arXiv AI
ReMAP: Lossless Residual Neural Lifting for Scalable MAP Inference in Arbitrary-Order Markov Random Fields
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arXiv Machine Learning
Sep 24
A lift for input-convex neural net training
The paper introduces the "lift" technique for training input‑convex neural networks, replacing the traditional non‑negative weight constraint enforced by projected gradient descent or a softplus map. By adding a learnable slack variable and an unconstrained network that processes a permutation‑invariant batch summary, the lift couples batch‑dependent latent weights to the gradient, increasing update variance and enabling faster escape from the softplus shoulder. Experiments show that when the softplus method stalls at the shoulder, the lift achieves tighter fits and reconstructs targets roughly three times faster, while both methods agree when the shoulder is rarely reached.
arXiv Machine Learning
Jun 4
When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks
arXiv:2606. 04476v1 Announce Type: new Abstract: In this paper, we study the gradient descent dynamics for jointly training both layers of a one-hidden-layer ReLU network to fit a linear target function.
arXiv Machine Learning
Jul 7
Direct Bethe Free Energy Minimization for Bayesian Neural Networks
arXiv:2605. 08446v3 Announce Type: replace Abstract: Bayesian neural networks are typically trained against the evidence lower bound (ELBO), whose Jensen gap closes only when the variational posterior is exact.
arXiv Machine Learning
Jul 16
Weight Feedback Computes the Jacobian Transpose Locally in Modern Deep Networks
arXiv:2607. 13380v1 Announce Type: new Abstract: Predictive Coding (PC) offers a biologically motivated alternative to backpropagation via local weight updates, yet routing error between layers still relies on an autograd Jacobian-transpose ($J^\top$) product - the last non-local operation in PC.
arXiv AI
Aug 6
The Hamilton-Jacobi Theory of Deep Learning
arXiv:2605. 28983v2 Announce Type: replace-cross Abstract: In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights.
arXiv Machine Learning
Sep 14
Dual-guided Hierarchical Edge Localization for Large-scale Optimal Transport Across Dimensions
The paper introduces HELLO, a hierarchical solver for large‑scale discrete optimal transport that reduces the problem to edge localization guided by dual potentials. HELLO uses a coarse‑to‑fine initialization across a recursive subsampling hierarchy and a refinement step that inserts the largest dual violators until a KKT residual tolerance is met, achieving linear memory usage. Experiments show that HELLO outperforms strong baselines by an order of magnitude in runtime while attaining lower transport objectives, and it scales to over a million samples in high‑dimensional settings, supporting various OT variants.