arXiv:2411.12876v2 Announce Type: replace-cross Abstract: Modern convolutional neural networks (CNNs) organize computation as a discrete stack of layers whose parameters are independently stored and learned, with the number of layers fixed as an architectural hyperparameter. In this work, we explore an alternative perspective: can network parameterization itself be modeled as a continuous dynamical system? We introduce Puppet-CNN, a framework that represents convolutional layer parameters as states evolving along a learned parameter flow governed by a neural ordinary differential equation (ODE). Under this formulation, layer parameters are generated through continuous evolution in parameter space, and the effective number of generated layers is determined by the integration horizon of the learned dynamics, which can be modulated by input complexity to enable input-adaptive computation. We validate this formulation on standard image classification benchmarks and demonstrate that continuous parameter dynamics can achieve competitive predictive performance while substantially reducing stored trainable parameters. These results suggest that viewing neural network parameterization through the lens of dynamical systems provides a structured and flexible design space for adaptive convolutional models.

arXiv:2411.15199v2 Announce Type: replace-cross Abstract: Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal for every input. In this work, we investigate input-adaptive generative dynamics for diffusion models, where the generation process itself adapts to the conditions of each sample. Instead of relying on a fixed diffusion trajectory, the proposed framework allows the generative dynamics to adjust across inputs according to their generation requirements. To enable this behavior, we train the diffusion backbone under varying horizons and noise schedules, so that it can operate consistently under different input-adaptive trajectories. Experiments on conditional image generation show that diffusion trajectories can vary across inputs while maintaining generation quality and reducing the average number of sampling steps. These results provide a proof of the concept that diffusion processes can benefit from input-adaptive generative dynamics rather than relying on a single fixed trajectory.