Accelerating Birkhoff Projection for Manifold-Constrained Hyper-Connections

• URL: http://arxiv.org/abs/2606.07574v1
• Date: Tue, 26 May 2026 13:11:08 GMT
• Title: Accelerating Birkhoff Projection for Manifold-Constrained Hyper-Connections
• Abstract summary: We develop an end-to-end acceleration framework for hyper-constrained hyper-connections (mHCs)<n>We focus on the practically important 4x4 Birkhoff projection setting and develop an end-to-end acceleration framework.
• Score: 6.932606401614012
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Manifold-constrained hyper-connections (mHCs) have recently been proposed as a principled extension of hyper-connections, where the residual mixing matrices are constrained to be doubly stochastic via projection onto the Birkhoff polytope. In practical mHC implementations, this constraint is enforced by Sinkhorn-Knopp iterations, and the backward pass relies on unrolling the iterative solver. This design introduces substantial computation and memory overhead, and may also yield inaccurate projections when the algorithm converges slowly on challenging inputs, undermining the intended norm-control and stability guarantees of mHCs. In this work, we focus on the practically important 4x4 Birkhoff projection setting and develop an end-to-end acceleration framework. By leveraging the dual formulation, we reduce the problem to a three-dimensional unconstrained convex problem and solve it with Newton's method, achieving fast convergence and high accuracy. For the backward pass, we replace the unrolled differentiation with implicit differentiation, yielding exact gradients without storing intermediate states. To exploit massive parallelism, we design a warp-level CUDA kernel that uses only register-level primitives, avoiding global and shared memory I/O. Extensive experiments against representative open-source baselines demonstrate that the proposed solver yields substantially more reliable doubly stochastic projections -- especially when the input magnitude is large -- and achieves significant end-to-end speedups (including the backward pass), reaching over 20x acceleration at large batch sizes while maintaining orders of magnitude smaller marginal errors.

Related papers

• Hardware-Aware QUBO Reformulation of Constrained Binary Optimization via the Walsh-Fourier Transform [1.3423094548772225]
  We present a novel framework for reformulating constrained binary optimization as Quadratic Unconstrained Binary Optimization (QUBO)<n>We show that this hardware-native surrogate can outperform denser full-pairwise projections, despite being drawn from a strictly smaller approximation space.<n>This advantage widens once the QUBO is embedded and sampled on quantum annealers, yielding samples with the lowest worst-case and mean objective gaps compared to unbalanced penalization and a hardware-blind projection onto all quadratic terms.
  arXiv  Detail & Related papers  (2026-07-28T23:45:18Z)
• OScaR: The Occam's Razor for Extreme KV Cache Quantization in LLMs and Beyond [50.440302567029654]
  Multi-modal intelligence has made the Key-Value cache a dominant memory bottleneck for efficient deployment.<n>In this work, we revisit the inherent limitations of the per-channel quantization paradigm.<n>We propose OScaR, an accurate and lightweight KV cache compression framework for X-LLMs.
  arXiv  Detail & Related papers  (2026-05-19T10:53:03Z)
• mHC-lite: You Don't Need 20 Sinkhorn-Knopp Iterations [5.518733929171501]
  Unconstrained residual matrices can compromise training stability.<n>DeepSeek's Manifold-Constrained Hyper-Connections (mHC) approximately projects these matrices onto the Birkhoff polytope via iterative Sinkhorn--Knopp (SK) normalization.
  arXiv  Detail & Related papers  (2026-01-09T11:19:14Z)
• Parallel Diffusion Solver via Residual Dirichlet Policy Optimization [88.7827307535107]
  Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature.<n>Existing solver-based acceleration methods often face significant image quality degradation under a low-dimensional budget.<n>We propose the Ensemble Parallel Direction solver (dubbed as EPD-EPr), a novel ODE solver that mitigates these errors by incorporating multiple gradient parallel evaluations in each step.
  arXiv  Detail & Related papers  (2025-12-28T05:48:55Z)
• MPQ-DMv2: Flexible Residual Mixed Precision Quantization for Low-Bit Diffusion Models with Temporal Distillation [74.34220141721231]
  We present MPQ-DMv2, an improved textbfMixed textbfPrecision textbfQuantization framework for extremely low-bit textbfDiffusion textbfModels.
  arXiv  Detail & Related papers  (2025-07-06T08:16:50Z)
• Two-dimensional Parallel Tempering for Constrained Optimization [0.3068068202044424]
  We introduce a two-dimensional extension of the powerful parallel tempering algorithm (PT)<n>The resulting two-dimensional parallel tempering algorithm (2D-PT) improves mixing in heavily constrained replicas.<n>The method applies broadly to constrained Ising problems and can be deployed on existing Ising machines.
  arXiv  Detail & Related papers  (2025-05-24T20:41:45Z)
• Smoothing ADMM for Sparse-Penalized Quantile Regression with Non-Convex Penalties [8.294148737585543]
  This paper investigates concave and clipped quantile regression in the presence of nonsecondary absolute and non-smooth convergence penalties. We introduce a novel-loop ADM algorithm with an increasing penalty multiplier, named SIAD, specifically for sparse regression.
  arXiv  Detail & Related papers  (2023-09-04T21:48:51Z)
• Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization [61.26619639722804]
  We propose a conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. The proposed method, equipped with an average gradient (SAG) estimator, requires only one sample per iteration. Nevertheless, it guarantees fast convergence rates on par with more sophisticated variance reduction techniques.
  arXiv  Detail & Related papers  (2022-02-26T19:10:48Z)
• Distributed stochastic optimization with large delays [59.95552973784946]
  One of the most widely used methods for solving large-scale optimization problems is distributed asynchronous gradient descent (DASGD) We show that DASGD converges to a global optimal implementation model under same delay assumptions.
  arXiv  Detail & Related papers  (2021-07-06T21:59:49Z)
• Hessian-Free High-Resolution Nesterov Acceleration for Sampling [55.498092486970364]
  Nesterov's Accelerated Gradient (NAG) for optimization has better performance than its continuous time limit (noiseless kinetic Langevin) when a finite step-size is employed. This work explores the sampling counterpart of this phenonemon and proposes a diffusion process, whose discretizations can yield accelerated gradient-based MCMC methods.
  arXiv  Detail & Related papers  (2020-06-16T15:07:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.