- The human-AI collaboration loop: AlphaEvolve is not autonomous research. Humans choose the problems, design evaluators, seed initial solutions, and interpret results. Alexander Novikov argues this back-and-forth is the whole point the system improves your questions as much as your answers.
- Keith Duggar probes the halting problem and evaluation cascade limitations. The researchers acknowledge the constraint but note that practical framing (time-bounded evaluation, evaluation cascades from cheap to expensive) sidesteps the theoretical issue for now.
- The recursive self-improvement question: AlphaEvolve improved the infrastructure that trains the models that power AlphaEvolve. The feedback loop exists but currently operates on a timescale of months.
SPONSOR MESSAGES:
***
Tufa AI Labs is a brand new research lab in Zurich started by Benjamin Crouzier focussed on o-series style reasoning and AGI. They are hiring a Chief Engineer and ML engineers. Events in Zurich.
GTC is coming, the premier AI conference, great opportunity to learn about AI. NVIDIA and partners will showcase breakthroughs in physical AI, AI factories, agentic AI, and inference. Register for virtual GTC for free, using Tims link (https://nvda.ws/4qQ0LMg)
Tufa AI Labs is a new research lab in Zurich started by Benjamin Crouzier focused on o-series style reasoning and AGI. They are hiring a Chief Engineer and ML engineers. Go to https://tufalabs.ai/
TIMESTAMPS:
00:00:00 Introduction: AlphaEvolves Breakthroughs and DeepMinds Lineage
00:11:24 Introducing AlphaEvolve: Evolutionary Architecture and LLM Pairing
00:16:56 The Halting Problem and Evaluation Constraints
00:23:20 Knowledge Augmentation: Meta-Prompting, Library Learning, and Self-Generated Data
00:29:08 Matrix Multiplication Breakthrough: From Strassen to 48 Multiplications
00:39:11 Problem Representation: Direct Solutions, Constructors, and Search Algorithms
00:46:06 Surprising Outcomes: What Researchers Did Not Expect
00:51:42 Hill Climbing, Program Synthesis, and Intelligibility
01:00:24 Real-World Applications: Complex Evaluations and Robotics
01:05:39 The Role of LLMs, Recursive Self-Improvement, and Future Directions
REFERENCES:
Blog Post:
[00:00:00] AlphaEvolve Blog Post
https://deepmind.google/discover/blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/
Paper:
[00:03:00] FunSearch
https://www.nature.com/articles/s41586-023-06924-6
[00:12:00] MAP-Elites
https://arxiv.org/abs/1504.04909
Person:
[00:11:24] Matej Balog
https://x.com/matejbalog
[00:14:10] Alexander Novikov
https://x.com/SashaVNovikov
Company:
[00:11:24] Tufa AI Labs
https://tufalabs.ai/
LINKS:
Full Transcript: https://app.rescript.info/share/de65b6ec8da83b261ce6018039fec289
Download PDF transcript: https://app.rescript.info/api/public/sessions/855d5b15e733d182/pdf
Guests:
Matej Balog: https://x.com/matejbalog
Alexander Novikov: https://x.com/SashaVNovikov")
![Learning at test time in LLMs [Jonas Hübotter]](https://i.ytimg.com/vi/vei7uf9wOxI/mqdefault.jpg "Learning at test time in LLMs [Jonas Hübotter]
Jonas Hübotter from ETH presents SIFT (Select Informative data for Fine-Tuning), a breakthrough algorithm that dramatically improves language model performance through test-time adaptation. Using intelligent data selection, SIFT achieves state-of-the-art results with a 3.8B parameter model - 30x smaller than previous approaches. The system combines a parametric controller with non-parametric memory to optimize training example selection, showing impressive results across mathematics, coding, and legal domains. This novel approach points toward more efficient and adaptable AI systems that can continuously improve through interaction.
This was the first physical meetup of Tufa AI Labs, are you an ML researcher interested in joining or presenting at one of these sessions? Please get in touch with Benjamin Crouzier benjamin@tufa.ai - https://tufalabs.ai/
SLIDES:
https://www.dropbox.com/scl/fi/sys3iasc63lgj8lm5t0ld/JONAS_SLIDES.pdf?rlkey=ak6ir61a2pyhrfuwyvgrdvq66&st=9cloopv9&dl=0
SPONSOR MESSAGE:
CentML offers competitive pricing for GenAI model deployment, with flexible options to suit a wide range of models, from small to large-scale deployments.
https://centml.ai/pricing/
Jonas Hübotter
Doctoral Researcher at ETH Zurich working on Active Fine-Tuning and Local Learning.
https://jonhue.github.io/
Test-Time Training on Nearest Neighbors for Large Language Models
https://arxiv.org/abs/2305.18466 (IMPORTANT BACKGROUND READING)
TOC:
1. SIFT Algorithm Core Concepts
[00:00:00] 1.1 Introduction to Test-Time Adaptation and SIFT Algorithm
[00:02:45] 1.2 The Pile Benchmark and Parameter Efficiency
[00:07:00] 1.3 Local Learning Models and Vapniks Principle
[00:12:33] 1.4 SIFT Performance and Domain-Specific Comparisons
2. Training and Data Selection Methods
[00:22:50] 2.1 Data Selection and Error Measurement Methods
[00:32:33] 2.2 Non-IID Training Experiments on MNIST
3. Scaling and Implementation and Audience QnA
[00:35:50] 3.1 Scaling Experiments to Larger Datasets and Models
[00:42:30] 3.2 Model Scaling and Performance Across Architectures
[00:44:25] 3.3 Exploration-Exploitation Trade-offs in Fine-tuning
[00:47:54] 3.4 Two-Stage Local Learning Architecture and SIFT Implementation
SHOWNOTES (transcript, references, best quotes etc):
https://www.dropbox.com/scl/fi/os3ny3sy446u07yldz0zg/JONAS_PRESENTS.pdf?rlkey=kmu2pxfx8xbmiy283diof0kj1&st=xi5ouc9t&dl=0
REFS:
[0:00:25] Paper: Efficiently Learning at Test-Time: Active Fine-Tuning of LLMs introducing SIFT algorithm for optimizing LLM performance through test-time fine-tuning (Jonas Hübotter, Sascha Bongni, Ido Hakimi, Andreas Krause)
https://arxiv.org/pdf/2410.08020
[0:02:45] The Pile: An 800GB Dataset of Diverse Text for Language Modeling - A comprehensive dataset comprising 22 diverse high-quality subsets for training large-scale language models (Leo Gao et al.)
https://arxiv.org/abs/2101.00027
[0:03:20] Language Models are Unsupervised Multitask Learners (GPT-2) -
https://cdn.openai.com/better-language-models/language_models_are_unsupervised_multitask_learners.pdf
[0:11:05] Vladimir Vapniks principle from Statistical Learning Theory: When solving a problem of interest, do not solve a more general problem as an intermediate step. Try to get the answer that you really need, but not a more general one.
https://www.amazon.com/Statistical-Learning-Information-Science-Statistics/dp/0387987800
[0:22:05] Paper discussed at ICML The Linear Representation Hypothesis and the Geometry of Large Language Models by Kiho Park et al.
https://arxiv.org/abs/2311.03658
[0:23:20] On choosing and bounding probability metrics - Paper discussing Total Variation (TV) distance and its applications in probability theory (ALISON L. GIBBS AND FRANCIS EDWARD SU)
https://arxiv.org/pdf/math/0209021
[0:33:25] MNIST dataset - Standard database of handwritten digits containing 60,000 training images and 10,000 test images of size 28x28 pixels (Yann LeCun, Corinna Cortes)
https://yann.lecun.com/exdb/mnist/
[0:35:50] CIFAR-100 dataset - A dataset of 32x32 color images in 100 classes, with 600 images per class (Alex Krizhevsky)
https://www.cs.toronto.edu/~kriz/cifar.html
[0:36:00] ImageNet - Large-scale hierarchical image database with over 14 million images organized according to the WordNet hierarchy (Jia Deng et al)
https://ieeexplore.ieee.org/document/5206848
[0:42:55] Llama 2: Collection of foundation and fine-tuned chat models ranging from 7B to 70B parameters (Hugo Touvron et al.)
https://arxiv.org/abs/2307.09288
[0:43:35] Scaling Instruction-Finetuned Language Models - Paper introducing Flan-T5, showing performance improvements through instruction finetuning (Hyung Won Chung et al.)
https://arxiv.org/abs/2210.11416
[0:45:10] Active Few-Shot Fine-Tuning methodology paper discussing exploration-exploitation trade-offs in the context of fine-tuning neural networks. (Jonas Hübotter et al.)
https://arxiv.org/abs/2402.15898")
