Leveraging the compositional nature of our world to expedite learning and facilitate generalization is a hallmark of human perception. In machine learning, on the other hand, achieving compositional generalization has proven to be an elusive goal, even for models with explicit compositional priors. To get a better handle on compositional generalization, we here approach it from the bottom up: Inspired by identifiable representation learning, we investigate compositionality as a property of the data-generating process rather than the data itself. This reformulation enables us to derive mild conditions on only the support of the training distribution and the model architecture, which are sufficient for compositional generalization. We further demonstrate how our theoretical framework applies to real-world scenarios and validate our findings empirically. Our results set the stage for a principled theoretical study of compositional generalization.

Since the inception of the classicalist vs. connectionist debate, it has been argued that the ability to systematically combine symbol-like entities into compositional representations is crucial for human intelligence. In connectionist systems, the field of disentanglement has gained prominence for its ability to produce explicitly compositional representations; however, it relies on a fundamentally representation of compositional structure that clashes with the foundations of deep learning. To resolve this tension, we extend Smolensky's Tensor Product Representation (TPR) and introduce, a representational form that encodes compositional structure in an inherently manner, along with, a theoretically-principled architecture designed specifically to learn Soft TPRs. Comprehensive evaluations in the visual representation learning domain demonstrate that the Soft TPR framework consistently outperforms conventional disentanglement alternatives -- achieving state-of-the-art disentanglement, boosting representation learner convergence, and delivering superior sample efficiency and low-sample regime performance in downstream tasks.

Since the inception of the classicalist vs. connectionist debate, it has been argued that the ability to systematically combine symbol-like entities into compositional representations is crucial for human intelligence. In connectionist systems, the field of disentanglement has gained prominence for its ability to produce explicitly compositional representations; however, it relies on a fundamentally symbolic, concatenative representation of compositional structure that clashes with the continuous, distributed foundations of deep learning. To resolve this tension, we extend Smolensky's Tensor Product Representation (TPR) and introduce Soft TPR, a representational form that encodes compositional structure in an inherently distributed, flexible manner, along with Soft TPR Autoencoder, a theoretically-principled architecture designed specifically to learn Soft TPRs. Comprehensive evaluations in the visual representation learning domain demonstrate that the Soft TPR framework consistently outperforms conventional disentanglement alternatives -- achieving state-of-the-art disentanglement, boosting representation learner convergence, and delivering superior sample efficiency and low-sample regime performance in downstream tasks. These findings highlight the promise of a distributed and flexible approach to representing compositional structure by potentially enhancing alignment with the core principles of deep learning over the conventional symbolic approach.

This paper presents a novel model design/algorithm for building compositional representations of sequences when (as in natural language or code) it is presumed that the sequences have salient latent structure that can be described as a binary tree. The method performs essentially at ceiling on two existing artificial datasets that were designed for this task, both of which have not been previously solved under comparable conditions. The method also performs reasonably well on a sentiment analysis task. Pros: The method is novel and solves a couple of prominent instances of an important open problem in deep learning for NLP and similar domains with latent structure: How to we build models that can efficiently learn and to build compositional representations using latent structure? This is interesting and likely to garner a reasonably large audience as a somewhat abstract/artificial result.

Since the inception of the classicalist vs. connectionist debate, it has been argued that the ability to systematically combine symbol-like entities into compositional representations is crucial for human intelligence. In connectionist systems, the field of disentanglement has gained prominence for its ability to produce explicitly compositional representations; however, it relies on a fundamentally symbolic, concatenative representation of compositional structure that clashes with the continuous, distributed foundations of deep learning. To resolve this tension, we extend Smolensky's Tensor Product Representation (TPR) and introduce Soft TPR, a representational form that encodes compositional structure in an inherently distributed, flexible manner, along with Soft TPR Autoencoder, a theoretically-principled architecture designed specifically to learn Soft TPRs. Comprehensive evaluations in the visual representation learning domain demonstrate that the Soft TPR framework consistently outperforms conventional disentanglement alternatives -- achieving state-of-the-art disentanglement, boosting representation learner convergence, and delivering superior sample efficiency and low-sample regime performance in downstream tasks. These findings highlight the promise of a distributed and flexible approach to representing compositional structure by potentially enhancing alignment with the core principles of deep learning over the conventional symbolic approach.

Compositionality is believed to be fundamental to intelligence. In humans, it underlies the structure of thought, language, and higher-level reasoning. In AI, compositional representations can enable a powerful form of out-of-distribution generalization, in which a model systematically adapts to novel combinations of known concepts. However, while we have strong intuitions about what compositionality is, there currently exists no formal definition for it that is measurable and mathematical. Here, we propose such a definition, which we call representational compositionality, that accounts for and extends our intuitions about compositionality. The definition is conceptually simple, quantitative, grounded in algorithmic information theory, and applicable to any representation. Intuitively, representational compositionality states that a compositional representation satisfies three properties. First, it must be expressive. Second, it must be possible to re-describe the representation as a function of discrete symbolic sequences with re-combinable parts, analogous to sentences in natural language. Third, the function that relates these symbolic sequences to the representation, analogous to semantics in natural language, must be simple. Through experiments on both synthetic and real world data, we validate our definition of compositionality and show how it unifies disparate intuitions from across the literature in both AI and cognitive science. We also show that representational compositionality, while theoretically intractable, can be readily estimated using standard deep learning tools. Our definition has the potential to inspire the design of novel, theoretically-driven models that better capture the mechanisms of compositional thought.

Analyzing sequential data is crucial in many domains, particularly due to the abundance of data collected from the Internet of Things paradigm. Time series classification, the task of categorizing sequential data, has gained prominence, with machine learning approaches demonstrating remarkable performance on public benchmark datasets. However, progress has primarily been in designing architectures for learning representations from raw data at fixed (or ideal) time scales, which can fail to generalize to longer sequences. This work introduces a \textit{compositional representation learning} approach trained on statistically coherent components extracted from sequential data. Based on a multi-scale change space, an unsupervised approach is proposed to segment the sequential data into chunks with similar statistical properties. A sequence-based encoder model is trained in a multi-task setting to learn compositional representations from these temporal components for time series classification. We demonstrate its effectiveness through extensive experiments on publicly available time series classification benchmarks. Evaluating the coherence of segmented components shows its competitive performance on the unsupervised segmentation task.