arXiv:2503. 13051v3 Announce Type: replace Abstract: Sorting and permutation learning are key concepts in optimization and machine learning, especially when organizing high-dimensional data into meaningful spatial layouts.
arXiv:2507. 13263v4 Announce Type: replace-cross Abstract: Bayesian Optimization (BO) is a powerful tool for black-box optimization, but its application to high-dimensional permutation spaces is severely limited by the challenge of defining scalable representations.
arXiv:2603. 17353v2 Announce Type: replace-cross Abstract: The finite symmetric group S_n provides a natural domain for permutations, yet learning probability distributions on S_n is challenging due to its factorially growing size and discrete, non-Euclidean structure.
The paper introduces Soft-OMP and Soft-IHT, permutation‑based variants of Orthogonal Matching Pursuit and Iterative Hard Thresholding that replace the non‑differentiable argsort with continuous soft‑sort operators. These differentiable algorithms enable the construction of fully trainable neural network architectures—OMP‑Net and IHT‑Net—while preserving the core greedy sparse recovery logic. The authors show both theoretically and numerically that the soft variants approximate their hard counterparts with controllable accuracy and can be extended to structured sparse recovery by learning structure‑aware weights.
arXiv:2606. 01111v1 Announce Type: new Abstract: Modern industrial recommender systems rely on thousands of heterogeneous features -- ranging from low-dimensional scalars (e.
arXiv:2608.06912v2 Announce Type: replace Abstract: Selecting the top-$k$ elements is a fundamental operation for inducing sparsity in large-scale models and optimization problems, enabling robust ex...
arXiv:2510. 14812v2 Announce Type: replace Abstract: Structured weight sparsity accelerates training and inference on modern GPUs, but it trails unstructured dynamic sparse training (DST) in accuracy especially at extreme sparsity.
GPart introduces a new parameter‑efficient fine‑tuning technique that directly maps a low‑dimensional trainable vector into the full weight space using a sparse, isometric partition matrix. Unlike LoRA, GPart eliminates the bilinear reconstruction step, preserving exact end‑to‑end isometry and reducing the checkpoint to just the vector and a random seed. Experiments across NLP, vision, and reasoning tasks show that GPart matches or surpasses existing PEFT methods while using far fewer parameters and offering a simpler, more tractable parameterization.
The paper introduces a new Gaussian Process kernel, GP‑Perm, that incorporates permutation invariance for Bayesian Optimization tasks involving well placement in Carbon Capture and Storage (CCS) projects. It compares sets via a stable divergence between their empirical representations and can be combined with standard kernels for additional inputs. The authors also explore a Deep Kernel Learning model using a Deep Sets architecture as a learned invariant baseline, evaluating both approaches on eight use cases, including seven synthetic benchmarks and a realistic CCS case study in the Johansen formation.
The paper presents a table‑free index for tapered memoization grids, enabling compact out‑of‑core evaluation of functions that depend on sorted arguments. By showing that the grid’s key set corresponds to multiset combinations, the authors derive a closed‑form O(d) ranking and unranking scheme that removes the need for large preprocessing tables and allows order‑free parallel construction. The resulting values‑only flat array uses significantly less memory than hash‑map memoization, offers faster query times once cache limits are exceeded, and remains operable with memory‑mapped storage beyond RAM.
ThinQuant introduces efficient rotation learning for low‑bit weight and activation quantization of large language models by reducing calibration data through a geometric selection of activations and solving a lower‑dimensional optimization problem via an ADMM algorithm. The method achieves comparable or better quantization performance with dramatically fewer calibration points, completing rotation calibration for Llama‑3‑70B in under 12 minutes and for Llama‑3.1‑405B in just over 2 hours on a single GPU. ThinQuant outperforms existing gradient‑free approaches such as DartQuant and gradient‑based SpinQuant in both speed and perplexity metrics on WikiText‑2.
arXiv:2608. 06912v1 Announce Type: new Abstract: The top-$k$ operation is a fundamental building block of modern sparse computation, enabling token routing, expert activation, memory selection, and attention pruning.
arXiv:2602. 14656v2 Announce Type: replace Abstract: Orthogonality constraints are ubiquitous in robust and probabilistic machine learning.