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A key-value cache is a key component of many services to provide low-latency and high-throughput data accesses to a huge amount of data. To improve the end-to-end performance of such services, a key-value cache must achieve a high cache hit ratio with high throughput. In this paper, we propose a new cache replacement algorithm, multi-step LRU, which achieves high throughput by efficiently exploiting SIMD instructions without using per-item additional memory (LRU metadata) to record information such as the last access timestamp. For a small set of items that can fit within a vector register, SIMD-based LRU management without LRU metadata is known (in-vector LRU). It remembers the access history by reordering items in one vector using vector shuffle instruction. In-vector LRU alone cannot be used for a caching system since it can manage only few items. Set-associative cache is a straightforward way to build a large cache using in-vector LRU as a building block. However, a naive set-associative cache based on in-vector LRU has a poorer cache hit ratio than the original LRU although it can achieve a high throughput. Our multi-step LRU enhances naive set-associative cache based on in-vector LRU for improving cache accuracy by taking both access frequency and access recency of items into account while keeping the efficiency by SIMD instructions. Our results indicate that multi-step LRU outperforms the original LRU and GCLOCK algorithms in terms of both execution speed and cache hit ratio. Multi-step LRU improves the cache hit ratios over the original LRU by implicitly taking access frequency of items as well as access recency into account. The cache hit ratios of multi-step LRU are similar to those of ARC, which achieves a higher a cache hit ratio in a tradeoff for using more LRU metadata.

In PT-quantum mechanics the generator of the dynamics of a physical system is not necessarily a self-adjoint Hamiltonian. It is now clear that this choice does not prevent to get a unitary time evolution and a real spectrum of the Hamiltonian, even if, most of the times, one is forced to deal with biorthogonal sets rather than with on orthonormal basis of eigenvectors. In this paper we consider some extended versions of the Heisenberg algebraic dynamics and we relate this analysis to some generalized version of Gibbs states and to their related KMS-like conditions. We also discuss some preliminary aspects of the Tomita-Takesaki theory in our context., Comment: In press in Complex Analysis and Operator Theory

The purpose of this article is twofold. First of all, the notion of $(D, E)$-quasi basis is introduced for a pair $(D, E)$ of dense subspaces of Hilbert spaces. This consists of two biorthogonal sequences $\{ \varphi_n \}$ and $\{ \psi_n \}$ such that $\sum_{n=0}^\infty \ip{x}{\varphi_n}\ip{\psi_n}{y}=\ip{x}{y}$ for all $x \in D$ and $y \in E$. Secondly, it is shown that if biorthogonal sequences $\{ \varphi_n \}$ and $\{ \psi_n \}$ form a $(D ,E)$-quasi basis, then they are generalized Riesz systems. The latter play an interesting role for the construction of non-self-adjoint Hamiltonians and other physically relevant operators., Comment: submitted to MJOM

Dropout is a simple but efficient regularization technique for achieving better generalization of deep neural networks (DNNs); hence it is widely used in tasks based on DNNs. During training, dropout randomly discards a portion of the neurons to avoid overfitting. This paper presents an enhanced dropout technique, which we call multi-sample dropout, for both accelerating training and improving generalization over the original dropout. The original dropout creates a randomly selected subset (called a dropout sample) from the input in each training iteration while the multi-sample dropout creates multiple dropout samples. The loss is calculated for each sample, and then the sample losses are averaged to obtain the final loss. This technique can be easily implemented by duplicating a part of the network after the dropout layer while sharing the weights among the duplicated fully connected layers. Experimental results using image classification tasks including ImageNet, CIFAR-10, and CIFAR-100 showed that multi-sample dropout accelerates training. Moreover, the networks trained using multi-sample dropout achieved lower error rates compared to networks trained with the original dropout. The additional computation cost due to the duplicated operations is not significant for deep convolutional networks because most of the computation time is consumed in the convolution layers before the dropout layer, which are not duplicated.

Continuing the analysis undertaken in previous articles, we discuss some features of non-self-adjoint operators and sesquilinear forms which are defined starting from two biorthogonal families of vectors, like the so-called generalized Riesz systems, enjoying certain properties. In particular we discuss what happens when they forms two $\D$-quasi bases., Comment: in press in Journal of Mathematical Physics

Data augmentation is a widely used technique in many machine learning tasks, such as image classification, to virtually enlarge the training dataset size and avoid overfitting. Traditional data augmentation techniques for image classification tasks create new samples from the original training data by, for example, flipping, distorting, adding a small amount of noise to, or cropping a patch from an original image. In this paper, we introduce a simple but surprisingly effective data augmentation technique for image classification tasks. With our technique, named SamplePairing, we synthesize a new sample from one image by overlaying another image randomly chosen from the training data (i.e., taking an average of two images for each pixel). By using two images randomly selected from the training set, we can generate $N^2$ new samples from $N$ training samples. This simple data augmentation technique significantly improved classification accuracy for all the tested datasets; for example, the top-1 error rate was reduced from 33.5% to 29.0% for the ILSVRC 2012 dataset with GoogLeNet and from 8.22% to 6.93% in the CIFAR-10 dataset. We also show that our SamplePairing technique largely improved accuracy when the number of samples in the training set was very small. Therefore, our technique is more valuable for tasks with a limited amount of training data, such as medical imaging tasks.

Ensembling multiple predictions is a widely used technique for improving the accuracy of various machine learning tasks. One obvious drawback of ensembling is its higher execution cost during inference. In this paper, we first describe our insights on the relationship between the probability of prediction and the effect of ensembling with current deep neural networks; ensembling does not help mispredictions for inputs predicted with a high probability even when there is a non-negligible number of mispredicted inputs. This finding motivated us to develop a way to adaptively control the ensembling. If the prediction for an input reaches a high enough probability, i.e., the output from the softmax function, on the basis of the confidence level, we stop ensembling for this input to avoid wasting computation power. We evaluated the adaptive ensembling by using various datasets and showed that it reduces the computation cost significantly while achieving accuracy similar to that of static ensembling using a pre-defined number of local predictions. We also show that our statistically rigorous confidence-level-based early-exit condition reduces the burden of task-dependent threshold tuning better compared with naive early exit based on a pre-defined threshold in addition to yielding a better accuracy with the same cost.

In this paper we define the notion of semi-regular biorthogonal pairs what is a generalization of regular biorthogonal pairs in Ref. \cite{hiroshi1} and show that if $(\{ \phi_{n} \} , \{ \psi_{n} \})$ is a semi-regular biorthogonal pair, then $\{ \phi_{n} \}$ and $\{ \psi_{n} \}$ are generalized Riesz bases. This result improves the results of Ref. \cite{h-t, hiroshi1, h-t2} in the regular case., Comment: 20pages

The first purpose of this paper is to show a method of constructing a regular biorthogonal pair based on the commutation rule: $ab-ba=I$ for a pair of operators $a$ and $b$ acting on a Hilbert space ${\cal H}$ with inner product $( \cdot | \cdot )$. Here, sequences $\{ \phi_{n} \}$ and $\{ \psi_{n} \}$ in a Hilbert space ${\cal H}$ are biorthogonal if $( \phi_{n} | \psi_{m})= \delta_{nm}$, $n,m=0,1, \cdots$, and they are regular if both $D_{\phi} \equiv Span \{ \phi_{n} \}$ and $D_{\psi} \equiv Span \{ \psi_{n} \}$ are dense in ${\cal H}$. Indeed, the assumption to construct the regular biorthogonal pair coincide with the definition of pseudo-bosons as originally given in Ref \cite{bagarello10}. Furthermore, we study the connections between the pseudo-bosonic operators $a, \; b, \; a^{\dagger}, \; b^{\dagger}$ and the pseudo-bosonic operators defined by a regular biorthogonal pair $(\{ \phi_{n} \}$, $\{ \psi_{n} \} )$ and an ONB $\mbox{ $e$}$ of ${\cal H}$ in appeared Ref \cite{hiroshi1}. The second purpose is to define and study the notion of ${\cal D}$-pseudo bosons in Ref \cite{bagarello13, bagarello2013} and give a method of constructing ${\cal D}$-pseudo bosons on some steps. Then it is shown that for any ONB $\mbox{ $e$}= \{ e_{n} \}$ in ${\cal H}$ and any operators $T$ and $T^{-1}$ in ${\cal L}^{\dagger} ( {\cal D})$, we may construct operators $A$ and $B$ satisfying ${\cal D}$-pseudo bosons, where ${\cal D}$ is a dense subspace in a Hilbert space ${\cal H}$ and ${\cal L}^{\dagger} ( {\cal D})$ the set of all linear operators $T$ from ${\cal D}$ to ${\cal D}$ such that $T^{\ast} {\cal D} \subset {\cal D}$, where $T^{\ast}$ is the adjoint of $T$. Finally, we give some physical examples of ${\cal D}$-pseudo bosons based on standard bosons by the method of constructing ${\cal D}$-pseudo bosons stated above., Comment: 16 pages

In \cite{b-i-t}, F. Bagarello, A. Inoue and C. Trapani investigated some operators defined by Riesz bases. These operators connect with ${\it quasi}$-${\it hermitian \; quantum \; mechanics}$, and its relatives. In this paper, we change the frameworks of these operators, and then almost results obtained in \cite{b-i-t} become trivial. Furthermore, we introduce a notion of generalized Riesz bases which is a generalization of Riesz bases and investigate some operators defined by generalized Riesz bases.