user: text: Write a concise one-sentence TLDR summary of the scientific paper content below.

Title: Training Neural Machines with Partial Traces

Paper content:
We present a novel approach for training neural abstract architectures which in- corporates (partial) supervision over the machine’s interpretable components.
To cleanly capture the set of neural architectures to which our method applies, we introduce the concept of a differential neural computational machine (∂NCM) and show that several existing architectures (e.g., NTMs, NRAMs) can be instantiated as a ∂NCM and can thus benefit from any amount of additional supervision over their interpretable components.
Based on our method, we performed a detailed experimental evaluation with both, the NTM and NRAM architectures, and showed that the approach leads to significantly better convergence and generalization capabilities of the learning phase than when training using only input-output examples.
Recently, there has been substantial interest in neural abstract machines that can induce programs from examples BID2 ; BID4 ; ; BID7 ; BID11 ; BID14 ; BID18 ; BID20 ; BID23 ; BID24 .
While significant progress has been made towards learning interesting algorithms BID8 , ensuring the training of these machines converges to the desired solution can be very challenging.
Interestingly however, even though these machines differ architecturally, they tend to rely on components (e.g., neural memory) that are more interpretable than a typical neural network (e.g., an LSTM).
A key question then is:Can we somehow provide additional amounts of supervision for these interpretable components during training so to bias the learning towards the desired solution?In
this work we investigate this question in depth. We
refer to the type of supervision mentioned above as partial trace supervision, capturing the intuition that more detailed information, beyond inputoutput examples, is provided during learning. To
study the question systematically, we introduce the notion of a differential neural computational machine (∂NCM), a formalism which allows for clean characterization of the neural abstract machines that fall inside our class and that can benefit from any amount of partial trace information. We
show that common architectures such as Neural Turing Machines (NTMs) and Neural Random Access Machines (NRAMs) can be phrased as ∂NCMs, useful also because these architectures form the basis for many recent extensions, e.g., BID8 ; BID9 ; BID11 . We
also explain why other machines such as the Neural Program Interpreter (NPI) BID18 or its recent extensions (e.g., the Neural Program Lattice BID15 ) cannot be instantiated as an ∂NCM and are thus restricted to require large (and potentially prohibitive) amounts of supervision. We
believe the ∂NCM abstraction is a useful step in better understanding how different neural abstract machines compare when it comes to additional supervision. We
then present ∂NCM loss functions which abstractly capture the concept of partial trace information and show how to instantiate these for both the NTM and the NRAM. We
also performed an extensive evaluation for how partial trace information affects training in both architectures. Overall
, our experimental results indicate that the additional supervision can substantially improve convergence while leading to better generalization and interpretability.To provide an intuition for the problem we study in this work, consider the simple task of training an NTM to flip the third bit in a bit stream (called Flip3rd) -such bitstream tasks have been extensively studied in the area of program synthesis (e.g., BID10 ; BID17 ). An example
input-output pair for this task could be examples, our goal is to train an NTM that solves this task. An example
NTM that generalizes well and is understandable is shown in FIG0 . Here, the
y-axis is time (descending), the x-axis is the accessed memory location, the white squares represent the write head of the NTM, and the orange squares represent the read head. As we can
see, the model writes the input sequence to the tape and then reads from the tape in the same order. However,
in the absence of richer supervision, the NTM (and other neural architectures) can easily overfit to the training set -an example of an overfitting NTM is shown in FIG0 . Here, the
traces are chaotic and difficult to interpret. Further,
even if the NTM generalizes, it can do so with erratic reads and writes, an example of which is shown in FIG0 . Here, the
NTM learns to read from the third bit (circled) with a smaller weight than from other locations, and also reads and writes erratically near the end of the sequence. This model
is less interpretable than the one in FIG0 because it is unclear how the model knows which the third bit actually is, or why a different read weight would help flip that bit.In this work we will develop principled ways for guiding the training of a neural abstract machine towards the behavior shown in FIG0 . For instance
, for Flip3rd, providing partial trace information on the NTM's read heads for 10% of the input-output examples is sufficient to bias the learning towards the NTM shown in FIG0 100% of the time.
We presented a method for incorporating (any amount of) additional supervision into the training of neural abstract machines.
The basic idea was to provide this supervision (called partial trace information) over the interpretable components of the machine and to thus more effectively guide the learning towards the desired solution.
We introduced the ∂NCM architecture in order to precisely capture the neural abstract machines to which our method applies.
We showed how to formulate partial trace information as abstract loss functions, how to instantiate common neural architectures such as NTMs and NRAMs as ∂NCMs and concretize the ∂NCM loss functions.
Our experimental results indicate that partial trace information is effective in biasing the learning of both NTM's and NRAM's towards better converge, generalization and interpretability of the resulting models.

assistant: text: We increase the amount of trace supervision possible to utilize when training fully differentiable neural machine architectures.