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The structure of extended affine Weyl symmetry group of higher Painlev\'e equations of $N$ periodicity depends on whether $N$ is even or odd. We find that for even $N$, the symmetry group ${\widehat A}^{(1)}_{N-1}$ contains the conventional B\"acklun
Externí odkaz:
http://arxiv.org/abs/2409.03534
Autor:
Ben-Kish, Assaf, Zimerman, Itamar, Abu-Hussein, Shady, Cohen, Nadav, Globerson, Amir, Wolf, Lior, Giryes, Raja
Long-range sequence processing poses a significant challenge for Transformers due to their quadratic complexity in input length. A promising alternative is Mamba, which demonstrates high performance and achieves Transformer-level capabilities while r
Externí odkaz:
http://arxiv.org/abs/2406.14528
Recent advances in efficient sequence modeling have led to attention-free layers, such as Mamba, RWKV, and various gated RNNs, all featuring sub-quadratic complexity in sequence length and excellent scaling properties, enabling the construction of a
Externí odkaz:
http://arxiv.org/abs/2405.16504
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Proceedings: OCNMP Conference, Bad Ems (Germany), 23-29 June 2024 (April 26, 2024) ocnmp:13294
The construction of Integrable Hierarchies in terms of zero curvature representation provides a systematic construction for a series of integrable non-linear evolution equations (flows) which shares a common affine Lie algebraic structure. The integr
Externí odkaz:
http://arxiv.org/abs/2403.16285
The Mamba layer offers an efficient selective state space model (SSM) that is highly effective in modeling multiple domains, including NLP, long-range sequence processing, and computer vision. Selective SSMs are viewed as dual models, in which one tr
Externí odkaz:
http://arxiv.org/abs/2403.01590
Publikováno v:
SciPost Phys. Proc., 014, 2023
The construction of negative grade KdV hierarchy is proposed in terms of a Miura-gauge transformation. Such gauge transformation is employed within the zero curvature representation and maps the Lax operator of the mKdV into its couterpart within the
Externí odkaz:
http://arxiv.org/abs/2312.14349
Publikováno v:
J. Phys.: Conf. Ser. 2667 (2023) 012027
The gauge-Miura correspondence establishes a map between the entire KdV and mKdV hierarchies, including positive and also negative flows, from which new relations besides the standard Miura transformation arise. We use this correspondence to classify
Externí odkaz:
http://arxiv.org/abs/2312.14101
Designing privacy-preserving deep learning models is a major challenge within the deep learning community. Homomorphic Encryption (HE) has emerged as one of the most promising approaches in this realm, enabling the decoupling of knowledge between the
Externí odkaz:
http://arxiv.org/abs/2311.08610
Families of DFAs (FDFAs) are a computational model recognizing $\omega$-regular languages. They were introduced in the quest of finding a Myhill-Nerode theorem for $\omega$-regular languages, and obtaining learning algorithms. FDFAs have been shown t
Externí odkaz:
http://arxiv.org/abs/2310.16022
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Proceedings: OCNMP Conference, Bad Ems (Germany), 23-29 June 2024 (April 15, 2024) ocnmp:13201
We present a construction of a class of rational solutions of the Painlev\'e V equation that exhibit a two-fold degeneracy, meaning that there exist two distinct solutions that share identical parameters. The fundamental object of our study is the or
Externí odkaz:
http://arxiv.org/abs/2310.01585