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Due to the surge of cloud-assisted AI services, the problem of designing resilient prediction serving systems that can effectively cope with stragglers and minimize response delays has attracted much interest. The common approach for tackling this problem is replication which assigns the same prediction task to multiple workers. This approach, however, is inefficient and incurs significant resource overheads. Hence, a learning-based approach known as parity model (ParM) has been recently proposed which learns models that can generate ``parities’’ for a group of predictions to reconstruct the predictions of the slow/failed workers. While this learning-based approach is more resource-efficient than replication, it is tailored to the specific model hosted by the cloud and is particularly suitable for a small number of queries (typically less than four) and tolerating very few stragglers (mostly one). Moreover, ParM does not handle Byzantine adversarial workers. We propose a different approach, named Approximate Coded Inference (ApproxIFER), that does not require training any parity models, hence it is agnostic to the model hosted by the cloud and can be readily applied to different data domains and model architectures. Compared with earlier works, ApproxIFER can handle a general number of stragglers and scales significantly better with the number of queries. Furthermore, ApproxIFER is robust against Byzantine workers. Our extensive experiments on a large number of datasets and model architectures show significant degraded mode accuracy improvement by up to 58% over ParM.