Table 10 presents the hyperparameters used to train dPads programmatic models.

Differentiable programs have recently attracted much interest due to their interpretability, compositionality, and their efficiency to leverage differentiable training. However, synthesizing differentiable programs requires optimizing over a combinatorial, rapidly exploded space of program architectures. Despite the development of effective pruning heuristics, previous works essentially enumerate the discrete search space of program architectures, which is inefficient. We propose to encode program architecture search as learning the probability distribution over all possible program derivations induced by a context-free grammar. This allows the search algorithm to efficiently prune away unlikely program derivations to synthesize optimal program architectures. To this end, an efficient gradient-descent based method is developed to conduct program architecture search in a continuous relaxation of the discrete space of grammar rules. Experiment results on four sequence classification tasks demonstrate that our program synthesizer excels in discovering program architectures that lead to differentiable programs with higher F1 scores, while being more efficient than state-of-the-art program synthesis methods.

This relaxed program is differentiable and can be trained end-to-end, and the resulting training loss is an approximately admissible heuristic that can guide the combinatorial search.

Table 10 presents the hyperparameters used to train dPads programmatic models.

Composing language models (LMs) into multi-step language programs and automatically optimizing their modular prompts is now a mainstream paradigm for building AI systems, but the tradeoffs in this space have only scarcely been studied before. We introduce LangProBe, the first large-scale benchmark for evaluating the architectures and optimization strategies for language programs, with over 2000 combinations of tasks, architectures, optimizers, and choices of LMs. Using LangProBe, we are the first to study the impact of program architectures and optimizers (and their compositions together and with different models) on tradeoffs of quality and cost. We find that optimized language programs offer strong cost--quality Pareto improvement over raw calls to models, but simultaneously demonstrate that human judgment (or empirical decisions) about which compositions to pursue is still necessary for best performance. We will open source the code and evaluation data for LangProBe.

Differentiable programs have recently attracted much interest due to their interpretability, compositionality, and their efficiency to leverage differentiable training. However, synthesizing differentiable programs requires optimizing over a combinatorial, rapidly exploded space of program architectures. Despite the development of effective pruning heuristics, previous works essentially enumerate the discrete search space of program architectures, which is inefficient. We propose to encode program architecture search as learning the probability distribution over all possible program derivations induced by a context-free grammar. This allows the search algorithm to efficiently prune away unlikely program derivations to synthesize optimal program architectures.

Toward combining inductive reasoning with perception abilities, we develop techniques for neurosymbolic program synthesis where perceptual input is first parsed by neural nets into a low-dimensional interpretable representation, which is then processed by a synthesized program. We explore several techniques for relaxing the problem and jointly learning all modules end-to-end with gradient descent: multitask learning; amortized inference; overparameterization; and a differentiable strategy for penalizing lengthy programs. Collectedly this toolbox improves the stability of gradient-guided program search, and suggests ways of learning both how to perceive input as discrete abstractions, and how to symbolically process those abstractions as programs.

Physics-informed Neural Networks (PINNs) have been widely used to obtain accurate neural surrogates for a system of Partial Differential Equations (PDE). One of the major limitations of PINNs is that the neural solutions are challenging to interpret, and are often treated as black-box solvers. While Symbolic Regression (SR) has been studied extensively, very few works exist which generate analytical expressions to directly perform SR for a system of PDEs. In this work, we introduce an end-to-end framework for obtaining mathematical expressions for solutions of PDEs. We use a trained PINN to generate a dataset, upon which we perform SR. We use a Differentiable Program Architecture (DPA) defined using context-free grammar to describe the space of symbolic expressions. We improve the interpretability by pruning the DPA in a depth-first manner using the magnitude of weights as our heuristic. On average, we observe a 95.3% reduction in parameters of DPA while maintaining accuracy at par with PINNs. Furthermore, on an average, pruning improves the accuracy of DPA by 7.81% . We demonstrate our framework outperforms the existing state-of-the-art SR solvers on systems of complex PDEs like Navier-Stokes: Kovasznay flow and Taylor-Green Vortex flow. Furthermore, we produce analytical expressions for a complex industrial use-case of an Air-Preheater, without suffering from performance loss viz-a-viz PINNs.