arXiv subjects

Thomas M. A. Fink

Publications and source records attributed to Thomas M. A. Fink.

9 recordsLinked to original sources

arXiv2026

Deep-layered machines have a built-in Occam's razor

Input-output maps are prevalent throughout science and technology. They are empirically observed to be biased towards simple outputs, but we don't understand why. To address this puzzle, we study the archetypal input-output map: a deep-layered machine in which every node is a Boolean function of all the nodes below it. We give an exact theory for the distribution of outputs, and we confirm our predictions through extensive computer experiments. As the network depth increases, the distribution becomes exponentially biased towards simple outputs. This suggests that deep-layered machines and other learning methodologies may be inherently biased towards simplicity in the models that they generate.

cond-mat.dis-nn↗

arXiv2022

Biological logics are restricted

Networks of gene regulation govern morphogenesis, determine cell identity and regulate cell function. But we have little understanding, at the local level, of which logics are biologically preferred or even permitted. To solve this puzzle, we studied the consequences of a fundamental aspect of gene regulatory networks: genes and transcription factors talk to each other but not themselves. Remarkably, this bipartite structure severely restricts the number of logical dependencies that a gene can have on other genes. We developed a theory for the number of permitted logics for different regulatory building blocks of genes and transcription factors. We tested our predictions against a simulation of the 19 simplest building blocks, and found complete agreement. The restricted range of biological logics is a key insight into how information is processed at the genetic level. It constraints global network function and makes it easier to reverse engineer regulatory networks from observed behavior.

q-bio.MN↗

arXiv2022

Regulatory motifs: structural and functional building blocks of genetic computation

Developing and maintaining life requires a lot of computation. This is done by gene regulatory networks. But we have little understanding of how this computation is organized. I show that there is a direct correspondence between the structural and functional building blocks of regulatory networks, which I call regulatory motifs. I derive a simple bound on the range of function that these motifs can perform, in terms of the local network structure. I prove that this range is a small fraction of all possible functions, which severely constrains global network behavior. Part of this restriction is due to redundancy in the function that regulatory motifs can achieve - there are many ways to perform the same task. Regulatory motifs help us understanding how genetic computation is organized and what it can achieve.

q-bio.MN↗

arXiv2021

A phase transition creates the geometry of the continuum from discrete space

Models of discrete space and space-time that exhibit continuum-like behavior at large lengths could have profound implications for physics. They may tame the infinities that arise from quantizing gravity, and dispense with the machinery of the real numbers, which has no direct observational support. Yet despite sophisticated attempts at formulating discrete space, researchers have failed to construct even the simplest geometries. We investigate graphs as the most elementary discrete models of two-dimensional space. We show that if space is discrete, it must be disordered, by proving that all planar lattice graphs exhibit the same taxicab metric as square grids. We give an explicit recipe for growing disordered discrete space by sampling a Boltzmann distribution of graphs at low temperature. We then propose three conditions which any discrete model of Euclidean space must meet: have a Hausdorff dimension of two, support unique straight lines and obey Pythagoras' theorem. Our model satisfies all three, making it the first discrete model in which continuum-like behavior is recovered at large lengths.

cond-mat.stat-mech↗

arXiv2019

The mathematical structure of innovation

Despite our familiarity with specific technologies, the origin of new technologies remains mysterious. Are new technologies made from scratch, or are they built up recursively from new combinations of existing technologies? To answer this, we introduce a simple model of recursive innovation in which technologies are made up of components and combinations of components can be turned into new components---a process we call technological recursion. We derive a formula for the extent to which technological recursion increases or decreases the likelihood of making new technologies. We test our predictions on historical data from three domains and find that technologies are not built up from scratch, but are the result of new combinations of existing technologies. This suggests a dynamical process by which known technologies were made and a strategy for accelerating the discovery of new ones.

physics.soc-ph↗

arXiv2014

Easily repairable networks

We introduce a simple class of distribution networks which withstand damage by being repairable instead of redundant. We prove a lower bound for the expected cost of repair, and show that for networks on the square and triangular lattice, this bound is achievable and results in a network with exactly three levels of structural hierarchy. We extend our results to networks subject to repeated attacks, in which the repairs themselves must be repairable. We find that, in exchange for a modest increase in repair cost, such networks are able to withstand any number of attacks.

physics.soc-ph↗

arXiv2013

Optimal scales in weighted networks

The analysis of networks characterized by links with heterogeneous intensity or weight suffers from two long-standing problems of arbitrariness. On one hand, the definitions of topological properties introduced for binary graphs can be generalized in non-unique ways to weighted networks. On the other hand, even when a definition is given, there is no natural choice of the (optimal) scale of link intensities (e.g. the money unit in economic networks). Here we show that these two seemingly independent problems can be regarded as intimately related, and propose a common solution to both. Using a formalism that we recently proposed in order to map a weighted network to an ensemble of binary graphs, we introduce an information-theoretic approach leading to the least biased generalization of binary properties to weighted networks, and at the same time fixing the optimal scale of link intensities. We illustrate our method on various social and economic networks.

physics.data-an↗

arXiv2013

Low-temperature behaviour of social and economic networks

Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely interconnected nodes. Several models, including ensembles of networks also known in social science as Exponential Random Graphs, have been proposed with the aim of reproducing each of these properties in isolation. Here we define a generalized ensemble of graphs by introducing the concept of graph temperature, controlling the degree of topological optimization of a network. We consider the temperature-dependent version of both existing and novel models and show that all the aforementioned topological properties can be simultaneously understood as the natural outcomes of an optimized, low-temperature topology. We also show that seemingly different graph models, as well as techniques used to extract information from real networks, are all found to be particular low-temperature cases of the same generalized formalism. One such technique allows us to extend our approach to real weighted networks. Our results suggest that a low graph temperature might be an ubiquitous property of real socio-economic networks, placing conditions on the diffusion of information across these systems.

cond-mat.dis-nn↗

arXiv2003

Stochastic Annealing

We demonstrate that is it possible to simulate a system in thermal equilibrium even when the energy cannot be evaluated exactly, provided the error distribution is known. This leads to an effective optimisation strategy for problems where the evaluation of each design can only be sampled statistically.

cond-mat.stat-mech↗