dysco-latent-dynamics-extraction

name	dysco-latent-dynamics-extraction
description	DYSCO (Dynamics via Contrastive Learning) - 多视角对比学习从噪声观测中提取潜在动力学系统。通过独立噪声视角分离信号与噪声，恢复潜在轨迹和支配动力学方程。
author	Paolo Muratore, Mackenzie Weygandt Mathis
arxiv_id	2606.1326
categories	["machine-learning","dynamical-systems","neuroscience","system-identification"]
tags	["contrastive-learning","latent-dynamics","system-identification","multi-view-learning","governing-equations","neural-dynamics","symbolic-discovery"]
created	2026-06-15T00:00:00.000Z
source	arXiv cs.LG/q-bio.NC

DYSCO: Extracting Governing Equations from Latent Dynamics

Overview

DYSCO (DYnamics via Contrastive Learning) is a multi-view temporal contrastive learning algorithm that jointly recovers latent trajectories and governing dynamics from noisy, high-dimensional measurements. It leverages multiple independent noisy views of the same underlying process to disentangle signal from noise.

Key Innovation

Multi-View Contrastive Framework

• Uses independent noisy views of same underlying process
• Separates signal from noise via contrastive learning
• Recovers latent trajectories AND governing dynamics simultaneously
• Symbolic recovery of governing equations in affine gauge

Problem Setting

Input: Noisy, high-dimensional observations
Challenge:
  - Short recordings
  - Noisy measurements
  - Coarsely sampled
  - Autocorrelated structure (e.g., fMRI)

Output:
  - Latent trajectories (signal)
  - Governing equations (symbolic)
  - Flow fields (dynamics)

Core Methodology

1. Multi-View Architecture

Views: Multiple independent noisy observations
       y₁(t) = g₁(x(t)) + noise₁
       y₂(t) = g₂(x(t)) + noise₂
       ...

Contrastive objective:
  - Align views of same latent state
  - Separate noise through independence

2. Temporal Contrastive Learning

• Temporal pairs: Same time point, different views
• Contrastive loss: Maximize agreement between views
• Noise separation: Independent noise → divergent representations

3. Functional Basis Parameterization

• Dynamics parameterized in structured functional basis
• Enables symbolic recovery of governing equations
• Affine gauge freedom allows interpretation

Theoretical Guarantees

Identifiability Results

• Strong identification up to affine indeterminacy
• Extends prior identifiability results to noisy nonlinear observations
• Guarantees for both Gaussian and Poisson noise

Key Conditions

1. Multiple independent noisy views
2. Weak coupling assumptions
3. Structured functional basis

Mathematical Framework

Latent Dynamics Model

$$\dot{x} = f(x)$$ where: