Inference using deep neural networks is often outsourced to the cloud since it is a computationally demanding task. However, this raises a fundamental issue of trust. How can a client be sure that the cloud has performed inference correctly? A lazy cloud provider might use a simpler but less accurate model to reduce its own computational load, or worse, maliciously modify the inference results sent to the client. We propose SafetyNets, a framework that enables an untrusted server (the cloud) to provide a client with a short mathematical proof of the correctness of inference tasks that they perform on behalf of the client. Specifically, SafetyNets develops and implements a specialized interactive proof (IP) protocol for verifiable execution of a class of deep neural networks, i.e., those that can be represented as arithmetic circuits. Our empirical results on three-and four-layer deep neural networks demonstrate the run-time costs of SafetyNets for both the client and server are low.

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After a Falcon 9 rocket stage burned up in the atmosphere, vaporised lithium and other metals drifted over Europe. A SpaceX rocket that burned up after re-entering the atmosphere unleashed a plume of vaporised metals over Europe, a type of pollution that is expected to increase as spacecraft and satellites multiply. The upper stage of a Falcon 9, which is designed to splash down in the Pacific Ocean for possible re-use, lost control due to engine failure and fell from orbit over the north Atlantic in February 2025. We're finally solving the puzzle of how clouds will affect our climate People across Europe saw fiery debris streaking through the sky, some of which crashed behind a warehouse in Poland. Seeing the news, Robin Wing at the Leibniz Institute of Atmospheric Physics in Germany and his colleagues turned on their lidar, an instrument for atmospheric sensing.

In this Appendix, we will derive the fixed-point equations for the order parameters presented in the main text, following and generalising the analysis in Ref. [ Saddle-point equations The saddle-point equations are derived straightforwardly from the obtained free energy functionally extremising with respect to all parameters. The zero-regularisation limit of the logistic loss can help us study the separability transition. N 5 + \ 1 p 0, 1 d 5. (66) As a result, given that \ 2( 0, 1 ], the smaller value for which E is finite is U This result has been generalised immediately afterwards by Pesce et al. Ref. [ 59 ] for the Gaussian case, we can obtain the following fixed-point equations, 8 > > > > > >< > > > > > >: E = Mean universality Following Ref. [ In our case, this condition is simpler than in Ref. [ We see that mean-independence in this setting is indeed verified. Numerical experiments Numerical experiments regarding the quadratic loss with ridge regularisation were performed by computing the Moore-Penrose pseudoinverse solution.

Then, to tackle the benchmark mentioned above, we present the Point-In-Context (PIC) to explore in-context learning for 3D point clouds.

The level sets of a Deep Neural Network (DNN) are known to capture important characteristics andproperties ofthenetwork.

Neural Information Processing Systems http://nips.cc/