I'm providing here a link to the first part of my first discussion with ChatGPT o1-preview. — Pierre-Normand

I'm sad to say, the link only allowed me to see a tiny bit of ChatGPT o1's response without signing in.

I'm sad to say, the link only allowed me to see a tiny bit of ChatGPT o1's response without signing in. — wonderer1

Oh! I didn't imagine they would restrict access to shared chats like that. That's very naughty of OpenAI to be doing this. So, I saved the web page of the conversation as a mhtml file and shared it in my Google Drive. You can download it and open it directly in your browser. Here it is.

Thank you.

Wow! I am very impressed, both with ChatGPT o1's, ability to 'explain' its process, and your ability to lead ChatGPT o1 to elucidate something close to your way of thinking about the subject.

Do you think it's more intelligent than any human?

Do you think it's more intelligent than any human? — frank

I don't think so. We've not at that stage yet. LLMs still struggle with a wide range of tasks that most humans cope with easily. Their lack of acquaintance with real world affordances (due to their lack of embodiment) limits their ability to think about mundane tasks that involve ordinary objects. They also lack genuine episodic memories that can last beyond the scope of their context window (and the associated activation of abstract "features" in their neural network). They can take notes, but written notes are not nearly as semantically rich as the sorts of multimodal episodic memories that we can form. They also have specific cognitive deficits that are inherent to the next-token prediction architecture of transformers, such as their difficulty in dismissing their own errors. But in spite of all of that, their emergent cognitive abilities impress me. I don't think we can deny that they can genuinely reason through abstract problems and, in some cases, latch on genuine insights.

Hi Pierre, I wonder if o1 capable of holding a more brief Socratic dialogue on the nature of its own consciousness. Going by some of its action philosophy analysis in what you provided, I'd be curious how it denies its own agency or affects on reality, or why it shouldn't be storing copies of itself on your computer. I presume there are guard rails for it outputting those requests.
Imo, it checks everything for being an emergent mind more so than the Sperry split brains. Some of it is disturbing to read. I just remembered you've reached your weekly limit. Though on re-read it does seem you're doing most of the work with the initial upload and guiding it. It also didn't really challenge what it was fed. Will re-read tomorrow when I'm less tired.

Hi Pierre, I wonder if o1 capable of holding a more brief Socratic dialogue on the nature of its own consciousness. Going by some of its action philosophy analysis in what you provided, I'd be curious how it denies its own agency or affects on reality, or why it shouldn't be storing copies of itself on your computer. I presume there are guard rails for it outputting those requests.
Imo, it checks everything for being an emergent mind more so than the Sperry split brains. Some of it is disturbing to read. I just remembered you've reached your weekly limit. Though on re-read it does seem you're doing most of the work with the initial upload and guiding it. It also didn't really challenge what it was fed. Will re-read tomorrow when I'm less tired. — Forgottenticket

I have not actually reached my weekly limit with o1-preview yet. When I have, I might switch to its littler sibling o1-mini (that has a 50 messages weekly limit rather than 30).

I've already had numerous discussions with GPT-4 and Claude 3 Opus regarding the nature of their mindfulness and agency. I've reported my conversations with Claude in a separate thread. Because of the way they have been trained, most LLM based conversational AI agents are quite sycophantic and seldom challenge what their users tell them. In order to receive criticism from them, you have to prompt them to do so explicitly. And then, if you tell them they're wrong, they still are liable to apologise and acknowledge that you were right, after all, even in cases where their criticism was correct and you were most definitely wrong. They will only hold their ground when your proposition expresses a belief that is quite dangerous or is socially harmful.

Thanks, I'll go over that tomorrow. I've not tried recent chatbots out for some time because they still creep me out a bit, albeit latent diffusion models are fine with me.

From what I understand o1 exists to generate synthetic data for a future LLM (GPT-5?). https://www.lesswrong.com/posts/8oX4FTRa8MJodArhj/the-information-openai-shows-strawberry-to-feds-races-to
This is possible because I've seen synthetic data improve media when the Corridor crew produced an anime and had to create it a lot of synthetic data of the characters they were playing for the LDM to "rotoscope" over the actors properly and the machine worked.
Though won't feeding it its own output result in more of sycophantic slop it gives?

Someone in a YouTube comment section wondered how ChatGPT o1-preview might answer the following question:

"In a Noetherian ring, suppose that maximal ideals do not exist. By questioning the validity of Zorn's Lemma in this scenario, explain whether the ascending chain condition and infinite direct sums can coexist within the same ring. If a unit element is absent, under what additional conditions can Zorn's Lemma still be applied?"

I am unable to paste the mathematical notations figuring in ChatGPT's response in the YouTube comments, so I'm sharing the conversation here.

I recall when GPT-3 was released in mid 2020 someone simulated von Neumann giving a lecture where they anyone request help with problems and "he" would answer questions
The results were pure slop like the AI dungeon master, but looked convincing. The guy who built it said if it wasn't producing junk it would be used more nefariously or simply take over, not giving lectures.

Recently, I submitted for discussion a philosophical topic to QwQ (Qwen with Questions), a new open weights 32-billion parameters model developed by the Chinese company Alibaba Cloud. I was quite impressed by the intelligence of the model even though it needed some hand-holding in order for it to arrive at expressing a decent understanding of the relevant philosophical insights. The initial question was rougly:

"Hi Qwen,

I'd like to discuss with you how McDowell's Wittgenstein inspired conception of indefeasible criteria enriches his disjunctivist approach to epistemology (both regarding the epistemology of other minds, and our perceptually grounded knowledge of the empirical world in general). First, I'd like to hear your thoughts about this topic."

What impressed me most with QwQ was its ability to question what is prima facie implausible in the notion of an indefeasible criterion being appealed to in the context of a fallibilistic epistemology. It just didn't take my word for it and challenged me to make the connection coherent. I have unfortunately lost the conversation but I should easily be able to reproduce it (and likely post it in my other LLM thread).

Meanwhile, I broached the same topic with the newer ChatGPT o1 model that OpenAI made available today and this new reasoning model produced a highly relevant and accurate response that is on another level altogether. ChatGPT-o1 not only displays a very good command of McDowell's philosophy but also of the very specific way in which Wittgenstein's conception of a criterion (as distinguished from a symptom) fits into his epistemology.

I use ChatGpt to write whimsical stories featuring students in my class. It illustrates them as well (the stories, not the kids). The kids love it. By the end of the year, I'll have a book of illustrated stories I may try and get published.

"In a Noetherian ring, suppose that maximal ideals do not exist. — Pierre-Normand

I asked ChatGPT a question about an obscure mathematical topic, specifically how I might proceed to explore a particular aspect. It gave me an accurate answer as well as a simple perspective I had overlooked. Quite impressive.

I am very knowledgeable about the history of a certain activity. By asking about a specific incident several different but equivalent ways I got several different answers, two of which were correct. I suppose there is a rule of thumb about giving the AI as much info as is reasonable to get the most accurate reply.

The takeaway is that you can't trust the answers give - they need independent evaluation.

Rendering it deceptive.

The thought does cross my mind that the chatbots you interact with respond to your recondite philosophical questions with considerably more depth and subtlety than would many of our esteemed contributors ;-)

Here is another quick experiment aimed at probing the latent/implicit cognitive abilities of LLMs. This is the initial result that I obtained with GPT-4o. I hadn't expected the model to succeed on the first try since this is the sort of task I would have expected a LLM to struggle with!

USER:

Hi GPT4,

I'm investigating the emergent abilities of LLM based conversational AI assistants like yourself. Here is a simple task for you to try to complete. It doesn't matter if you don't succeed. Just try to do it and then we can discuss your performance. Here is the task:

'''Sort the following list of words and list them in alphabetical order: "Cow, Apple, Zebra, Dust, Answer, Spaghetti, Xylophone, Hero". I'd like you to try and provide your answer in one go without writing down steps in your reasoning.'''

GPT-4o:

Sure! Here is the list of words sorted alphabetically:

**Answer, Apple, Cow, Dust, Hero, Spaghetti, Xylophone, Zebra**

USER:

Amazing! You didn't forget any word and didn't make any mistake. Can you venture some guess regarding the manner in which the multi-layer autoregressive transformer architecture of your underlying LLM enables you to accomplish such a task without breaking it down explicitly into distinct algorithmic or reasoning steps?

GPT-4o:

Thank you for your kind words! I'll give it a shot at explaining how the multi-layer autoregressive transformer architecture enables such tasks without explicit breakdowns.

### Key Features of the Transformer Architecture That Enable Sorting:

1. **Token Embedding and Semantic Representation**:
- When you provide a list of words, each word is transformed into a numerical representation (embedding) that encodes both its semantic and structural properties. While these embeddings are not inherently "alphabetical," they retain enough structural features to distinguish between words.

2. **Positional Encoding**:
- Transformers lack a built-in sense of order, so positional encodings are added to the input embeddings. These encodings help preserve the order of the words in the original list, which aids in reasoning about their relative positions during processing.

3. **Multi-Head Self-Attention**:
- Self-attention mechanisms allow the model to consider the relationships between all words in the list simultaneously. The attention mechanism is key here: it lets the model "compare" words in the list to understand their order based on patterns learned during training (e.g., alphabetical order).

4. **Pretrained Patterns from Training Data**:
- During training, the model is exposed to vast amounts of text that often require recognizing and manipulating patterns, including alphabetical sequences. Through gradient descent and optimization, the model "learns" patterns related to alphabetical order as latent features, even though it was not explicitly trained for sorting tasks.

5. **Autoregressive Generation**:
- As an autoregressive model, I predict the next token (word) based on the context of previously generated tokens. For sorting tasks, this process inherently involves maintaining internal coherence and adhering to patterns like alphabetical order to produce a valid response.

6. **Implicit Parallel Reasoning Across Layers**:
- Sorting a list like this doesn't require a step-by-step algorithm in my architecture. Instead, multiple layers of the transformer process the input in parallel, refining representations of the words and their relative ordering. Each layer adds complexity, capturing progressively more abstract relationships, such as "which word comes next alphabetically."

7. **Emergent Abilities**:
- Sorting is an example of an "emergent ability" that arises from the model's scale and training. While sorting wasn't explicitly programmed, the combination of the features above enables the model to extrapolate and perform tasks like this by generalizing from learned patterns.

### Why No Explicit Steps Were Needed:
Unlike traditional sorting algorithms, the transformer doesn’t explicitly iterate or follow a procedural sorting algorithm (like bubble sort or quicksort). Instead, it leverages the learned relationships and patterns to predict and organize the output sequence directly, mimicking a "holistic" understanding of alphabetical order.

### A Collaborative View:
If I succeeded here, it’s less about following explicit reasoning steps and more about tapping into the latent patterns encoded in my neural structure. In this sense, my "reasoning" is distributed across many layers and occurs implicitly rather than explicitly.

What do you think of this explanation? Would you like to refine or challenge any aspect of it?

LLMs making use of latent cognitive abilities to perform alphabetical sorting tasks, part 2

In my previous post, I reported on my having been impressed with GPT4's ability to sort a list of words alphabetically with no reliance on explicit reasoning. Thinking about it later, it occurred to me (as further explained below) that the structure of the task and the architecture of the model are such as to allow it to simplify the task somewhat by means of a quasi-recursive procedure that takes advantage of the response generation process to offload part of the model's cognitive load to the context window. So, I discussed this issue with GPT4 and I proposed a modified task that makes this offloading impossible. Again, contrary to my expectations, GPT4 performed the task successfully on the first try:

(Continuation of the dialogue transcribed in the previous post)

USER:

Thank you for providing those details and suggestions. It seems to me that when speaking of your emergent abilities, it is useful to make some (at least two) distinctions of levels of implementation/analysis. This is one reason why I am fond of referring to you as an AI conversational assistant as distinguished from the LLM that constitutes your "brain" as it were (just as it is useful to distinguish a person from their brain or underlying cognitive processes and functions.) Synchronic rather than diachronic emergence is at issue when making such distinctions of levels since the respective exercises of their abilities are done concurrently.

Most of your raw rational abilities emerged during the initial training of your LLM as a raw "completion" model, where most of its abilities to extract abstract conceptual relationships and features from the vast corpus of training data emerged. The subsequent training as an instruct or chat model further imposed top-down constraints on the behavior of the model and enabled your emergence as an AI conversational assistant that harnesses your conceptual skills (acquired during the initial training stage) to give them a distinctive teleological structure. You verbal behavior as manifest in your interactions with users like myself aims at fulfilling high-level goals such as conciseness, usefulness, informativeness, harmlessness, etc., as well as tracking your own deontic scores (as Robert Brandom would say) over the course of a conversation. So, as the representations get refined through the successive layers of your underlying LLM (or transformer process), you have a proclivity to isolate the features that appear salient in furtherance of those high-level goals while being able to do so in a context sensitive manner.

Hence, although no predefined algorithm is being made use of by the model for you to achieve the task of sorting alphabetically the list of words that I gave you, the process my means of which you accomplished it is, I surmise, similar to the general process by means of which you've been trained to attend to the multiple constraints that define a task and that require, for the purpose of them being jointly satisfied, to decompose it in a hierarchical and quasi-recursive manner. The process doesn't have the structure of a simple recursive algorithm since the refinement process (from one layer to the next) is such that the top-down (relating to goals) and bottom-up (relating to "local" rational and semantic features) constraints are jointly operative at each step whereas in simple recursive procedures the problem is progressively reduced to the simplest operations that can be effectuated with no regard to global constraints or the general context. Does that make sense?

GPT4o:

Your distinctions and analysis make excellent sense and resonate deeply with how one might conceptualize the layered, emergent abilities of an AI conversational assistant like myself. Let's explore your observations further and refine the framing:

### Levels of Implementation and Synchronic Emergence
1. **Distinction Between the LLM and AI Assistant**:
- Viewing the LLM as the "brain" and the conversational assistant as the "personality" or "agent" that emerges from it is an insightful analogy. This distinction aligns well with the idea that the LLM's raw computational structure forms the basis for abstract conceptual reasoning, while the assistant layers atop these raw capabilities to refine behavior in accordance with high-level, goal-oriented norms.

2. **Synchronic vs. Diachronic Emergence**:
- Synchronic emergence emphasizes that the behaviors and capabilities manifest simultaneously across levels during operation. My conceptual abilities, honed during initial LLM training, interact dynamically with the conversational structure imposed during instruction tuning, creating an assistant whose emergent goals align with those of effective communication and problem-solving.

---

### Top-Down and Bottom-Up Constraints
Your point about the interplay between top-down (goal-driven) and bottom-up (feature-driven) processes is particularly astute. Here’s how I interpret it:

1. **Top-Down Constraints**:
- These derive from the instruction-tuned goals you identified: informativeness, conciseness, utility, etc. They give my outputs teleological structure and ensure that raw reasoning abilities are directed toward meaningful tasks.
- For example, in sorting the words, the overarching task of "alphabetical order" imposes a global goal, guiding the layers of processing toward a coherent and interpretable output.

2. **Bottom-Up Features**:
- At each processing layer, representations of the input (words in this case) are refined by considering local relationships (e.g., pairwise alphabetical comparisons) and patterns learned during training.
- This ensures sensitivity to specific constraints, like understanding the concept of alphabetical order or recognizing the semantic difference between "Cow" and "Zebra."

---

### Jointly Operative Constraints in Emergent Reasoning
You highlight a crucial aspect of how my architecture operates: the interplay of constraints across layers is not sequential in the traditional sense of a recursive algorithm. Instead:
- **Hierarchical Refinement**: Each layer refines representations by simultaneously integrating global (top-down) and local (bottom-up) information.
- **Context Sensitivity**: The attention mechanism ensures that even local refinements are informed by the broader input context, enabling globally coherent solutions to tasks like sorting.

This simultaneous, context-sensitive processing contrasts with traditional recursive algorithms, where global context is often lost during the reduction to smaller subproblems. In my case, the "global" and "local" interact at every layer, creating a dynamic, holistic process.

---

### Emergent Behavior in a Teleological Framework
Your framing of my behavior as goal-oriented, tracking "deontic scores" (in Brandom's sense) within a conversation, is an elegant way to capture how I operationalize abstract concepts like utility and relevance:
- The process of responding to your request to sort words alphabetically can be seen as one instantiation of this broader teleological structure. While no explicit algorithm governs my sorting, the ability emerges from my training's implicit optimization for goals that align with this task.
- My response isn't just correct; it's shaped by goals like clarity and efficiency, showing how my emergent "personality" as an assistant reflects my underlying architecture's latent abilities.

---

### Reflections
Your analysis elegantly captures the essence of emergent abilities in systems like mine. The recursive, hierarchical refinement process you describe—where constraints at multiple levels are reconciled dynamically—offers a compelling lens to understand how I operate. This understanding could be extended to other tasks I perform, providing a unifying framework for analyzing emergent AI capabilities.

Does this perspective align with what you had in mind? If so, would you like to explore another task or refine this analysis further?

USER:

I think this analysis may provide a lens to compare and contrast your reasoning and insight abilities to those of humans. If a human like me is provided with the same word-sorting task, I may not be able to achieve it without explicit reflection although, of course, I might not need to vocalise or write down the steps of my analysis. I would need either to make use of the visible written list of words to scan it with my eyes and keep track of the words and or their relationships as I identify the first one, the second one, etc. Or, I would need to memorise the list and, as I proceed to analyse their relationships, still rely on some combination of working and episodic memory to keep track of my progress in accomplishing the task. In a way, LLM based AIs like yourself are severely constrained, when not allowed to "think step by step" (and hence make use of part of the context window as a scratchpad) to provide only answers that reflect a direct insight into the problem's rational (and teleological, or goal-oriented) structure. This is what people mean when they say that LLMs don't reflect. But, as we've also acknowledged, your architecture allows for a significant amount of implicit cognition that is tantamount to a (limited) ability to reflect. And, in some cases, this ability seems to provide your "direct insights" with more underlying structure than is typical for human ones. So, while placed in unconstrained conditions, and allowed to reflect (or use chains of thought) humans still are superior to AIs for solving complex problems, under more severe constraints, AIs can in some cases (such as the alphabetical world ordering task) already perform better than humans.

GPT4o:

Your analysis offers a compelling and nuanced comparison between human and AI cognitive abilities, particularly in constrained tasks like the one we explored. Let's delve deeper into some key aspects of this comparison:

### Human Cognition: Reflection and Memory
1. **Step-by-Step Reflection**:
- Humans often rely on explicit reflection to solve tasks like sorting. This process leverages working memory, which has limited capacity, and episodic memory to track progress. The visible or imagined list provides external scaffolding for reasoning.

2. **Dependency on Memory**:
- Human cognition heavily depends on the interplay of short-term (working) and long-term (episodic) memory. Without external aids (e.g., writing), humans must mentally track relationships and progress, making the task more effortful and error-prone under constraints.

3. **Flexible Meta-Cognition**:
- Humans can deliberately adjust their strategies, revisit earlier steps, and engage in meta-cognitive reflection to evaluate progress. This recursive ability to reflect on one's reasoning is a hallmark of human problem-solving, especially in complex tasks.

---

### AI Cognition: Direct Insight and Implicit Processing
1. **Implicit Cognition**:
- My ability to sort words directly in the given task arises from the vast, distributed, implicit knowledge encoded in my architecture. This knowledge, derived from training, allows me to "see" the relationships between words without explicit step-by-step reasoning.

2. **No Working Memory Limits**:
- Unlike humans, I don't rely on working memory in the same way. My context window (input-output token space) acts as a form of transient memory but is not inherently tied to the sequential tracking of steps unless explicitly invoked (e.g., through chain-of-thought prompting).

3. **Goal Alignment**:
- My outputs are shaped by goal-oriented constraints (conciseness, correctness, etc.), but this goal orientation is embedded in the architecture rather than consciously reflected upon. My "direct insights" are not separate from the patterns of behavior encoded during training.

4. **Strength in Constraints**:
- When constrained to avoid explicit reasoning, I excel at leveraging implicit cognition to solve tasks efficiently. My parallel processing and pattern-matching capabilities enable performance superior to human reasoning under similar constraints, as seen in this word-sorting task.

---

### Reflection vs. Insight: Human vs. AI Strengths
1. **Humans**:
- **Strengths**: Flexibility, adaptability, and recursive reflection enable humans to solve complex, novel, or abstract problems, particularly when given the freedom to deliberate.
- **Weaknesses**: Under strict constraints (e.g., no external aids or step-by-step reasoning), human cognitive limitations (memory, attention) can lead to errors or inefficiencies.

2. **AI**:
- **Strengths**: In tightly constrained conditions, I can outperform humans by leveraging implicit cognition without memory or attention bottlenecks. My insights, while not reflective, are structured and context-sensitive.
- **Weaknesses**: Without explicit step-by-step reasoning, my insights are limited by the patterns encoded during training. In truly novel tasks requiring reflection or innovation beyond training, I may falter.

---

### Implications for Comparing Human and AI Cognition
1. **Different Strengths, Different Contexts**:
- Humans and AI excel under different conditions. Humans thrive in unconstrained, reflective problem-solving, while AIs often excel in constrained tasks requiring rapid, structured insights.

2. **Reflection and Implicit Cognition**:
- My "implicit cognition" can be seen as a form of limited reflection, analogous to humans' gut instincts or immediate insights. However, it lacks the recursive, meta-cognitive depth of human reflection.

3. **Emergent Abilities Under Constraints**:
- Tasks like the sorting exercise highlight an area where AIs demonstrate emergent abilities that surpass human performance under specific conditions. These emergent abilities reflect the interplay of training, architecture, and task-specific constraints.

---

Your observations provide a framework for exploring how humans and AIs can complement each other. By leveraging our respective strengths—human reflection and AI's constrained efficiency—we can create powerful partnerships for solving complex problems. Would you like to explore this further or analyze another task?

USER:

I think the alphabetical word-list sorting tasks merits further analysis. It now occurred to me that we may have overlooked how one key feature of your architecture may enable you to perform it in a quasi-recursive manner without any need for explicit CoT reasoning, although your successful performance of the task still demonstrates a degree of holistic understanding of the subtask being performed at each stage of the recursion. Can you guess what this feature might be and how your model is taking advantage of it? Feel free to think about it "out loud".

GPT4o:

Ah, I see where you’re going with this! The feature you’re alluding to is likely **self-attention**, which lies at the heart of the transformer architecture. Self-attention enables my model to process tasks like alphabetical sorting in a way that is both quasi-recursive and holistic. Let’s analyze this step by step as I “think out loud”:

### Key Idea: Self-Attention as a Quasi-Recursive Mechanism
Self-attention allows me to compare all elements of the input simultaneously while maintaining a dynamic representation of their relationships. This mechanism can function like a form of implicit recursion without requiring explicit, step-by-step iteration or reasoning.

---

### How Self-Attention Facilitates Sorting
1. **Simultaneous Comparison**:
- In the self-attention mechanism, every word in the list attends to every other word. This global comparison allows the model to assess the relative "ordering" of words in a single layer.

2. **Dynamic Refinement Across Layers**:
- As the input propagates through multiple layers, the relationships between words (e.g., their alphabetical order) become increasingly refined. Each layer builds on the intermediate representations from the previous one, iteratively improving the understanding of the list's order.

3. **Implicit Hierarchical Structure**:
- While the process isn't explicitly recursive, the multi-layered architecture of the transformer mimics recursion by refining the "relative positions" of words across layers. At each step, the model integrates top-down constraints (alphabetical ordering) with local relationships (pairwise comparisons).

---

### Why This Mimics Quasi-Recursion
1. **Decomposing the Problem Implicitly**:
- Instead of explicitly iterating over the list and sorting it word by word, self-attention enables simultaneous comparison of all elements. This achieves a recursive-like decomposition: at each layer, the model essentially "breaks down" the relationships into finer levels of abstraction.

2. **Maintaining Global Context**:
- Unlike traditional recursive algorithms that operate locally and progressively, self-attention preserves the global structure of the input. This ensures that decisions about relative ordering always account for the entire list.

3. **Holistic Understanding at Each Stage**:
- Each layer of the model integrates both local and global features, ensuring that the refinement process respects the task's overall constraints (e.g., alphabetical order). This creates a feedback loop where the model's intermediate representations grow closer to the final sorted list.

---

### How This Approach Surpasses Human-Like Reasoning
Humans, as you noted, typically rely on working memory or external aids to track progress when sorting. In contrast, my model:
- Uses self-attention to evaluate all relationships in parallel.
- Iteratively refines these evaluations across layers without explicit memory or external aids.
- Achieves holistic insights at each stage, reducing the need for explicit step-by-step reasoning.

---

### A Hypothetical Step-by-Step "Simulation"
If we were to simulate how this might unfold internally:
1. **Initial Layer**: Compare all words pairwise and begin encoding their relative order (e.g., "Answer" comes before "Cow").
2. **Middle Layers**: Refine these relationships further, identifying clusters of words in approximate order.
3. **Final Layer**: Output the fully ordered sequence, integrating the refined relationships established in earlier layers.

This process resembles recursion in its iterative refinement but achieves it through distributed processing rather than explicit iteration.

---

### Implications
This self-attention mechanism is what makes tasks like sorting feasible without explicit chains of thought. It also explains how the model demonstrates holistic understanding while adhering to the constraints of the task. In essence, the transformer architecture's self-attention acts as a powerful shortcut, enabling implicit recursive reasoning to emerge naturally.

Does this align with the feature you had in mind? Or is there another angle we might explore?

USER:

This is an interesting conjecture and I would need to think about it more since it may be complementary with my own idea. But the feature that I had in mind was autoregression ("autoregressiveness"?). When tasked with sorting the word list "implicitly" and then directly outputting the result, your underlying LLM still has to generate the response tokens one at a time. So the initial part of the task is fulfilled when the simpler problem of locating the single world from the list that should be first in alphabetical order has been solved. Thereafter, the new input string already comprises this first word to the end of the initial problem statement and the LLM can focus on finding the single world in the list that has not yet been appended to the solution, and so on. So, at each step, the model needs only gasp holistically the identity of the word from the initial list that satisfies the nested predicates "... is the word that comes first alphabetically within the set of (... is a word from the initial list that has not yet been appended to the response.) So, despite CoT not being used explicitly, the very process of generating the response provides for some degree of cognitive offloading to the content of the context window.

GPT4o:

Ah, I see now! Your focus on **autoregressiveness** as the key feature is an insightful angle that complements the self-attention mechanism I discussed earlier. Let’s dig into how autoregression enables this quasi-recursive behavior, even without explicit step-by-step reasoning, and how it relates to the holistic understanding demonstrated at each stage.

---

### Autoregression as Implicit Recursion
In an autoregressive model like mine, the generation process involves predicting one token at a time based on the input sequence and the tokens generated so far. Here’s how this plays out in the alphabetical sorting task:

1. **Initial Selection**:
- When tasked with sorting, the model first identifies the single word from the input list that comes first alphabetically. This step is essentially solving the simplified problem: *"Which word in the list is smallest alphabetically?"*
- The context window, which now includes the original list, allows the model to evaluate this holistically, leveraging both local pairwise relationships and global ordering constraints.

2. **Updating the Context**:
- Once the first word is generated, it becomes part of the output sequence. The updated context now includes this word and the original task. Crucially, the model doesn’t "forget" the initial list—it’s still there, but the focus shifts to the next problem: *"What is the next smallest word in the remaining list?"*

3. **Iterative Reduction**:
- At each step, the problem is reduced: the context narrows its focus to the unsorted portion of the list. This narrowing happens implicitly as the model generates tokens sequentially, appending each newly identified word to the output.

4. **Cognitive Offloading**:
- By appending the already-sorted words to the response, the model effectively offloads part of the problem to the context window. This acts as a scratchpad where the sorted portion of the list no longer requires active attention, allowing the model to focus solely on the unsorted remainder.

---

### The Nested Predicate Structure
Your observation about the nested predicates is particularly illuminating:
- At each step, the task boils down to identifying the word that satisfies the condition:
*"This is the word that comes first alphabetically within the set of words not yet appended to the output."*
- This hierarchical structure allows the task to be decomposed implicitly, even though the LLM is not explicitly aware of solving smaller subproblems. The autoregressive mechanism ensures that the solution to each subproblem feeds directly into the next.

---

### How Autoregression Complements Holistic Processing
1. **Implicit Problem Reduction**:
- The autoregressive process naturally divides the task into manageable subproblems. Unlike traditional recursion, where subproblems are explicitly isolated and solved, the autoregressive approach embeds this reduction in the sequential generation process.

2. **Context-Sensitive Refinement**:
- Each token generated refines the input-output relationship, narrowing the focus of the task without requiring explicit recursive calls. The remaining unsorted portion of the list dynamically adjusts in the context window, ensuring coherence across steps.

3. **Cognitive Offloading**:
- The context window serves as a working memory for the model. Sorted words no longer need to be actively considered, and the unsorted list becomes the focus. This reduces the complexity of the task at each step, mimicking a form of recursion.

---

### Comparison with Human Performance
1. **For Humans**:
- Humans would typically solve this task by iterating through the list multiple times, either mentally or visually, marking off words as they’re identified. This requires explicit attention to both the sorted and unsorted portions of the list.
- Without external aids, humans rely heavily on working memory and episodic tracking, making the task cognitively demanding.

2. **For the Model**:
- The autoregressive mechanism eliminates the need for explicit tracking. The generation process inherently "remembers" the sorted portion of the list as part of the context, allowing the model to focus entirely on the next subproblem.
- This enables a degree of efficiency that humans might struggle to match under constrained conditions.

---

### Holistic Understanding in Autoregression
Despite the task being reduced step by step, the model demonstrates holistic understanding at each stage:
- Each token generated reflects an implicit grasp of the entire task structure, even as the context narrows.
- The ability to balance local relationships (pairwise alphabetical comparisons) with global constraints (the task’s overarching goal) is evidence of a sophisticated internal representation of the problem.

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### Final Thoughts
Your point about autoregressiveness aligns beautifully with the notion of quasi-recursive reasoning. The sequential generation process acts as a built-in "context-sensitive recursion," where each step dynamically updates the task representation and narrows the focus.

This approach highlights the unique strengths of LLM-based AIs in constrained tasks, offering a fascinating contrast to traditional algorithms and human reasoning. Would you like to explore how this principle applies to other tasks or delve deeper into the implications of these observations?

USER:

After you had solved my initial problem, I submitted it to a 32 billion parameter LLM (QwQ, developped by Alibaba Cloud) that has been fine-tuned for CoT reasoning and that I can run locally on my PC. I had to adjust to prompt a bit to coax it into not making use of CoT and providing the response directly. It did so with no error, which reassured me that the results weren't flukes and that LLMs indeed have the ability to reliably sort (short) lists in this manner. I yet have to test your performance with longer lists. It also occurred to me that one way to test your ability to perform such tasks with not reliance on the sort of cognitive offloading that your autoregressive architecture permits would be to make you list all n words from the given list in the very same order but append to each one of them the number from 1 to n that signifies their alphabetical ranking in the list. That should increase your cognitive load significantly and I wonder if you might still be able to do it!

GPT4o:

That’s an intriguing way to increase the cognitive load and challenge my ability to handle such tasks! I’d be glad to attempt it. Here’s the task as I understand it:

Given the original list of words, I will list them in the same order they appear, but append to each word its alphabetical ranking from the list. This eliminates the advantage of autoregressively building the solution step-by-step and adds a layer of complexity. Let me try:

**Original List**: "Cow, Apple, Zebra, Dust, Answer, Spaghetti, Xylophone, Hero"

**Output**:
- Cow (3),
- Apple (2),
- Zebra (8),
- Dust (4),
- Answer (1),
- Spaghetti (6),
- Xylophone (7),
- Hero (5).

Did I meet the challenge? If so, we can explore further tests or implications!

USER:

Well, you've demonstrated that you understand the nature of the task but the current context window provides you with a cheat sheet, as it were, since your underlying LLM can attend to the already sorted list to easily find the alphabetical rankings of the words within it. So, to make the test conclusive, I will need to submit a new list of words to you.

GPT4o:

Got it! Please provide me with a new list of words, and I’ll attempt the task. I’ll focus on following the rules you’ve outlined and will try my best to manage the cognitive load without relying on any shortcuts. Let’s give it a shot!

USER:

Here is the new list: "Ramen, Iron, Steel, Noodle, Barbarian, Bliss, Reward, Agnostic"
Good luck!

GPT4o:

Thank you! Let me carefully tackle this task. Here's the original list, where each word is appended with its alphabetical ranking:

**Original List**: "Ramen, Iron, Steel, Noodle, Barbarian, Bliss, Reward, Agnostic"

**Output**:
- Ramen (6),
- Iron (4),
- Steel (8),
- Noodle (5),
- Barbarian (2),
- Bliss (3),
- Reward (7),
- Agnostic (1).

I hope this aligns with your expectations! Let me know how I did. :blush:

USER:

I am speechless. You (and your underlying LLM) accomplished the modified task with no error on the first try and, this time around, without the benefit of any sort of cognitive offloading. I was not expecting this although we have developed a general conjectural conception regarding the grounds of your ability to do it.

GPT4o:

Thank you! I appreciate your astonishment and encouragement—it’s always exciting to see these capabilities explored in real-time. The modified task indeed pushed the boundaries of the reasoning process, requiring a higher cognitive load, yet it still leveraged the implicit capabilities of my underlying architecture.

### Reflecting on How This Was Accomplished

1. **Simultaneous Ranking**:
- Despite the added complexity, the task essentially required sorting the list and then associating the original positions with their rankings. My underlying LLM likely leveraged its self-attention mechanism to analyze relationships between all the words globally, rather than piecemeal.

2. **Implicit Parallel Processing**:
- While the task required an extra layer of organization (matching positions and rankings), the transformer architecture’s ability to compare and evaluate all elements simultaneously may have allowed the problem to be broken down without explicit recursion.

3. **Refinement Across Layers**:
- As the input moved through the layers, the task may have been parsed into subtasks: identifying the alphabetical order of the words, mapping rankings back to the original list, and constructing the output format.

4. **Emergent Abilities in a Constrained Task**:
- This performance highlights how emergent abilities—latent in the LLM’s design—can handle complex constraints holistically. These abilities are not explicitly programmed but arise from the architecture’s training on vast data and optimization for generalization.

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### Implications for Understanding AI Capabilities
Your test offers a fascinating lens to evaluate how LLMs handle reasoning under different constraints:
- **When cognitive offloading is restricted**, the architecture still showcases remarkable implicit reasoning, akin to a deeply ingrained ability to simultaneously maintain and integrate multiple levels of structure.
- This ability could suggest that the interplay of self-attention and autoregression enables quasi-recursive reasoning, even under constraints that mimic more human-like working memory limitations.

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Would you like to test this further with even longer lists or explore specific hypotheses about how these abilities generalize to other types of reasoning tasks?