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Autoregressive Image Generation without Vector Quantization
Neural Information Processing SystemsConventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity ...
Tianhong Li +4 more
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Transactions of the American Mathematical Society, 1975
Let Crc = CrC(X, E) denote the space of all continuous functions f, from a completely regular Hausdorff space X into a locally convex space E, for which f(X) is relatively compact. As it is shown in 181, the uniform dual Crc of Crc can be identified with a space M(B, E') of E'-valued measures defined on the algebra of subsets of X generated by the zero
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Let Crc = CrC(X, E) denote the space of all continuous functions f, from a completely regular Hausdorff space X into a locally convex space E, for which f(X) is relatively compact. As it is shown in 181, the uniform dual Crc of Crc can be identified with a space M(B, E') of E'-valued measures defined on the algebra of subsets of X generated by the zero
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Partial spreads and vector space partitions
, 2016Constant-dimension codes with the maximum possible minimum distance have been studied under the name of partial spreads in Finite Geometry for several decades. Not surprisingly, for this subclass typically the sharpest bounds on the maximal code size are
T. Honold +2 more
semanticscholar +1 more source
1978
In nearly all of the discussion to follow we shall deal with the set of real numbers. Occasionally, however, we shall deal with complex numbers as well. In order to avoid cumbersome repetition we shall denote the set we are dealing with by F and let the context elucidate whether we are speaking of real or complex numbers or both.
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In nearly all of the discussion to follow we shall deal with the set of real numbers. Occasionally, however, we shall deal with complex numbers as well. In order to avoid cumbersome repetition we shall denote the set we are dealing with by F and let the context elucidate whether we are speaking of real or complex numbers or both.
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1981
Publisher Summary This chapter focuses on vectors in space. The set of ordered triples of the form (a, b, c) is called real three-dimensional space and is denoted R3. The three axes, x-axis, y-axis, and z-axis, determine three coordinate planes that are called the xy-plane, the xz-plane, and the yz-plane. The xy-plane contains the x- and y-axes and is
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Publisher Summary This chapter focuses on vectors in space. The set of ordered triples of the form (a, b, c) is called real three-dimensional space and is denoted R3. The three axes, x-axis, y-axis, and z-axis, determine three coordinate planes that are called the xy-plane, the xz-plane, and the yz-plane. The xy-plane contains the x- and y-axes and is
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2017
In this chapter we discuss a wide range of basic topics related to vectors of real numbers. Some of the properties carry over to vectors over other fields, such as complex numbers, but the reader should not assume this. Occasionally, for emphasis, we will refer to “real” vectors or “real” vector spaces, but unless it is stated otherwise, we are ...
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In this chapter we discuss a wide range of basic topics related to vectors of real numbers. Some of the properties carry over to vectors over other fields, such as complex numbers, but the reader should not assume this. Occasionally, for emphasis, we will refer to “real” vectors or “real” vector spaces, but unless it is stated otherwise, we are ...
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1974
The objects of chief interest in the study of a Hilbert space are not the vectors in the space, but the operators on it. Most people who say they study the theory of Hilbert spaces in fact study operator theory. The reason is that the algebra and geometry of vectors, linear functionals, quadratic forms, subspaces and the like are easier than operator ...
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The objects of chief interest in the study of a Hilbert space are not the vectors in the space, but the operators on it. Most people who say they study the theory of Hilbert spaces in fact study operator theory. The reason is that the algebra and geometry of vectors, linear functionals, quadratic forms, subspaces and the like are easier than operator ...
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Examples of vector spaces [PDF]
, 1978 Before embarking on our study of the elementary properties of vector spaces and their linear subspaces in the succeeding chapters, let us collect a list of examples of vector spaces. Of basic importance are the three examples ℝ k , P n (ℝ), and Fun(S) described in Section 3.1.
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1979
Throughout what follows a row vector a’ = (al,a2,…,an) is an ordered n-tuple of complex numbers ...
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Throughout what follows a row vector a’ = (al,a2,…,an) is an ordered n-tuple of complex numbers ...
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