Building, Reusing, and Generalizing Abstract Representations from Concrete Sequences

We sincerely thank Reviewer z6tL for the thoughtful and encouraging feedback. We are glad that the reviewer found the paper novel and well-written, with significant contributions to the field of abstraction in AI. Below, we address the specific weaknesses and questions raised.

Some small presentation issues in the appendix: equation in line 1020 is too long, figure 7 has a red line from a word processor, figure 8 has a red line that seems to be an error

Thank you for pointing this out. We have corrected the equation and the figures.

While I did praise the comprehensive evaluation, it is almost too much content; it was difficult for me to understand the model without referring to the appendix. I suggest including information about the set up in the main text to improve clarity.

Thank you for the suggestion, we have moved critical parts describing the model from the appendix to the main text.

Since the model builds up chunks by considering frequencies of adjacent chunks, there might be a limit to the expressivity of the formed abstraction. For example, while it might be able to capture the pattern of two chunks consistently being n chunks apart (if the intermediate chunks are all members of the set representing a variable), it cannot capture a pattern of two chunks being a variable number of chunks apart, where the number of chunks is determined by a symbol being present in the sequence.

Thank you for the question. There is also a limit of HVM's expressivity: HVM will not be able to capture a pattern of two chunks being a variable number of chunks apart, indicated by a particular symbol embedded in the sequence. We have added this point in the limitation section (l 520).

Thank you for addressing my concerns. I have no other questions and will be maintaining my score.

What is the relationship between this model and other Bayesian Wake-Sleep class of algorithms, like the older Helmholtz machine or the newer generation such as DreamCoder?

Thank you for highlighting the connection to Bayesian Wake-Sleep algorithms. We address the comparison between our model with the two other models below:

Helmholtz Machine The HVM certainly has some relationship with both these models - although they are rather at opposite ends of a spectrum. The Helmholtz machine involves hierarchical generative and recognition models, and is certainly one of the inspirations for the sort of coupling between the two that we have also exploited. However, its hierarchy is not focused on sequences, and, for various reasons, its sequential extension (the Helmholtz machine through time) did not work well, partly because it did not include the sort of iterative processing that we employed in the HVM.

DreamCoder Conversely, the DreamCoder is perhaps best seen as a much more sophisticated and complex recognition model mapping an input into a potentially generating program. Dream coder solves domain-specific tasks by generating programs such as list processing and logo graphics. Dream coder starts with a library of primitive functions that operate on such tasks, and synthesis programs from the library to solve these tasks. DreamCoder contains a wake phase and the sleep phase. During the wake phase, the neural recognition model proposes programs to solve the given tasks. During the abstraction sleep stage, it finds frequently used program combinations as reusable components. During the dreaming sleep stage, the dream coder samples programs from the learned library which defines hypothetical tasks to train the neural recognition model. Dreamcoder and other program synthesis approaches differ from HVM in two primary aspects. One is that the program synthesis approach applies to problems in symbolic tasks in which an input and output is given, different from HVM which takes sequence data. Secondly, the program synthesis approach needs to be initiated with a library of primitive functions, which subtly demands expert knowledge and application domains, whereas HVM does not assume any program primitives and are initialized with an empty dictionary. Thus inference/recognition in the HVM is sufficiently simple that it does not need the extensive machinery inherent to DreamCoder.

We have added discussions about these models to the related work section (l 501).

We thank Reviewer dGcC for their detailed and constructive review. We appreciate the recognition of our algorithm as “really innovative” and the evaluation as “rigorous” with insightful touches on human behavior. We address the comments and questions by the reviewer below.

I think the paper can mainly be improved in clarity. I think adding some more information on what datasets are being used would be useful. For example, line 310: " BabyLM language dataset, which contain text snippets from a collection of data domains" what data domains are there? It was hard for me to understand what kind of data this was.

We agree that providing more explicit descriptions of the data domains will enhance clarity. Specifically, we have revised the text to explain that the BabyLM dataset includes text snippets from domains such as conversational child-directed speech, narrative stories, and other linguistically rich environments (l 298).

For Figure 5, I think the authors should plot the difference between the conditions rather than the conditions themselves.

We appreciate the suggestion to reformat Figure 5 for better interpretability. We have updated the plot to show the difference between the control and variable conditions, which more clearly highlights where HVM outperforms the LLMs. We have moved the individual likelihood plots to the supplement.

I get the feeling that this algorithm isn't quite as scalable as other powerful sequence learning technologies we have today such as LLMs. This is not to say the algorithm is not useful because of that, because of course you do get more interesting structure and interpretability out of it (and it's also a better model of how humans do sequence learning). But I think this is at least worth mentioning in the discussion.

Scalability is indeed a key area for future work. While our current work focuses on cognitive plausibility and interpretability rather than efficiency at large scales, we recognize that scaling up would be a very appealing prospect. We have added a section in the discussion addressing the scalability limitations and potential future directions. Specifically, we propose that HVM could be used as a preprocessing step to extract hierarchical tokens for sequence prediction models, such as transformers, thereby serving as a bridge between interpretability and scalable sequence modeling. We have included additional information about scaling up in the discussion section (l 538).

(minor weakness) I think a potential missed opportunity for this algorithm is interpreting the discovered variables on specific datasets that we know have rich hierarchical structure. For example, can you use this algorithm on musical notes to recover leitmotifs? But there is enough work here that this can count as future work.

We also appreciate the idea of testing HVM on datasets with known hierarchical structures, such as musical sequences or motifs in classical compositions. While this is beyond the scope of our current work, we agree that such applications could yield valuable insights. We have added this as a direction for future work in the manuscript (l 534).

We thank Reviewer NkSJ for their thoughtful and constructive feedback. We are glad that our contributions were appreciated, especially the novel theoretical framework and the connection to cognitive science.

The paper's comparison to LLMs is relatively narrow and focuses primarily on a specific sequence recall task and limited to short sequences, and therefore seems slightly contrived situation. The paper would benefit from explorations of slightly more complex abstraction tasks to study the general applicability of their method.

We appreciate your comment. Our initial aim was to ground HVM's performance in well-understood human sequence learning paradigms. We agree that evaluating HVM on more complex abstraction tasks would strengthen our claims about generalizability and the benefits of hierarchical abstraction. As we do not have data from humans doing a more complex task, in this comparison, we can only stop at the scope of the human experiment. However, the sequences are on a cognitive scale not short, as the length goes beyond working memory span and are challenging to remember. To address this, we propose adding a comparison where HVM and LLMs are evaluated purely on artificial datasets with higher levels of abstraction. Although human performance data would not be available for such tasks, the comparison could highlight differences in learning and transfer complexity between HVM and LLMs. We have added a discussion in the paper and consider including a new table summarizing these comparisons.We could compare HVM with LLM on sequences with more complex hierarchies, in this case the human data might be missing, and the comparison would be purely between the cognitive model and LLMs. Maybe we can have a table about this comparison on the learning and transfer complexity.

Limited Discussion of Related Work: The comparisons in the paper are quite limited and don't adequately address the rich literature on sequence compression and pattern detection. A single example I have in mind of a similar cogntiively-inspired latent variable learning model is CSCGs (https://pmc.ncbi.nlm.nih.gov/articles/PMC8062558/), but there are more.

We appreciate your comment. We agree that broadening our literature review will improve the paper’s depth. George et al. proposed the clone-structured cognitive map as a neural model that replicates observation for different contexts in a cloned higher-order markov chain, and show that CSCG exerts neuronal properties in the hippocampus. This model addresses sequence learning on an algorithmic level and has a neural implementation focus, whereas our model addresses questions on the computational level. We expect future work to bring this computational model of abstract chunk learning to an implementational level. We have addressed cognitive models like CSCGs (as mentioned) in the related work section and discuss how our approach differentiates from these models (l 507).

We thank Reviewer RUZK for their detailed feedback and constructive suggestions. We are glad the reviewer found the model an "interesting, sensible, and original improvement over HCM" and appreciated the work ‘s connection to neuroscience, cognitive science and linguistic audience. Below, we address the reviewer’s comments, including weaknesses, questions, and minor suggestions.

Many of the main experiments were conducted on data from a generative model that fits exactly the modeling assumptions for HVM (or tasks inspired by these assumptions)

We acknowledge the reviewer’s concern that some experiments rely on a generative model designed to align with HVM’s assumptions. The generative model was not created to give HVM an unfair advantage but rather to simulate hierarchical structures that are characteristic of certain real-world sequences. This approach mirrors common practices in sequence learning research (e.g., Teh et al., 2006; Milan et al., 2016). Moreover, the generative model itself has merit for studying hierarchical data. As noted, we also evaluated HVM on natural language data to demonstrate its generalization capabilities beyond synthetic datasets. We have clarified this justification in the revised manuscript (l 220, l 497) and emphasized the importance of showing HVM's robustness on natural datasets as critical validation.

Hierarchical Dirichlet processes and related models (perhaps most famously many variants of topic models) have been used and discussed exhaustively in the ML, linguistics, and cognitive science literature. But an in-depth discussion and technical comparison of HVM against these is currently missing.

We appreciate the reviewer’s suggestion to compare HVM with other important and influential models. HVM shares an hierarchical nature with a variety of models; however, it differs from topics models, such as Latent Dirichlet Allocation (LDA) by being aimed specifically at sequences rather than treating documents as ‘bags of words’ that can be clustered in a high-dimensional space. It also differs from HDP, which captures clustering over sequences but lacks the library of reusable chunks and variables central to HVM. We have expanded the related work section to include a more detailed discussion of these distinctions (l 503).

From a cognitive perspective, a severe limitation is that learning in HVM strongly depends on initial learned representations and the order in which learning experiences are represented.

We recognize that HVM's reliance on initial learned representations and order of learning experiences introduces an order dependency. This characteristic, while potentially limiting, is consistent with findings in cognitive science. Human learning mechanisms can be highly order-sensitive and curriculum dependent: the sequence in which information is presented influences learning and memory. In language learning, children acquire more complex compounds as they develop (Newport 1977): stages of child language acquisition follow the geometry of the syntactic tree, with early stages of acquisition corresponding to learning lower parts of the adult syntactic tree, which keeps growing with the development of the child (Friedman et al., 2021, Snow et al., 1972, and Fernald et al., 1989). This sort of path dependency afflicts any online learning system that lacks an arbitrarily large memory buffer. It is therefore also important for conventional machine learning systems. We have expanded on this characteristic in the discussion, providing references to the cognitive literature, commenting on the statistical limitation, but resource advantage (l520).

Reference:

1. Catherine E. Snow. 1972. Mothers’ speech to children learning language. Child Development, 43(2):549– 565.
2. Anne Fernald, Traute Taeschner, Judy Dunn, Mechthild Papousek, Bénédicte de Boysson-Bardies, and Ikuko Fukui. 1989. A cross-language study of prosodic modifications in mothers’ and fathers’ speech to preverbal infants. Journal of Child Language.
3. Elissa. Newport, Henry Gleitman, and Lila Gleitman. 1977. Mother, id rather do it myself: Some effects and non-effects of maternal speech style. In Catherine E. Snow and Charles A. Ferguson, editors, Talking to Children, pages 109–149. Cambridge University Press.
4. Friedmann, N., Belletti, A. & Rizzi, L., (2021) “Growing trees: The acquisition of the left periphery”, Glossa: a journal of general linguistics 6(1): 131.
5. Yee Whye Teh. A hierarchical Bayesian language model based on Pitman-Yor processes. 2006
6. Kieran Milan, Joel Veness, James Kirkpatrick, Michael Bowling, Anna Koop, and Demis Hassabis. The Forget-me-not Process.

I am not sure whether there is a big take-away other than saying LLMs in-context learning on this task is different from the model and different from human learning on this task. ... The work is very interesting to a comp. neurosci. audience and a comp. linguistics audience, but its impact in the ML and AI community is likely to be quite limited (nonetheless, a part of the ICLR audience has a background in the aforementioned fields).

Thank you for raising the question about the implications of different behavior of LLMs, humans, and HVM on the cognitive task. This section is included in the paper because LLMs have been reported as having emergent abilities such as solving mathematical problems and reasoning tasks (Webb 2023, Kojima 2022). This has raised the (popular, but controversial) idea that given sufficient training LLMs may exceed human intelligence . However, controversy has accompanied the findings that LLMs do not learn to generalize on symbolic tasks, and particularly those that involve abstract representation (Trott 2022, Ransom 2022) and compositional operations (Dentella 2024).

It therefore becomes especially important to use a task that unearths the aspects of LLM that differ from human cognition, and find out whether there are features inside a more conventional cognitive model that might provide the missing component. Our observations about the match between human data and the HVM suggest make it a candidate. Along similar lines, the experiment can be adapted to evaluate other types of model for their ability to abstract. Therefore, we expect this task to appeal to a broad audience beyond cognitive scientists and linguists. We have also updated our experimental comparison to include more recent large language models.

To clarify this point, we have also changed the LLM section to substantiate the importance of comparing LLM with humans and cognitive models (l 374). We have also highlighted HVM’s potential as a preprocessing tool for tokenization in neural sequence models, enabling them to leverage hierarchical abstractions (l 522).

Reference:

1. Kojima, T., Gu, S.S., Reid, M., Matsuo, Y., Iwasawa, Y.: Large language models are zero-shot reasoners. NeurIPS 2022
2. S. Trott, C. Jones, T. Chang, J. Michaelov, B. Bergen, Do large language models know what humans know? arXiv [Preprint] (2022).
3. Han, S. J., Ransom, K. J., Perfors, A., & Kemp, C. (2022). Human-like property induction is a challenge for large language models. In Proceedings of the annual meeting of the cognitive science society (Vol. 44, No. 44).
4. Dentella, V., Günther, F., Murphy, E. et al. Testing AI on language comprehension tasks reveals insensitivity to underlying meaning. Sci Rep 14, 28083 (2024).

The work and claims could be strengthened by evaluating on more datasets that focus on abstraction, but have not been generated by the authors. This is only relevant for a major revision.

Thank you for the comment. We are aware of datasets such as BIG-bench, that evaluates abstraction by computing similarities between multiple-choice words based on text queries (Srivastava et al. 2023), or the ARC challenge which is designed with symbolic reasoning in a graphical setting. Both these benchmarks operate in domains that are more complicated than the simple sequence setting that we study. Furthermore, our algorithm is too simple to be plugged directly into abstraction tasks that are based on language description or symbolic reasoning. We have taken this suggestion as a reference for future work to apply such models on benchmarks.

Topic models and various forms of hierarchical latent variable models have been used and discussed extensively in linguistics, machine learning, and cognitive science. How does the HVM relate to commonly used topic models (LDA, and more modern ones)? Ideally this is discussed on a technical level in detail, but at the least it needs to be included with more detail in the related work discussion.

Please see our brief discussion above comparing the sequence learning models proposed with topic models (l 511). We have expanded the related work section and the discussion to make these points explicitly, within the confines of the length limit.

How does the generative model relate to the Hierarchical Dirichlet Process (Teh et al. 2006)?

The HDP is a very attractive model of sequences - which is even used by some to characterize everything from sequence learning in humans to the structure of the songs of Bengalese finches. However, HVM differs from hierarchical Dirichlet Process (HDP) models in the nature of its library (which is more flexible than in the HDP); and it also differs from fragment grammar methods by having the notion of variables that are ‘interior’ to chunks. Thus, HVM is endowed with the sort of flexibility that is critical for characterizing sequences with rich hierarchical structure, including natural languages.