NeurIPS 2026 论文列表

Complementarity Determining Regions (CDRs) are critical segments of an antibody that facilitate binding to specific antigens. Current computational methods for CDR design rely on reconstruction losses and do not jointly optimize binding energy, a crucial metric of antibody efficacy. Rather, binding energy optimization is performed via computationally expensive Online Reinforcement Learning (RL) pipelines that rely heavily on unreliable binding-energy estimators. In this paper, we propose AbFlowNet, a novel generative framework that integrates GFlowNet with Diffusion models. By framing each diffusion step as a state in the GFlowNet framework, AbFlowNet jointly optimizes standard diffusion losses and binding energy by directly incorporating energy signals into the training process, thereby unifying diffusion and reward optimization in a single procedure. Experimental results show that AbFlowNet outperforms the base diffusion model by 3.06% in amino acid recovery, 20.40% in geometric reconstruction (RMSD), and 3.60% in binding energy improvement ratio. ABFlowNet also decreases Top-1 total energy and binding energy errors by 24.8% and 38.1%, which is competitive with AbDPO's expensive online RL optimization without pseudo-labeling the test dataset or requiring computationally expensive synthetic CDR sampling.

Spatial cognition requires stable neural manifolds of orientation and location that track self-motion and sensory cues. Continuous attractors provide a natural dynamical principle, but learning such mechanisms that form and control manifolds with theoretical guarantees remains difficult. We propose Spatial Energy Attractor Learning (SEAL), a theory of neurodynamics learning for spatial cognition, where continuous spatial representations arise as learned low-energy manifolds in Hopfield energy landscapes through population-level Fourier energy learning. For head-direction and grid-cell systems, Fourier energy landscapes yield ring and torus attractors with learned normal attraction and input-driven tangent transport. We prove that Fourier construction is a special case of a general Hopfield-compatible energy extension whose autonomous dynamics preserve energy descent and whose expressive energy families approximate target attractor energies and restoring fields. Experiments on HD and grid-cell populations show that the learned energies restore perturbed states to ring and torus manifolds, stabilize velocity-driven moving bumps across multiple input regimes, and induce continuous-attractor interactive structures with local excitation and surround inhibition. Together, these results provide a stable, learnable, and biologically interpretable energy-based account of continuous spatial representation.

We propose the Grid Efficient Transport Optimization Linear Programming (GETO-LP) model, a novel formulation of the Fixed-Support Wasserstein barycenter problem for $M$ probability distributions supported on $d$-dimensional grids. While standard LP models require $O(MN^2)$ variables, the GETO-LP model requires only $O(dMN^{1+\frac{1}{d}})$, with $N$ being the total number of points in the grid support. Despite the reduced number of variables, our formulation is \emph{exact}, meaning that its solution fully characterizes both the barycenter $\nu$ and the optimal transport plans between $\nu$ and each of the $M$ input distributions without additional optimization steps. We validate the GETO-LP model via extensive comparisons with classical and entropic regularization solvers, demonstrating its effectiveness on both synthetic data and real-world applications such as color palette manipulation and medical data averaging. Overall, our approach provides an effective formulation for the Wasserstein barycenter problem, offering a memory-efficient alternative that naturally integrates with other existing computational frameworks.