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  • Founded by Jim and Marilyn Simons, we’re a private philanthropy advancing mathematics and basic science.

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Bringing people and ideas together to fund, conduct, and share transformative science.

Our grants advance knowledge and strengthen connections between science and society.

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Founded by Jim and Marilyn Simons, we’re a private philanthropy advancing mathematics and basic science.

Work with us on the frontier of basic science research.

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The Flatiron Institute is a research center that uses computational science to advance fields like physics, biology, and astronomy.

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Featured

Dissecting mechanisms of hyperarousal in autism and related disorders using the Simons Sleep Project

Funded Work

Gravity Follows Newton’s and Einstein’s Rules, Even at Cosmic Scales

April 15, 2026

Scientists Capture Superconductivity’s ‘Dancing Pairs’ for First Time, Filling Gap in Decades-Old Theory

April 15, 2026

How SURFiN Fellowships Jump-Started These 3 Neuroscience Students’ STEM Careers

March 18, 2026

Topology and Complexity

November 19, 2014

Results

  1. A Network of Biologically Inspired Rectified Spectral Units (ReSUs) Learns Hierarchical Features Without Error Backpropagation

    Publication
    We introduce a biologically inspired, multilayer neural architecture composed of Rectified Spectral Units (ReSUs). Each ReSU projects a recent window of its input history onto a canonical direction …
  2. Neurons as Detectors of Coherent Sets in Sensory Dynamics

    Publication
    We model sensory streams as observations from high-dimensional stochastic dynamical systems and conceptualize sensory neurons as self-supervised learners of compact representations of such dynamics. From prior …
  3. Reading Qubits with Sequential Weak Measurements: Limits of Information Extraction

    Publication
    Quantum information processing and computation requires high accuracy qubit configuration readout. In many practical schemes, the initial qubit configuration has to be inferred from readout that is a …
  4. Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states

    Publication
    Whether the ground state of the square lattice Hubbard model exhibits superconductivity remains a major open question, central to understanding high temperature cuprate superconductors and ultra-cold fermions …
  5. Toward Robustness across Cosmological Simulation Models IllustrisTNG, SIMBA, Astrid, and Swift-Eagle

    Publication
    The rapid advancement of large-scale cosmological simulations has opened new avenues for cosmological and astrophysical research. However, the increasing diversity among cosmological simulation models presents a challenge …
  6. Neural Network-Augmented Pfaffian Wave-functions for Scalable Simulations of Interacting Fermions

    Publication
    Developing accurate numerical methods for strongly interacting fermions is crucial for improving our understanding of various quantum many-body phenomena, especially unconventional superconductivity. Recently, neural quantum states have …
  7. In-Context Denoising with One-Layer Transformers: Connections between Attention and Associative Memory Retrieval

    Publication
    We introduce in-context denoising, a task that refines the connection between attention-based architectures and dense associative memory (DAM) networks, also known as modern Hopfield networks. Using …
  8. In-Context Denoising with One-Layer Transformers: Connections between Attention and Associative Memory Retrieval

    Publication
    We introduce in-context denoising, a task that refines the connection between attention-based architectures and dense associative memory (DAM) networks, also known as modern Hopfield networks. Using …
  9. Normative framework for deriving neural networks with multi-compartmental neurons and non-Hebbian plasticity

    Publication
    An established normative approach for understanding the algorithmic basis of neural computation is to derive online algorithms from principled computational objectives and evaluate their compatibility with anatomical and …
  10. Unlocking the Potential of Similarity Matching: Scalability, Supervision and Pre-training

    Publication
    While effective, the backpropagation (BP) algorithm exhibits limitations in terms of biological plausibility, computational cost, and suitability for online learning. As a result, there has been a growing …
  11. Coordinated drift of receptive fields in Hebbian/anti-Hebbian network models during noisy representation learning

    Publication
    Recent experiments have revealed that neural population codes in many brain areas continuously change even when animals have fully learned and stably perform their tasks. This representational ‘drift …
  12. Toward a Geometrical Understanding of Self-supervised Contrastive Learning

    Publication
    Self-supervised learning (SSL) is currently one of the premier techniques to create data representations that are actionable for transfer learning in the absence of human annotations. Despite …
  13. Deep Learning the Functional Renormalization Group

    Publication
    We perform a data-driven dimensionality reduction of the scale-dependent four-point vertex function characterizing the functional renormalization group (FRG) flow for the widely studied two-dimensional …
  14. Neural Circuits for Dynamics-Based Segmentation of Time Serie

    Publication
    The brain must extract behaviorally relevant latent variables from the signals streamed by the sensory organs. Such latent variables are often encoded in the dynamics that generated the …
  15. Quantification of gas concentrations in NO/NO2/C3H8/NH3 mixtures using machine learning

    Publication
    We employ machine learning to decode the composition of unknown gas mixtures from the output of an array of four electrochemical sensors. The sensors use metal oxide electrodes …
  16. Spatial Transformer K-Means

    Publication
    Yanis Bahroun
  17. Neural Circuits for Dynamics-Based Segmentation of Time Series

    Publication
    The brain must extract behaviorally relevant latent variables from the signals streamed by the sensory organs. Such latent variables are often encoded in the dynamics that generated the …
  18. Neural optimal feedback control with local learning rules

    Publication
    A major problem in motor control is understanding how the brain plans and executes proper movements in the face of delayed and noisy stimuli. A prominent framework for …
  19. A Normative and Biologically Plausible Algorithm for Independent Component Analysis

    Publication
    The brain effortlessly solves blind source separation (BSS) problems, but the algorithm it uses remains elusive. In signal processing, linear BSS problems are often solved by Independent Component …
  20. Shadow tomography based on informationally complete positive operator-valued measure

    Publication
    Recently introduced shadow tomography protocols use “classical shadows” of quantum states to predict many target functions of an unknown quantum state. Unlike full quantum state tomography, shadow tomography …
  21. A Similarity-preserving Neural Network Trained on Transformed Images Recapitulates Salient Features of the Fly Motion Detection Circuit

    Publication
    Learning to detect content-independent transformations from data is one of the central problems in biological and artificial intelligence. An example of such problem is unsupervised learning of …
  22. A Biologically Plausible Neural Network for Multichannel Canonical Correlation Analysis

    Publication
    Cortical pyramidal neurons receive inputs from multiple distinct neural populations and integrate these inputs in separate dendritic compartments. We explore the possibility that cortical microcircuits implement canonical correlation …
  23. A biologically plausible neural network for multi-channel Canonical Correlation Analysis

    Publication
    Cortical pyramidal neurons receive inputs from multiple distinct neural populations and integrate these inputs in separate dendritic compartments. We explore the possibility that cortical microcircuits implement Canonical Correlation …
  24. Interpretable Image Clustering via Diffeomorphism-Aware K-Means

    Publication
    We design an interpretable clustering algorithm aware of the nonlinear structure of image manifolds. Our approach leverages the interpretability of K-means applied in the image space while …
  25. Clustering is semi-definitely not that hard: Nonnegative SDP for manifold disentangling

    Publication
    In solving hard computational problems, semidefinite program (SDP) relaxations often play an important role because they come with a guarantee of optimality. Here, we focus on a popular …
  26. Why Do Similarity Matching Objectives Lead to Hebbian/Anti-Hebbian Networks?

    Publication
    Modeling self-organization of neural networks for unsupervised learning using Hebbian and anti-Hebbian plasticity has a long history in neuroscience. Yet derivations of single-layer networks with …

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