The paper discusses how backpropagation enables deep learning but does not inherently organize parameters for reusable functional components, leading to weight entanglement where overlapping parameter sets hinder independent modification. It introduces weight operators—parameterized modules that can be composed at inference—to address this, proposing a two-stage learning process that first infers operator composition and then updates only the selected operators. Vector Networks (VNs) are presented as an implementation that couples operator selection to local error-driven updates, demonstrating that learned operators can be recombined in unseen ways while keeping updates confined to the relevant parameter sets.
arXiv:2606. 21497v2 Announce Type: replace-cross Abstract: Modern deep neural networks are trained using error backpropagation, which requires sequential forward and backward computations across network layers.
arXiv:2510. 22450v3 Announce Type: replace-cross Abstract: The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons.
Over the past decade, deep neural networks (DNNs) have achieved remarkable success on complex machine-learning tasks, yet the theoretical foundations of their performance remain incomplete. From a statistical viewpoint, a natural question is: can DNNs attain feature-learning and prediction consistency comparable to that of classical models?
CrossGMN introduces a graph metanetwork that processes a trained source network and an initialized target network simultaneously, enabling equivariant cross‑architecture weight‑space transformations. By preserving symmetry through cross‑network message passing, CrossGMN can refine target network initializations while remaining invariant to source permutations and equivariant to target permutations. Experiments demonstrate that CrossGMN accelerates knowledge distillation, transfers across datasets without retraining, and unifies compression from diverse source architectures into a common target architecture.
arXiv:2602. 12952v3 Announce Type: replace Abstract: Adapting large pre-trained models to downstream tasks often produces task-specific parameter updates that are expensive to relearn for every model variant.
arXiv:2606. 19538v1 Announce Type: new Abstract: Convolutional networks, recurrent networks, and transformers each encode different inductive biases -- locality, sequential memory, and content-dependent pairwise interaction -- and have remained mathematically distinct since their inception.
arXiv:2512. 24780v2 Announce Type: replace Abstract: Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking.
arXiv:2606. 00130v2 Announce Type: replace-cross Abstract: Large deep neural networks are costly to store and deploy because inference must move and evaluate many parameters.
arXiv:2406. 09770v2 Announce Type: replace-cross Abstract: Solving multi-objective optimization problems for large deep neural networks is a challenging task due to the complexity of the loss landscape and the expensive computational cost of training and evaluating models.
arXiv:2601. 06441v2 Announce Type: replace Abstract: Learning activation functions has emerged as a promising direction in deep learning, allowing networks to adapt activation mechanisms to task-specific demands.
arXiv:2606. 11123v1 Announce Type: new Abstract: Backpropagation (BP) is widely viewed as biologically implausible, in part because it requires feedback weights to be the transpose of forward weights for error propagation.
arXiv:2609.38081v1 Announce Type: new Abstract: On a single task, deep networks can learn many solutions, depending on their optimizer, training data, architecture, and hyperparameters. Many of these...