Paper:
Learning to Remember More with Less Memorization
Memory-augmented neural networks consisting of a neural controller and an external memory have shown potentials in long-term sequential learning. Current RAM-like memory models maintain memory accessing every timesteps, thus they do not effectively leverage the short-term memory held in the controller. We hypothesize that this scheme of writing is suboptimal in memory utilization and introduces redundant computation. To validate our hypothesis, we derive a theoretical bound on the amount of information stored in a RAM-like system and formulate an optimization problem that maximizes the bound. The proposed solution dubbed Uniform Writing is proved to be optimal under the assumption of equal timestep contributions. To relax this assumption, we introduce modifications to the original solution, resulting in a solution termed Cached Uniform Writing. This method aims to balance between maximizing memorization and forgetting via overwriting mechanisms. Through an extensive set of experiments, we empirically demonstrate the advantages of our solutions over other recurrent architectures, claiming the state-of-the-arts in various sequential modeling tasks.

Review:
This paper deals with Memory Augmnted Neural Networks (MANN) and introduces an algorithm which allows full writes to the dense memory to be only exectued every L timesteps. The controller produces a hidden output at most timestps, whih is appended to a cache. Every L steps, soft attention is used to combine this cache of N hidden states to a single one, and then this is used as the input hidden state for the controller, with the outputs performing a write in the full memory M, along with clearing the cache.
The authors first derive "Uniform Writing" (UW) which updates the memory at regular intervals instead of every timestep. The derivation is based on the "contribution" which is norm of the gradient of some input timestep to some hidden state (potentially at a different timestep). I am not clear on whether this terminology for the quantity is novel, if this is the case maybe the authors should state this more clearly. UW says that if all timesteps are equally important, and only D writes can be made in a sequence of length T, then writes should be done every T/(D+1) steps. I have not checked the proof in detail but this seems reasonable that it would maximise the contribution quantity introduced. I am less clear on whether this is obviously the right thing to do - sometimes this value is referred to in relation to information, but that term does not strictly seem to be being used in the information theory sense (no mention of bits or nats anywhere). Regardless, as the authors point out, in real problems there are obviously timesteps which have less or no useful information, and clearly UW is mostly defined in order to build towards CUW.
CUW expands on UW by adding the cache of different hidden states, and using soft attention over them. This feels like a reasonable step, although I would presume there are times when the L hidden states were collected over timesteps with no information, and so the resulting write is not that useful, and times when all of hte L timesteps contain different useful information. In these circumstances it seems like the problem of getting the *useful* information into the memory is still present, as the single write done with the averaged hidden state will need to contain lots of information, which may be more ideal written with several timesteps.
The experiments are well described and overall the paper seems reproducable. The standard toy datasets of copy / reverse / sinusoid are used. The results are interesting - regular DNC with memory size 50 performs surprisingly badly on clean Sinusoid, my guess would be that with hyperparameter tuning this could be improved upon. I'm not sure that using exactly the same hyperparameters for a wide variety of models is appropriate - even with optimizers like Adam and RMSProp, I would want to see at least some sweeping for the best hyperparams, and then graphs like figure 3 should show error bars averaged across multiple runs with the best per-model hyperparameters. However, The DNC with CUW seems to perform well across all synthetic tasks.
There is no mention of Adaptive Computation Time/ACT (Graves, https://arxiv.org/abs/1603.08983) throughout the paper, which is surprising considering Alex Graves' models form two of the baselines used throughout the paper. ACT aims to execute an RNN a variable number of times, usually to do >1 timestep of processing for a single timestep of input. In the context of this paper, I believe it could be adapted to do either zero or one steps of computation per timestep, and that would yield a very comparable network where the LSTM controller always executes, and writes to the memory only happen sometimes. Given that it allows a learned process to decide whether to write, as opposed to having a fixed L which separates full writes, this should have the potential to outperform CUW, as it could learn that at certain times, writes must happen at every step. In my view ACT is attempting to solve essentially the same problem as this paper, so it should either be included as a baseline, or the manuscript should be updated to explain why this is not an appropriate comparison.
I think this is an interesting paper, trying to make progress on an important problem. The results look good, but I can only give a borderline score due to missing ACT numbers, and a few other unclear points. The addition of ACT experiments, and error bars on certain results, would change my mind here.
Notes:
"No solution has been proposed to help MANNs handle ultra long sequence" - (Rae et al 2016) is an attempt to do this, by improving the complexity of reads / writes. This allows bigger memory and longer sequences to be processed.
"Current MANNS only support dense writing" - presumably this means dense as in 'every timestep', but this terminology is overloaded - you could consider NTM / DNC as doing dense writing, and then work of Rae et al 2016 doing sparse writing.
In my experience training these kind of RNNs can have reasonably high variance across seeds - figures 2 & 3 should have error bars, and especially Table 4 as that contains the most important results. Getting 99 percent accuracy when previous SOTA is only 0.1% lower is only really meaningful if the standard deviation across seeds is very small.
Appendix A: the 'by induction' result - I believe there is an error, it should be:
h_t = \sigma_{i=1}^t U_{t-i}W x_i + C
As W is applied to inputs, before the repeated applications of U? I believe the rest of the derivation still holds the same, after the correction.