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A Compositional Kernel Model for Feature Learning 特征学习的组合核模型
IF 2.5 2区 数学
Applied and Computational Harmonic Analysis Pub Date : 2026-09-01 DOI: 10.1016/j.acha.2026.101923
Feng Ruan,Keli Liu,Michael Jordan
{"title":"A Compositional Kernel Model for Feature Learning","authors":"Feng Ruan,Keli Liu,Michael Jordan","doi":"10.1016/j.acha.2026.101923","DOIUrl":"https://doi.org/10.1016/j.acha.2026.101923","url":null,"abstract":"","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"43 1","pages":"101923"},"PeriodicalIF":2.5,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Noisy phase retrieval from subgaussian measurements 从亚高斯测量中提取噪声相位
IF 2.5 2区 数学
Applied and Computational Harmonic Analysis Pub Date : 2026-09-01 DOI: 10.1016/j.acha.2026.101926
Haiyang Peng,Deren Han,Linbin Li,Meng Huang
{"title":"Noisy phase retrieval from subgaussian measurements","authors":"Haiyang Peng,Deren Han,Linbin Li,Meng Huang","doi":"10.1016/j.acha.2026.101926","DOIUrl":"https://doi.org/10.1016/j.acha.2026.101926","url":null,"abstract":"","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"39 1","pages":"101926"},"PeriodicalIF":2.5,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Matrix Discrepancy for Representations of Finite Groups 有限群表示的矩阵不一致
IF 2.5 2区 数学
Applied and Computational Harmonic Analysis Pub Date : 2026-09-01 DOI: 10.1016/j.acha.2026.101924
Afonso S. Bandeira,Helmut Bölcskei
{"title":"Matrix Discrepancy for Representations of Finite Groups","authors":"Afonso S. Bandeira,Helmut Bölcskei","doi":"10.1016/j.acha.2026.101924","DOIUrl":"https://doi.org/10.1016/j.acha.2026.101924","url":null,"abstract":"","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"29 4 1","pages":"101924"},"PeriodicalIF":2.5,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Playing with Time: Dilation and Time Encoding 玩时间：扩张和时间编码
IF 2.5 2区 数学
Applied and Computational Harmonic Analysis Pub Date : 2026-08-27 DOI: 10.1016/j.acha.2026.101921
Marek Hilton, Pier Luigi Dragotti
{"title":"Playing with Time: Dilation and Time Encoding","authors":"Marek Hilton, Pier Luigi Dragotti","doi":"10.1016/j.acha.2026.101921","DOIUrl":"https://doi.org/10.1016/j.acha.2026.101921","url":null,"abstract":"The samples resulting from a time encoding machine (TEM) are intrinsically non-uniform and thus typical strategies for reconstruction rely on transforming the time encoded samples into an equivalent non-uniform sampling problem. In this work we take an alternative perspective and consider how integrate-and-fire time encoded samples represent uniform sampling on an equivalent ‘amplitude’-domain signal. From this perspective, existing reconstruction strategies are readily applicable but only for a limited class of signals. To remedy this, we propose a modification of the typical sampling hardware to create a new time-dilating integrate-and-fire sampler (TDIF) that can sample and reconstruct a broader range of signals. We show that, in amplitude-domain, dilation of time measurements is an almost equivalent operation to filtering in the time-domain. Thus signals can be sampled with arbitrary sampling kernels in amplitude-domain by dilating time measurements. We show that non-negative piecewise constant signals can be perfectly reconstructed from their sparse dilated time encodings.","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"6 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148884857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay 幂律衰减下解析谱算法的泛化误差曲线
IF 2.5 2区 数学
Applied and Computational Harmonic Analysis Pub Date : 2026-08-26 DOI: 10.1016/j.acha.2026.101920
Yicheng Li, Weiye Gan, Zuoqiang Shi, Qian Lin
{"title":"Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay","authors":"Yicheng Li, Weiye Gan, Zuoqiang Shi, Qian Lin","doi":"10.1016/j.acha.2026.101920","DOIUrl":"https://doi.org/10.1016/j.acha.2026.101920","url":null,"abstract":"The generalization error curve of a kernel regression method concerns the exact order of the generalization error under various source conditions, noise levels, and choices of the regularization parameter, rather than only the minimax rate. In this work, under mild assumptions, we rigorously characterize the generalization error curves of kernel gradient descent and, more generally, of a large class of analytic spectral algorithms in kernel regression. Consequently, we sharpen the near-inconsistency result for kernel interpolation and clarify the saturation effects of kernel regression algorithms with higher qualification. Motivated in part by neural tangent kernel theory, these results greatly improve our understanding of the generalization behavior of wide neural networks. A novel technical contribution, the analytic functional argument, may also be of independent interest.","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"133 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148853332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constraints for Stable Sampling on the Sphere 球面上稳定采样的约束
IF 2.5 2区 数学
Applied and Computational Harmonic Analysis Pub Date : 2026-08-25 DOI: 10.1016/j.acha.2026.101922
Martin Ehler, Karlheinz Gröochenig
{"title":"Constraints for Stable Sampling on the Sphere","authors":"Martin Ehler, Karlheinz Gröochenig","doi":"10.1016/j.acha.2026.101922","DOIUrl":"https://doi.org/10.1016/j.acha.2026.101922","url":null,"abstract":"We derive quantitative volume constraints for sampling measures <ce:italic>μ<ce:inf loc=\"post\">t</ce:inf></ce:italic> on the unit sphere <mml:math altimg=\"si1.svg\"><mml:msup><mml:mi mathvariant=\"double-struck\">S</mml:mi><mml:mi>d</mml:mi></mml:msup></mml:math> that satisfy Marcinkiewicz-Zygmund inequalities for polynomials of degree <ce:italic>t</ce:italic>. Using precise localization estimates for Jacobi polynomials, we obtain explicit upper and lower bounds on the <ce:italic>μ<ce:inf loc=\"post\">t</ce:inf></ce:italic>-mass of geodesic balls at the natural scale <mml:math altimg=\"si2.svg\"><mml:msup><mml:mi>t</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>. Whereas constants are typically left implicit in the literature, we place special emphasis on fully explicit constants, so that the results are genuinely quantitative. Moreover, these bounds yield quantitative constraints for the <ce:italic>s</ce:italic>-dimensional Hausdorff volume of Marcinkiewicz-Zygmund sampling sets and, in particular, optimal lower bounds for the length of Marcinkiewicz-Zygmund curves.","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"9 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148853333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Fourier ratio: A unifying measure of complexity for recovery, localization, and learning 傅里叶比率：用于恢复、定位和学习的复杂性的统一度量
IF 2.6 2区 数学
Applied and Computational Harmonic Analysis Pub Date : 2026-07-01 Epub Date: 2026-06-27 DOI: 10.1016/j.acha.2026.101904
W. Burstein, A. Iosevich, H. Nathan
{"title":"The Fourier ratio: A unifying measure of complexity for recovery, localization, and learning","authors":"W. Burstein,&nbsp;A. Iosevich,&nbsp;H. Nathan","doi":"10.1016/j.acha.2026.101904","DOIUrl":"10.1016/j.acha.2026.101904","url":null,"abstract":"<div><div>We introduce a generalized Fourier ratio, the ℓ<sup>1</sup>/ℓ<sup>2</sup> norm ratio of coefficients in a <em>arbitrary</em> orthonormal system, as a single, basis-invariant measure of <em>effective dimension</em> that governs fundamental limits across signal recovery, localization, and learning. First, we prove that functions with small Fourier ratio can be stably recovered from random missing samples via ℓ<sup>1</sup> minimization, extending and clarifying compressed sensing guarantees for general bounded orthonormal systems. Second, we establish a sharp <em>localization obstruction</em>: any attempt to localize recovery to subslices of a product space necessarily inflates the Fourier ratio by a factor scaling with the square root of the slice count, demonstrating that global complexity cannot be distributed locally. Finally, we show that the same parameter controls key complexity-theoretic measures: it provides explicit upper bounds on Kolmogorov rate-distortion description length and on the statistical query (SQ) dimension of the associated function class. These results unify analytic, algorithmic, and learning-theoretic constraints under a single complexity parameter, revealing the Fourier ratio as a fundamental invariant in information-theoretic signal processing.</div></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"85 ","pages":"Article 101904"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A resolution of the Gaussian hyperplane tessellation conjecture on the sphere 球面上高斯超平面镶嵌猜想的解译
IF 2.6 2区 数学
Applied and Computational Harmonic Analysis Pub Date : 2026-07-01 Epub Date: 2026-06-09 DOI: 10.1016/j.acha.2026.101903
Sjoerd Dirksen, Nigel Q․ D. Strachan
{"title":"A resolution of the Gaussian hyperplane tessellation conjecture on the sphere","authors":"Sjoerd Dirksen,&nbsp;Nigel Q․ D. Strachan","doi":"10.1016/j.acha.2026.101903","DOIUrl":"10.1016/j.acha.2026.101903","url":null,"abstract":"<div><div>We investigate how many hyperplanes with independent standard Gaussian directions one needs to produce a <em>δ</em>-uniform tessellation of a subset <em>S</em> of the Euclidean sphere, meaning that for any pair of points in <em>S</em> the fraction of hyperplanes separating them corresponds to their geodesic distance up to an additive error <em>δ</em>. It was conjectured that, up to certain positive multiplicative constants, <span><math><mrow><msup><mi>δ</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup><msub><mi>w</mi><mo>*</mo></msub><msup><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow></math></span> Gaussian random hyperplanes are necessary and sufficient for this purpose, where <em>w</em><sub>*</sub>(<em>S</em>) is the Gaussian complexity of <em>S</em>. We falsify this conjecture by constructing a set <em>S</em> where, up to constants, <span><math><mrow><msup><mi>δ</mi><mrow><mo>−</mo><mn>3</mn></mrow></msup><msub><mi>w</mi><mo>*</mo></msub><msup><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow></math></span> Gaussian hyperplanes are necessary and sufficient.</div></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"85 ","pages":"Article 101903"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148356332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unitary invariants of the finite Heisenberg group 有限Heisenberg群的酉不变量
IF 2.6 2区 数学
Applied and Computational Harmonic Analysis Pub Date : 2026-07-01 Epub Date: 2026-06-27 DOI: 10.1016/j.acha.2026.101906
Josh Katz
{"title":"Unitary invariants of the finite Heisenberg group","authors":"Josh Katz","doi":"10.1016/j.acha.2026.101906","DOIUrl":"10.1016/j.acha.2026.101906","url":null,"abstract":"<div><div>Unitary invariants-polynomials in both the variables and their conjugates-often separate orbits in far lower degree than ordinary polynomial invariants, yet their separating power is little studied. We illustrate this for the finite Heisenberg group <em>H<sub>N</sub></em>: although <span><math><mrow><mi>C</mi><msup><mrow><mo>[</mo><mi>V</mi><mo>]</mo></mrow><msub><mi>H</mi><mi>N</mi></msub></msup></mrow></math></span> has no nonconstant invariants below degree N, degree-six unitary invariants (a Heisenberg analogue of the bispectrum) already separate generic <em>H<sub>N</sub></em>-orbits up to a global phase, and a single degree-N polynomial invariant resolves the phase, giving full generic orbit separation. The construction rests on results from phase retrieval. This gives a concrete case where the minimal separating degree for unitary invariants is dramatically lower than for polynomial invariants.</div></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"85 ","pages":"Article 101906"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the role of the Double Fourier Sphere method in fast algorithms on SO(3) 重傅立叶球法在SO(3)快速算法中的作用
IF 2.6 2区 数学
Applied and Computational Harmonic Analysis Pub Date : 2026-07-01 Epub Date: 2026-06-24 DOI: 10.1016/j.acha.2026.101907
Ralf Hielscher, Erik Wünsche
{"title":"On the role of the Double Fourier Sphere method in fast algorithms on SO(3)","authors":"Ralf Hielscher,&nbsp;Erik Wünsche","doi":"10.1016/j.acha.2026.101907","DOIUrl":"10.1016/j.acha.2026.101907","url":null,"abstract":"<div><div>We analyze the Double Fourier Sphere (DFS) method on the rotation group <span><math><mrow><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math></span> in the frequency domain and demonstrate its central role in fast algorithms. Fast Fourier algorithms on <span><math><mrow><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math></span> are commonly formulated as a Wigner transform - mapping harmonic to Fourier coefficients - followed by a Fourier transform. We revisit this formulation and interpret the Wigner transform as an explicit realization of the DFS method, lifting functions from <span><math><mrow><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math></span> to <span><math><msup><mrow><mi>T</mi></mrow><mn>3</mn></msup></math></span>. In this context, we analyze the Sobolev regularity loss induced by this lifting. Furthermore, we compare different Wigner transform implementations, examine additional symmetry enhancements, and observe that the direct method is often faster and more stable than the fast polynomial transform approaches.</div></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"85 ","pages":"Article 101907"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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