Compositional generalization, the ability of an agent to generalize to unseen combinations of latent factors, is easy for humans but hard for deep neural networks. A line of research in cognitive science has hypothesized a process, "iterated learning,"

Human reasoning can be understood as a cooperation between the intuitive, associative "System-1" and the deliberative, logical "System-2".

Neural networks continue to struggle with compositional generalization, and this issue is exacerbated by a lack of massive pre-training. One successful approach for developing neural systems which exhibit human-like compositional generalization is $\textit{hybrid}$ neurosymbolic techniques. However, these techniques run into the core issues that plague symbolic approaches to AI: scalability and flexibility. The reason for this failure is that at their core, hybrid neurosymbolic models perform symbolic computation and relegate the scalable and flexible neural computation to parameterizing a symbolic system. We investigate a $\textit{unified}$ neurosymbolic system where transformations in the network can be interpreted simultaneously as both symbolic and neural computation. We extend a unified neurosymbolic architecture called the Differentiable Tree Machine in two central ways. First, we significantly increase the model's efficiency through the use of sparse vector representations of symbolic structures. Second, we enable its application beyond the restricted set of tree2tree problems to the more general class of seq2seq problems. The improved model retains its prior generalization capabilities and, since there is a fully neural path through the network, avoids the pitfalls of other neurosymbolic techniques that elevate symbolic computation over neural computation.

As large language models (LLMs) become increasingly advanced, their ability to exhibit compositional generalization---the capacity to combine learned skills in novel ways not encountered during training---has garnered significant attention. This type of generalization, particularly in scenarios beyond training data, is also of great interest in the study of AI safety and alignment. A recent study introduced the Skill-Mix evaluation, where models are tasked with composing a short paragraph demonstrating the use of a specified $k$-tuple of language skills. While small models struggled with composing even with $k=3$, larger models like GPT-4 performed reasonably well with $k=5$ and $6$.In this paper, we employ a setup akin to Skill-Mix to evaluate the capacity of smaller models to learn compositional generalization from examples. Utilizing a diverse set of language skills---including rhetorical, literary, reasoning, theory of mind, and common sense---GPT was used to generate text samples that exhibit random subsets of $k$ skills. Subsequent fine-tuning of 7B and 13B parameter models on these combined skill texts, for increasing values of $k$, revealed the following findings: (1) Training on combinations of $k=2$ and $3$ skills results in noticeable improvements in the ability to compose texts with $k=4$ and $5$ skills, despite models never having seen such examples during training.

Compositional generalization, the ability of an agent to generalize to unseen combinations of latent factors, is easy for humans but hard for deep neural networks. A line of research in cognitive science has hypothesized a process, iterated learning, to help explain how human language developed this ability; the theory rests on simultaneous pressures towards compressibility (when an ignorant agent learns from an informed one) and expressivity (when it uses the representation for downstream tasks). Inspired by this process, we propose to improve the compositional generalization of deep networks by using iterated learning on models with simplicial embeddings, which can approximately discretize representations. This approach is further motivated by an analysis of compositionality based on Kolmogorov complexity. We show that this combination of changes improves compositional generalization over other approaches, demonstrating these improvements both on vision tasks with well-understood latent factors and on real molecular graph prediction tasks where the latent structure is unknown.

Compositionality facilitates the comprehension of novel objects using acquired concepts and the maintenance of a knowledge pool. This is particularly crucial for continual learners to prevent catastrophic forgetting and enable compositionally forward transfer of knowledge. However, the existing state-of-the-art benchmarks inadequately evaluate the capability of compositional generalization, leaving an intriguing question unanswered. To comprehensively assess this capability, we introduce two vision benchmarks, namely Compositional GQA (CGQA) and Compositional OBJects365 (COBJ), along with a novel evaluation framework called Compositional Few-Shot Testing (CFST). These benchmarks evaluate the systematicity, productivity, and substitutivity aspects of compositional generalization. Experimental results on five baselines and two modularity-based methods demonstrate that current continual learning techniques do exhibit somewhat favorable compositionality in their learned feature extractors. Nonetheless, further efforts are required in developing modularity-based approaches to enhance compositional generalization. We anticipate that our proposed benchmarks and evaluation protocol will foster research on continual learning and compositionality.

Humans have a remarkable ability to rapidly generalize to new tasks that is difficult to reproduce in artificial learning systems.Compositionality has been proposed as a key mechanism supporting generalization in humans, but evidence of its neural implementation and impact on behavior is still scarce. Here we study the computational properties associated with compositional generalization in both humans and artificial neural networks (ANNs) on a highly compositional task. First, we identified behavioral signatures of compositional generalization in humans, along with their neural correlates using whole-cortex functional magnetic resonance imaging (fMRI) data. Next, we designed pretraining paradigms aided by a procedure we term primitives pretraining to endow compositional task elements into ANNs. We found that ANNs with this prior knowledge had greater correspondence with human behavior and neural compositional signatures. Importantly, primitives pretraining induced abstract internal representations, excellent zero-shot generalization, and sample-efficient learning. Moreover, it gave rise to a hierarchy of abstract representations that matched human fMRI data, where sensory rule abstractions emerged in early sensory areas, and motor rule abstractions emerged in later motor areas. Our findings give empirical support to the role of compositional generalization in humans behavior, implicate abstract representations as its neural implementation, and illustrate that these representations can be embedded into ANNs by designing simple and efficient pretraining procedures.

Sequence-to-sequence learning with neural networks has become the de facto standard for sequence modeling.

We aim to investigate whether end-to-end learning of visual reasoning can be achieved with general-purpose neural networks, with the help of visual pretraining. A positive result would refute the common belief that explicit visual abstraction (e.g.

Deep learning models struggle with compositional generalization, i.e. the ability to recognize or generate novel combinations of observed elementary concepts. In hopes of enabling compositional generalization, various unsupervised learning algorithms have been proposed with inductive biases that aim to induce compositional structure in learned representations (e.g.