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We speculate that transient chaos is inevitable when we train models to solve hard problems: sensitivity is needed to support hard computations, but the tradeoff is unpredictable inference cost

Why does this matter? Reasoning tends to exhibit “overthinking” Two similar prompts produce reasoning traces with 10x differences in length and thus token cost

We show the formation of fractal basins by training a loop transformer to solve integer linear regression. A bifurcation occurs mid-training: the transformer figures out how to solve unseen examples, but fractal basins appear.

Saddle scrambling allows reasoning models to check more possible solutions. We calculate the fast Lyapunov indicator (which measures how strongly transiently chaotic a trajectory is). It correlates with how many solutions the reasoning model visits before converging

High-dimensional dynamics are a “Plinko” game. Trajectories start in nearby places and converge to the same answer, but saddles cause them to take many different routes as they scatter off different incorrect answers

What causes transient chaos? Reasoning gets stuck near incorrect solutions, which the latent dynamics encode as saddle points. We visualize these excursions via PCA. Given two adjacent initial conditions, one solves the puzzle quickly; the other gets stuck near the wrong solution

How do fractals form? Dynamical systems form long, sensitive transients due to transient chaos: initial conditions start adjacent, but they take very different routes to the same equilibrium (the final answer). Natural cases include turbulence and biological networks

When we give models harder problem cases, the fractals become stronger. We think that fractal basins are thus a generic physical effect when models tru to map hard problems onto analogue systems

Where you start reasoning has a huge effect on how long it takes to converge. We color initial conditions by the convergence time. We see fractals across all architectures + tasks, ranging from Mazes to Countdown math puzzles

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Alexandra Weber @toedtoad.bsky.social · 31/08/2026

Our group discovered that reasoning models produce fractals when asked to solve hard problems. We can use nonlinear dynamics to probe the thinking processes of recurrent depth models on Sudoku, mathematics, and even ARC-AGI (1/N) arxiv.org/abs/2609.04963

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My first paper is officially out in @currentbiology.bsky.social ! We found that snake embryos coil due to a mismatch in growth rates between the gut and spine. This tight coil is one of the reasons why snakes are able to get so long. Read the paper here!

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Deepak Krishnamurthy @deepakkrish.bsky.social · 31/08/2026

Thrilled to share that I’ll be starting as an Assistant Professor in Mechanical Engineering at UC Berkeley in January 2027! @ucberkeleyofficial.bsky.social @berkeleyengineer.bsky.social I’ll be launching the Deep Lab for Microbial Biomechanics. 🧵 1/8

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JAX Genomic Education @jaxeducation.bsky.social · 31/08/2026

💡 Learn to design behavioral workflows, apply ML approaches to behavioral modeling, and connect behavior to neural and experimental manipulations. Register: www.jax.org/education-an... Organized by: @vivekdna.bsky.social @antihebbiann.bsky.social @gordonberman.bsky.social @goldenneuron.bsky.social

Flyer for the Application of Machine Learning for Automated Quantification of Behavior Short Course. See the event webpage for more information at www.jax.org/autobehavior.

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Ben Fulcher @bendfulcher.bsky.social · 04/08/2026

pyhctsa is out! A native Python port of the majority of the hctsa feature library (highly comparative time-series analysis). Thousands of interpretable time-series features available via a pip install. Built by Joshua Moore. Paper: doi.org/10.21105/jos... Code: github.com/DynamicsAndN...

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Mattia Serra @mattiaserra.bsky.social · 28/05/2025

📣 Preprint alert! We developed a framework to uncover Coherent Structures in flows on dynamic surfaces—revealing dynamic attractors, repellers and deformation directions in nematic vesicles, pancreatic spheroids, and beating zebrafish hearts. @sreejithsanthosh.bsky.social biorxiv.org/content/10.1...

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William Gilpin @wgilpin.bsky.social · 31/05/2026

thank you! i'm really excited about it. we are trying to get something similar working for PDEs now but measuring "OOD" for them has been trickier than expected

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Aishik Ghosh @aishikghosh.bsky.social · 19/03/2026

The Machine Learning for Fundamental Physics School is back! This time bigger and in a new location: Georgia Institute of Technology (@gtsciences.bsky.social)! We can cover the domestic travel and accommodation of most students and ECRs participating. Apply soon! indico.global/event/17000/

indico.global

Machine Learning for Fundamental Physics School (ML4FP) 2026

The Machine Learning for Fundamental Physics School (ML4FP) 2026 will be held at the Georgia Institute of Technology from June 1 to June 5, 2026. The event is organized with support from Oak Ridge Nat...

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Reposted by William Gilpin

Suraj Shankar 🏳️‍🌈 @surajshankar.bsky.social · 27/02/2026

Delighted this paper is out! Soft solids fracture in complex ways. Can we control it using structure and activity? Yes, using defects that localize energy injection for targeted failure! Amazing work combining exp, theory & ML by Sheng Chen and collab with Murrell lab (Yale).

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The work was inspired by recent works on small transformers, which isolate surprising behaviors like in-context k-nearest neighbors, and even in-context learning of small MLPs. See Garg et a 2022l: arxiv.org/abs/2208.01066 and Reddy 2024: arxiv.org/abs/2312.03002 (10/N)

You can think of our setting as a minimized version of SciML foundation models (FM) do. For example, PDE FMs are trained at one Reynolds number, but can forecast different Reynolds numbers. Likewise, physiology FM zero-shot new subjects, who are likely distinct dynamical systems

The agreement improves as out-of-distribution loss drops. We repeated these experiments across a hundred different models trained on different systems, using the dysts ODE library. (8/N)

The results agree, suggesting that small transformers learn transfer operators from the context during testing. They especially capture longer-lived modes, like the invariant distribution and long-lived metastable states (leading eigenvectors) (7/N)

So transformers infer when tokens arise from a higher-dimensional attractor. How does this enable OOD forecasts? We sample transitions between pairs of k-grams (time-delay embedded inputs), and compare to transition probabilities on the original, full state space. (6/N)

How is this possible? We extract the conditional probabilities of the small transformer and find that it time delay embeds its univariate input. When test data comes from a higher dimensional system, attention rollouts become higher-rank, i.e. an adaptive delay embedding. (5/N)

We can also see this in the loss curves. We see epoch-wise double descent for our in-distribution test data (a different trajectory from the same ODE), but we see a second double descent for out-of-distribution data from an unseen ODE. (4/N)

in our new paper we shrink this phenomenon down: we fully-train a small Chronos-like transformer to forecast exactly one dynamical system, and then test its ability to forecast a second dynamical system. Even in this restricted setting, it works much better than expected. (3/N)

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Last year, we noticed that off-the-shelf time series foundation models, which never saw ODE during training, forecast chaotic systems surprisingly well, even without fine-tuning. (2/N)

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Research Corporation for Science Advancement @rescorp.org · 12/02/2026

How do time series foundation models forecast unseen dynamical systems? In new experiments, we find that small transformers learn to approximate transfer operators in-context. (1/N) arxiv.org/abs/2602.18679

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RCSA welcomes 24 early career teacher-scholars in chemistry, physics, and astronomy as recipients of its 2026 #CottrellScholar Awards. Each awardee receives $120,000. Congratulations to this exceptional class!

rescorp.org

2026 Cottrell Scholar Awards

Research Corporation for Science Advancement, America's first foundation dedicated wholly to science, has named 24 early career scholars in chemistry, physics, and astronomy as recipients of its 2026 ...

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Eddie Lee @handle.invalid · 27/12/2025

I’m very happy to announce that I will joining #Seoul National University’s #SNU #physics department as Assistant Professor in Fall of 2026!

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Prakash Lab @ Miami @vprakashlab.bsky.social · 23/12/2025

🚨 POSTDOC OPENING 🚨 NIH-funded Bio-Fluid Mechanics Postdoc in my lab @univmiami.bsky.social Hofstenia miamia | cilia-driven flows | behavior & neuroscience Collab w/ Mansi Srivastava @harvard.edu 🕒 Start: Jan–Feb 2026 ⏳ 1 yr, renewable | Email me ASAP! #Postdoc #Biophysics #FluidDynamics

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Eddie Lee @handle.invalid · 08/07/2025

I'm excited to say that one of the most exploratory and thought-provoking papers I've worked on in recent years was just accepted at Physical Review Research. Preprint here: arxiv.org/abs/2502.21072 #physics #innovation 🧪🦋 @apsphysics.bsky.social

arxiv.org

Innovation-exnovation dynamics on trees and trusses

Innovation and its complement exnovation describe the progression of realized possibilities from the past to the future, and the process depends on the structure of the underlying graph. For example, ...

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William Gilpin @wgilpin.bsky.social · 17/06/2025

hi david, thank you very much :)

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This work was inspired by amazing recent work on transients by the dynamical systems community: Analogue KSAT solvers, slowdowns in gradient descent during neural network training, and chimera states in coupled oscillators. (12/N)

For the Lotka-Volterra case, optimal coordinates are the right singular vectors of the species interaction matrix. You can experimentally estimate these with O(N) operations using Krylov-style methods: perturb the ecosystem, and see how it reacts. (11/N)

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This variation influences how we reduce the dimensionality of biological time series. With non-reciprocal interactions (like predator prey), PCA won’t always separate timescales. The optimal dimensionality-reducing variables (“ecomodes”) should precondition the linear problem (10/N)

As a consequence of ill-conditioning, large ecosystems become excitable: small changes cause huge differences in how they approach equilibrium. Using the FLI, a metric invented by astrophysicists to study planetary orbits, we see caustics indicating variation in solve path (9/N)

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How would hard optimization problems arise in nature? I used genetic algorithms to evolve ecosystems towards supporting more biodiversity, and they became more ill-conditioned—and thus more prone to supertransients. (8/N)

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So ill-conditioning isn’t just something numerical analysts care about. It’s a physical property that measures computational complexity, which translates to super long equilibration times in large biological networks with trophic overlap (7/N)

More precisely: the expected equilibration time of a random Lotka-Volterra system scales with the condition number of the species interaction matrix. The scaling matches the expected scaling of the solvers that your computer uses to do linear regression (6/N)

We can think of ecological dynamics as an analogue constraint satisfaction problem. As the problem becomes more ill-conditioned, the ODEs describing the system take longer to “solve” the problem of who survives and who goes extinct (5/N)

But is equilibrium even relevant? In high dimensions, stable fixed points might not be reachable in finite time. Supertransients due to unstable solutions that trap dynamics for increasingly long durations. E.g, pipe turbulence is supertransient (laminar flow is globally stable) (4/N)

Dynamical systems are linear near fixed points, so May used random matrix theory to show large random ecosystems are usually unstable. The biodiversity we see in the real world requires finer-tuned structure from selection, niches, et al. that recover stability (3/N)

A celebrated result in mathematical biology is Robert May’s “stability vs complexity” tradeoff. In large biological networks, we can’t possibly measure all N^2 interactions among N species, genes, neurons, etc. What is our null hypothesis for their behavior? (2/N)