with 3d plots| Toby Lam’s Blog
without eigendecomposition| Toby Lam’s Blog
Figure 1 There is lots of fractal-like behaviour in NNs. Not all the senses in which fractal-like-behaviour is used are the same; Figure 2 finds fractals in a transformer residual stream for example, but there are fractal loss landscapes, fractal optimiser paths… I bet some of these things connect pretty well. Let‘s find out. 1 Fractal loss landscapes More loss landscape management here [Andreeva et al. (2024); Hennick and Baerdemacker (2025); ]. Estimation theory for fractal qualities ...| The Dan MacKinlay stable of variably-well-consider’d enterprises
Disentangled representation learning| The Dan MacKinlay stable of variably-well-consider’d enterprises
How can we model and solve multi-agent coordination problems in AlgebraicJulia?| blog.algebraicjulia.org
1 Key Research Directions| The Dan MacKinlay stable of variably-well-consider’d enterprises
Normalising flows for PDE learning. Figure 1 Lipman et al. (2023) seems to be the origin point, extended by Kerrigan, Migliorini, and Smyth (2024) to function-valued PDEs. Figure 2: An illustration of our FFM method. The vector field (in black) transforms a noise sample drawn from a Gaussian process with a Matérn kernel (at ) to the function (at ) via solving a function space ODE. By sampling many such , we define a conditional path of measures approximately interpolating between and the f...| The Dan MacKinlay stable of variably-well-consider’d enterprises
Diffusion models for PDE learning. Figure 1 Slightly confusing terminology, because we are using diffusion models to learn PDEs, but the PDEs themselves are often used to model diffusion processes. Also sometimes the diffusion models that do the modelling aren’t actually diffusive, but are based on Poisson flow generative models. Naming things is hell. 1 Classical diffusion models TBD 2 Poisson Flow generative models These are based on non-diffusive physics but also seem to be used to simu...| The Dan MacKinlay stable of variably-well-consider’d enterprises
Figure 1 Placeholder. Levers for Biological Progress - by Niko McCarty In order for 50-100 years of biological progress to be condensed into 5-10 years of work, we’ll need to get much better at running experiments quickly and also collecting higher-quality datasets. This essay focuses on how we might do both, specifically for the cell. Though my focus in this essay is narrow — I don’t discuss bottlenecks in clinical trials, human disease, or animal testing — I hope others will take o...| The Dan MacKinlay stable of variably-well-consider’d enterprises
Rewrite rules are organized via a graphical syntax into discrete-time simulations which can be understood as agent-based models. This representation is transparent, compositional, and serializable.| blog.algebraicjulia.org
In the previous post, we defined a general approach for composing dynamical systems based on the mathematics of operads and operad algebras. In this post, we explore an undirected composition syntax in which dynamical systems compose by sharing resources. We also get a taste of hierarchical composition, i.e. composing systems which are themselves composites.| blog.algebraicjulia.org
Informally, many models are specified as compositions of primitive dynamical systems. In this series of posts, we make this modular specification formal by introducing a computing framework from composing open dynamical systems. In this first post of the series, we examine directed theories for composition.| blog.algebraicjulia.org
This blog post is written as a dialogue between two imaginary characters, one of them representing myself (H) and the other a stubborn straw man (S). It is broken into four parts: the dogma, the insight, the decoy, and the clues. If you do not feel like reading the whole thing, you can skip to […] The post Breaking Free from Neural Networks and Dynamical Systems first appeared on Life Is Computation.| Life Is Computation
We will see that the 3D plot of \(x^2 + (y+zi)^2 = 1\) contains a circle and a hyperbola, where \(i\) is the imaginary number. Beyond the visuals, this helps us understand the (complex) eigenvalues of real matrices.| Toby Lam’s Blog