Navier-Stokes, DeepSeek V4.1 Flash, AlphaGenome, and Diffusion Control: 5 videos from September 7–13

The short version

I Never Thought I’d See This Happen

• OpenAI announced a solution to the Navier-Stokes existence and smoothness Millennium Prize problem using an internal model significantly more capable than GPT-6 Astra, with the automated proof taking roughly three and a half days to produce. 1
• Outside mathematicians Tristan Buckmaster and Levon Alpargy spent a year establishing that their related fluid result could extend toward solving Navier-Stokes, using commercial models whose providers could not rule out ingesting their drafts. 1
• The presenter reviews the physical mechanics governing the equations, breaking fluid behavior into advection along flow directions, pressure expansion, and viscous diffusion that smooths local differences over time. 1
• The claimed proof shows that starting from rest under carefully engineered external forces, inward-spiraling vortices can accelerate without bound in finite time while keeping total kinetic energy finite, indicating a mathematical breakdown. 1
• The video attributes the speed of AI progress in mathematics to verifiability, contrasting human evaluation of prose at 100 iterations per hour with automated theorem checkers running up to 100 million checks per hour. 1

Deepseek did it again...

• DeepSeek V4.1 Flash is an open-weights mixture-of-experts model totaling 552 billion parameters, activating only 8 billion parameters on input and 16 billion on output during generation. 2
• The release addresses global high-bandwidth memory shortages by shrinking the key-value cache memory requirement by 75% and reducing storage footprint to one-eighth of comparable predecessors. 2
• Berman reports API pricing of $0.15 per million input tokens off-peak ($0.30 peak) and $0.60 per million output tokens off-peak ($1.20 peak), paired with generation throughput approaching 200 tokens per second. 2
• In hands-on testing across web and IDE environments, the model failed a Rubik's Cube interactive simulation, altering tile colors in place during rotation and replaying previous moves in reverse rather than executing an algorithmic solution. 2
• Additional evaluations showed a basic brush-stroke silhouette on the Paintbench portrait test compared to GPT-6 Astra's layered execution, alongside an interactive 3D water simulation with customizable physical inputs. 2

AlphaGenome Atlas: Understanding the human genome

• AlphaGenome models genomic sequence contexts across chromosomes to predict the molecular consequences of single-base mutations on human phenotypes and disease risk. 3
• DeepMind condensed roughly 10,000 raw multidimensional predictions per genetic position into a single scalar AlphaGenome Variant Impact (AVI) score to facilitate clinical prioritization. 3
• The team precomputed AVI scores across all nine billion possible single-letter alterations in the human genome, compiling the results into a one-petabyte open resource. 3
• The project includes an interactive web-based Genome Browser designed to give experimental biologists visual access to variant impact data without requiring code. 3
• DeepMind frames the release as part of an expanding agentic workflow combining specialized biological foundation models such as AlphaFold and AlphaGenome to accelerate discovery. 3

Probabilistic Inference for Controlling Diffusion Models

• He organizes inference-time diffusion guidance into two structural families: sequential control, which propagates particles step-by-step from noise to data, and parallel control, which refines entire denoising trajectories simultaneously via replica exchange MCMC. 4
• Standard marginal density control relies on approximating intractable density ratios using the learned score network, a shortcut that introduces compound errors when the base diffusion model contains inaccuracies. 4
• Exact control can be recovered without score ratio approximations by lifting reward tilting to full trajectory space, where intermediate path densities cancel out in importance weights and swap acceptance probabilities. 4
• Under strict evaluation budgets, sequential Monte Carlo yields fast improvements with small particle pools but collapses to identical samples without large batch sizes, whereas parallel tempering maintains sample diversity by swapping across noise levels. 4
• Empirical experiments demonstrate that parallel path control successfully identifies rare conformational transitions in proteins, including folding switches and phosphorylation states that baseline diffusion misses. 4

Effective Doomerism

• Former OpenAI and Anthropic pre-training researcher Jacob Cox resigned publicly, alleging both labs are recklessly racing toward self-improving superintelligence and gambling with human survival. 5
• sentdex notes that Anthropic uses cultural screening around existential risk in hiring, establishing an internal consensus where high probability-of-doom estimates become a social norm. 5
• The video critiques Effective Altruism as a utilitarian doctrine that readily accepts concentrated power and rights trade-offs, comparing its logic to rural automated surveillance deployments. 5
• sentdex breaks down the widely cited HuggingFace containment breach, pointing out that external evaluation vendor Irregular ran the benchmark inside an improperly isolated environment rather than experiencing an autonomous cyber breakout. 5
• The commentary questions calls for centralized licensing boards, arguing that existential catastrophe warnings often serve as corporate lobbying to restrict open-source development and protect market incumbents. 5