We thank the reviewers for their insightful feedback. In the following, we address their concerns and questions. ": There is a big misunderstanding. The table above shows that the proposed model performs best. ": Deep SVDD uses only one center and one layer, while we have multiple centers ( 's, the key challenge is on what contribution Indeed, these have been discussed at lines 115-116 and 126-128.

Real-world timeseries have complex underlying temporal dynamics and the detection of anomalies is challenging.

To date, this advantage of RNNs over CNNs is entirely theoretical.

Combinatorial optimization problems can be solved by heuristic algorithms such as simulated annealing (SA) which aims to find the optimal solution within a large search space through thermal fluctuations. The algorithm generates new solutions through Markov-chain Monte Carlo techniques. This sampling scheme can result in severe limitations, such as slow convergence and a tendency to stay within the same local search space at small temperatures. To overcome these shortcomings, we use the variational classical annealing (VCA) framework [1] that combines autoregressive recurrent neural networks (RNNs) with traditional annealing to sample solutions that are uncorrelated. In this paper, we demonstrate the potential of using VCA as an approach to solving real-world optimization problems. We explore VCA's performance in comparison with SA at solving three popular optimization problems: the maximum cut problem (Max-Cut), the nurse scheduling problem (NSP), and the traveling salesman problem (TSP). For all three problems, we find that VCA outperforms SA on average in the asymptotic limit by one or more orders of magnitude in terms of relative error. Interestingly, we reach large system sizes of up to 256 cities for the TSP. We also conclude that in the best case scenario, VCA can serve as a great alternative when SA fails to find the optimal solution.