Modulated
Neural ODEs
I.A. Auzina, Ç. Yıldız, S. Magliacane, M. Bethge and E. Gavves
Modulated NODEs
I.A. Auzina, Ç. Yıldız, S. Magliacane, M. Bethge and E. Gavves
Key Idea:
length, mass
length of limbs
influence dynamics
influence reconstruction
color of a ball
color of clothes
does setting apart dynamic states from
underlying static factors of variation improve existing model performance?
Modulated NODEs
Key Idea:
does setting apart dynamic states from
underlying static factors of variation improve existing model performance?
I.A. Auzina, Ç. Yıldız, S. Magliacane, M. Bethge and E. Gavves
\mathbf{z}_0
Latent Space
Encoding
Network
Decoding
Network
Forward
Simulation
(ODE)
\mathbf{d}
Dynamics Modulator
Modulator Prediction
Network
\mathbf{s}
Modulator Prediction
Network
Static Modulator
Latent NODE
(Chen et al., 2018)
ours
MoNODE (2023)
Parameters of an ODE
Style of a digit
influence dynamics
influence reconstruction
Modulated NODEs
\mathbf{d} \sim p(\mathbf{d}) ~\quad \textit{// dynamics modulator} \\
\mathbf{s} \sim p(\mathbf{s}) ~~\quad \textit{// static modulator} \\
\mathbf{z}_0 \sim p(\mathbf{z}_0) \quad \textit{// latent ODE state} \\
Generative Model
\mathbf{x}_i \sim p_{\phi}(\mathbf{x}_i \mid \mathbf{z}_i ~;~ \mathbf{s}).
\mathbf{z}_i = \mathbf{z}_0 + \int_{t_0}^{t_i} \mathbf{f}_{\mathbf{\theta}}(\mathbf{z}(\tau);\mathbf{d})~d \tau \\
implicit, point-estimates
ELBO (Chen, 2018)
I.A. Auzina, Ç. Yıldız, S. Magliacane, M. Bethge and E. Gavves
Modulated NODEs
I.A. Auzina, Ç. Yıldız, S. Magliacane, M. Bethge and E. Gavves
A general framework
Latent NODE
(Chen et al., 2018)
Second Order NODE
(Norcliffe et al., 2020)
Latent Second Order NODE
(Yildiz et al., 2019)
Heavy Ball NODE
(Xia et al., 2021)
can be applied to most x-NODE
Modulated NODEs
A general framework
that improves forecasting and generalization
Sinusoidal Data
Latent NODE
(Chen et al., 2018)
ours Mo-xNODE
Heavy Ball NODE
(Xia et al., 2021)
I.A. Auzina, Ç. Yıldız, S. Magliacane, M. Bethge and E. Gavves
Modulated NODEs
A general framework
that improves forecasting and generalization
Sinusoidal Data
Latent NODE
(Chen et al., 2018)
ours Mo-xNODE
Heavy Ball NODE
(Xia et al., 2021)
I.A. Auzina, Ç. Yıldız, S. Magliacane, M. Bethge and E. Gavves
Modulated NODEs
A general framework
that is easier to train
Sinusoidal Data
ours: Mo-xNODE
NODE (Chen et al., 2018)
SONODE (Norcliffe et al., 2020)
HBNODE (Xia et al., 2021)
I.A. Auzina, Ç. Yıldız, S. Magliacane, M. Bethge and E. Gavves
Modulated NODEs
A general framework
that disentangles underlying factors
Table 2. R^2 scores to predict the unknown Factors of Variation from inferred latents. Higher is better.
d
~
\frac{dx}{dt} = \alpha x - \beta xy
\frac{dy}{dt} = \delta xy - \gamma y
dynamics
modulator
PP parameters
I.A. Auzina, Ç. Yıldız, S. Magliacane, M. Bethge and E. Gavves
Modulated NODEs
that improves performance
on real world data
Table 3. Test MSE and standard deviation. Lower is better.
MoNODE
NODE
I.A. Auzina, Ç. Yıldız, S. Magliacane, M. Bethge and E. Gavves
Thank you for your attention
I.A. Auzina, Ç. Yıldız, S. Magliacane, M. Bethge and E. Gavves
Modulated NODEs
All experiments and models publicly available at:
Modulated NODEs NeurIPS 2023
By iaa
