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Cloud applications based on the "Functions as a Service" (FaaS) paradigm have become very popular. Yet, due to their stateless nature, they must frequently interact with an external data store, which limits their performance. To mitigate this issue, we introduce OFC, a transparent, vertically and horizontally elastic in-memory caching system for FaaS platforms, distributed over the worker nodes. OFC provides these benefits cost-effectively by exploiting two common sources of resource waste: (i) most cloud tenants overprovision the memory resources reserved for their functions because their footprint is non-trivially input-dependent and (ii) FaaS providers keep function sandboxes alive for several minutes to avoid cold starts. Using machine learning models adjusted for typical function input data categories (e.g., multimedia formats), OFC estimates the actual memory resources required by each function invocation and hoards the remaining capacity to feed the cache. We build our OFC prototype based on enhancements to the OpenWhisk FaaS platform, the Swift persistent object store, and the RAM-Cloud in-memory store. Using a diverse set of workloads, we show that OFC improves by up to 82 % and 60 % respectively the execution time of single-stage and pipelined functions.