dysco-latent-dynamics-extraction

name	dysco-latent-dynamics-extraction
description	DYSCO (Dynamics via Contrastive Learning) - Multi-view temporal contrastive learning for extracting governing equations from latent dynamics. Identifies dynamical systems from noisy high-dimensional observations with theoretical identifiability guarantees.
keywords	["contrastive learning","dynamical systems","latent dynamics","governing equations","system identification","neural recordings","representation learning","scientific discovery","multi-view learning"]
version	1.0.0
arxiv_id	2606.1326
authors	Paolo Muratore, Mackenzie Weygandt Mathis
published	2026-06-11T00:00:00.000Z
categories	["cs.LG","q-bio.NC"]

DYSCO: Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learning

Overview

This paper presents DYSCO, a multi-view temporal contrastive learning algorithm that jointly recovers latent trajectories and governing dynamics from noisy, high-dimensional measurements. The framework enables symbolic recovery of governing equations within an affine gauge with theoretical identifiability guarantees.

Key Innovation: Multi-view contrastive learning + functional basis parameterization → disentangle signal from noise + recover symbolic dynamics

Core Question: How can we identify latent dynamical systems from noisy, high-dimensional observations (e.g., neural recordings)?

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Methodology

1. Multi-View Contrastive Learning Framework

Core Idea: Use multiple independent noisy views of same underlying process to separate signal from noise

# Problem formulation
y_t^i = g_i(x_t) + ε_t^i  # i = 1, 2, ..., K views
# x_t: latent trajectory (unknown)
# g_i: observation function (nonlinear, unknown)
# ε_t^i: observation noise (Gaussian or Poisson)

Key Assumption: Views are independent conditioned on latent state

2. Contrastive Learning Objective

Temporal contrastive loss:

L_contrastive = -log(exp(sim(x_t, x_{t+τ}) / τ)
                     / Σ_s exp(sim(x_t, x_s) / τ))

Positive pairs: (x_t, x_{t+τ}) - temporally adjacent samples (same trajectory)

Negative pairs: (x_t, x_s) - samples from different trajectory segments

3. Functional Basis Parameterization

Dynamics representation:

dx/dt = f(x) = Σ_{k=1}^K θ_k · φ_k(x)
# φ_k: basis functions (polynomial, neural network, etc.)
# θ_k: coefficients to identify

Advantages:

1. Structured parameterization → symbolic recovery
2. Sparse basis → interpretable equations
3. Flexible basis → adapts to dynamics complexity

4. Joint Optimization