Publications (144)
Diffusion Models are Evolutionary Algorithms
Yanbo Zhang, Benedikt Hartl, Hananel Hazan +1
In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolutio…
Lattice models for non-Fermi liquid metals
Michael Levin, T. Senthil
We present two 2D lattice models with non-Fermi liquid metallic phases. We show that the low energy physics of these models is exactly described by a Fermi sea of fractionalized qu…
Positive Alignment: Artificial Intelligence for Human Flourishing
Ruben Laukkonen, Seb Krier, Chloé Bakalar +13
Existing alignment research is dominated by concerns about safety and preventing harm: safeguards, controllability, and compliance. This paradigm of alignment parallels early psych…
Bio-inspired AI: Integrating Biological Complexity into Artificial Intelligence
Nima Dehghani, Michael Levin
The pursuit of creating artificial intelligence (AI) mirrors our longstanding fascination with understanding our own intelligence. From the myths of Talos to Aristotelian logic and…
Automated shapeshifting for function recovery in damaged robots
Sam Kriegman, Stephanie Walker, Dylan Shah +3
A robot's mechanical parts routinely wear out from normal functioning and can be lost to injury. For autonomous robots operating in isolated or hostile environments, repair from a…
A short proof of ToruÅczyk's Characterization Theorems
Jan J. Dijkstra, Michael Levin, Jan van Mill
We present short proofs of ToruÅczyk's well-known characterization theorems of the Hilbert cube and Hilbert space, respectively.
Neuroevolution of Decentralized Decision-Making in N-Bead Swimmers Leads to Scalable and Robust Collective Locomotion
Benedikt Hartl, Michael Levin, Andreas Zöttl
Many microorganisms swim by performing larger non-reciprocal shape deformations that are initiated locally by molecular motors. However, it remains unclear how decentralized shape…
SBMLtoODEjax: Efficient Simulation and Optimization of Biological Network Models in JAX
Mayalen Etcheverry, Michael Levin, Clément Moulin-Frier +1
Advances in bioengineering and biomedicine demand a deep understanding of the dynamic behavior of biological systems, ranging from protein pathways to complex cellular processes. B…
A mean field approach for string condensed states
Michael Levin, Xiao-Gang Wen
We describe a mean field technique for quantum string (or dimer) models. Unlike traditional mean field approaches, the method is general enough to include string condensed phases i…
Neurons as hierarchies of quantum reference frames
Chris Fields, James F. Glazebrook, Michael Levin
Conceptual and mathematical models of neurons have lagged behind empirical understanding for decades. Here we extend previous work in modeling biological systems with fully scale-i…
On p-adic actions raising dimension by 2
Michael Levin
Raymond and Wiliams constructed an action of the p-adic integers on an n-dimensional compactum, n>1, with the orbit space of dimension n+2. The author earlier presented a simplifie…
A Little Rank Goes a Long Way: Random Scaffolds with LoRA Adapters Are All You Need
Hananel Hazan, Yanbo Zhang, Benedikt Hartl +1
How many of a neural network's parameters actually encode task-specific information? We investigate this question with LottaLoRA, a training paradigm in which every backbone weight…
Modeling somatic computation with non-neural bioelectric networks
Santosh Manicka, Michael Levin
The field of basal cognition seeks to understand how adaptive, context-specific behavior occurs in non-neural biological systems. Embryogenesis and regeneration require plasticity…
Braiding statistics of loop excitations in three dimensions
Chenjie Wang, Michael Levin
While it is well known that three dimensional quantum many-body systems can support non-trivial braiding statistics between particle-like and loop-like excitations, or between two…
Equilibrium flow: From Snapshots to Dynamics
Yanbo Zhang, Michael Levin
Scientific data, from cellular snapshots in biology to celestial distributions in cosmology, often consists of static patterns from underlying dynamical systems. These snapshots, w…
Oncomorphic neural agent populations for resource-limited sequential learning
Philip Greulich, Michael Levin, Rosalia Moreddu
Distributed artificial intelligence (AI) often operates under sequential task exposure, uneven compute, and decentralized coordination. Here, we present a cancer-inspired, or oncom…
Deconfined quantum criticality and Neel order via dimer disorder
Michael Levin, T. Senthil
Recent results on the nature of the quantum critical point between Neel and valence bond solid(VBS) ordered phases of two dimensional quantum magnets are examined by an attack from…
Collective states of non-abelian quasiparticles in a magnetic field
Michael Levin, Bertrand I. Halperin
Motivated by the physics of the Moore-Read ν= 1/2 state away from half-filling, we investigate collective states of non-abelian e/4 quasiparticles in a magnetic field. We consider…
Some mapping theorems for extensional dimension
Michael Levin, Wayne Lewis
We present some results related to theorems of Pasynkov and Torunczyk on the geometry of maps of finite dimensional compacta.
Scale invariant robot behavior with fractals
Sam Kriegman, Amir Mohammadi Nasab, Douglas Blackiston +4
Robots deployed at orders of magnitude different size scales, and that retain the same desired behavior at any of those scales, would greatly expand the environments in which the r…
Protected edge modes without symmetry
Michael Levin
We discuss the question of when a gapped 2D electron system without any symmetry has a protected gapless edge mode. While it is well known that systems with a nonzero thermal Hall…
A property of C_p[0,1]
Michael Levin
We prove that for every finite dimensional compact metric space there is an open continuous linear surjection from onto . The proof makes use of embeddings i…
Vanishing Hall conductance for commuting Hamiltonians
Carolyn Zhang, Michael Levin, Sven Bachmann
We consider the process of flux insertion for ground states of almost local commuting projector Hamiltonians in two spatial dimensions. In the case of finite dimensional local Hilb…
Topological invariants for gauge theories and symmetry-protected topological phases
Chenjie Wang, Michael Levin
We study the braiding statistics of particle-like and loop-like excitations in 2D and 3D gauge theories with finite, Abelian gauge group. The gauge theories that we consider are ob…
Universal acyclic resolutions for arbitrary coefficient groups
Michael Levin
We prove that for every compactum and every integer there are a compactum of and a surjective -map $r: Z \lo X$ such that for every abe…
Fractional topological insulators
Michael Levin, Ady Stern
We analyze generalizations of two dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems. These states, which we call fra…
On dimensionally exotic maps
Alexander Dranishnikov, Michael Levin
We call a value of a map dimensionally regular if . It was shown in \cite{first-exotic} that if a map between comp…
On actions of abelian Cantor groups
Michael Levin
By a Cantor group we mean a topological group homeomorphic to the Cantor set. The author earlier proved that every compact metric space of rational cohomological dimension n can be…
Extensions of maps to M(Z_m,1)
Jerzy Dydak, Michael Levin
We show that a Moore space M(Z_m,1) is an absolute extensor for finite dimensional metrizable spaces of cohomological dimension dim_{Z_m} \leq 1.
Generalizations and limitations of string-net models
Chien-Hung Lin, Michael Levin
We ask which topological phases can and cannot be realized by exactly soluble string-net models. We answer this question for the simplest class of topological phases, namely those…
Covering spaces by balls
Vladimir P. Fonf, Michael Levin, Clemente Zanco
We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space by closed balls each of positive radius, some point e…
Exactly soluble lattice models for non-abelian states of matter in 2 dimensions
Maciej Koch-Janusz, Michael Levin, Ady Stern
Following an earlier construction of exactly soluble lattice models for abelian fractional topological insulators in two and three dimensions, we construct here an exactly soluble…
Open Questions about Time and Self-reference in Living Systems
Samson Abramsky, Wolfgang Banzhaf, Leo S. D. Caves +5
Living systems exhibit a range of fundamental characteristics: they are active, self-referential, self-modifying systems. This paper explores how these characteristics create chall…
An embedding theorem for mean dimension
Michael Levin
Let (X,Z) be a minimal dynamical system on a compact metric X and k an integer such that mdim X< k. We show that (X,Z) admits an equivariant embedding in the shift (D^k)^Z where D…
Survival, decay, and topological protection in non-Hermitian quantum transport
Mark S. Rudner, Michael Levin, Leonid S. Levitov
Non-Hermitian quantum systems can exhibit unique observables characterizing topologically protected transport in the presence of decay. The topological protection arises from windi…
A Max Pressure Algorithm for Traffic Signals Considering Pedestrian Queues
Hao Liu, Vikash V. Gayah, Michael Levin
This paper proposes a novel max-pressure (MP) algorithm that incorporates pedestrian traffic into the MP control architecture. Pedestrians are modeled as being included in one of t…
Rational acyclic resolutions
Michael Levin
Let X be a compactum such that dim_Q X < n+1, n>1. We prove that there is a Q-acyclic resolution r: Z-->X from a compactum Z of dim < n+1. This allows us to give a complete descrip…
Closed orbits for the diagonal group and well-rounded lattices
Michael Levin, Uri Shapira, Barak Weiss
Curt McMullen showed that every compact orbit for the action of the diagonal group on the space of lattices contains a well-rounded lattice. We extend this to all closed orbits.
Heuristically Adaptive Diffusion-Model Evolutionary Strategy
Benedikt Hartl, Yanbo Zhang, Hananel Hazan +1
Diffusion Models represent a significant advancement in generative modeling, employing a dual-phase process that first degrades domain-specific information via Gaussian noise and r…
Competency of the Developmental Layer Alters Evolutionary Dynamics in an Artificial Embryogeny Model of Morphogenesis
Lakshwin Shreesha, Michael Levin
Biological genotypes do not code directly for phenotypes; developmental physiology is the control layer that separates genomes from capacities ascertained by selection. A key aspec…
Casimir repulsion between metallic objects in vacuum
Michael Levin, Alexander P. McCauley, Alejandro W. Rodriguez +2
We give an example of a geometry in which two metallic objects in vacuum experience a repulsive Casimir force. The geometry consists of an elongated metal particle centered above a…
Tensor-entanglement renormalization group approach to 2D quantum systems
Zheng-Cheng Gu, Michael Levin, Xiao-Gang Wen
Traditional mean-field theory is a simple generic approach for understanding various phases. But that approach only applies to symmetry breaking states with short-range entanglemen…
Metabolic limits on classical information processing by biological cells
Chris Fields, Michael Levin
Biological information processing is generally assumed to be classical. Measured cellular energy budgets of both prokaryotes and eukaryotes, however, fall orders of magnitude short…
A Z-set unknotting theorem for Nobeling spaces
Michael Levin
We prove a -set unknotting theorem for Nobeling spaces. This generalizes a result obtained by S. Ageev for a restricted class of -sets. The theorem is proved for a certain mo…
Longitudinal analysis of gene expression profiles using functional mixed-effects models
Maurice Berk, Cheryl Hemingway, Michael Levin +1
In many longitudinal microarray studies, the gene expression levels in a random sample are observed repeatedly over time under two or more conditions. The resulting time courses ar…
Constraints on order and disorder parameters in quantum spin chains
Michael Levin
We derive general constraints on order and disorder parameters in Ising symmetric spin chains. Our main result is a theorem showing that every gapped, translationally invariant, Is…
Advancing the Scientific Method with Large Language Models: From Hypothesis to Discovery
Yanbo Zhang, Sumeer A. Khan, Adnan Mahmud +10
With recent Nobel Prizes recognising AI contributions to science, Large Language Models (LLMs) are transforming scientific research by enhancing productivity and reshaping the scie…
Classification and analysis of two dimensional abelian fractional topological insulators
Michael Levin, Ady Stern
We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasipar…
A free energy principle for generic quantum systems
Chris Fields, Karl Friston, James F. Glazebrook +1
The Free Energy Principle (FEP) states that under suitable conditions of weak coupling, random dynamical systems with sufficient degrees of freedom will behave so as to minimize an…
Anomaly indicators for time-reversal symmetric topological orders
Chenjie Wang, Michael Levin
Some time-reversal symmetric topological orders are anomalous in that they cannot be realized in strictly two-dimensions without breaking time reversal symmetry; instead, they can…
Characterizing Nobeling spaces
Michael Levin
It is shown that Nobeling spaces are uniquely determined by the universal extension and embedding properties.
Universal lower bound on topological entanglement entropy
Isaac H. Kim, Michael Levin, Ting-Chun Lin +2
Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law, with a constant correction term known as the topological entanglement entropy (T…
Quantum ether: photons and electrons from a rotor model
Michael Levin, Xiao-Gang Wen
We give an example of a purely bosonic model -- a rotor model on the 3D cubic lattice -- whose low energy excitations behave like massless U(1) gauge bosons and massless Dirac ferm…
Neural cellular automata: applications to biology and beyond classical AI
Benedikt Hartl, Michael Levin, Léo Pio-Lopez
Neural Cellular Automata (NCA) represent a powerful framework for modeling biological self-organization, extending classical rule-based systems with trainable, differentiable (or e…
Braiding statistics approach to symmetry-protected topological phases
Michael Levin, Zheng-Cheng Gu
We construct a 2D quantum spin model that realizes an Ising paramagnet with gapless edge modes protected by Ising symmetry. This model provides an example of a "symmetry-protected…
Cell-like resolutions preserving cohomological dimensions
Michael Levin
We prove that for every compactum X with dim_Z X <= n >= 2 there is a cell-like resolution r: Z --> X from a compactum Z onto X such that dim Z <= n and for every integer k and eve…
Detecting topological order in a ground state wave function
Michael Levin, Xiao-Gang Wen
A large class of topological orders can be understood and classified using the string-net condensation picture. These topological orders can be characterized by a set of data (N, d…
Tensor-entanglement renormalization group approach to topological phases
Zheng-Cheng Gu, Michael Levin, Xiao-Gang Wen
The tensor-entanglement renormalization group approach is applied to Hamiltonians that realize a class of topologically ordered states -- string-net condensed states. We analyze ph…
A union theorem for mean dimension
Michael Levin
Let (X,Z) be a dynamical system on a compact metric X and let X be the countable union of closed invariant subsets X_i, i in N. We prove that mdim X =sup {mdim X_i : i in N}.
Weak symmetry breaking in two dimensional topological insulators
Chenjie Wang, Michael Levin
We show that there exist two dimensional (2D) time reversal invariant fractionalized insulators with the property that both their boundary with the vacuum and their boundary with a…
Nernst and Ettingshausen effects in gapped quantum materials
Michael Levin, Anton Kapustin, Lev Spodyneiko
We investigate whether there could exist topological invariants of gapped 2D materials related to dissipationless thermoelectric transport at low temperatures. We give both macrosc…
Stability of topological superconducting qubits with number conservation
Matthew F. Lapa, Michael Levin
The study of topological superconductivity is largely based on the analysis of simple mean-field models that do not conserve particle number. A major open question in the field is…
BraiNCA: brain-inspired neural cellular automata and applications to morphogenesis and motor control
Léo Pio-Lopez, Benedikt Hartl, Michael Levin
Most of the Neural Cellular Automata (NCAs) defined in the literature have a common theme: they are based on regular grids with a Moore neighborhood (one-hop neighbour). They do no…
Morphological computational capacity of Physarum polycephalum
Suyash Bajpai, Aviva Lucas-DeMott, Nirosha J Murugan +2
While computational capacity limits of the universe and carbon-based life have been estimated, a stricter bound for aneural organisms has not been established. Physarum polycephalu…
Technological Approach to Mind Everywhere (TAME): an experimentally-grounded framework for understanding diverse bodies and minds
Michael Levin
Synthetic biology and bioengineering provide the opportunity to create novel embodied cognitive systems (otherwise known as minds) in a very wide variety of chimeric architectures…
Scalable sim-to-real transfer of soft robot designs
Sam Kriegman, Amir Mohammadi Nasab, Dylan Shah +5
The manual design of soft robots and their controllers is notoriously challenging, but it could be augmented---or, in some cases, entirely replaced---by automated design tools. Mac…
Solvable models for neutral modes in fractional quantum Hall edges
Chris Heinrich, Michael Levin
We describe solvable models that capture how impurity scattering in certain fractional quantum Hall edges can give rise to a neutral mode --- i.e. an edge mode that does not carry…
A dimensional property of Cartesian product
Michael Levin
We show that the Cartesian product of three hereditarily infinite dimensional compact metric spaces is never hereditarily infinite dimensional. It is quite surprising that the proo…
Is the electrostatic force between a point charge and a neutral metallic object always attractive?
Michael Levin, Steven G. Johnson
We give an example of a geometry in which the electrostatic force between a point charge and a neutral metallic object is repulsive. The example consists of a point charge centered…
Giving Simulated Cells a Voice: Evolving Prompt-to-Intervention Models for Cellular Control
Nam H. Le, Patrick Erikson, Yanbo Zhang +2
Guiding biological systems toward desired states, such as morphogenetic outcomes, remains a fundamental challenge with far-reaching implications for medicine and synthetic biology.…
Closing the Loop on Morphogenesis: A Mathematical Model of Morphogenesis by Closed-Loop Reaction-Diffusion
Joel Grodstein, Michael Levin
Morphogenesis, the establishment and repair of emergent complex anatomy by groups of cells, is a fascinating and biomedically-relevant problem. One of its most fascinating aspects…
What Lives? A meta-analysis of diverse opinions on the definition of life
Reed Bender, Karina Kofman, Blaise Agüera y Arcas +1
The question of "what is life?" has challenged scientists and philosophers for centuries, producing an array of definitions that reflect both the mystery of its emergence and the d…
Symmetry-Twisted Multi-Entropies: Order Parameters for 2D SPT Phases
Ramanjit Sohal, Michael Levin, Ruben Verresen
The paper proposes two nonlocal order parameters based on symmetry‑twisted multi‑entropies that can detect and distinguish all 2D bosonic symmetry‑protected topological phases with…
Many-body systems with spurious modular commutators
Julian Gass, Michael Levin
Recently, it was proposed that the chiral central charge of a gapped, two-dimensional quantum many-body system is proportional to a bulk ground state entanglement measure known as…
Topological constraints on self-organisation in locally interacting systems
Francesco Sacco, Dalton A R Sakthivadivel, Michael Levin
All intelligence is collective intelligence, in the sense that it is made of parts which must align with respect to system-level goals. Understanding the dynamics which facilitate…
Equivariant embedding of finite-dimensional dynamical systems
Yonatan Gutman, Michael Levin, Tom Meyerovitch
We prove an equivariant version of the classical Menger-Nobeling theorem regarding topological embeddings: Whenever a group acts on a finite-dimensional compact metric space $X…
Resolving rational cohomological dimension via a Cantor group action
Michael Levin
By a Cantor group we mean a topological group homeomorphic to the Cantor set. We show that a compact metric space of rational cohomological dimension can be obtained as the orb…
Slime mould: the fundamental mechanisms of cognition
Jordi Vallverdu, Oscar Castro, Richard Mayne +7
The slime mould Physarum polycephalum has been used in developing unconventional computing devices for in which the slime mould played a role of a sensing, actuating, and computing…
Extensions of maps to the projective plane
Jerzy Dydak, Michael Levin
It is proved that for a 3-dimensional compact metrizable space X the infinite real projective space is an absolute extensor of X if and only if the real projective plane is an abso…
Rényi-like entanglement probe of the chiral central charge
Julian Gass, Michael Levin
We propose a ground state entanglement probe for gapped, two-dimensional quantum many-body systems that involves taking powers of reduced density matrices in a particular geometric…
Classical Sorting Algorithms as a Model of Morphogenesis: self-sorting arrays reveal unexpected competencies in a minimal model of basal intelligence
Taining Zhang, Adam Goldstein, Michael Levin
The emerging field of Diverse Intelligence seeks to identify, formalize, and understand commonalities in behavioral competencies across a wide range of implementations. Especially…
On compacta not admitting a stable intersection in R^n
Michael Levin
Compacta X and Y are said to admit a stable intersection in R^n if there are maps f : X -> R^n and g : Y -> R^n such that for every sufficiently close continuous approximations f'…
Particle-hole symmetry and the Pfaffian state
Michael Levin, Bertrand I. Halperin, Bernd Rosenow
We consider the properties of the Moore-Read Pfaffian state under particle-hole conjugation. We show that the particle-hole conjugate of the Pfaffian state - or "anti-Pfaffian" sta…
Loop braiding statistics in exactly soluble 3D lattice models
Chien-Hung Lin, Michael Levin
We construct two exactly soluble lattice spin models that demonstrate the importance of three-loop braiding statistics for the classification of 3D gapped quantum phases. The two m…
Fermi surface change across a deconfined quantum critical point
Ribhu K. Kaul, Alexei Kolezhuk, Michael Levin +2
The quantum phase transitions of metals have been extensively studied in the rare-earth "heavy electron" materials, the cuprates, and related compounds. The Fermi surface of the me…
Hole dynamics in an antiferromagnet across a deconfined quantum critical point
Ribhu K. Kaul, Alexei Kolezhuk, Michael Levin +2
We study the effects of a small density of holes, delta, on a square lattice antiferromagnet undergoing a continuous transition from a Neel state to a valence bond solid at a decon…
Language Game: Talking to Non-Human Systems
Yanbo Zhang, Michael Levin
Language carries thought and coordination among humans but rarely reaches further along the spectrum of diverse intelligence. Yet non-neural systems -- from gene regulatory network…
Particle-hole symmetry and electromagnetic response of a half-filled Landau level
Michael Levin, Dam Thanh Son
We derive exact physical consequences of particle-hole symmetry of the state of electrons in a strong magnetic field. We show that if the symmetry is not spontaneously bro…
The Free Energy Principle drives neuromorphic development
Chris Fields, Karl Friston, James F. Glazebrook +2
We show how any system with morphological degrees of freedom and locally limited free energy will, under the constraints of the free energy principle, evolve toward a neuromorphic…
A free Z-action by isometries on a compact metric space which is not embeddable into a cubical shift
Alexander Dranishnikov, Michael Levin
We construct an example announced in the title. It answers in a strong way a well-known open problem in topological dynamics. In fact our construction is an existence theorem. It i…
Memory via Temporal Delays in weightless Spiking Neural Network
Hananel Hazan, Simon Caby, Christopher Earl +2
A common view in the neuroscience community is that memory is encoded in the connection strength between neurons. This perception led artificial neural network models to focus on c…
Quantized pumping and phase diagram topology of interacting bosons
Erez Berg, Michael Levin, Ehud Altman
Interacting lattice bosons at integer filling can support two distinct insulating phases, which are separated by a critical point: the Mott insulator and the Haldane insulator[Phys…
Acyclic resolutions for arbitrary groups
Michael Levin
We prove that for every abelian group G and every compactum X with there is a G-acyclic resolution $r: Z \lo X$ from a compactum Z with a…
Tensor renormalization group approach to 2D classical lattice models
Michael Levin, Cody P. Nave
We describe a simple real space renormalization group technique for two dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the sa…
ZapGPT: Free-form Language Prompting for Simulated Cellular Control
Nam H. Le, Patrick Erickson, Yanbo Zhang +2
Human language is one of the most expressive tools for conveying intent, yet most artificial or biological systems lack mechanisms to interpret or respond meaningfully to it. Bridg…
Fermions, strings, and gauge fields in lattice spin models
Michael Levin, Xiao-Gang Wen
We investigate the general properties of lattice spin models with emerging fermionic excitations. We argue that fermions always come in pairs and their creation operator always has…
The Causally Emergent Alignment Hypothesis: Causal Emergence Aligns with and Predicts Final Reward in Reinforcement Learning Agents
Federico Pigozzi, Michael Levin
A hallmark of life on Earth is the ability of agents to exert causal power and be drivers of subsequent events. This is key to cognition at all scales. Causal emergence, measuring…
Symmetry enriched string-nets: Exactly solvable models for SET phases
Chris Heinrich, Fiona Burnell, Lukasz Fidkowski +1
We construct exactly solvable models for a wide class of symmetry enriched topological (SET) phases. Our construction applies to 2D bosonic SET phases with finite unitary onsite sy…
Mutual Chern-Simons theory for Z_2 topological order
Su-Peng Kou, Michael Levin, Xiao-Gang Wen
We study several different topological ordered states in frustrated spin systems. The effective theories for those different Z_2 topological orders all have the same form --…
Effect of slowly decaying long-range interactions on topological qubits
Etienne Granet, Michael Levin
We study the robustness of topological ground state degeneracy to long-range interactions in quantum many-body systems. We focus on slowly decaying two-body interactions that scale…