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We introduce MiniMax-01 series, including MiniMax-Text-01 and MiniMax-VL-01, which are comparable to top-tier models while offering superior capabilities in processing longer contexts. The core lies in lightning attention and its efficient scaling. To maximize computational capacity, we integrate it with Mixture of Experts (MoE), creating a model with 32 experts and 456 billion total parameters, of which 45.9 billion are activated for each token. We develop an optimized parallel strategy and highly efficient computation-communication overlap techniques for MoE and lightning attention. This approach enables us to conduct efficient training and inference on models with hundreds of billions of parameters across contexts spanning millions of tokens. The context window of MiniMax-Text-01 can reach up to 1 million tokens during training and extrapolate to 4 million tokens during inference at an affordable cost. Our vision-language model, MiniMax-VL-01 is built through continued training with 512 billion vision-language tokens. Experiments on both standard and in-house benchmarks show that our models match the performance of state-of-the-art models like GPT-4o and Claude-3.5-Sonnet while offering 20-32 times longer context window. We publicly release MiniMax-01 at https://github.com/MiniMax-AI., Comment: A technical report from MiniMax. The authors are listed in alphabetical order. We open-sourced our MiniMax-01 at https://github.com/MiniMax-AI

In this paper, we characterize smooth projective surfaces on which every integral pseudoeffective divisor has an integral Zariski decomposition., Comment: 7 pages, thanks the referee for useful comments, accepted by the Journal of Algebra and Its Applications. Comments are Welcome!

Let $X$ be a smooth projective surface and the closed Mori cone $\overline{\mathrm{NE}}(X)=\sum\mathbb R_{\ge0}[C_i]$ with some curves $C_i$ on $X$. We say that $X$ satisfies the bounded cohomology property if there exists a constant $c_X>0$ such that $h^1(\mathcal O_X(C))\le c_Xh^0(\mathcal O_X(C))$ for every curve $C$ on $X$. When the Picard number $\rho(X)=2$, we prove that $X$ satisfies the bounded cohomology property if one of the following holds: (i) the Kodaira dimension $\kappa(X)\le1$, (ii) the Iitaka dimension $\kappa(X,C_1)=1$ and $C_2^2<0$ and (iii) $\kappa(X,C_1)=\kappa(X,C_2)=1$. Moreover, we show that $X$ with the arbitrary Picard number satisfies the bounded cohomology property if each $C_i$ has $\kappa(X,C_i)=1$., Comment: 13 pages, comments are welcome!

Unforeseen particle accelerator interruptions, also known as interlocks, lead to abrupt operational changes despite being necessary safety measures. These may result in substantial loss of beam time and perhaps even equipment damage. We propose a simple yet powerful binary classification model aiming to forecast such interruptions, in the case of the High Intensity Proton Accelerator complex at the Paul Scherrer Institut. The model is formulated as logistic regression penalized by least absolute shrinkage and selection operator, based on a statistical two sample test to distinguish between unstable and stable states of the accelerator. The primary objective for receiving alarms prior to interlocks is to allow for countermeasures and reduce beam time loss. Hence, a continuous evaluation metric is developed to measure the saved beam time in any period, given the assumption that interlocks could be circumvented by reducing the beam current. The best-performing interlock-to-stable classifier can potentially increase the beam time by around 5 min in a day. Possible instrumentation for fast adjustment of the beam current is also listed and discussed., Comment: 12 pages, 13 figures

Particle accelerators are complex facilities that produce large amounts of structured data and have clear optimization goals as well as precisely defined control requirements. As such they are naturally amenable to data-driven research methodologies. The data from sensors and monitors inside the accelerator form multivariate time series. With fast pre-emptive approaches being highly preferred in accelerator control and diagnostics, the application of data-driven time series forecasting methods is particularly promising. This review formulates the time series forecasting problem and summarizes existing models with applications in various scientific areas. Several current and future attempts in the field of particle accelerators are introduced. The application of time series forecasting to particle accelerators has shown encouraging results and the promise for broader use, and existing problems such as data consistency and compatibility have started to be addressed., Comment: 13 pages, 11 figures

Under the framework of dynamics on normal projective varieties by Kawamata, Nakayama and Zhang \cite{Kawamata85,Nakayama10,NZ09,NZ10,Zhang16}, Hu and the author \cite{HL21}, we may reduce Kawaguchi-Silverman conjecture for automorphisms $f$ on normal projective threefolds $X$ with either the canonical divisor $K_X$ is trivial or negative Kodaira dimension to the following two case: (i) $f$ is a primitively automorphism of a weak Calabi-Yau threefold (ii) $X$ is a rationally connected threefold. And we prove Kawaguchi-Silverman conjecture is true for automorphisms of normal projective varieties $X$ with the irregularity $q(X)\ge\dim X-1$. Finally, we discuss Kawaguchi-Silverman conjecture on normal projective varieties with Picard number two., Comment: 16 pages, thanks the referee for useful comments, accepted by International Journal of Mathematics. arXiv admin note: text overlap with arXiv:2208.02616

In this paper we first note a result of birational automorphisms with bounded degree of projective varieties related with the Zariski dense orbit conjecture (ZDO) and the Zariski density of periodic points. Next, we give a reduced result of ZDO for automorphisms of projective threefolds, and showed ZDO for automorphisms of projective varieties $X$ with the irregularity $q(X)\ge\dim X-1$., Comment: 12 papes, this is a note of Zariski dense orbit conjecture. The original title is revised. Welcome to comments!

We say a smooth projective surface $X$ satisfies the bounded cohomology property if there exists a positive constant $c_X$ such that $h^1(\mathcal O_X(C))\le c_Xh^0(\mathcal O_X(C))$ for every prime divisor $C$ on $X$. Let the closed Mori cone $\mathrm{NE}(X)=\mathbb R_{\ge0}[C_1]+\mathbb R_{\ge0}[C_2]$ such that $C_1$ and $C_2$ with $C_2^2<0$ are some curves on $X$. If either (i) the Kodaira dimension $\kappa(X)\le1$ or (ii) $\kappa(X)=2$, the irregularity $q(X)=0$ and the Iitaka dimension $\kappa(X,C_1)=1$, then we prove that $X$ satisfies the bounded cohomology property., Comment: 9 pages, to appear in Communications in Algebra, minor revision

The beam interruptions (interlocks) of particle accelerators, despite being necessary safety measures, lead to abrupt operational changes and a substantial loss of beam time. A novel time series classification approach is applied to decrease beam time loss in the High Intensity Proton Accelerator complex by forecasting interlock events. The forecasting is performed through binary classification of windows of multivariate time series. The time series are transformed into Recurrence Plots which are then classified by a Convolutional Neural Network, which not only captures the inner structure of the time series but also utilizes the advances of image classification techniques. Our best performing interlock-to-stable classifier reaches an Area under the ROC Curve value of $0.71 \pm 0.01$ compared to $0.65 \pm 0.01$ of a Random Forest model, and it can potentially reduce the beam time loss by $0.5 \pm 0.2$ seconds per interlock.

The following conjecture arose out of discussions between B. Harbourne, J. Ro\'e, C. Cilberto and R. Miranda: for a smooth projective surface $X$ there exists a positive constant $c_X$ such that $h^1(\mathcal O_X(C))\le c_X h^0(\mathcal O_X(C))$ for every prime divisor $C$ on $X$. When the Picard number $\rho(X)=2$, we prove that if either the Kodaira dimension $\kappa(X)=1$ and $X$ has a negative curve or $X$ has two negative curves, then this conjecture holds for $X$., Comment: 6 pages, to appear in Communications in Algebra, minor revision

We collect some results on endomorphisms on projective varieties related with the Kawaguchi-Silverman conjecture. We discuss certain condition on automorphism groups of projective varieties and positivity conditions on leading real eigendivisors of self-morphisms. We prove Kawaguchi-Silverman conjecture for endomorphisms on projective bundles on a smooth Fano variety of Picard number one. In the last section, we discuss endomorphisms and augmented base loci of their eigendivisors., Comment: 11 pages

Let $X$ be a projective variety of dimension $n\ge1$ over an algebraically closed field of arbitrary characteristic. We prove a Fujiki-Lieberman type theorem on the structure of the automorphism group of $X$. Let $G$ be a group of zero entropy automorphisms of $X$ and $G_0$ the set of elements in $G$ which are isotopic to the identity. We show that after replacing $G$ by a suitable finite-index subgroup, $G/G_0$ is a unipotent group of the derived length at most $n-1$. This result was first proved by Dinh, Oguiso and Zhang for compact K\"ahler manifolds., Comment: 10 pages,comments are welcome! Accepted by International Journal of Mathematics

Let $X$ be a normal projective variety of dimension $n$ and $G$ an abelian group of automorphisms such that all elements of $G\setminus \{\mathrm{id}\}$ are of positive entropy. Dinh and Sibony showed that $G$ is actually free abelian of rank $\le n - 1$. The maximal rank case has been well understood by De-Qi Zhang. We aim to characterize the pair $(X, G)$ such that $\mathrm{rank} G = n - 2$., Comment: to appear in Canad. J. Math., minor revision

The following conjecture arose out of discussions between B. Harbourne, J. Ro\'e, C. Cilberto and R. Miranda: for a smooth projective surface $X$ there exists a positive constant $c_X$ such that $h^1(\mathcal O_X(C))\le c_X h^0(\mathcal O_X(C))$ for every prime divisor $C$ on $X$. We show that the conjecture is true for some smooth projective surfaces with Picard number 2., Comment: 11 pages

We characterize the integral Zariski decomposition of a smooth projective surface with Picard number 2 to partially solve a problem of B. Harbourne, P. Pokora, and H. Tutaj-Gasinska [Electron. Res. Announc. Math. Sci. 22 (2015), 103--108]., Comment: 8 pages,Mathematische Nachrichten