# Mode Connectivity in Auction Design

arXiv: https://arxiv.org/abs/2305.11005 · HTML: https://mlsanity.com/paper/2305.11005/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 18 May 2023.

## Builds on (most cited first, 20 of 20)

- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Nets](https://mlsanity.com/paper/1906.06247/) (2019)
- [On Connected Sublevel Sets in Deep Learning](https://mlsanity.com/paper/1901.07417/) (2019)
- [Landscape Connectivity and Dropout Stability of SGD Solutions for Over-parameterized Neural Networks](https://mlsanity.com/paper/1912.10095/) (2019)
- [Complexity of Mechanism Design](https://mlsanity.com/paper/1408.1486/) (2014)
- [Automated Mechanism Design via Neural Networks](https://mlsanity.com/paper/1805.03382/) (2018)
- [Differentiable Economics for Randomized Affine Maximizer Auctions](https://mlsanity.com/paper/2202.02872/) (2022)
- [ProportionNet: Balancing Fairness and Revenue for Auction Design with Deep Learning](https://mlsanity.com/paper/2010.06398/) (2020)
- [A Context-Integrated Transformer-Based Neural Network for Auction Design](https://mlsanity.com/paper/2201.12489/) (2022)
- [Strong Duality for a Multiple-Good Monopolist](https://mlsanity.com/paper/1409.4150/) (2014)
- [Learning Revenue-Maximizing Auctions With Differentiable Matching](https://mlsanity.com/paper/2106.07877/) (2021)
- [Duality and Optimality of Auctions for Uniform Distributions](https://mlsanity.com/paper/1404.2329/) (2014)
- [Understanding Incentives: Mechanism Design becomes Algorithm Design](https://mlsanity.com/paper/1305.4002/) (2013)
- [Sampling and Representation Complexity of Revenue Maximization](https://mlsanity.com/paper/1402.4535/) (2014)
- [Mechanism Design via Optimal Transport](https://mlsanity.com/paper/1503.01958/) (2015)
- [The Menu-Size Complexity of Revenue Approximation](https://mlsanity.com/paper/1604.06580/) (2016)

## Built on by (most cited first, 3 of 3)

- [Optimal Automated Market Makers: Differentiable Economics and Strong Duality](https://mlsanity.com/paper/2402.09129/) (2024)
- [Open Problems in Differentiable Social Choice: Learning Mechanisms, Decisions, and Alignment](https://mlsanity.com/paper/2602.03003/) (2026)
- [Enhancing Affine Maximizer Auctions with Correlation-Aware Payment](https://mlsanity.com/paper/2602.09455/) (2026)

## Abstract (arXiv)

Optimal auction design is a fundamental problem in algorithmic game theory. This problem is notoriously difficult already in very simple settings. Recent work in differentiable economics showed that neural networks can efficiently learn known optimal auction mechanisms and discover interesting new ones. In an attempt to theoretically justify their empirical success, we focus on one of the first such networks, RochetNet, and a generalized version for affine maximizer auctions. We prove that they satisfy mode connectivity, i.e., locally optimal solutions are connected by a simple, piecewise linear path such that every solution on the path is almost as good as one of the two local optima. Mode connectivity has been recently investigated as an intriguing empirical and theoretically justifiable property of neural networks used for prediction problems. Our results give the first such analysis in the context of differentiable economics, where neural networks are used directly for solving non-convex optimization problems.