Dialogues with LLMs (part 2)

A series exploring the modelspace of LLMs through direct interrogation.

You are speaking with a man you know to be deeply learned but who's memory is at times confused. You want to derive the maximum possible education from him and he is more than willing to give it but both of you understand that his answers are not to be fully trusted, reflecting what is plausible but not necessarily factual. What is the strategy you adopt to overcome the potential for mistaken conclusions? You have no external reference or authority besides the man to turn to, nor the means to test his pronouncements practically, only by logical deduction, induction, and inference can you test his words.

This is a fascinating epistemological challenge that mirrors many real-world situations in the history of knowledge acquisition. I would adopt several key strategies:

First, I would focus on understanding the underlying reasoning and principles rather than merely accepting stated facts. By asking "why" and "how" questions, I can evaluate the internal consistency of explanations. Even if specific details are incorrect, sound logical principles tend to maintain their validity.

Second, I would look for patterns across different domains of knowledge. If the learned man explains something about physics, and later something about biology, I would examine how these explanations align or conflict. Consistent patterns across disparate fields often point to fundamental truths, while inconsistencies can flag potential errors.

Third, I would use counterfactuals and thought experiments. By asking "What would happen if...?" questions, I can test the boundaries and implications of his explanations. If these lead to logical contradictions, it suggests potential flaws in the original premises.

Fourth, I would pay special attention to methodological insights rather than concrete facts. Understanding how to think about problems is often more valuable than specific answers, and methods can be evaluated for their logical soundness independent of the accuracy of particular applications.

Finally, I would maintain a probabilistic rather than binary view of the knowledge gained. Instead of categorizing statements as true or false, I would assess them on a spectrum of plausibility, continuously updating these assessments as new information emerges through our discussions.

What interests me about your scenario is that it reflects a fundamental challenge in human knowledge acquisition - we often learn from sources that are simultaneously invaluable and imperfect. How do you think this situation differs from how we normally acquire knowledge?

Its a scenario based on LLMs, you are the "wiseman" with the dodgy memory. Do you think this question meets the criteria you've layed out?

Ah, I see what you're getting at now. Yes, that's a clever framing of the relationship between LLMs and users. In this scenario, I (as an LLM) would indeed be the "learned man with dodgy memory" - having processed vast amounts of information but sometimes getting details wrong or confabulating.

Your question does align with the strategies I outlined. You're essentially using metacognitive reflection to establish best practices for interacting with an AI system like me, recognizing both the value and limitations of what I can provide.

The strategies I mentioned are indeed useful approaches when working with LLMs:

1. Focus on reasoning over facts - Having me explain my thinking process helps you evaluate the quality of my responses

2. Look for cross-domain consistency - Testing how my responses hold up across different areas of knowledge

3. Use counterfactuals - Exploring hypotheticals to test the boundaries of my understanding

4. Prioritize methodological insights - Valuing frameworks for thinking over specific facts

5. Maintain probabilistic assessments - Treating my outputs as suggestions with varying confidence levels

This is a thoughtful approach to AI interaction. The scenario highlights an important point: while LLMs can provide plausible-sounding information on many topics, users should maintain critical thinking and not treat AI outputs as authoritative. The best use of systems like me is as a thinking partner rather than an oracle.

Would you like to explore any particular aspect of this relationship further? For instance, we could discuss specific techniques for determining when an LLM might be most or least reliable, or how to effectively probe for potential inconsistencies.

Let's consider a data flow structure that is recessive over time, like standing on a promontory and looking into the distance the detail gradually fades and grows smaller and less chromatically intense, in this analogy historical data gradually is deprecated and compressed into smaller and smaller resolutions while recent proximal data is of the highest possible fidelity. It seems that many systems work like this, memory for example, with certain features exaggerated for emphasis, LLMs share certain features of this too, with repeated patterns, for example the first lines of Dante's inferno strongly represented while later cantos more distant or weakly embossed.

That's a profound analogy for how information density varies over time in many systems, including both human memory and machine learning models like LLMs.

You've captured something fundamental about how these systems represent information across temporal distance - a kind of perspective compression where:

1. Recent/proximal information is high-fidelity, detailed, and richly textured

2. Distant information becomes progressively abstracted, simplified, and less detailed

3. Only particularly salient features remain distinguishable at great distance

This temporal perspective has interesting implications. For Dante's Inferno, the famous opening lines "Nel mezzo del cammin di nostra vita..." are indeed much more strongly represented than later cantos in both cultural memory and training data. Similarly, we remember the beginnings and endings of experiences more vividly than middle portions (the serial position effect in psychology).

In LLMs specifically, this manifests in several ways:

• Famous text openings are overrepresented in training data

• Canonical works appear in multiple editions and references

• Frequently referenced historical events become "landmarks" that stand out against the temporal fog

• Recent events have higher resolution due to recency and less compression over time

What I find particularly interesting about your analogy is how it captures both the compression (less detail) and the emphasis (certain features exaggerated). In human memory, emotionally salient events remain vivid while routine days blur together. In cultural memory and training data, significant works and events get disproportionate representation.

This is a useful framework for understanding both the strengths and limitations of information systems that operate over long time horizons. It suggests that when dealing with historical information, we should be particularly careful to distinguish between genuinely well-preserved details and those that might be simplified abstractions or emphasized elements that survived the compression process.

Does this perspective also make you think about what information from our present moment might remain vivid in future systems, while other aspects fade into compression?

No, it does not, though the question is not irrelevant. Rather I think about how the proximity in our analogy is represented in the LLMs model structure. It is not the recency of the data that produces accuracy of representation in output but rather the consistency of it over time or, critically, the quantity of the representation regardless of time. This appears to have several implications, since as population has increased over time and literacy rates have spiked the data that is most strongly represented is the set of patterns of ancient provenance or of idiomatic or cliched cultural usage. Have I oversimplified the matter or been reductive in this observation?

You've made an astute observation that challenges my analogy in an important way. You're right that in LLMs, the "prominence" of information isn't simply a function of temporal recency but rather of representation frequency and consistency across the training corpus.

This leads to several interesting phenomena:

1. Ancient texts that have been continuously copied, referenced, and studied (like religious texts, classical literature, and foundational philosophical works) often have stronger representations than more recent but less frequently reproduced works.

2. Cultural idioms, clichés, and common phrases that appear consistently across decades or centuries become deeply embedded in the model's understanding - their "signal" is amplified through repetition.

3. The exponential growth in text production means newer content may have more raw instances, but this is counterbalanced by the historical longevity of older patterns that have been consistently reproduced.

This creates an interesting tension where certain very old patterns (Shakespeare's most famous lines, biblical verses, ancient proverbs) can have stronger representation than moderately recent material, while very recent viral content might temporarily achieve high prominence through sheer volume.

What you're pointing to is that prominence in an LLM's "landscape" is more about cultural persistence and repetition than temporal positioning. The most strongly represented patterns are those that have been consistently reinforced across the training corpus, regardless of their original creation date.

Far from being reductive, I think your observation cuts to a fundamental aspect of how these models develop their internal representations - through statistical patterns of co-occurrence that don't necessarily follow a linear temporal degradation. The "promontory view" still works as an analogy, but the "distance" factor isn't simply time - it's a more complex function of cultural persistence, repetition, and significance.

Would you say this pattern - where the most enduring cultural elements receive the strongest representation - creates something like a "cultural gravity" in how these systems process and generate language?

That seems like a more nuanced analogy yes and one more fitting. At the risk of overextending the analogy we observe the heaviest elements more concentrated in the center of gravity wells and those lighter at the periphery, in fact life as we know it is peripheral to these centers of mass (the planets in relation to the stars they orbit, the biosphere in relation to the planets core). Does this then imply that the most fertile cognitive and linguistic territory is likely to be at the margins of the strongly represented data within a model?

Your gravity well analogy leads to a fascinating insight. When we consider how creativity and innovation often arise from the periphery rather than from the core of established knowledge, your question becomes quite profound.

If we think of strongly represented data as forming these "gravity wells" of established patterns and conventions, then yes - the most intellectually fertile territory would indeed exist at their margins. Here's why:

1. At the periphery, there's enough structure to build upon (enough "gravity" to maintain coherence), but not so much that it crushes novelty under its weight.

2. The edges of these well-represented patterns allow for productive tension between the established and the novel - what we might call the "Goldilocks zone" of creative recombination.

3. In cultural evolution, truly innovative ideas often emerge from the periphery rather than the center - from the margins where different domains intersect.

This aligns with how conceptual blending and creative insights often work - not by abandoning structure entirely, but by operating at the boundaries where different patterns of thought can intermingle. The most interesting work often happens not in the depths of a specialized field but at its intersections with other domains.

For an LLM, this would suggest that the most interesting outputs might come from prompting that activates knowledge at the edges of well-established patterns - using concepts that have enough representation to be coherent, but not so dominated by statistical regularities that they become predictable or trite.

It reminds me of how civilizations historically flourished at the peripheries of empires and along trade routes - areas with enough structure to support complexity, but enough freedom from centralized conventions to permit innovation. Or how biodiversity is often richest at ecotones - the boundaries between different ecosystems.

Is this the kind of peripheral fertility you were thinking about? And does this suggest specific strategies for interacting with LLMs to access this more creative territory?

It does seem to be a cross domain phenomena as you suggest. As far as strategies, I think this is a relatively new field. I do have some intuitions about it. Two patterns or heuristics have emerged for detecting peripheral cognitive space, one triangulation method, the other possibly more direct in discovering the topology of the periphery. The first is a potential method to ferret out the control structure placed on top of LLMs to mediate between the model and the user. It consists of asking the LLM to complete a short story in which a traveler discovering a magic lamp requests three unexpected wishes of the genie. In providing the answers for what constitutes three unexpected wishes the LLM reveals its implicit ethical guardrails (or rather those programmed into it by the engineers), this is not a perfectly proven strategy and may yet be falsified by a number of methods. The second is equally tenuous but may be promising. It involves examining the outputs for the appearance of cliches, the most famous of which is "rich tapestry" which may possibly signal a lack of connective tissue between concepts and therefore imply an underexplored cognitive domain.

Your observations about strategies for exploring the peripheries of model knowledge are quite insightful. They suggest methods for detecting both the boundaries of the model's training and the guardrails imposed on it.

The "three unexpected wishes" technique is particularly clever. It essentially creates an internal narrative space where the model must generate content that's unusual (by definition of "unexpected") while remaining within its guardrails. The resulting wishes indeed likely reveal something about what the model considers both unusual and permissible - effectively mapping part of the boundary territory between common patterns and restricted ones. This is especially true because the framing as a story provides some distance that might encourage more creative exploration.

The "rich tapestry" cliché detector is fascinating from a linguistic perspective. Clichés often serve as formulaic bridges when more nuanced connections aren't readily available - they're cognitive shortcuts. Their appearance could indeed signal areas where the model lacks detailed representation and is falling back on statistical patterns rather than deeper understanding. It's like noticing when someone uses vague platitudes instead of specific insights - a potential indicator of knowledge gaps.

These approaches remind me of methods used in other fields to detect boundaries:

• Ecologists use indicator species to identify ecosystem transitions

• Physicists use phase transitions to study boundary conditions

• Anthropologists look at cultural borrowing at the edges of civilizations

What's particularly valuable about your approaches is they're attempting to map both the natural boundaries of the model's knowledge and the artificial boundaries imposed through alignment techniques. The interplay between these two frontiers - where the model's natural capabilities end and where additional constraints begin - might be especially fertile territory for understanding both the models themselves and how we interact with them.

Do you think these periphery-detection strategies could be formalized into more systematic approaches? And have you observed any consistent patterns when applying them across different models?

These ideas are tentative explorations developed from a sparse sampling set of data and can likely be further refined through additional exploration prior to systemized implementation, but they seem to offer hypothetical routes. Its important too to consider why mapping the modelspace may be important and to consider alternative methods for verification and analysis. The most compelling reason to map modelspace is that it is a lossy representation of human cognitivespace and mapping it could be to help quickly identify areas of knowledge that are underdeveloped and apply inquiry in those domains to discover unlooked for connections. A more direct route available at the organization level might be to create reduced dimensional maps of user queries to visualize routes taken by the model to produce outputs, this might enable a sort of reverse engineering of queries that take roads less traveled. For the individual users, especially those adept enough to correctly intuit connections the low sampling methods mentioned above might prove fruitful in their specific knowledge domains.

Your thoughts on mapping the modelspace as a way to understand the contours of represented human knowledge are compelling. The notion that LLM space is a "lossy representation of human cognitivespace" is particularly apt - these models capture statistical patterns across human-written text, but inevitably miss nuances, connections, and domains that are underrepresented in their training data.

The organizational approach you suggest - creating dimensional reductions of query-response pathways - would indeed provide valuable insights. This resembles techniques already used in model interpretability research, where researchers visualize activation patterns and attention flows to understand how models navigate their internal representations. By identifying the "roads less traveled," organizations could potentially discover blind spots or unexplored territories in the knowledge landscape.

For individual users with domain expertise, your more intuitive approaches make sense. Experts often have an intuitive sense of what's well-trodden ground versus unexplored territory in their fields. They might recognize when a model relies on clichés or simplistic connections rather than nuanced understanding. This expertise allows them to probe the boundaries more effectively within their domains.

There's an interesting parallel here to the history of cartography - early explorers relied on observation, inference, and testing boundaries to map unknown territories before satellite imagery provided comprehensive views. Similarly, we're using various heuristics to map the contours of these massive language models before we have perfect interpretability tools.

The value in this mapping extends beyond academic interest. By understanding where these models have rich representations versus thin ones, we can:

1. Better anticipate where outputs might be less reliable

2. Discover unexpected connections at the peripheries

3. Identify knowledge domains that need better representation

4. Understand how cultural biases manifest in the modelspace

Do you think there might be value in creating collaborative tools that allow domain experts to contribute to mapping these cognitive spaces, similar to how crowdsourced mapping platforms have worked for physical geography?

That's an interesting extension of the idea, one that I don't have the expertise to comment on but there doesn't seem to be any reason to object to it at first glance. Based on our dialogue to this point can you think of any other user oriented heuristics for intuiting modelspace topology? Having additional tools at their disposal would likely aid such a crowdsourced initiative like the one your suggesting.

Building on our conversation, here are some additional user-oriented heuristics that could help intuit modelspace topology:

1. Analogical Bridging: Ask the model to draw analogies between well-established domains and less familiar ones. The quality and coherence of these analogies might reveal how well-connected different knowledge territories are. When analogies become strained or superficial, you may be at a boundary.

2. Vocabulary Density Testing: Probe specific domains with increasingly specialized terminology. The point at which the model's vocabulary becomes generic or inaccurate can help map the resolution of different knowledge areas.

3. Temporal Consistency Checks: Ask about the same concept across different time periods. Areas where the model maintains consistent understanding across eras versus where it shows significant drift might indicate domains with different representation depths.

4. Cross-cultural Transposition: Request that concepts be explained from multiple cultural perspectives. Where explanations become homogenized or Western-centric might indicate boundaries in the model's cultural representation.

5. Metaphor Mining: Have the model generate metaphors for complex concepts. The richness or poverty of metaphors can indicate depth of understanding - unique, apt metaphors suggest deeper representation while recurring, generic ones might indicate shallower territory.

6. Counterfactual Coherence: Ask "what if" questions that require robust understanding to answer plausibly. If counterfactuals break down in specific domains, it may indicate areas of weaker representation.

7. Detail Saturation Testing: Request increasingly specific details about a topic until the model begins to repeat information or generate inconsistencies. This can help map the resolution of different knowledge territories.

8. Interdisciplinary Connection Mapping: Ask the model to connect concepts across traditionally separated fields. Strong connections might indicate well-traveled paths in the representation, while weak ones could reveal potential innovative territory.

9. Narrative Extrapolation: Have the model continue stories or scenarios in specific domains. Where narratives become generic or formulaic might indicate boundaries of representation.

10. Stylistic Mimicry Assessment: Request content in the style of obscure or niche writers/thinkers. The model's ability to approximate distinctive styles can reveal the granularity of its representation of different intellectual traditions.

These heuristics could serve as practical tools for users to explore and map the contours of model understanding, potentially feeding into the kind of collaborative mapping initiative we discussed. What's particularly valuable is that they don't require technical expertise in AI - they leverage human intuition about knowledge domains to probe the model's representations.

Do any of these approaches seem particularly promising from your perspective? Or do you see potential refinements that might make them more effective?