Biologically Plausible Model for Nonlinear Dimensionality Reduction

Idea Proposed

Model structure of the Hebbian t-SNE. (A) Three-layer feedforward model including the input layer X, the middle layer Z, and the output layer Y. The transformation from X to Z is fixed. The synaptic weight matrix W from the middle to output layers is plastic, regulated by the presynaptic and postsynaptic neurons and global factor D. The global factor D is determined by x̂ diff and ŷ diff that calculate input and output similarities, respectively. The input similarity x̂ diff is based on the input difference ∥X(t) − X(t − 1)∥2 and axonal signal a from the middle layer. (B) Hypothetical elements implementing Hebbian t-SNE in the Drosophila olfactory circuit

Why Dimensionality Reduction Matters

Our sensory systems receive high-dimensional data—visual, auditory, and chemical signals—that must be processed efficiently. The brain transforms this complex input into low-dimensional representations that drive behavior. In artificial intelligence, dimensionality reduction helps with:

Data Visualization: t-SNE and UMAP (Uniform Manifold Approximation and Projection) make high-dimensional data understandable.
Feature Extraction: Reducing redundant information while preserving critical patterns.
Improved Learning: Simplifies downstream processing for AI and machine learning models.

The Biological Inspiration

The olfactory system in Drosophila provides a real-world model for dimensionality reduction. It consists of three key layers:

Projection Neurons (PNs) → Input Layer (X): Receives raw sensory input.
Kenyon Cells (KCs) → Middle Layer (Z): Expands data into a high-dimensional, sparse representation.
Mushroom Body Output Neurons (MBONs) → Output Layer (Y): Reduces data back to a low-dimensional form for decision-making.

This structure is remarkably similar to neural networks used in machine learning, making it a natural candidate for biologically plausible AI.

How Hebbian t-SNE Works

Unlike traditional t-SNE, which relies on gradient descent, Hebbian t-SNE leverages three-factor Hebbian learning, a biologically inspired rule for synaptic plasticity. The process consists of three main steps:

Step 1: Compute Input Similarities

High-dimensional input data (X) is analyzed to determine similarities.
Similarity is measured using a Gaussian function, ensuring that close points are weighted more heavily.

Step 2: Compute Output Similarities

The low-dimensional representation (Y) is adjusted to match the input structure.
Instead of a Gaussian, t-SNE uses a t-distribution, preventing the “crowding problem.”

Step 3: Adjust Synaptic Weights Using Hebbian Learning

The network updates connections based on three-factor Hebbian plasticity:
- Presynaptic activity (Z)
- Postsynaptic activity (Y)
- A global modulatory signal (D), similar to dopamine
The rule strengthens connections between neurons that fire together, leading to self-organized clustering of similar data points.

Key Advantages of Hebbian t-SNE

Unsupervised Learning – No labeled data required. Biologically Plausible – Mimics real neural circuits. Works for Nonlinear Data – Captures hidden structures beyond PCA. Supports Real-Time Learning – Can handle streaming data. Dopaminergic Modulation – Incorporates neuromodulatory control for adaptive learning.

Applications and Future Implications

🚀 Neuroscience: Understanding brain function and sensory processing. 🚀 AI & Machine Learning: Creating more biologically inspired models. 🚀 Robotics: Enhancing perception and decision-making in autonomous systems. 🚀 Data Science: Providing new ways to visualize and cluster high-dimensional datasets.

How Hebbian t-SNE Differs from Traditional t-SNE

Feature	Traditional t-SNE	Hebbian t-SNE
Learning Method	Gradient Descent	Hebbian Learning
Computational Cost	High	Lower
Biological Basis?	No	Yes
Handles Streaming Data?	No	Yes
Uses Dopamine-Like Modulation?	No	Yes

Sources & citation

Kensuke Yoshida, Taro Toyoizumi, A biological model of nonlinear dimensionality reduction. Sci. Adv.11,eadp9048(2025).DOI:10.1126/sciadv.adp9048