We introduce an online active exploration algorithm for data-efficiently learning an abstract symbolic model of an environment. Our algorithm is divided into two parts: the first part quickly generates an intermediate Bayesian symbolic model from the data that the agent has collected so far, which the agent can then use along with the second part to guide its future exploration towards regions of the state space that the model is uncertain about. We show that our algorithm outperforms random and greedy exploration policies on two different computer game domains. The first domain is an Asteroids-inspired game with complex dynamics but basic logical structure. The second is the Treasure Game, with simpler dynamics but more complex logical structure.

A popular trend in recent years is using symbolic planning models with reinforcement learning (RL) algorithms.

Machine Learning has proved its ability to produce accurate models - but the deployment of these models outside the machine learning community has been hindered by the difficulties of interpreting these models.

We introduce an online active exploration algorithm for data-efficiently learning an abstract symbolic model of an environment. Our algorithm is divided into two parts: the first part quickly generates an intermediate Bayesian symbolic model from the data that the agent has collected so far, which the agent can then use along with the second part to guide its future exploration towards regions of the state space that the model is uncertain about. We show that our algorithm outperforms random and greedy exploration policies on two different computer game domains. The first domain is an Asteroids-inspired game with complex dynamics but basic logical structure. The second is the Treasure Game, with simpler dynamics but more complex logical structure.

It is therefore possible to learn the symbols by naively collecting samples from the environment, for example by random exploration.

International series in pure and applied mathematics.

Machine Learning has proved its ability to produce accurate models - but the deployment of these models outside the machine learning community has been hindered by the difficulties of interpreting these models.

Neurosymbolic AI (NSAI) has recently emerged to mitigate limitations associated with deep learning (DL) models, e.g. quantifying their uncertainty or reason with explicit rules. Hence, TinyML hardware will need to support these symbolic models to bring NSAI to embedded scenarios. Yet, although symbolic models are typically compact, their sparsity and computation resolution contrasts with low-resolution and dense neuro models, which is a challenge on resource-constrained TinyML hardware severely limiting the size of symbolic models that can be computed. In this work, we remove this bottleneck leveraging a tight hardware/software integration to present a complete framework to compute NSAI with TinyML hardware. We focus on symbolic models realized with tractable probabilistic circuits (PCs), a popular subclass of probabilistic models for hardware integration. This framework: (1) trains a specific class of hardware-efficient \emph{deterministic} PCs, chosen for the symbolic task; (2) \emph{compresses} this PC until it can be computed on TinyML hardware with minimal accuracy degradation, using our $n^{th}$-root compression technique, and (3) \emph{deploys} the complete NSAI model on TinyML hardware. Compared to a 64b precision baseline necessary for the PC without compression, our workflow leads to significant hardware reduction on FPGA (up to 82.3\% in FF, 52.6\% in LUTs, and 18.0\% in Flash usage) and an average inference speedup of 4.67x on ESP32 microcontroller.

Given the demand for responsible and trustworthy AI for education, this study evaluates symbolic, sub-symbolic, and neural-symbolic AI (NSAI) in terms of generalizability and interpretability. Our extensive experiments on balanced and imbalanced self-regulated learning datasets of Estonian primary school students predicting 7th-grade mathematics national test performance showed that symbolic and sub-symbolic methods performed well on balanced data but struggled to identify low performers in imbalanced datasets. Interestingly, symbolic and sub-symbolic methods emphasized different factors in their decision-making: symbolic approaches primarily relied on cognitive and motivational factors, while sub-symbolic methods focused more on cognitive aspects, learnt knowledge, and the demographic variable of gender -- yet both largely overlooked metacognitive factors. The NSAI method, on the other hand, showed advantages by: (i) being more generalizable across both classes -- even in imbalanced datasets -- as its symbolic knowledge component compensated for the underrepresented class; and (ii) relying on a more integrated set of factors in its decision-making, including motivation, (meta)cognition, and learnt knowledge, thus offering a comprehensive and theoretically grounded interpretability framework. These contrasting findings highlight the need for a holistic comparison of AI methods before drawing conclusions based solely on predictive performance. They also underscore the potential of hybrid, human-centred NSAI methods to address the limitations of other AI families and move us closer to responsible AI for education. Specifically, by enabling stakeholders to contribute to AI design, NSAI aligns learned patterns with theoretical constructs, incorporates factors like motivation and metacognition, and strengthens the trustworthiness and responsibility of educational data mining.