Stardust: Compiling Sparse Tensor Algebra to a Reconfigurable Dataflow Architecture

We introduce Stardust, a compiler that compiles sparse tensor algebra to reconfigurable dataflow architectures (RDAs). Stardust introduces new user-provided data representation and scheduling language constructs for mapping to resource-constrained accelerated architectures. Stardust uses the information provided by these constructs to determine on-chip memory placement and to lower to the Capstan RDA through a parallel-patterns rewrite system that targets the Spatial programming model. The Stardust compiler is implemented as a new compilation path inside the TACO open-source system. Using cycle-accurate simulation, we demonstrate that Stardust can generate more Capstan tensor operations than its authors had implemented and that it results in 138$\times$ better performance than generated CPU kernels and 41$\times$ better performance than generated GPU kernels.Comment: 15 pages, 13 figures, 6 tables

JaxPruner: A concise library for sparsity research

This paper introduces JaxPruner, an open-source JAX-based pruning and sparse training library for machine learning research. JaxPruner aims to accelerate research on sparse neural networks by providing concise implementations of popular pruning and sparse training algorithms with minimal memory and latency overhead. Algorithms implemented in JaxPruner use a common API and work seamlessly with the popular optimization library Optax, which, in turn, enables easy integration with existing JAX based libraries. We demonstrate this ease of integration by providing examples in four different codebases: Scenic, t5x, Dopamine and FedJAX and provide baseline experiments on popular benchmarks.Comment: Jaxpruner is hosted at http://github.com/google-research/jaxprune

Nachruf auf Rudolf Trostel (1928 - 2016)

Im Februar dieses Jahres hat uns ein großer Mechaniker verlassen

ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS

We study the homological algebra of bimodules over involutive associative algebras. We show that Braun’s definition of involutive Hochschild cohomology in terms of the complex of involution-preserving derivations is indeed computing a derived functor: the Z/2-invariants intersected with the center. We then introduce the corresponding involutive Hochschild homology theory and describe it as the derived functor of the pushout of Z/2-coinvariants and abelianization

On Dirac Factorization, Fractional Calculus, and Polynomial Linearization

We postulate the existence of fractional order derivative operators that satisfy a semi-group property in order to further factor the Klein-Gordon equation in Dirac's fashion. The analog of Dirac's matrices are found and we study the generalization of the Dirac algebra generated by these matrices. In this way, a hierarchy of generalized Clifford algebras is formed. We then apply this procedure to Schr\"odinger's equation, and examine the resulting coefficients before moving to a more general setting in which we study the linearization of polynomials with coefficients that do not commute with the indeterminates. Partial differential equations with non-constant coefficients are the archetypal example in this setting.Comment: 15 page

Chasing non-diagonal cycles in a certain system of algebras of operations

The mod 2 universal Steenrod algebra Q is a non-locally finite homogeneous quadratic algebra closely related to the ordinary mod 2 Steenrod algebra and the Lambda algebra. The algebra Q provides an example of a Koszul algebra which is a direct limit of a family of certain non-Koszul algebras Rk's. In this paper we see how far the several Rk's are to be Koszul by chasing in their cohomology non-trivial cocycles of minimal homological degre

Free Bicommutative Algebras

2000 Mathematics Subject Classification: Primary 17A50, Secondary 16R10, 17A30, 17D25, 17C50.Algebras with identities a(bc)=b(ac), (ab)c=(ac)b is called bicommutative. Bases and the cocharacter sequence for free bicommutative algebras are found. It is shown that the exponent of the variety of bicommutaive algebras is equal to 2