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Title: Neural network gradient-based learning of black-box function interfaces

Paper content:
Deep neural networks work well at approximating complicated functions when provided with data and trained by gradient descent methods.
At the same time, there is a vast amount of existing functions that programmatically solve different tasks in a precise manner eliminating the need for training.
In many cases, it is possible to decompose a task to a series of functions, of which for some we may prefer to use a neural network to learn the functionality, while for others the preferred method would be to use existing black-box functions.
We propose a method for end-to-end training of a base neural network that integrates calls to existing black-box functions.
We do so by approximating the black-box functionality with a differentiable neural network in a way that drives the base network to comply with the black-box function interface during the end-to-end optimization process.
At inference time, we replace the differentiable estimator with its external black-box non-differentiable counterpart such that the base network output matches the input arguments of the black-box function.
Using this ``Estimate and Replace'' paradigm, we train a neural network, end to end, to compute the input to black-box functionality while eliminating the need for intermediate labels.
We show that by leveraging the existing precise black-box function during inference, the integrated model generalizes better than a fully differentiable model, and learns more efficiently compared to RL-based methods.
End-to-end supervised learning with deep neural networks (DNNs) has taken the stage in the past few years, achieving state-of-the-art performance in multiple domains including computer vision BID25 , natural language processing BID23 BID10 , and speech recognition BID29 .
Many of the tasks addressed by DNNs can be naturally decomposed to a series of functions.
In such cases, it might be advisable to learn neural network approximations for some of these functions and use precise existing functions for others.
Examples of such tasks include Semantic Parsing and Question Answering.
Since such a decomposition relies partly on precise functions, it may lead to a superior solution compared to an approximated one based solely on a learned neural model.
Decomposing a solution into trainable networks and existing functions requires matching the output of the networks to the input of the existing functions, and vice-versa.
The input and output are defined by the existing functions' interface.
We shall refer to these functions as black-box functions (bbf), focusing only on their interface.
For example, consider the question: "Is 7.2 greater than 4.5?"
Given that number comparison is a solved problem in symbolic computation, a natural solution would be to decompose the task into a two-step process of
(i) converting the natural language to an executable program, and
(ii) executing the program on an arithmetic module.
While a DNN may be a good fit forWe propose an alternative approach called Estimate and Replace that finds a differentiable function approximation, which we term black-box estimator, for estimating the black-box function.
We use the black-box estimator as a proxy to the original black-box function during training, and by that allow the learnable parts of the model to be trained using gradient-based optimization.
We compensate for not using any intermediate labels to direct the learnable parts by using the black-box function as an oracle for training the black-box estimator.
During inference, we replace the black-box estimator with the original non-differentiable black-box function.End-to-end training of a solution composed of trainable components and black-box functions poses several challenges we address in this work-coping with non-differentiable black-box functions, fitting the network to call these functions with the correct arguments, and doing so without any intermediate labels.
Two more challenges are the lack of prior knowledge on the distribution of inputs to the black-box function, and the use of gradient-based methods when the function approximation is near perfect and gradients are extremely small.
This work is organized as follows: In Section 2, we formulate the problem of decomposing the task to include calls to a black-box function.
Section 3 describes the network architecture and training procedures.
In Section 4, we present experiments and comparison to Policy Gradient-based RL, and to fully neural models.
We further discuss the potential and benefits of the modular nature of our approach in Section 6.
Interpretability via Composability Lipton (2016) identifies composability as a strong contributor to model interpretability.
They define composability as the ability to divide the model into components and interpret them individually to construct an explanation from which a human can predict the model's output.
The Estimate and Replace approach solves the black-box interface learning problem in a way that is modular by design.
As such, it provides an immediate interpretability benefit.
Training a model to comply with a well-defined and well-known interface inherently supports model composability and, thus, directly contributes to its interpretability.For example, suppose you want to let a natural language processing model interface with a WordNet service to receive additional synonym and antonym features for selected input words.
Because the WordNet interface is interpretable, the intermediate output of the model to the WordNet service (the words for which the model requested additional features) can serve as an explanation to the model's final prediction.
Knowing which words the model chose to obtain additional features for gives insight to how it made its final decision.Reusability via Composability An additional clear benefit of model composability in the context of our solution is reusability.
Training a model to comply with a well-defined interface induces well-defined module functionality which is a necessary condition for module reuse.
Current solutions for learning using black-box functionality in neural network prediction have critical limitations which manifest themselves in at least one of the following aspects:
(i) poor generalization,
(ii) low learning efficiency,
(iii) under-utilization of available optimal functions, and
(iv) the need for intermediate labels.In this work, we proposed an architecture, termed EstiNet, and a training and deployment process, termed Estimate and Replace, which aim to overcome these limitations.
We then showed empirical results that validate our approach.Estimate and Replace is a two-step training and deployment approach by which we first estimate a given black-box functionality to allow end-to-end training via back-propagation, and then replace the estimator with its concrete black-box function at inference time.
By using a differentiable estimation module, we can train an end-to-end neural network model using gradient-based optimization.
We use labels that we generate from the black-box function during the optimization process to compensate for the lack of intermediate labels.
We show that our training process is more stable and has lower sample complexity compared to policy gradient methods.
By leveraging the concrete black-box function at inference time, our model generalizes better than end-to-end neural network models.
We validate the advantages of our approach with a series of simple experiments.
Our approach implies a modular neural network that enjoys added interpretability and reusability benefits.Future Work We limit the scope of this work to tasks that can be solved with a single black-box function.
Solving the general case of this problem requires learning of multiple black-box interfaces, along unbounded successive calls, where the final prediction is a computed function over the output of these calls.
This introduces several difficult challenges.
For example, computing the final prediction over a set of black-box functions, rather than a direct prediction of a single one, requires an additional network output module.
The input of this module must be compatible with the output of the previous layer, be it an estimation function at training time, or its black-box function counterpart at inference time, which belong to different distributions.
We reserve this area of research for future work.As difficult as it is, we believe that artificial intelligence does not lie in mere knowledge, nor in learning from endless data samples.
Rather, much of it is in the ability to extract the right piece of information from the right knowledge source for the right purpose.
Thus, training a neural network to intelligibly interact with black-box functions is a leap forward toward stronger AI.

assistant: text: Training DNNs to interface w\ black box functions w\o intermediate labels by using an estimator sub-network that can be replaced with the black box after training