5.2 KiB
| authors | citekey | publish_date | publisher | location | pages | last_import | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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katzReluplexEfficientSMT2017 | 2017-01-01 | Springer International Publishing | Cham | 97-117 | 2025-05-15 |
Indexing Information
Published: 2017-01
DOI 10.1007/978-3-319-63387-9_5 ISBN 978-3-319-63387-9 #Airborne-Collision-Avoidance-System, #Deep-Neural-Networks-DNNs, #Rectified-Linear-Unit-ReLU, #ReLU-Function, #Satisfiability-Modulo-Theories-SMT
#InFirstPass
[!Abstract] Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees about their behavior. We present a novel, scalable, and efficient technique for verifying properties of deep neural networks (or providing counter-examples). The technique is based on the simplex method, extended to handle the non-convex Rectified Linear Unit (ReLU) activation function, which is a crucial ingredient in many modern neural networks. The verification procedure tackles neural networks as a whole, without making any simplifying assumptions. We evaluated our technique on a prototype deep neural network implementation of the next-generation airborne collision avoidance system for unmanned aircraft (ACAS Xu). Results show that our technique can successfully prove properties of networks that are an order of magnitude larger than the largest networks verified using existing methods.>[!seealso] Related Papers
Annotations
Notes
!Reluplex- An Efficient SMT Solver for Verifying Deep Neural Networks-Note
Highlights From Zotero
[!done] Important The technique is basedon the simplex method, extended to handle the non-convex RectifiedLinear Unit (ReLU ) activation function, which is a crucial ingredientin many modern neural networks. The verification procedure tacklesneural networks as a whole, without making any simplifying assump-tions. We evaluated our technique on a prototype deep neural networkimplementation of the next-generation airborne collision avoidance sys-tem for unmanned aircraft (ACAS Xu). Results show that our techniquecan successfully prove properties of networks that are an order of mag-nitude larger than the largest networks verified using existing methods. 2025-05-13 4:42 pm
[!done] Important Past efforts at verifying properties of DNNs with ReLUs have had to make significant simplifying assumptions [3,10]—for instance, by considering only small input regions in which all ReLUs are fixed at either the activeor inactive state [3], hence making the problem convex but at the cost of beingable to verify only an approximation of the desired property 2025-05-13 4:45 pm
[!tip] Brilliant We propose a novel, scalable, and efficient algorithm for verifying propertiesof DNNs with ReLUs. We address the issue of the activation functions headon, by extending the simplex algorithm—a standard algorithm for solving LP instances—to support ReLU constraints. This is achieved by leveraging the piece-wise linear nature of ReLUs and attempting to gradually satisfy the constraintsthat they impose as the algorithm searches for a feasible solution. We call the algorithm Reluplex, for “ReLU with Simplex”. 2025-05-13 4:46 pm
[!highlight] Highlight The problem’s NP-completeness means that we must expect the worst-case performance of the algorithm to be poor. However, as is often the case with SAT and SMT solvers, the performance in practice can be quite reasonable; 2025-05-13 4:47 pm
[!highlight] Highlight Our contributions can be summarized as follows. We (i) present Reluplex,an SMT solver for a theory of linear real arithmetic with ReLU constraints; (ii) show how DNNs and properties of interest can be encoded as inputs to Reluplex; (iii) discuss several implementation details that are crucial to performance and scalability, such as the use of floating-point arithmetic, bound derivation for ReLU variables, and conflict analysis; and (iv) conduct a thorough evaluationon the DNN implementation of the prototype ACAS Xu system, demonstratingthe ability of Reluplex to scale to DNNs that are an order of magnitude largerthan those that can be analyzed using existing techniques. 2025-05-13 4:48 pm
Follow-Ups
[!example] are trained over a finiteset of inputs and outputs and are expected to generalize, i.e. to behave correctly for previously-unseen inputs. However, it has been observed that DNNs can react in unexpected and incorrect ways to even slight perturbations of their inputs [34].
- #Follow-Up
[!example] DNN verification is experi-mentally beyond the reach of general-purpose tools such as linear programming(LP) solvers or existing satisfiability modulo theories (SMT) solvers [3,10,31], and thus far, dedicated tools have only been able to handle very small networks (e.g. a single hidden layer with only 10 to 20 hidden nodes [30,31]).
- #Follow-Up