Neurosymbolic Programming for Science Jennifer J. Sun CaltechMegan Tjandrasuwita

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Neurosymbolic Programming for Science

Jennifer J. Sun∗

Caltech

Megan Tjandrasuwita∗

MIT CSAIL

Atharva Sehgal∗

UT Austin

Armando Solar-Lezama

MIT CSAIL

Swarat Chaudhuri

UT Austin

Yisong Yue

Caltech

Omar Costilla-Reyes †

MIT CSAIL

Abstract

Neurosymbolic Programming (NP) techniques have the potential to accelerate

scientiﬁc discovery. These models combine neural and symbolic components to

learn complex patterns and representations from data, using high-level concepts or

known constraints. NP techniques can interface with symbolic domain knowledge

from scientists, such as prior knowledge and experimental context, to produce

interpretable outputs. We identify opportunities and challenges between current NP

models and scientiﬁc workﬂows, with real-world examples from behavior analysis

in science: to enable the use of NP broadly for workﬂows across the natural and

social sciences.

1 Introduction

One of the grand challenges in the artiﬁcial intelligence and scientiﬁc communities is to ﬁnd an AI

scientist: an artiﬁcial agent that can automatically design, test, and infer scientiﬁc hypotheses from

data. This application poses several distinct challenges for existing learning techniques because of the

need to ensure that new theories are consistent with prior scientiﬁc knowledge, as well as to enable

scientists to reason about the implications of new hypotheses and experimental designs.

The distinct requirements of scientiﬁc discovery have pushed the community to explore expressive

yet symbolically interpretable techniques such as symbolic regression [Cranmer, 2020], interpretable

machine learning [Ustun and Rudin, 2017, Doshi-Velez and Kim, 2017, Kleinberg et al., 2018,

McGrath et al., 2021], as well as program synthesis [Koksal et al., 2013, Ellis et al., 2022]. These

techniques have helped the community make signiﬁcant progress in a number of applications, such as

those discussed in Goodwin et al. [2022] and Sapoval et al. [2022], but we are still far from solving

the grand challenge.

We focus on the opportunities and challenges behind an important class of learning techniques based

on Neurosymbolic Programming (NP) [Chaudhuri et al., 2021]. These techniques combine neural and

symbolic reasoning to build expressive models that incorporate prior expert knowledge and strong

constraints on model behavior and structure. NP is capable of producing symbolic representations of

theories that can be analyzed and manipulated to answer rich counterfactuals.

NP empowers a new line of attack on the grand AI scientist challenge: represent scientiﬁc hypotheses

as programs in a Domain Speciﬁc Language (DSL) and use neurosymbolic program synthesis to

automatically discover these programs (Figure 1). Users can incorporate complex prior knowledge

(e.g., known features and constraints) into the design of the DSL. The NP learning algorithms can

then follow classic scientiﬁc reasoning principles to ﬁnd predictive programs. Also, models learned

this way are often similar to code that human domain experts write during manual scientiﬁc modeling.

∗Equal contribution

†Corresponding author: costilla@mit.edu

NeurIPS 2022 AI for Science Workshop.

arXiv:2210.05050v2 [cs.AI] 7 Nov 2022

Choose

Research

Question

Scientiﬁc Process

Generate

Hypothesis

Experimental

Setup /

Data Collection

Analysis Interpretation Report to

Community

NP Lifecycle

Data Curation

(Sec 3.1)

Encoding Domain

Knowledge

(Sec 3.2)

NP Model

Training

(Sec 3.3; 3.4)

Evaluation &

Interpretability

(Sec 3.5; Sec 3.6)

Deployment

(Sec 3.7)

Iterative

Domain

Knowledge

World

Figure 1: Synergy between the scientiﬁc and neurosymbolic programming workﬂow.

Collectively, these characteristics enable a transparent and interactive process where an AI system

and a human expert collaborate on evidence-based reasoning and the discovery of new scientiﬁc facts.

Here, we use behavior analysis as a concrete, illustrative example. We start with an introduction to

NP (Section 2), then outline challenges and opportunities for future research (Section 3).

Behavior analysis as running example.

We chose behavior analysis as an example use case for

several reasons. Behavioral data is spatiotemporal, which is a common data type across the sciences.

Correspondingly, underlying challenges are shared in other domains, from monitoring vital signs to

modeling physical systems, to studying the dynamics of chemical reactions. Additionally, behavioral

data illustrate common challenges with scientiﬁc data. These datasets often contain rare behaviors

with noisy and imperfect data and can vary signiﬁcantly in relevant time scales (e.g., milliseconds vs

hours). Datasets also vary across labs, organisms/systems, and experimental setups. Finally, automatic

behavior quantiﬁcation is becoming increasingly crucial in many ﬁelds, such as neuroscience, ecology,

biology, and healthcare. As computational behavior analysis and neurosymbolic learning are both

developing research areas, there are many exciting opportunities to explore at their intersection.

Background on behavior analysis.

An important objective of behavior analysis is to quantify

behavior from video using continuous or discrete representations. We focus on the case of animal

behavior analysis in science [Anderson and Perona, 2014, Datta et al., 2019], where there are diverse

organisms and naturalistic behaviors. A common approach is ﬁrst to perform animal pose tracking

from video [Mathis et al., 2018, Pereira et al., 2022], then categorize behaviors of interest from animal

pose [Segalin et al., 2021] (as discussed later in Figure 4). From an NP perspective, this approach can

be viewed as learning a symbolically interpretable intermediate representation (tracked keypoints).

Existing challenges in behavior analysis.

Similar to other scientiﬁc ﬁelds, data collection and

annotation are expensive for behavioral experiments. Analyzing data is also time-consuming and

expensive since specialized domain expertise is required for identifying behaviors of interest and

extracting knowledge. Models need to interface efﬁciently with scientists and data at both the inputs

and outputs from the scientiﬁc process (Figure 1). For NP models, leveraging domain expertise in the

form of behavioral attributes has been demonstrated to improve data efﬁciency [Sun et al., 2021] and

interpretability [Tjandrasuwita et al., 2021].

There is a variety of domain expertise that requires new algorithmic designs to integrate into the NP

workﬂow, such as experimental context, existing ethograms, and scientiﬁc spatiotemporal constraints.

Incorporating such domain knowledge has the potential to enable NP models to be more robust

to noisy and imperfect data, and enable new scientiﬁc inquiries that were too expensive to study

previously. Furthermore, when black-box models are used for studying behavior, it is difﬁcult to

diagnose errors and explain model outputs [Rudin, 2019]. NP models have the potential to produce

symbolic descriptions of behavior (Figure 2), which enables experts to connect model interpretations

with other parts of the behavior analysis workﬂow, e.g., describing behavioral differences across

different strains of mice. Finally, to enable the use of NP models in real-world science workﬂows,

these models must be scalable and produce robustly reproducible interpretations.

(a) Example of a domain-speciﬁc language for neurosymbolic programming.

(b) A neurosymbolic program.

Figure 2: Examples of NP for learning programs in mouse social behavior [Shah et al., 2020].

2 Neurosymbolic Programming Techniques

Neurosymbolic programs incorporate latent representations from neural networks and symbols that

explicitly capture pre-existing human knowledge, and connect these elements using rich architectures

that mirror classic models of computation. The programs, assumed to belong to a DSL, are learned

using a combination of gradient-based optimization, probabilistic methods, and symbolic techniques.

Anatomy of a Neurosymbolic Program.

In general, a neurosymbolic program comprises its discrete

architecture and continuous parameters. Consider the neurosymbolic program in Figure 2b, obtained

from DSL 2a, which comprises logical symbolic operations such as “if” statements, as well as

functions with continuous parameters. The architecture includes all the discrete symbolic choices that

form the structure of the program (such as whether to have an “if” statement and where to place it

relative to other operations), and “programming” this architecture is analogous to architecture design

in neural networks (e.g., whether to use convolutions, recurrent units, attention, etc.).

Space of Neurosymbolic Programs.

The range of NP methods varies in the degree to which they use

neural versus symbolic reasoning (Figure 3). The two ends of the spectrum correspond to purely neural

(a 1D convolutional network) and purely symbolic (a human-written program) models, respectively.

The techniques close to the center are neurosymbolic: the model in the center-left is a neurosymbolic

encoder [Zhan et al., 2021], while the model in the center-right is a program with differentiable

parameters for behavior analysis [Tjandrasuwita et al., 2021]. From a deﬁnitional perspective, purely

neural and purely symbolic programs can be considered special cases of neurosymbolic programs,

although we typically do not refer to those as neurosymbolic programs for practical purposes.

To illustrate the strengths and weaknesses of each model in Figure 3, assume that we have a scientiﬁc

hypothesis to test on a dataset. On the right side, the fully symbolic model would involve an expert-

written program that encodes the hypothesis in a general programming language. This program

requires no learnable parameters, is fully interpretable and, if needed, can be iteratively improved.

However, this method is also brittle, and the program must be engineered to handle all the dynamics

of the dataset. This is intractable for models with complex dynamics. On the left side, the purely

neural model would model the hypothesis directly using the dataset. Such models ﬁt well to the

dataset but offer limited interpretability and control over the generated hypothesis, which can make

def is_attacking(fly, tgt):

f2t_angle = atan((tgt.y-fly.y) / (tgt.x - fly.x))

rel_angle = |fly.abs_angle - f2t_angle|

return fly.speed > 2 and rel_angle < 0.1

Neural Symbolic

Black-box,

many parameters

Interpretable via visualizations,

few parameters

Interpretable,

no parameters

Interpretable via visualizations,

few parameters (symbolic),

many parameters (neural)

Properties

Visualization

Name 1D Convolutional Network Neurosymbolic Encoder Differentiable Program Human-written Program

Symbolic

Neural

Input

Encoding

Feature Weights

Channel 1 Channel 2

Figure 3: Space of neurosymbolic programming models in behavior analysis, including purely neural

(left), purely symbolic (right), and neurosymbolic (two in middle)

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NeurosymbolicProgrammingforScienceJenniferJ.SunCaltechMeganTjandrasuwitaMITCSAILAtharvaSehgalUTAustinArmandoSolar-LezamaMITCSAILSwaratChaudhuriUTAustinYisongYueCaltechOmarCostilla-ReyesyMITCSAILAbstractNeurosymbolicProgramming(NP)techniqueshavethepotentialtoacceleratescienticdiscovery.Thesemodel...

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