Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Revisiting Frank-Wolfe for Structured Nonconvex Optimization
Authors: Hoomaan Maskan, Yikun Hou, Suvrit Sra, Alp Yurtsever
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we present numerical experiments demonstrating the effectiveness of the proposed method compared to other projection-free algorithms. ... We evaluate the empirical performance of the proposed framework through numerical experiments, comparing it with other FW algorithms on quadratic assignment problems and the alignment of partially observed embeddings. ... In this section, we numerically evaluate DC-FW on solving the quadratic assignment problem (QAP) and alignment of partially observed embeddings. |
| Researcher Affiliation | Academia | Hoomaan Maskan Yikun Hou Suvrit Sra Alp Yurtsever Umeå University, Sweden Technical University of Munich, Germany |
| Pseudocode | Yes | Algorithm 1 DC-FW 1: Input: initial point x1 D, target accuracy ϵ > 0 2: for t = 1, 2, . . . do 3: Initialize Xt,1 = xt 4: for k = 1, 2, . . . do 5: St,k = arg minx D f(Xt,k) g(xt), x 6: Dt,k = St,k Xt,k 7: if f(Xt,k) g(xt), Dt,k ϵ/2 then 8: set xt+1 = Xt,k and break 9: end if 10: Xt,k+1 = Xt,k + ηt,k Dt,k // use ηt,k = 2/(k + 1), or the strategies in (5) or (6) 11: end for 12: end for |
| Open Source Code | Yes | Justification: We will disclose all the code used in our experimental results. |
| Open Datasets | Yes | The goal in QAP is to find a permutation that optimally aligns two matrices A and B Rn n. This amounts to minimizing a nonconvex quadratic objective function over the set of permutation matrices, an NP-Hard combinatorial optimization problem. A promising approach to approximate QAP is to use the following convex-hull relaxation (Vogelstein et al., 2015): ... The QAPLIB benchmark datasets (Burkard et al., 1997). We use the 300-dimensional English and French word embeddings from the Fast Text library (Bojanowski et al., 2017) as the source and target embeddings, selecting the 10,000 most common words from each dictionary. We used a heuristic stochastic variant of the proposed DC-FW algorithm and the stochastic Frank-Wolfe (FW) algorithm (Pokutta et al., 2020) to train neural networks with constrained parameters on two classification datasets: CIFAR-10 and CIFAR-100 (Krizhevsky & Hinton, 2009). |
| Dataset Splits | No | The paper mentions using well-known datasets like QAPLIB, Fast Text embeddings, CIFAR-10, and CIFAR-100. It also specifies selecting 10,000 words from each dictionary for embedding alignment and modeling partial observations with a probability of 0.1, and training on CIFAR datasets. However, it does not explicitly provide specific training/validation/test split percentages, sample counts, or clear references to standard predefined splits for any of these datasets in a way that would allow direct reproduction of data partitioning without external knowledge. |
| Hardware Specification | Yes | Simulations were run on a single core of an Intel Xeon Gold 6132 processor using MATLAB 2021a. ... All experiments were conducted using Python (3.9.5) and Py Torch (2.0.1) on an NVIDIA A100 GPU. |
| Software Dependencies | Yes | Simulations were run on a single core of an Intel Xeon Gold 6132 processor using MATLAB 2021a. ... All experiments were conducted using Python (3.9.5) and Py Torch (2.0.1) on an NVIDIA A100 GPU. |
| Experiment Setup | Yes | All methods start from the same initial point, obtained by projecting the sum of a normalized matrix of ones and an i.i.d. standard Gaussian random matrix onto the Birkhoff polytope. ... We compute the gap at the initial point, denoted as ϵ0, and terminate the algorithms once the gap reaches 0.001 ϵ0. Additionally, we impose a maximum iteration limit of 108. For both DC-FW and FW, we used the exact line-search method for step-size selection... We employed an adaptive strategy where the tolerance ϵt is updated dynamically. We fixed a multiplication parameter β = 0.8, and initially we set ϵ1 = β ϵ0. Then, at each iteration t, we update the tolerance as follows: if the gap falls below ϵt, we decrease the tolerance by setting ϵt+1 = βϵt. Otherwise, we keep it unchanged, ϵt+1 = ϵt. ... We choose regularization parameter λ = 10 4. All algorithms are initialized at the origin. ... All models were initialized using the same seed and trained for 100 epochs with a batch size of 256. ... This is followed by a 2 2 max pooling layer and a dropout layer with a 0.01 probability. ... The example is based on the hyperparameters L = 10, c = 10 for DC-FW and FW. Furthermore, DC-FW with hyper-parameter L = 10, demonstrates superior performance compared to the FW method and in both training and validation. |