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Minimizing smooth Kurdyka-{\L}ojasiewicz functions via generalized descent methods: Convergence rate and complexity
Masoud Ahookhosh, Susan Ghaderi, Alireza Kabgani, Morteza Rahimi
https://arxiv.org/abs/2511.10414 https://arxiv.org/pdf/2511.10414 https://arxiv.org/html/2511.10414
arXiv:2511.10414v1 Announce Type: new
Abstract: This paper addresses the generalized descent algorithm (DEAL) for minimizing smooth functions, which is analyzed under the Kurdyka-{\L}ojasiewicz (KL) inequality. In particular, the suggested algorithm guarantees a sufficient decrease by adapting to the cost function's geometry. We leverage the KL property to establish the global convergence, convergence rates, and complexity. A particular focus is placed on the linear convergence of generalized descent methods. We show that the constant step-size and Armijo line search strategies along a generalized descent direction satisfy our generalized descent condition. Additionally, for nonsmooth functions by leveraging the smoothing techniques such as forward-backward and high-order Moreau envelopes, we show that the boosted proximal gradient method (BPGA) and the boosted high-order proximal-point (BPPA) methods are also specific cases of DEAL, respectively. It is notable that if the order of the high-order proximal term is chosen in a certain way (depending on the KL exponent), then the sequence generated by BPPA converges linearly for an arbitrary KL exponent. Our preliminary numerical experiments on inverse problems and LASSO demonstrate the efficiency of the proposed methods, validating our theoretical findings.
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Learning Linear Regression with Low-Rank Tasks in-Context
Kaito Takanami, Takashi Takahashi, Yoshiyuki Kabashima
https://arxiv.org/abs/2510.04548 https://a…

Learning Linear Regression with Low-Rank Tasks in-Context
In-context learning (ICL) is a key building block of modern large language models, yet its theoretical mechanisms remain poorly understood. It is particularly mysterious how ICL operates in real-world applications where tasks have a common structure. In this work, we address this problem by analyzing a linear attention model trained on low-rank regression tasks. Within this setting, we precisely characterize the distribution of predictions and the generalization error in the high-dimensional li…

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The Prodigy:
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#TheProdigy
https://littleorangeua1.bandcamp.com/track/the-prodigy-diesel-power-pain-shut-your-mouth-littleorangeua-version
https://open.spotify.com/track/2zKT0JYK2Ap1YgWMXoibnP

Stability and Superconductivity of Ternary Polyhydrides
Dmitrii V. Semenok, Di Zhou, Wuhao Chen, Alexander G. Kvashnin, Andrey V. Sadakov, Toni Helm, Pedro N. Ferreira, Christoph Heil, Vladimir M. Pudalov, Ivan A. Troyan, Viktor V. Struzhkin
https://arxiv.org/abs/2509.22877

Stability and Superconductivity of Ternary Polyhydrides
We review five years of experimental and theoretical attempts (2020-2025) to enhance the superconducting critical temperature ($\textit{T$_c$}$) of hydrogen-rich compounds by alloying binary superhydrides with additional elements. Despite predictions of higher $\textit{T$_c$}$ in ternary systems such as La-Y-H, La-Ce-H, and Ca-Mg-H, experiments consistently show that the maximum $\textit{T$_c$}$ in disordered ternary superhydrides does not exceed that of the best binary parent hydrides within e…

🇺🇦 #NowPlaying on #BBC6Music's #HuwStephens
The Prodigy:
🎵 Diesel Power
#TheProdigy
https://littleorangeua1.bandcamp.com/track/the-prodigy-diesel-power-pain-shut-your-mouth-littleorangeua-version
https://open.spotify.com/track/2zKT0JYK2Ap1YgWMXoibnP