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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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We convene scientists, mathematicians, and thinkers to share ideas and explore new questions.

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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

Results

  1. Task-Induced Representational Invariances Depend on Learning Objective in Deep RL

    Publication
    Reinforcement Learning (RL) has long served as a model for goal-directed animal behavior in neuroscience. Modern deep RL has shown remarkable success across many domains, further strengthening …
  2. Two Speeds of Learning: A Representation-Readout Decomposition of Grokking and Double Descent

    Publication
    Training loss and accuracy are the standard signals used to monitor generalization during deep neural network training. Two well-documented phenomena complicate this picture: in grokking, train loss …
  3. Spectral Analysis of Representational Similarity with Limited Neurons

    Publication
    Measuring representational similarity between neural recordings and computational models is challenging due to constraints on the number of neurons that can be recorded simultaneously. In this work, we …
  4. Estimating Dimensionality of Neural Representations from Finite Samples

    Publication
    The global dimensionality of a neural representation manifold provides rich insight into the computational process underlying both artificial and biological neural networks. However, all existing measures of global …
  5. Linear Readout of Neural Manifolds with Continuous Variables

    Publication
    Brains and artificial neural networks compute with continuous variables such as object position or stimulus orientation. However, the complex variability in neural responses makes it difficult to link …
  6. Diagnosing Generalization Failures from Representational Geometry Markers

    Publication
    Generalization, the ability to perform well beyond the training context, is a hallmark of biological and artificial intelligence, yet anticipating unseen failures remains a central challenge. Conventional approaches …
  7. Emergent Manifold Separability during Reasoning in Large Language Models

    Publication
    Chain-of-Thought (CoT) prompting significantly improves reasoning in Large Language Models, yet the temporal dynamics of the underlying representation geometry remain poorly understood. We investigate these dynamics …
  8. Neural population geometry and optimal coding of tasks with shared latent structure

    Publication
    Animals can recognize latent structures in their environment and apply this information to efficiently navigate the world. Several works argue that the brain supports these abilities by forming …
  9. Sparse input representations explain odor discrimination in complex, concentration-varying mixtures

    Publication
    In natural environments, animals must detect behaviorally relevant odors despite variability in both odor mixture composition and stimulus intensity. Although mice can identify salient odors embedded in complex …
  10. Effective computations for hippocampal place cell phenomena in sparse untrained random networks

    Publication
    … explain many features of place cell network activity, suggesting that simple biologically-plausible architectures can realize representations of spatial experience that are robust, flexible, and spontaneous.
  11. Statistical mechanics of support vector regression

    Publication
    A key problem in deep learning and computational neuroscience is relating the geometrical properties of neural representations to task performance. Here, we consider this problem for continuous decoding …
  12. Feature Learning beyond the Lazy-Rich Dichotomy: Insights from Representational Geometry

    Publication
    Integrating task-relevant information into neural representations is a fundamental ability of both biological and artificial intelligence systems. Recent theories have categorized learning into two regimes: the rich …
  13. Variations in neuronal selectivity create efficient representational codes

    Publication
    Our visual capabilities depend on neural response properties in visual areas of our brains. Neurons exhibit a wide variety of selective response properties, but the reasons for this …
  14. Variations in neuronal selectivity create efficient representational geometries for perception

    Publication
    Our visual capabilities depend on neural response properties in visual areas of our brains. Neurons exhibit a wide variety of selective response properties, but the reasons for this …
  15. The Geometry of Prompting: Unveiling Distinct Mechanisms of Task Adaptation in Language Models

    Publication
    Decoder-only language models have the ability to dynamically switch between various computational tasks based on input prompts. Despite many successful applications of prompting, there is very limited …
  16. Geometry Linked to Untangling Efficiency Reveals Structure and Computation in Neural Populations

    Publication
    From an eagle spotting a fish in shimmering water to a scientist extracting patterns from noisy data, many cognitive tasks require untangling overlapping signals. Neural circuits achieve this …
  17. Nonlinear classification of neural manifolds with contextual information

    Publication
    Understanding how neural systems efficiently process information through distributed representations is a fundamental challenge at the interface of neuroscience and machine learning. Recent approaches analyze the statistical and …
  18. Estimating Neural Representation Alignment from Sparsely Sampled Inputs and Features

    Publication
    In both artificial and biological systems, the centered kernel alignment (CKA) has become a widely used tool for quantifying neural representation similarity. While current CKA estimators typically correct …
  19. Contrastive-equivariant self-supervised learning improves alignment with primate visual area IT

    Publication
    Models trained with self-supervised learning objectives have recently matched or surpassed models trained with traditional supervised object recognition in their ability to predict neural responses of object …
  20. How to optimize neuroscience data utilization and experiment design for advancing brain models of visual and linguistic cognition?

    Publication
    In recent years, neuroscience has made significant progress in building large-scale artificial neural network (ANN) models of brain activity and behavior. However, there is no consensus on …
  21. Representational learning by optimization of neural manifolds in an olfactory memory network

    Publication
    Higher brain functions depend on experience-dependent representations of relevant information that may be organized by attractor dynamics or by geometrical modifications of continuous “neural manifolds”. To explore …
  22. Task-Relevant Covariance from Manifold Capacity Theory Improves Robustness in Deep Networks

    Publication
    Analysis of high-dimensional representations in neuroscience and deep learning traditionally places equal importance on all points in a representation, potentially leading to significant information loss. Recent advances …
  23. Estimating the Spectral Moments of the Kernel Integral Operator from Finite Sample Matrices

    Publication
    Analyzing the structure of sampled features from an input data distribution is challenging when constrained by limited measurements in both the number of inputs and features. Traditional approaches …
  24. Geometric changes in monkey V4 and IT neural responses during visual category learning

    Publication
    Behavior changes over the course of learning a task. This behavioral change is due to shifts in neural responses that support improved performance. Here, we investigated how the …
  25. Towards an Improved Understanding and Utilization of Maximum Manifold Capacity Representations

    Publication
    Maximum Manifold Capacity Representations (MMCR) is a recent multi-view self-supervised learning (MVSSL) method that matches or surpasses other leading MVSSL methods. MMCR is intriguing because it …
  26. Neural Manifold Capacity Captures Representation Geometry, Correlations, and Task-Efficiency Across Species and Behaviors

    Publication
    The study of the brain encompasses multiple scales, including temporal, spatial, and functional aspects. To integrate understanding across these different levels and modalities, it requires developing quantification methods …
  27. Probing Biological and Artificial Neural Networks with Task-dependent Neural Manifolds

    Publication
    In recent years, growth in our understanding of the computations performed in both biological and artificial neural networks has largely been driven by either low-level mechanistic studies …
  28. Efficient coding of natural images using maximum manifold capacity representations

    Publication
    The efficient coding hypothesis posits that sensory systems are adapted to the statistics of their inputs, maximizing mutual information between environmental signals and their representations, subject to biological …

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