---
authors:

  - "Dutta, Souradeep"
  
  - "Jha, Susmit"
  
  - "Sankaranarayanan, Sriram"
  
  - "Tiwari, Ashish"
  
  - "Dutle, Aaron"
  
  - "Muñoz, César"
  
  - "Narkawicz, Anthony"
  
citekey: "duttaOutputRangeAnalysis2018"
publish_date: 2018-01-01
publisher: "Springer International Publishing"
location: "Cham"
pages: 121-138
last_import: 2025-05-12
---

# Indexing Information
Published: 2018-01

**DOI**
[10.1007/978-3-319-77935-5_9](https://doi.org/10.1007/978-3-319-77935-5_9)
**ISBN**
[978-3-319-77935-5](https://www.isbnsearch.org/isbn/978-3-319-77935-5)



#ToRead


>[!Abstract]
>Given a neural network (NN) and a set of possible inputs to the network described by polyhedral constraints, we aim to compute a safe over-approximation of the set of possible output values. This operation is a fundamental primitive enabling the formal analysis of neural networks that are extensively used in a variety of machine learning tasks such as perception and control of autonomous systems. Increasingly, they are deployed in high-assurance applications, leading to a compelling use case for formal verification approaches. In this paper, we present an efficient range estimation algorithm that iterates between an expensive global combinatorial search using mixed-integer linear programming problems, and a relatively inexpensive local optimization that repeatedly seeks a local optimum of the function represented by the NN. We implement our approach and compare it with Reluplex, a recently proposed solver for deep neural networks. We demonstrate applications of our approach to computing flowpipes for neural network-based feedback controllers. We show that the use of local search in conjunction with mixed-integer linear programming solvers effectively reduces the combinatorial search over possible combinations of active neurons in the network by pruning away suboptimal nodes.>[!seealso] Related Papers
>

# Annotations
## Notes
![[Paper Notes/Output Range Analysis for Deep Feedforward Neural Networks.md]]

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