Out-Of-Domain (OOD) generalization is a significant challenge in learning dynamical systems, especially when they exhibit bifurcation, a sudden topological transition triggered by a model parameter crossing a critical threshold. A prevailing belief is that machine learning models, unless equipped with strong priors, struggle to generalize across bifurcations due to the abrupt changes in data characteristics. Contrary to this belief, we demonstrate that context-dependent Neural Ordinary Differential Equations (NODEs), trained solely on localized, pre-bifurcation, symmetric data and without physics-based priors, can still identify post-bifurcation, symmetry-breaking behaviors, even in a zero-shot manner. We interpret this capability to the model's implicit utilization of topological invariants, particularly the Poincaré index, and offer a formal explanation based on the Poincaré–Hopf theorem. We derive the conditions under which NODEs can recover—or erroneously hallucinate—broken symmetries without explicit training. Building on this insight, we showcase a topological regularizer inspired by the Poincaré–Hopf theorem and validate it empirically on phase transitions of systems described by the Landau–Khalatnikov equation.

We study structure-preserving low-dimensional representation of a data manifold embedded in a high-dimensional observation space based on variational auto-encoders (VAEs). We approach this by decomposing the data manifold $\mathcal{M}$ as $\mathcal{M} = \mathcal{M} / G \times G$, where $G$ and $\mathcal{M} / G$ are a group of symmetry transformations and a quotient space of $\mathcal{M}$ up to $G$, respectively. From this perspective, we define the structure-preserving representation of such a manifold as a latent space $\mathcal{Z}$ which is isometrically isomorphic (i.e., distance-preserving) to the quotient space $\mathcal{M} / G$ rather $\mathcal{M}$ (i.e., symmetry-preserving). To this end, we propose a novel auto-encoding framework, named isometric quotient VAEs (IQVAEs), that can extract the quotient space from observations and learn the Riemannian isometry of the extracted quotient in an unsupervised manner. Empirical proof-of-concept experiments reveal that the proposed method can find a meaningful representation of the learned data and outperform other competitors for downstream tasks.

Inductive transfer learning aims to learn from a small amount of training data for the target task by utilizing a pre-trained model from the source task. Most strategies that involve large-scale deep learning models adopt initialization with the pre-trained model and fine-tuning for the target task. However, when using over-parameterized models, we can often prune the model without sacrificing the accuracy of the source task. This motivates us to adopt model pruning for transfer learning with deep learning models. In this paper, we propose PAC-Net, a simple yet effective approach for transfer learning based on pruning. PAC-Net consists of three steps: Prune, Allocate, and Calibrate (PAC). The main idea behind these steps is to identify essential weights for the source task, fine-tune on the source task by updating the essential weights, and then calibrate on the target task by updating the remaining redundant weights. Under the various and extensive set of inductive transfer learning experiments, we show that our method achieves state-of-the-art performance by a large margin.

This paper presents a deep neural network based test vector generation method for dynamic verification of memory devices. The proposed method is built on reinforcement learning framework, where the action is input stimulus on device pins and the reward is coverage score of target circuitry. The developed agent efficiently explores high-dimensional and large action space by using policy gradient method with Å-nearest neighbor search, transfer learning, and replay buffer. The generated test vectors attained the coverage score of 100% for fifteen representative circuit blocks of modern DRAM design. The output vector length was only 7% of the human-created vector length.

Time-reversal symmetry, which requires that the dynamics of a system should not change with the reversal of time axis, is a fundamental property that frequently holds in classical and quantum mechanics. In this paper, we propose a novel loss function that measures how well our ordinary differential equation (ODE) networks comply with this time-reversal symmetry; it is formally defined by the discrepancy in the time evolutions of ODE networks between forward and backward dynamics. Then, we design a new framework, which we name as Time-Reversal Symmetric ODE Networks (TRS-ODENs), that can learn the dynamics of physical systems more sample-efficiently by learning with the proposed loss function. We evaluate TRS-ODENs on several classical dynamics, and find they can learn the desired time evolution from observed noisy and complex trajectories. We also show that, even for systems that do not possess the full time-reversal symmetry, TRS-ODENs can achieve better predictive performances over baselines.