Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy desired constraints or exhibit desired properties is difficult. In practice, expensive heuristic search or reinforcement learning algorithms are often employed. In this paper, we investigate the use of conditional generative models which directly attack this inverse problem, by modeling the distribution of discrete structures given properties of interest. Unfortunately, the maximum likelihood training of such models often fails with the samples from the generative model inadequately respecting the input properties. To address this, we introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We avoid high-variance score-function estimators that would otherwise be required by sampling from an approximation to the normalized rewards, allowing simple Monte Carlo estimation of model gradients. We test our methodology on two tasks: generating molecules with user-defined properties and identifying short python expressions which evaluate to a given target value. In both cases, we find improvements over maximum likelihood estimation and other baselines.

Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For example, when programming a neural network, conditionals and iteration cannot be used everywhere; they can break the derivatives necessary for gradient-based learning to work. This limits the class of differentiable algorithms we can directly express, imposing restraints on how we build neural networks and differentiable programs more generally. However, these restraints are not fundamental. Recent work shows conditionals can be first-class, by compiling them into differentiable form as linear neurons. Similarly, this work shows iteration can be first-class -- by compiling to linear recurrent neurons. We present a minimal typed, higher-order and linear programming language with iteration called $\textsf{Cajal}\scriptstyle(\mathbb{\multimap}, \mathbb{2}, \mathbb{N})$. We prove its programs compile correctly to recurrent neurons, allowing discrete algorithms to be expressed in a differentiable form compatible with gradient-based learning. With our implementation, we conduct two experiments where we link these recurrent neurons against a neural network solving an iterative image transformation task. This determines part of its function prior to learning. As a result, the network learns faster and with greater data-efficiency relative to a neural network programmed without first-class iteration. A key lesson is that recurrent neurons enable a rich interplay between learning and the discrete structures of ordinary programming.

Weaknesses: The improvements over Maximum Likelihood are very moderate and no comparisons are made with more computationally expensive RL approaches (at least on the small QM9 dataset it would be interesting). It would be very interesting to see the performance tradeoff between the proposed approach and the Monte Carlo estimation of the expectation term in Eq 11. One of the promising features of generative algorithms for molecules is their supposed ability to capture a complex statistical distribution of plausible molecules that can be made, paid for, stored in a vial, etc. The approximately 100 million molecules that have been made and the couple of billions that can be confidently said to be makeable are samples from that distribution. It is not clear how much of chemical space is in that manifold.

The authors propose an RL-inspired way of fitting a conditional generative model to the training data with the aim of generating discrete structures, such as molecules, satisfying some desired properties. Unlike policy gradients in RL, the proposed algorithm does not require sampling from the model/policy, instead approximating the expectation of interest using the training data reweighted with the normalized rewards. This is done to avoid high gradient variance of policy gradient algorithms. The reviewers liked the novelty of the approach to this important problem. While the experimental results are not spectacular and there were some concerns about missing RL baselines and connections to reward-augmented ML, the author response addressed them in large part.

Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy desired constraints or exhibit desired properties is difficult. In practice, expensive heuristic search or reinforcement learning algorithms are often employed. In this paper, we investigate the use of conditional generative models which directly attack this inverse problem, by modeling the distribution of discrete structures given properties of interest. Unfortunately, the maximum likelihood training of such models often fails with the samples from the generative model inadequately respecting the input properties.

This paper devises a novel kernel function for structured natural language data. In the field of Natural Language Processing, feature extraction consists of the following two steps: (1) syntactically and semantically analyzing raw data, i.e., character strings, then representing the results as discrete structures, such as parse trees and dependency graphs with part-of-speech tags; (2) creating (possibly high-dimensional) numerical feature vectors from the discrete structures. The new kernels, called Hier- archical Directed Acyclic Graph (HDAG) kernels, directly accept DAGs whose nodes can contain DAGs. HDAG data structures are needed to fully reflect the syntactic and semantic structures that natural language data inherently have. In this paper, we define the kernel function and show how it permits efficient calculation.

Kernels on discrete structures evaluate pairwise similarities between objects which capture semantics and inherent topology information. Existing kernels on discrete structures are only developed by topology information(such as adjacency matrix of graphs), without considering original attributes of objects. This paper proposes a two-phase paradigm to aggregate comprehensive information on discrete structures leading to a Discount Markov Diffusion Learnable Kernel (DMDLK). Specifically, based on the underlying projection of DMDLK, we design a Simple Hypergraph Kernel Convolution (SHKC) for hidden representation of vertices. SHKC can adjust diffusion steps rather than stacking convolution layers to aggregate information from long-range neighborhoods which prevents over-smoothing issues of existing hypergraph convolutions. Moreover, we utilize the uniform stability bound theorem in transductive learning to analyze critical factors for the effectiveness and generalization ability of SHKC from a theoretical perspective. The experimental results on several benchmark datasets for node classification tasks verified the superior performance of SHKC over state-of-the-art methods.

We propose an algorithmic approach for synthesizing linear hybrid automata from time-series data. Unlike existing approaches, our approach provides a whole family of models. Each model in the family is guaranteed to capture the input data up to a precision error {\epsilon}, in the following sense: For each time series, the model contains an execution that is {\epsilon}-close to the data points. Our construction allows to effectively choose a model from this family with minimal precision error {\epsilon}. We demonstrate the algorithm's efficiency and its ability to find precise models in two case studies.

Genetic algorithms (GA) are a family of heuristics which are empirically good at providing a decent answer in many cases, although they are rarely the best option for a given domain. You mention derivative-based algorithms, but even in the absence of derivatives there are plenty of derivative-free optimization algorithms that perform way better than GAs. See this and this answer for some ideas. What many standard optimization algorithms have in common (even derivative-free methods) is the assumption that the underlying space is a smooth manifold (perhaps with a few discrete dimensions), and the function to optimize is somewhat well-behaved. However, not all functions are defined on a smooth manifold.

This paper proposes a new approach to feature selection based on a statistical feature mining technique for sequence and tree kernels. Since natural language data take discrete structures, convolution kernels, such as sequence and tree kernels, are advantageous for both the concept and accuracy of many natural language processing tasks. However, experiments have shown that the best results can only be achieved when limited small substructures are dealt with by these kernels. This paper discusses this issue of convolution kernels and then proposes a statistical feature selection that enable us to use larger substructures effectively. The proposed method, in order to execute efficiently, can be embedded into an original kernel calculation process by using substructure mining algorithms. Experiments on real NLP tasks confirm the problem in the conventional method and compare the performance of a conventional method to that of the proposed method.