# Neural tuning and representational geometry

arXiv: https://arxiv.org/abs/2104.09743 · HTML: https://mlsanity.com/paper/2104.09743/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2021.

## Built on by (most cited first, 30 of 31)

- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [Beyond Geometry: Comparing the Temporal Structure of Computation in Neural Circuits with Dynamical Similarity Analysis](https://mlsanity.com/paper/2306.10168/) (2023)
- [The Influence of Learning Rule on Representation Dynamics in Wide Neural Networks](https://mlsanity.com/paper/2210.02157/) (2022)
- [Soft Matching Distance: A metric on neural representations that captures single-neuron tuning](https://mlsanity.com/paper/2311.09466/) (2023)
- [What Representational Similarity Measures Imply about Decodable Information](https://mlsanity.com/paper/2411.08197/) (2024)
- [Representational dissimilarity metric spaces for stochastic neural networks](https://mlsanity.com/paper/2211.11665/) (2022)
- [The Topology and Geometry of Neural Representations](https://mlsanity.com/paper/2309.11028/) (2023)
- [Neural Population Geometry Reveals the Role of Stochasticity in Robust Perception](https://mlsanity.com/paper/2111.06979/) (2021)
- [Interpretable statistical representations of neural population dynamics and geometry](https://mlsanity.com/paper/2304.03376/) (2023)
- [A Rubric for Human-like Agents and NeuroAI](https://mlsanity.com/paper/2212.04401/) (2022)
- [Neural Networks as Paths through the Space of Representations](https://mlsanity.com/paper/2206.10999/) (2022)
- [Multilevel Interpretability Of Artificial Neural Networks: Leveraging Framework And Methods From Neuroscience](https://mlsanity.com/paper/2408.12664/) (2024)
- [Stochastic Forward-Forward Learning through Representational Dimensionality Compression](https://mlsanity.com/paper/2505.16649/) (2025)
- [Understanding Neural Coding on Latent Manifolds by Sharing Features and Dividing Ensembles](https://mlsanity.com/paper/2210.03155/) (2022)
- [Response Theory via Generative Score Modeling](https://mlsanity.com/paper/2402.01029/) (2024)
- [Contrastive Self-Supervised Learning As Neural Manifold Packing](https://mlsanity.com/paper/2506.13717/) (2025)
- [Emergent behavior and neural dynamics in artificial agents tracking turbulent plumes](https://mlsanity.com/paper/2109.12434/) (2021)
- [Divergent representations of ethological visual inputs emerge from supervised, unsupervised, and reinforcement learning](https://mlsanity.com/paper/2112.02027/) (2021)
- [A space of goals: the cognitive geometry of informationally bounded agents](https://mlsanity.com/paper/2111.03699/) (2021)
- [Axiomatizing Neural Networks via Pursuit of Subspaces](https://mlsanity.com/paper/2605.20534/) (2026)
- [Stimulus symmetries can confound representational similarity analyses](https://mlsanity.com/paper/2605.21324/) (2026)
- [Conditioned Direct Feedback Alignment via Activity and Error Geometry](https://mlsanity.com/paper/2607.18574/) (2026)
- [On the Level Sets and Invariance of Neural Tuning Landscapes](https://mlsanity.com/paper/2212.13285/) (2022)
- [Supervised Quadratic Feature Analysis: Information Geometry Approach for Dimensionality Reduction](https://mlsanity.com/paper/2502.00168/) (2025)
- [Decomposing stimulus-specific sensory neural information via diffusion models](https://mlsanity.com/paper/2505.11309/) (2025)
- [Predicting Brain Morphogenesis via Physics-Transfer Learning](https://mlsanity.com/paper/2509.05305/) (2025)
- [Emergence of Spatial Representation in an Actor-Critic Agent with Hippocampus-Inspired Sequence Generator](https://mlsanity.com/paper/2510.09951/) (2025)
- [Beyond Routing: Characterising Expert Tuning and Representation in Vision Mixture-of-Experts](https://mlsanity.com/paper/2605.20610/) (2026)
- [Similarity-based representation factorization for revealing interpretable dimensions in representational data](https://mlsanity.com/paper/2605.26921/) (2026)
- [Hyperbolic Neural Population Geometry Benefits Computation](https://mlsanity.com/paper/2606.10238/) (2026)

## Abstract (arXiv)

A central goal of neuroscience is to understand the representations formed by brain activity patterns and their connection to behavior. The classical approach is to investigate how individual neurons encode the stimuli and how their tuning determines the fidelity of the neural representation. Tuning analyses often use the Fisher information to characterize the sensitivity of neural responses to small changes of the stimulus. In recent decades, measurements of large populations of neurons have motivated a complementary approach, which focuses on the information available to linear decoders. The decodable information is captured by the geometry of the representational patterns in the multivariate response space. Here we review neural tuning and representational geometry with the goal of clarifying the relationship between them. The tuning induces the geometry, but different sets of tuned neurons can induce the same geometry. The geometry determines the Fisher information, the mutual information, and the behavioral performance of an ideal observer in a range of psychophysical tasks. We argue that future studies can benefit from considering both tuning and geometry to understand neural codes and reveal the connections between stimulus, brain activity, and behavior.