Our results settle the complexity status regarding these parameters number of dimensions and number of ReLUs if the network is assumed to compute the ReLU case, we show fixed-parameter tractability for the combined parameter four ReLUs (or two linear threshold neurons) with zero training error. Finally, in We also answer a question by Froese et al. [2022, JAIR] proving W[1]-hardness for dimensions, which excludes any polynomial-time algorithm for constant dimension. Khalife and Basu [2022, IPCO] showing that both problems are NP-hard for two eral questions are still open. We answer questions by Arora et al. [2018, ICLR] and complexity of these problems has been studied numerous times in recent years, sevsidering ReLU and linear threshold activation functions.

The simultaneous rise of machine learning as a service and concerns over user privacy have increasingly motivated the need for private inference (PI). While recent work demonstrates PI is possible using cryptographic primitives, the computational overheads render it impractical. State-of-art deep networks are inadequate in this context because the source of slowdown in PI stems from the ReLU operations whereas optimizations for plaintext inference focus on reducing FLOPs. In this paper we re-think ReLU computations and propose optimizations for PI tailored to properties of neural networks. Specifically, we reformulate ReLU as an approximate sign test and introduce a novel truncation method for the sign test that significantly reduces the cost per ReLU. These optimizations result in a specific type of stochastic ReLU. The key observation is that the stochastic fault behavior is well suited for the fault-tolerant properties of neural network inference. Thus, we provide significant savings without impacting accuracy. We collectively call the optimizations Circa and demonstrate improvements of up to 4.7 storage and 3 runtime over baseline implementations; we further show that Circa can be used on top of recent PI optimizations to obtain 1.8 additional speedup.

We consider the problem of learning function classes computed by neural networks with various activations (e.g. ReLU or Sigmoid), a task believed to be computationally intractable in the worst-case. A major open problem is to understand the minimal assumptions under which these classes admit provably efficient algorithms. In this work we show that a natural distributional assumption corresponding to {\em eigenvalue decay} of the Gram matrix yields polynomial-time algorithms in the non-realizable setting for expressive classes of networks (e.g.

Wealso compare CoPrivwith SOTA network optimization methods, including SNL, MetaPruning, etc. CoPriv achieves 9.98 and 3.88 online and total communication reduction with a higher accuracy compared to SNL,respectively.

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