conceptual understanding as well as practically using them in your deep learning models. We start with sparsity. If your goal was to optimize your brain for storage, you can often trim a lot of useless trivia etc. while retaining the model’s performance? In this chapter we introduce the intuition behind sparsity, different possible methods of picking the connections and nodes to prune, and how to prune a given get you excited yet? Let’s learn about these techniques together! Model Compression Using Sparsity Sparsity or Pruning refers to the technique of removing (pruning) weights during the model training

Synthetic Data  Generate data with specific data characteristics  Systematic evaluation w/ datasize, sparsity, etc  Inappropriate for certain topics: compression, ML accuracy  “Real” Data Repositories  0 [J. Sommer, M. Boehm, A. V. Evfimievski, B. Reinwald, P. J. Haas: MNC: Structure- Exploiting Sparsity Estimation for Matrix Expressions. SIGMOD 2019] 15 706.015 Introduction to Scientific Writing #Guidelines] [J. Sommer, M. Boehm, A. V. Evfimievski, B. Reinwald, P. J. Haas: MNC: Structure- Exploiting Sparsity Estimation for Matrix Expressions. SIGMOD 2019] 27 706.015 Introduction to Scientific Writing

Semi-supervised Learning (Contd.) Constrained Clustering Distance Metric Learning Manifold based Learning Sparsity based Learning (Compressed Sensing) Feng Li (SDU) Overview September 6, 2023 40 / 57 Constrained

quantization as described in chapter 2. We could also incorporate compression techniques such as sparsity, k-means clustering, etc. which will be discussed in the later chapters. 2. Even after compression

N. Shazeer. Switch transformers: Scaling to trillion parameter models with simple and efficient sparsity. CoRR, abs/2101.03961, 2021. URL https://arxiv.org/ abs/2101.03961. L. Gao, S. Biderman, S. Black

containing sparse arrays. Returns dtype [Series] Series with the count of columns with each type and sparsity (dense/sparse) See also: ftypes Return ftypes (indication of sparse/dense and dtype) in this object Returns pandas.Series The data type of each column. See also: pandas.DataFrame.ftypes Dtype and sparsity information. 1336 Chapter 6. API Reference pandas: powerful Python data analysis toolkit, Release containing sparse arrays. Returns dtype [Series] Series with the count of columns with each type and sparsity (dense/sparse) See also: ftypes Return ftypes (indication of sparse/dense and dtype) in this object

C::Sparse, update::Cint) Update an LDLt or LLt Factorization F of A to a factorization of A ± C*C'. If sparsity preserving factorization is used, i.e. L*L' == P*A*P' then the new factor will be L*L' == P*A*P' sparse matrices differ from their dense counterparts in that the resulting matrix follows the same sparsity pattern as a given sparse matrix S, or that the resulting sparse matrix has density d, i.e. each dimensions m x n with structural zeros at S[I[k], J[k]]. This method can be used to construct the sparsity pattern of the matrix, and is more efficient than using e.g. sparse(I, J, zeros(length(I))). For

C::Sparse, update::Cint) Update an LDLt or LLt Factorization F of A to a factorization of A ± C*C'. If sparsity preserving factorization is used, i.e. L*L' == P*A*P' then the new factor will be L*L' == P*A*P' sparse matrices differ from their dense counterparts in that the resulting matrix follows the same sparsity pattern as a given sparse matrix S, or that the resulting sparse matrix has density d, i.e. each dimensions m x n with structural zeros at S[I[k], J[k]]. This method can be used to construct the sparsity pattern of the matrix, and is more efficient than using e.g. sparse(I, J, zeros(length(I))). For

C::Sparse, update::Cint) Update an LDLt or LLt Factorization F of A to a factorization of A ± C*C'. If sparsity preserving factorization is used, i.e. L*L' == P*A*P' then the new factor will be L*L' == P*A*P' sparse matrices differ from their dense counterparts in that the resulting matrix follows the same sparsity pattern as a given sparse matrix S, or that the resulting sparse matrix has density d, i.e. each dimensions m x n with structural zeros at S[I[k], J[k]]. This method can be used to construct the sparsity pattern of the matrix, and is more efficient than using e.g. sparse(I, J, zeros(length(I))). For

matrix-matrix mul�plica�on (#30372). • Sparse vector outer products are more performant and maintain sparsity in products of the form kron(u, v'), u * v', and u .* v' where u and v are sparse vectors or column sparse matrices differ from their dense counterparts in that the resul�ng matrix follows the same sparsity pa�ern as a given sparse matrix S, or that the resul�ng sparse matrix has density d, i.e. each matrix