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THEOREM 3.1. Given MNC sketches $ h_{A} $ and $ h_{B} $ for matrices A and B, the output sparsity $ s_{C} $ of the matrix product C = A B can be exactly computed under the assumptions A1 and A2
Algorithm 1 MNC Sparsity Estimation
Input: MNC sketches $ h_{A} $ and $ h_{B} $ for matrices A and B
Output: Output sparsity $ s_{C} $
1: // a) basic and extended sparsity estimation, incl upper 0 码力 |
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| 2 年前 3 jpg)
## Structured and Unstructured Sparsity
- Lots of 'free' wins from exploring sparsity in modern ML models
- Can often prune models to 80%+ sparsity(with retraining)
- Massive speedups 0 码力 |
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| 1 年前 3 Synthetic Data
■ Generate data with specific data characteristics
■ Systematic evaluation w/ datasize, sparsity, etc distributions?
■ Inappropriate for certain topics: compression, ML accuracy
## “Real” jpg)
[J. Sommer, M. Boehm, A. V. Evfimievski, B. Reinwald, P. J. Haas: MNC: Structure-Exploiting Sparsity Estimation for Matrix Expressions. SIGMOD 2019]
[J. Sommer, M. Boehm, A. V. Evfimievski, B. Reinwald, P. J. Haas: MNC: Structure-Exploiting Sparsity Estimation for Matrix Expressions. SIGMOD 2019]
 to further improve H. Zhang, H. Zhang, D. Zhao, and W. Liang. Conditional memory via scalable lookup: A new axis of sparsity for large language models. CoRR, abs/2601.07372, 2026. doi: 10.48550/ARXIV.2601. 07372. URL https://doi 0 码力 |
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| 1 月前 3 Learning (Contd.)
• Constrained Clustering
• Distance Metric Learning
• Manifold based Learning
• Sparsity based Learning (Compressed Sensing)
## Constrained Clustering
When we have any of the following: 0 码力 |
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| 2 年前 3 Houston, TX, USA
$ ^{4} $ Target Corporation; Sunnyvale, CA, USA
MNC: Structure-Exploiting Sparsity Estimation for Matrix Expressions
Johanna Sommer
IBM Germany
Matthias Boehm
Graz University 0 码力 |
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| 2 年前 3 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 0 码力 |
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| 2 年前 3 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 0 码力 |
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| 2 年前 3 update::Cint)
Update an LDLt or LLt Factorization F of A to a factorization of $ A \pm C^{*}C^{*} $
If sparsity preserving factorization is used, i.e. $ L^{*}L^{*} $ == $ P^{*}A^{*}P^{*} $ then the new factor 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 0 码力 |
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| 2 年前 3
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《Efficient Deep Learning Book》[EDL] Chapter 5 - Advanced Compression Techniquesconceptual 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 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 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 training0 码力 | 34 页 | 3.18 MB | 2 年前3