The Gradient: Perspectives on AI

David Pfau: Manifold Factorization and AI for Science

The Gradient: Perspectives on AI

Show Notes

Episode 130 I spoke with David Pfau about: * Spectral learning and ML * Learning to disentangle manifolds and (projective) representation theory * Deep learning for computational quantum mechanics * Picking and pursuing research problems and directions David’s work is really (times k for some very large value of k) interesting—I’ve been inspired to descend a number of rabbit holes because of it. (if you listen to this episode, you might become as cool as this guy) While I’m at it — I’m still hovering around 40 ratings on Apple Podcasts. It’d mean a lot if you’d consider helping me bump that up! Enjoy—and let me know what you think! David is a staff research scientist at Google DeepMind. He is also a visiting professor at Imperial College London in the Department of Physics, where he supervises work on applications of deep learning to computational quantum mechanics. His research interests span artificial intelligence, machine learning and scientific computing. Find me on Twitter for updates on new episodes, and reach me at [email protected] for feedback, ideas, guest suggestions. I spend a lot of time on this podcast—if you like my work, you can support me on Patreon :) You can also support upkeep for the full Gradient team/project through a paid subscription on Substack! Subscribe to The Gradient Podcast: Apple Podcasts | Spotify | Pocket Casts | RSSFollow The Gradient on Twitter Outline: * (00:00) Intro * (00:52) David Pfau the “critic” * (02:05) Scientific applications of deep learning — David’s interests * (04:57) Brain / neural network analogies * (09:40) Modern ML systems and theories of the brain * (14:19) Desirable properties of theories * (18:07) Spectral Inference Networks * (19:15) Connections to FermiNet / computational physics, a series of papers * (33:52) Deep slow feature analysis — interpretability and findings on eigenfunctions * (39:07) Following up on eigenfunctions (there are indeed only so many hours in a day; I have been asking the Substack people if they can ship 40-hour days, but I don’t think they’ve gotten to it yet) * (42:17) Power iteration and intuitions * (45:23) Projective representation theory * (46:00) ??? * (46:54) Geomancer and learning to decompose a manifold from data * (47:45) we consider the question of whether you will spend 90 more minutes of this podcast episode (there are not 90 more minutes left in this podcast episode, but there could have been) * (1:08:47) Learning embeddings * (1:11:12) The “unexpected emergent property” of Geomancer * (1:14:43) Learned embeddings and disentangling and preservation of topology * n/b I still haven’t managed to do this in colab because I keep crashing my instance when I use s3o4d :( * (1:21:07) What’s missing from the ~ current (deep learning) paradigm ~ * (1:29:04) LLMs as swiss-army knives * (1:32:05) RL and human learning — TD learning in the brain * (1:37:43) Models that cover the Pareto Front (image below) * (1:46:54) AI accelerators and doubling down on transformers * (1:48:27) On Slow Research — chasing big questions and what makes problems attractive * (1:53:50) Future work on Geomancer * (1:55:35) Finding balance in pursuing interesting and lucrative work * (2:00:40) Outro Links: * Papers * Natural Quantum Monte Carlo Computation of Excited States (2023) * Making sense of raw input (2021) * Integrable Nonparametric Flows (2020) * Disentangling by Subspace Diffusion (2020) * Ab initio solution of the many-electron Schrödinger equation with deep neural networks (2020) * Spectral Inference Networks (2018) * Connecting GANs and Actor-Critic Methods (2016) * Learning Structure in Time Series for Neuroscience and Beyond (2015, dissertation) * Robust learning of low-dimensional dynamics from large neural ensembles (2013) * Probabilistic Deterministic Infinite Automata (2010) * Other * On Slow Research * “I just want to put this out here so that no one ever says ‘we can just get around the data limitations of LLMs with self-play’ ever again.

More from The Gradient: Perspectives on AI

Jan 22, 2026

Episode 144 Happy New Year! This is one of my favorite episodes of the year — for the fourth time, Nathan Benaich and I did our yearly roundup of AI news and advancements, including selections from this year’s State of AI Report. If you’ve stuck around and continue to listen, I’m really thankful you’re here. I love hearing from you. You can find Nathan and Air Street Press here on Substack and on Twitter, LinkedIn, and his personal site. Check out his writing at press.airstreet.com. Find me on Twitter (or LinkedIn if you want…) for updates on new episodes, and reach me at [email protected] for feedback, ideas, guest suggestions. Outline * (00:00) Intro * (00:44) Air Street Capital and Nathan world * Nathan’s path from cancer research and bioinformatics to AI investing * The “evergreen thesis” of AI from niche to ubiquitous * Portfolio highlights: Eleven Labs, Synthesia, Crusoe * (03:44) Geographic flexibility: Europe vs. the US * Why SF isn’t always the best place for original decisions * Industry diversity in New York vs. San Francisco * The Munich Security Conference and Europe’s defense pivot * Playing macro games from a European vantage point * (07:55) VC investment styles and the “solo GP” approach * Taste as the determinant of investments * SF as a momentum game with small information asymmetry * Portfolio diversity: defense (Delian), embodied AI (Syriact), protein engineering * Finding entrepreneurs who “can’t do anything else” * (10:44) State of AI progress in 2025 * Momentous progress in writing, research, computer use, image, and video * We’re in the “instruction manual” phase * The scale of investment: private markets, public markets, and nation states * (13:21) Range of outcomes and what “going bad” looks like * Today’s systems are genuinely useful—worst case is a valuation problem * Financialization of AI buildouts and GPUs * (14:55) DeepSeek and China closing the capability gap * Seven-month lag analysis (Epoch AI) * Benchmark skepticism and consumer preferences (”Coca-Cola vs. Pepsi”) * Hedonic adaptation: humans reset expectations extremely quickly * Bifurcation of model companies toward specific product bets * (18:29) Export controls and the “evolutionary pressure” argument * Selective pressure breeds innovation * Chinese companies rushing to public markets (Minimax, ZAI) * (21:30) Reasoning models and test-time compute * Chain of thought faithfulness questions * Monitorability tax: does observability reduce quality? * User confusion about when models should “think” * AI for science: literature agents, hypothesis generation * (23:53) Chain of thought interpretability and safety * Anthropomorphization concerns * Alignment faking and self-preservation behaviors * Cybersecurity as a bigger risk than existential risk * Models as payloads injected into critical systems * (27:26) Commercial traction and AI adoption data * Ramp data: 44% of US businesses paying for AI (up from 5% in early 2023) * Average contract values up to $530K from $39K * State of AI survey: 92% report productivity gains * The “slow takeoff” consensus and human inertia * Use cases: meeting notes, content generation, brainstorming, coding, financial analysis * (32:53) The industrial era of AI * Stargate and XAI data centers * Energy infrastructure: gas turbines and grid investment * Labs need to own models, data, compute, and power * Poolside’s approach to owning infrastructure * (35:40) Venture capital in the age of massive GPU capex * The GP lives in the present, the entrepreneur in the future, the LP in the past * Generality vs. specialism narratives * “Two or 20”: management fees vs. carried interest * Scaling funds to match entrepreneur ambitions * (40:10) NVIDIA challengers and returns analysis * Chinese challengers: 6x return vs. 26x on NVIDIA * US challengers: 2x return vs. 12x on NVIDIA * Grok acquired for $20B; Samba Nova markdown to $1.6B * “The tide is lifting all boats”—demand exceeds supply * (44:06) The hardware lottery and ar

Nov 26, 2025

Episode 143 I spoke with Iason Gabriel about: * Value alignment * Technology and worldmaking * How AI systems affect individuals and the social world Iason is a philosopher and Senior Staff Research Scientist at Google DeepMind. His work focuses on the ethics of artificial intelligence, including questions about AI value alignment, distributive justice, language ethics and human rights. You can find him on his website and Twitter/X. Find me on Twitter (or LinkedIn if you want…) for updates, and reach me at [email protected] for feedback, ideas, guest suggestions. Outline * (00:00) Intro * (01:18) Iason’s intellectual development * (04:28) Aligning language models with human values, democratic civility and agonism * (08:20) Overlapping consensus, differing norms, procedures for identifying norms * (13:27) Rawls’ theory of justice, the justificatory and stability problems * (19:18) Aligning LLMs and cooperation, speech acts, justification and discourse norms, literacy * (23:45) Actor Network Theory and alignment * (27:25) Value alignment and Iason’s starting points * (33:10) The Ethics of Advanced AI Assistants, AI’s impacts on social processes and users, personalization * (37:50) AGI systems and social power * (39:00) Displays of care and compassion, Machine Love (Joel Lehman) * (41:30) Virtue ethics, morality and language, virtue in AI systems vs. MacIntyre’s conception in After Virtue * (45:00) The Challenge of Value Alignment * (45:25) Technologists as worldmakers * (51:30) Technological determinism, collective action problems * (55:25) Iason’s goals with his work * (58:32) Outro Links Papers: * AI, Values, and Alignment (2020) * Aligning LMs with Human Values (2023) * Toward a Theory of Justice for AI (2023) * The Ethics of Advanced AI Assistants (2024) * A matter of principle? AI alignment as the fair treatment of claims (2025)

Dec 26, 2024

Episode 142 Happy holidays! This is one of my favorite episodes of the year — for the third time, Nathan Benaich and I did our yearly roundup of all the AI news and advancements you need to know. This includes selections from this year’s State of AI Report, some early takes on o3, a few minutes LARPing as China Guys……… If you’ve stuck around and continue to listen, I’m really thankful you’re here. I love hearing from you. You can find Nathan and Air Street Press here on Substack and on Twitter, LinkedIn, and his personal site. Check out his writing at press.airstreet.com. Find me on Twitter (or LinkedIn if you want…) for updates on new episodes, and reach me at [email protected] for feedback, ideas, guest suggestions.

Dec 12, 2024

Episode 141 I spoke with Professor Philip Goff about: * What a “post-Galilean” science of consciousness looks like * How panpsychism helps explain consciousness and the hybrid cosmopsychist view Enjoy! Philip Goff is a British author, idealist philosopher, and professor at Durham University whose research focuses on philosophy of mind and consciousness. Specifically, it focuses on how consciousness can be part of the scientific worldview. He is the author of multiple books including Consciousness and Fundamental Reality, Galileo's Error: Foundations for a New Science of Consciousness and Why? The Purpose of the Universe. Find me on Twitter for updates on new episodes, and reach me at [email protected] for feedback, ideas, guest suggestions. Subscribe to The Gradient Podcast: Apple Podcasts | Spotify | Pocket Casts | RSSFollow The Gradient on Twitter Outline: * (00:00) Intro * (01:05) Goff vs. Carroll on the Knowledge Arguments and explanation * (08:00) Preferences for theories * (12:55) Curiosity (Grounding, Essence) and the Knowledge Argument * (14:40) Phenomenal transparency and physicalism vs. anti-physicalism * (29:00) How Exactly does Panpsychism Help Explain Consciousness * (30:05) The argument for hybrid cosmopsychism * (36:35) “Bare” subjects / subjects before inheriting phenomenal properties * (40:35) Bundle theories of the self * (43:35) Fundamental properties and new subjects as causal powers * (50:00) Integrated Information Theory * (55:00) Fundamental assumptions in hybrid cosmopsychism * (1:00:00) Outro Links: * Philip’s homepage and Twitter * Papers * Putting Consciousness First * Curiosity (Grounding, Essence) and the Knowledge Argument

Nov 21, 2024

Hi everyone! If you’re a new subscriber or listener, welcome. If you’re not new, you’ve probably noticed that things have slowed down from us a bit recently. Hugh Zhang, Andrey Kurenkov and I sat down to recap some of The Gradient’s history, where we are now, and how things will look going forward. To summarize and give some context: The Gradient has been around for around 6 years now – we began as an online magazine, and began producing our own newsletter and podcast about 4 years ago. With a team of volunteers — we take in a bit of money through Substack that we use for subscriptions to tools we need and try to pay ourselves a bit — we’ve been able to keep this going for quite some time. Our team has less bandwidth than we’d like right now (and I’ll admit that at least some of us are running on fumes…) — we’ll be making a few changes: * Magazine: We’re going to be scaling down our editing work on the magazine. While we won’t be accepting pitches for unwritten drafts for now, if you have a full piece that you’d like to pitch to us, we’ll consider posting it. If you’ve reached out about writing and haven’t heard from us, we’re really sorry. We’ve tried a few different arrangements to manage the pipeline of articles we have, but it’s been difficult to make it work. We still want this to be a place to promote good work and writing from the ML community, so we intend to continue using this Substack for that purpose. If we have more editing bandwidth on our team in the future, we want to continue doing that work. * Newsletter: We’ll aim to continue the newsletter as before, but with a “Best from the Community” section highlighting posts. We’ll have a way for you to send articles you want to be featured, but for now you can reach us at our [email protected]. * Podcast: I’ll be continuing this (at a slower pace), but eventually transition it away from The Gradient given the expanded range. If you’re interested in following, it might be worth subscribing on another player like Apple Podcasts, Spotify, or using the RSS feed. * Sigmoid Social: We’ll keep this alive as long as there’s financial support for it. If you like what we do and/or want to help us out in any way, do reach out to [email protected]. We love hearing from you. Timestamps * (0:00) Intro * (01:55) How The Gradient began * (03:23) Changes and announcements * (10:10) More Gradient history! On our involvement, favorite articles, and some plugs Some of our favorite articles! There are so many, so this is very much a non-exhaustive list: * NLP’s ImageNet moment has arrived * The State of Machine Learning Frameworks in 2019 * Why transformative artificial intelligence is really, really hard to achieve * An Introduction to AI Story Generation * The Artificiality of Alignment (I didn’t mention this one in the episode, but it should be here) Places you can find us! Hugh: * Twitter * Personal site * Papers/things mentioned! * A Careful Examination of LLM Performance on Grade School Arithmetic (GSM1k) * Planning in Natural Language Improves LLM Search for Code Generation * Humanity’s Last Exam Andrey: * Twitter * Personal site * Last Week in AI Podcast Daniel: * Twitter * Substack blog * Personal site (under construction)

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