Plasticity -- a neural network's ability to adapt to new tasks -- is critical for continual and transfer learning. Existing measures, such as effective rank, dead neuron fraction, and weight norm, lack theoretical grounding and correlate poorly with performance on new tasks. We introduce local redundancy, an information-theoretic measure derived from universal compression theory. We define local redundancy as the worst-case redundancy of a local model family -- parameters in an infinitesimal neighborhood along gradient directions -- and show this is a principled measure of plasticity. Although local redundancy is intractable to compute exactly, we prove that the expected squared gradient norm on a synthetic memorization task provides an efficiently computable lower bound. Experiments on continual image classification and time series transfer learning demonstrate that local redundancy predicts downstream performance better than existing measures and enables pretraining checkpoint selection where validation loss plateaus.
On-device federated learning (FL) enables privacy-preserving and personalized model training on resource-constrained devices such as smartphones and IoT nodes. To reduce communication cost, sign-based methods (e.g., signSGD) transmit one-bit gradients. However, exposing gradient…
A watermark in a generative model's output is usually asked only whether a text is machine-made. The same mark can do more: attribute it to the user who produced it, extract a hidden payload, or localize the part that survives editing. These form a forensic ladder, and we ask wha…
How diffusion models circumvent the curse of dimensionality to learn complex distributions over high dimensional spaces from a finite training set, instead of memorizing it, remains a fundamental mystery. To address this, we introduce analytically tractable Bayesian information r…
Local causal discovery is a scalable alternative to global structure learning. However, it can struggle to identify valid adjustment sets in data-scarce settings because of finite-sample uncertainty, incomplete local neighborhoods, and unresolved Markov equivalence. Although many…
While autoregressive models optimize the exact data likelihood via the chain rule, diffusion models are typically trained with denoising objectives. We develop conservation laws based on generalized extrinsic information transfer (GEXIT) functions for a broad class of memoryless…
We present a complete formal proof that transformer architectures, when their internal update mechanisms satisfy a Bayes joint-distribution condition, implement exact Bayesian posterior inference. Working within the measure-theoretic kernel framework, we define a hierarchy of abs…