Abstraction and Analogies with LLMs

I was listening to a recent episode of the Machine Learning Street Talk podcast (a very fine podcast!).

Specifically:

• How Do AI Models Actually Think?, Laura Ruis.

Fantastic episode! Just great. I need a re-listen.

Early in the conversation they touch on (I’m paraphrasing, probably wrongly) whether LLMs think/reason as Douglas Hofstadter suggests, abstracting via a collection of analogies. It’s agreed they do.

The host touches on Hofstadter’s often repeated quote:

…every concept we have is essentially nothing but a tightly packaged bundle of analogies, …all we do when we think is to move fluidly from concept to concept — in other words, to leap from one analogy-bundle to another — …lastly, that such concept-to-concept leaps are themselves made via analogical connection.

In my head, I store it something like:

Abstraction is a bag of analogies.

Or:

Abstract concepts are an ensemble of perspectives.

The latter for sure.

I’m not a philosophy of AI guy, so this is probably common stuff, but it lit me up.

Okay, let’s see what our friend gpt4o has to say:

(edited lightly by me for readability)

Douglas Hofstadter’s idea that abstraction is a “bag of analogies” is a profound insight into how human cognition works.

This notion reflects his broader views on how we understand and process concepts. He argues that abstraction—the process of creating general concepts from specific instances—is deeply rooted in our ability to make analogies between different experiences and ideas.

Explanation:

1. What Does He Mean by “Bag of Analogies”?

   • Hofstadter suggests that when we think abstractly, we draw from a reservoir of analogous experiences, ideas, and concepts stored in our minds.
   • For example, our understanding of “freedom” might come from various analogies: a bird flying, a prisoner being released, or a child running freely in a field. Each of these is an instance of the abstract concept tied together by similarity.
   • Instead of defining abstract concepts through rigid rules, humans often rely on these loose, analogy-based connections.

2. Why Is This Significant?

   • This view challenges traditional notions in AI and philosophy that abstraction is a purely logical or rule-based process.
   • It emphasizes the fluid, creative, and subjective nature of human thought, showing how abstraction is grounded in personal and cultural experiences.

3. How Does This Relate to Hofstadter’s Work?

   • This idea is central to his research on analogy-making, as seen in projects like Copycat, where he tried to model how computers might replicate human-like analogy-making.
   • His books, especially Gödel, Escher, Bach and I Am a Strange Loop, are filled with examples of how analogies underpin both simple concepts and complex thought.

A Quotation for Reference:

One possible quotation capturing this idea appears in Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander:

“Every concept we have is essentially a package of analogies, a bundle of thought-pathways that work together to capture the essence of a category as it exists in our minds.”

Further Elaboration:

This statement encapsulates the idea that concepts are not isolated entities; they exist within networks of relationships, built through analogies we’ve drawn over time. For Hofstadter, analogy-making is not just a part of thinking—it is thinking. The ability to see one thing in terms of another is what allows us to generalize, create new ideas, and even understand abstract concepts like self and consciousness.

Cool.

For the record, I found GEB very clever but repetitive/boring and “I Am a Strange Loop” very readable (as intended). Probably due for a re-read.

Sorry, I guess. I know how the kids love GEB. Maybe I’m too dumb.

I have not read “Surfaces and Essences”. Added to my to-read list.

Our LLM friend, all to eager to please, likes the connection of Hofstadter’s idea about abstraction/analogy and ML ensembles:

Douglas Hofstadter’s idea that abstraction is a “bag of analogies” can be compellingly related to the concept of ensembles in machine learning (ML). Here’s how the two concepts intersect:

1. Analogies as Models in an Ensemble

• In Hofstadter’s view, abstraction emerges from combining many analogies to form a cohesive understanding. This is akin to how an ensemble of models in ML combines diverse models to produce better generalizations.
• Just as each analogy in Hofstadter’s “bag” captures a facet of an abstract idea, each model in an ensemble captures a different aspect of the data. Together, these models contribute to a more nuanced and robust decision-making process.

2. Diversity and Complementarity

• Analogies are diverse and context-dependent, meaning different analogies can highlight different aspects of the same concept.
• Similarly, ensembles thrive on diversity. Techniques like bagging (e.g., Random Forests) and boosting (e.g., Gradient Boosting Machines) work by aggregating models trained on different subsets of data or with varying perspectives on the same problem. This diversity improves generalization, akin to how a wide range of analogies enrich understanding.

3. Weighted Contributions

• In Hofstadter’s theory, not all analogies are equally important; some resonate more strongly depending on the context.
• In ensembles, models can have varying weights depending on their reliability or relevance for specific predictions. Techniques like weighted voting in ensemble methods reflect this principle, paralleling how the human mind prioritizes certain analogies in abstraction.

4. Reducing Overfitting and Bias

• Abstraction helps humans generalize across situations by synthesizing a “big picture” from specific instances, avoiding rigid over-reliance on one analogy.
• Similarly, ensembles reduce overfitting by averaging out the biases and overfitting tendencies of individual models. The “bag of analogies” helps prevent any single analogy (or model) from dominating and misrepresenting the abstraction (or prediction).

5. Creating New Patterns

• Hofstadter emphasizes that abstraction and analogy-making allow for creativity—forming novel concepts from familiar patterns.
• Ensembles, especially methods like stacking, where the predictions of base models are fed into a meta-model, can create new, emergent patterns of understanding by leveraging insights from multiple base learners.

Table: Shared Themes Between Hofstadter’s Idea and Ensembles

Practical Implication: How This View Can Inspire ML

Understanding abstraction as a process rooted in analogy can inspire new ensemble methods:

1. Analogy-Based Model Selection: Design ensembles where each model explicitly represents an analogy or interpretation of the data (e.g., models trained on different feature transformations or subsets).
2. Dynamic Weighting: Just as the mind emphasizes certain analogies depending on context, ensembles could use context-aware weighting, where models are weighted dynamically based on the current input.
3. Interpretable Ensembles: Hofstadter’s insights could motivate research into interpretable ensembles, where the contribution of each model (or analogy) to the final abstraction (or prediction) is transparent.

Fine.

And what does gpt4o think about Hofstadter’s notion as it relates to how LLMs “think”?

(I really should look up Laura’s work on this, or other academics, would perplexity find the papers I wonder?)

Douglas Hofstadter’s idea that abstraction is a “bag of analogies” aligns intriguingly with how large language models (LLMs) like GPT work, “think,” and “reason.” While LLMs are not conscious or capable of true understanding, their mechanisms echo some of the patterns Hofstadter describes in human cognition. Here’s how:

1. Analogies in LLMs: Patterns in Contextual Embeddings

• LLMs are trained to predict the next word in a sequence by analyzing vast datasets and identifying patterns across contexts. This is akin to how humans draw analogies from prior experiences to make sense of new situations.
• For LLMs:
  • Each word or concept is represented as a high-dimensional vector embedding.
  • Relationships between these embeddings are analogous to Hofstadter’s analogies, as they capture similarities and associations between concepts based on usage patterns in the training data.
• Example: If a model “knows” that a king is related to a queen like a man is to a woman, it is essentially creating analogies within the structure of its embeddings.

2. Generative Reasoning as an Emergent “Bag of Analogies”

• Hofstadter’s view suggests that reasoning emerges from combining multiple analogies to form a coherent abstraction. Similarly, LLMs generate responses by synthesizing patterns from diverse contexts.
• When an LLM generates a sentence, it implicitly draws from a vast “bag” of training data:
  • Analogous examples influence the prediction process.
  • For instance, when reasoning about a new topic, the LLM might use patterns seen in similar linguistic structures to generate plausible, contextually appropriate responses.

3. Hierarchies of Meaning

• Hofstadter emphasizes that abstraction is built on layers of analogies. LLMs operate in a similar way:
  • Lower levels: The model understands patterns of individual words and phrases (e.g., syntactic relationships).
  • Higher levels: The model integrates these into larger, more abstract ideas (e.g., coherent narratives or reasoning chains).
  • This mirrors how humans stack analogies to move from specific instances to broader concepts.

4. Creativity and Novelty

• Hofstadter ties creativity to analogy-making—combining familiar concepts in new ways. LLMs often generate novel responses by recombining elements of their training data in previously unseen ways.
• Example:
  • Given a prompt like “What if cats could talk?”, an LLM might “reason” by analogizing from other examples of anthropomorphized animals in stories and constructing a response based on these analogies.

5. Limitations: True Understanding vs. Pattern Matching

While LLMs exhibit behaviors that resemble Hofstadter’s “bag of analogies,” there are key differences:

• LLMs:
  • Work by statistical pattern matching rather than true understanding or reasoning.
  • Their “analogies” are implicit in the training data and embeddings, not conscious or deliberate.
• Humans:
  • Actively generate and evaluate analogies, adapting them to context and purpose.
  • Analogies are rooted in lived experiences and a subjective sense of meaning.

These differences highlight the gap between human cognition as a strange loop (a self-aware system) and LLMs, which are sophisticated but ultimately unselfconscious machines.

6. Hofstadter’s Critiques of AI and LLMs

Hofstadter has been skeptical of AI systems, arguing that they lack the rich, meaning-based understanding central to human cognition. For instance:

• He might view LLMs as vast repositories of “shallow analogies,” incapable of forming the deep, recursive self-referential patterns that underpin true reasoning and abstraction.
• LLMs do not create analogies intentionally; their responses are emergent phenomena from probabilistic calculations, not genuine conceptual leaps.

How Hofstadter’s Ideas Could Inspire Better LLMs

1. Explicit Analogy-Making Mechanisms:

   • Future LLMs could include mechanisms to explicitly construct analogies rather than rely on implicit patterns.
   • For example, they could compare embeddings more dynamically and explicitly map relationships between concepts.

2. Self-Referential Capabilities:

   • Hofstadter’s idea of a “strange loop” suggests that true reasoning involves systems that can reflect on themselves. Incorporating feedback loops into LLMs might enhance their ability to reason recursively.

3. Contextual Adaptation:

   • Hofstadter’s emphasis on context-sensitive analogy-making could inspire LLMs to better weigh and adapt their responses based on nuanced context, rather than relying on static training data patterns.

Summary

Hofstadter’s “bag of analogies” resonates deeply with how LLMs operate:

• Both rely on synthesizing patterns to make sense of input.
• Both construct abstractions through the aggregation of contextual relationships. However, LLMs lack the conscious intent, deep understanding, and self-referential awareness central to Hofstadter’s view of cognition. While LLMs excel at mimicking human-like reasoning, bridging the gap between statistical pattern recognition and true analogy-making remains a frontier for AI research.

Good stuff.