Researchers have introduced tropical circuits with scalar multiplication gates, which utilize operations like max, addition, and multiplication by a positive constant. The study establishes exponential size lower bounds for these circuits when computing maximum weight directed spanning trees and maximum weight bipartite perfect matchings. This work also demonstrates an exponential size difference between monotone and non-monotone maxout neural networks, which are extensions of ReLU networks, highlighting that input-convex neural networks may require significantly larger sizes than their unrestricted counterparts to represent the same functions. AI
IMPACT This research may lead to a better understanding of the trade-offs between model size and expressivity in neural networks, particularly for models with enforced convexity constraints.
RANK_REASON The cluster contains an academic paper detailing theoretical computer science research.
- Input-convex neural networks
- Input-Convex Neural Networks (ICNNs)
- Maximum Weight Bipartite Perfect Matchings
- Maximum Weight Directed Spanning Trees
- Maxout Neural Networks
- Monotone Maxout Neural Networks
- ReLU neural networks
- Scalar Multiplication Gates
- Tropical Circuits
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