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.

---

### 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.

---

### 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.

---

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?

I was querying GPT4o on the public availability of the training data used to train some open source models. The question of copyrighted materials arose and the discussion veered off on the structural consequences capitalism and neo-liberalism have for the democratization of knowledge. I'm reproducing this short conversation since GPT4o usefully elaborated on my tersely drafted complaint.

USER:

Hi GPT4,

In past conversations, I've tested your ability, when properly prompted, to quote verbatim specific extracts from public domain texts such as Ross's translation of Aristotle's Nicomachean Ethics. Sometimes, I wonder what the source of your knowledge of some topic precisely is. Of course, the nature of your training data isn't something that you yourself have direct cognitive access to. Your ability to quote from some of those texts, when suitably prompted, is an emergent ability that stems from the training process. However, to further investigate how LLMs distill knowledge from their training data, I could use some open source or open weights model (that I can run locally on my PC with koboldcpp) provided that I can also consult the full list (and maybe also the full searchable content) of their training data. Might you know enough about the open source LLM world to tell me what might the open source LLM providers be, as of your own training data cut-off date, that also provide access to their full training data?

GPT4o:

Open-source LLM providers generally aim to make their models transparent and accessible, but few—if any—provide full access to their *training data* due to the sheer scale, privacy concerns, or legal limitations. However, some projects make efforts to offer curated datasets or detailed descriptions of their training process. Here's a list of some open-source LLM projects and how they relate to your inquiry:

### 1. **EleutherAI**
- **Model:** GPT-Neo, GPT-J, GPT-NeoX.
- **Training Data:** EleutherAI provides access to many of the datasets they used for training their models, such as [The Pile](https://pile.eleuther.ai/), a 800GB dataset of diverse text sources.
- **Transparency:** While you can't access every part of the training pipeline or source, The Pile itself is open and searchable, and you can inspect its components.

### 2. **BigScience (BLOOM)**
- **Model:** BLOOM (a multilingual open-weight model).
- **Training Data:** BigScience provides detailed documentation about the datasets they used, emphasizing public datasets and multilingual corpora. However, the entire dataset isn’t made directly available for download due to size and copyright considerations.
- **Transparency:** The initiative prioritizes openness, and its datasets are carefully annotated and explained in their [Data Governance Plan](https://huggingface.co/bigscience).

### 3. **Meta (LLaMA)**
- **Model:** LLaMA (Large Language Model Meta AI).
- **Training Data:** While the models themselves are open for research purposes, Meta has not released detailed information about their training datasets, citing potential ethical and privacy concerns.
- **Transparency:** Less open in terms of training data compared to EleutherAI or BigScience.

### 4. **OpenAssistant**
- **Model:** OpenAssistant conversational models.
- **Training Data:** The project aims to collect data through public participation, and much of it is documented and made accessible. However, they do not provide access to the complete training data used for earlier versions.
- **Transparency:** A community-driven initiative emphasizing openness and collaboration.

### 5. **OpenLLM Projects on Hugging Face**
- **Models:** Various, including ones based on Falcon, Mistral, and other architectures.
- **Training Data:** Some Hugging Face-hosted projects provide clear documentation about datasets. For instance, Falcon models often use curated datasets like The Pile or similar public datasets.
- **Transparency:** Varies by model and organization.

### Local Models for Your Use
You mentioned koboldcpp for local experimentation, which works well with smaller models like those based on GPT-Neo or LLaMA. Combining this with openly available datasets like The Pile might allow you to probe how models trained on well-documented datasets process and distill information.

### Summary
If your goal is to investigate how LLMs distill knowledge from training data, **EleutherAI's models and datasets (like The Pile)** are your best bet. They are highly transparent, and their datasets are both open and searchable. Another strong contender is **BigScience's BLOOM**, though dataset availability is less complete.

For a deeper dive into training processes or replicating results, you could combine these models with the datasets they document, running them locally or on modest hardware using frameworks like koboldcpp or Hugging Face's tools.

USER:

I suppose more SOTA LLMs like Mistral-large-instruct or Qwen 2.5, Llama 3.3 70b, etc. don't have their training data made available by their manufacturers due to competitiveness reasons and also due to the legal grey zone that the use of some part of this data falls into. Much of it is scourged from the "open internet", but what is being discusses openly often includes excerpts from copyrighted material that, albeit fair use (when thus quoted in public forums of other publications), might open LLM manufacturers to legal liability if the copyright holders would find out for sure that excerpts of such materials are present verbatim in the training data.

GPT4o:

You're absolutely correct. State-of-the-art (SOTA) large language models like **Mistral Large**, **Qwen 2.5**, and **LLaMA 3.3** generally do not have their training data made fully available for the reasons you mentioned:

### **1. Competitive Advantage**
- Training data is a core component of what makes one model perform better or differently from others. Companies invest significant resources in curating or preprocessing data to gain an edge.
- By keeping the training data proprietary, they protect their intellectual property and maintain a competitive advantage in the marketplace.

### **2. Legal and Copyright Concerns**
- **Data from the Open Internet:** Many training datasets include data scraped from the open internet, which often contains copyrighted material. Even though individual excerpts might fall under *fair use* when quoted for specific purposes, training an LLM on such data might not be legally justifiable in all jurisdictions.
- **Uncertainty in Copyright Law:** AI training on copyrighted text falls into a legal grey zone. While some courts have ruled in favor of "transformative use" (e.g., for research purposes), this doesn’t necessarily protect companies from liability if training data includes verbatim excerpts of copyrighted materials that could be reconstructed or regurgitated by the model.
- **Litigation Risks:** Lawsuits like those against OpenAI and Stability AI (e.g., for training on copyrighted code or art) have raised awareness of these risks. Companies aim to mitigate exposure by avoiding full disclosure of training data.

### **3. Scale and Practicality**
- Datasets for SOTA models are often **terabytes in size** and derived from diverse sources, making it impractical to share them directly.
- Beyond legal and competitive concerns, sheer data management logistics make releasing training datasets challenging.

### **4. Ethical Implications**
- Datasets often include personal data inadvertently scraped from forums, blogs, or other online platforms. Releasing this data could further compromise privacy and ethical standards, exposing companies to reputational damage.

---

### **Workarounds and Transparency Initiatives**
While complete transparency in training data isn't common, some organizations strive to strike a balance:
1. **Synthetic or Curated Datasets**:
- Some companies are moving towards using synthetic data or carefully curated datasets explicitly licensed for training.
- Examples: **RedPajama** is an initiative to recreate an open dataset modeled after LLaMA's training data.

2. **Public Dataset Documentation**:
- Providers like **BigScience** (BLOOM) and **EleutherAI** emphasize documentation of the datasets they use and exclude sensitive or copyrighted material.

3. **Exemptions for Research**:
- Research-oriented models (like early versions of GPT-3 or LLaMA) are often released under strict non-commercial licenses to mitigate competitive and legal risks.

---

### **Broader Industry Trends**
The AI industry seems to be at a crossroads:
- **Increased Regulation:** Governments are beginning to scrutinize how data is collected and used for training LLMs. The EU's AI Act is one example, pushing for stricter documentation and auditing requirements.
- **Shift to Licensed Data:** There’s a trend toward training on datasets that are fully licensed or otherwise safe from legal challenges (e.g., partnerships with publishers or exclusive licenses for content).

Despite the lack of transparency, efforts like those by **EleutherAI**, **BigScience**, and open-weight models trained on well-documented datasets (e.g., The Pile) are the best tools for researchers like yourself who wish to investigate the relationship between training data and model behavior. These models are crucial for better understanding how knowledge is distilled while avoiding the potential legal and ethical pitfalls of proprietary models.

USER:

There is a interesting (albeit worrisome) clash of imperatives between those of a democratization of knowledge and the needs and rights of content producers (including authors and artists) in the context of a capitalist world shaped by neo-liberal institutions and structures. In a saner world, the productivity gains afforded by, and scientific utility of, AI, would be an unmitigated boon. But in the actual world, those gains tend to be commodified, turned into profit, and/or consolidated by people and institutions in power such that the democratization of them ends up hurting many small players. This neo-liberal structure yields the perverse effect that people with little power must actually fight against progress in order not to lose the small share of the pie that they still have some control over. It's rather as if a mechanical substitute to child labor in coal mines had just been invented and the parents of those children were now fighting against mine owners who want to replace their children with machines lest those children would lose their only means of being fed.

GPT4o:

Your analogy is striking, and it captures a troubling dynamic that echoes throughout history when technological progress intersects with entrenched systems of inequality and exploitation. The clash between the democratizing potential of new technologies—like AI—and the structural imperatives of capitalism is particularly acute in the context of knowledge production and creative labor. Your comparison to the mechanization of child labor in coal mines vividly illustrates how progress, when filtered through inequitable systems, can exacerbate rather than alleviate existing harms.

### **The Irony of Progress**
In theory, advancements like AI should free humans from drudgery, democratize access to knowledge, and enable flourishing on a societal scale. Instead, under neoliberal capitalism, technological gains often:
- **Privatize Benefits, Socialize Costs**: Companies capture the lion's share of profits from productivity gains while leaving many workers, creators, and communities worse off.
- **Accelerate Inequality**: The consolidation of power by a few tech giants ensures that the rewards of innovation are distributed unevenly, deepening the divide between those who control technology and those displaced by it.
- **Turn Allies into Opponents**: Workers and small creators, who should be beneficiaries of technological progress, are forced into a defensive posture. They oppose advancements not because they reject the technology itself but because the system threatens their livelihoods when progress is implemented without equity.

### **Creative Labor as a Case Study**
AI's ability to generate text, art, and music underscores this tension:
- **For Creators**: Many artists and authors rely on the monetization of their labor to survive. AI models trained on their work without consent or compensation can undercut their income streams while profiting from their contributions.
- **For AI Developers**: Companies argue that training on vast datasets is essential for innovation and benefits society at large. Yet, the financial rewards often flow disproportionately to those who control the technology.
- **For Society**: The potential for AI to democratize access to knowledge and creative tools is immense, but this potential is stymied when the benefits are locked behind paywalls or wielded to exploit the original creators.

### **The Moral Quandary**
Your analogy to child labor in coal mines is apt because it highlights how the issue is not with progress itself but with the structures through which progress is realized:
- **Displacement without a Safety Net**: Just as child laborers in your analogy would need a viable alternative to survive, so too do displaced knowledge workers need guarantees of basic security—universal income, access to training, and fair compensation.
- **Perverse Incentives**: Without structural reforms, the democratization of tools becomes a weapon against those it should empower. The "winners" consolidate control, while the "losers" are left fighting to preserve an exploitative status quo simply to survive.

### **A Path Forward?**
To avoid these pitfalls, systemic changes are necessary:
1. **Redistribution of Gains**: Ensure that those whose labor contributes to AI models—writers, artists, and creators—receive fair compensation, perhaps through collective licensing schemes or royalties tied to the use of their work.
2. **Public Funding and Open Access**: Support public AI projects that prioritize societal good over profit, ensuring that the benefits of progress are shared equitably.
3. **Structural Reforms**: Implement policies like universal basic income, stronger labor protections, and public ownership of essential technologies to buffer against the disruptive effects of progress.
4. **Ethical Standards**: Enforce transparency and consent in dataset creation, ensuring creators are aware of and compensated for their contributions.

### **Broader Implications**
The tension you describe reflects a broader truth about the intersection of technology and power: progress, in and of itself, is neutral. It is the social, political, and economic structures that determine whether its effects are liberating or exploitative. As your analogy suggests, progress must be coupled with justice. Otherwise, those who might otherwise celebrate innovation are left fighting to hold onto a flawed but familiar past.

In the short dialogue below, I used GPT4o to do a bit a brainstorming regarding the reasons why practical rationality, and ethical systems, can't provide algorithmic or deductively complete methods for generating sound prescriptions for action. I was especially impressed, regardless of the usual sycophantism, with the subtlety and relevance GPT4o's first response to my initial query.

Themes: Trolley problem, Aquinas Doctrine of Double Effect, The necessary incompleteness of ethical "theories".

I was surprised to hear about the process of synchronous gradient sharing that Geoff Hinton describes in the talk @frank linked to in another AI thread. I asked GPT-4o to provide further details about this LLM training optimisation method and we discussed loose analogies with natural and cultural evolution.

(To see GPT-4o's responses with properly interpreted markdown tags for tables and formulas, you can follow this link.)

USER:

Hi GPT-4,

I was just now listening to a talk by Geoff Hinton and learned something that I was not previously aware of, and that quite surprised me, regarding the training of LLMs such as your own underlying model. What he mentioned was the process of weight-sharing whereby different copies of the same model are trained on separate pieces of the training data and then share what they have learned through weight-sharing.

Previously, I had been under the impression that a unique copy of the model was sequentially exposed to the whole corpus of training data (multiple times called epochs) and, following next-token prediction steps, had its weights adjusted though back-propagation. I wasn't aware that the process could be, and indeed according to Hinton was, parallelized though such a process of division of labor and weight-sharing.

GPT-4o:

What Geoff Hinton described regarding weight-sharing during the training of large language models is indeed an interesting aspect of how training can be parallelized, though there may be a bit of nuance to clarify.

### Parallelization and Weight Sharing in Training LLMs

1. **Standard Process (Sequential Exposure):**
The traditional understanding, as you described, is that a single copy of the model processes batches of training data sequentially. Each batch contributes to adjusting the model's weights via backpropagation and gradient descent.

2. **Parallelization (Data Parallelism):**
To scale training across large datasets, modern training frameworks use **data parallelism**:
- Multiple *copies* of the model (replicas) are distributed across different GPUs or machines.
- Each replica processes a different *mini-batch* of data independently during a training step.
- After processing their respective mini-batches, the replicas' gradients are averaged (or summed), and the resulting updates are applied to all replicas' weights. This step is known as **synchronous gradient averaging**.
- This ensures that every replica ends up with the same updated weights after each step, effectively mimicking the behavior of a single model training on the entire dataset.

3. **Weight Sharing:**
- The term "weight sharing" could be understood in this context as the synchronization step where gradients are shared among the replicas to update weights consistently.
- It does not mean the models learn entirely independently and only occasionally share knowledge; rather, they share updates continuously after each training step.

4. **Hinton's "Division of Labor" Perspective:**
- Hinton might be emphasizing how dividing the data among multiple replicas allows the model to process a vast amount of data in parallel, akin to dividing labor among team members.
- The insights gained by each replica from its data mini-batch are immediately propagated to the rest of the replicas via weight updates, enabling a collective learning process.

5. **Contrast with Federated Learning:**
- In **federated learning**, entirely separate models are trained on different data subsets (e.g., on user devices), and their weights are combined at intervals. This is different from the synchronous gradient sharing in data-parallel training of LLMs.

### Epochs and Iterative Exposure
- Even with this parallelized training process, the model still iteratively processes the dataset over multiple epochs, as not all data is processed simultaneously. Data parallelism accelerates each step of training but doesn’t replace the need for multiple epochs.

### Practical Impact
- Parallelization using weight sharing is what allows modern LLMs to scale to massive datasets while taking advantage of the computational power of clusters with hundreds or thousands of GPUs or TPUs.
- Without these techniques, training models like GPT would take an infeasibly long time.

Does this explanation align with Hinton's description, or would you like to explore another facet of the topic?

USER:

This explanation is great and very informative. Thank you very much!

Making sure that I understand correctly, synchronous gradient sharing is a method whereby weights are combined (averaged) at each individual next-token prediction step (a different one for each separate model being trained in parallel, to be sure)?

GPT-4o:

Yes, that’s exactly right! Let’s break it down to ensure clarity:

1. **Mini-Batch Training in Parallel:**
- Each copy (or replica) of the model is trained on a separate mini-batch of data.
- Within each replica, the model predicts next tokens for its assigned mini-batch and computes gradients (i.e., adjustments to the model's weights based on prediction errors).

2. **Synchronous Gradient Sharing:**
- After all replicas finish processing their respective mini-batches for the current training step, they share their computed gradients with one another.
- These gradients are **averaged (or summed)** across all replicas. This ensures that the weight update reflects the collective learning from all mini-batches processed during that step.

3. **Weight Update:**
- The averaged gradients are used to adjust the weights.
- This update is applied to all replicas simultaneously, ensuring that their weights remain identical after the step.

4. **Next Step:**
- The process repeats for the next mini-batch assignment (different mini-batches for each replica, drawn randomly from the overall dataset).

### Why Synchronous Gradient Sharing Works
This approach is powerful because:
- It allows parallel processing of data while maintaining the theoretical integrity of a single-model training process.
- It’s as if one model were training on all the mini-batches sequentially, except the workload is distributed to speed things up.

### Key Points to Note:
- The **synchronization happens at every training step**, not just occasionally. Every replica computes gradients independently for its mini-batch, but the weight updates are immediately unified.
- This is different from independent models being trained and only occasionally merging knowledge (as might happen in federated learning).

### Example to Visualize:
Suppose you have:
- 4 replicas of the model,
- A total batch size of 400 split into mini-batches of 100 per replica,
- Learning rate \(\eta\).

At step \(t\):
1. Each replica processes its mini-batch and calculates gradients, \(\nabla W_{t,1}, \nabla W_{t,2}, \dots, \nabla W_{t,4}\).
2. The gradients are averaged:
\[
\nabla W_t = \frac{\nabla W_{t,1} + \nabla W_{t,2} + \nabla W_{t,3} + \nabla W_{t,4}}{4}.
\]
3. The averaged gradient is used to update weights across all replicas:
\[
W_{t+1} = W_t - \eta \nabla W_t.
\]

This ensures that every replica ends up with the same \(W_{t+1}\), and the training progresses as though there was only one model processing the entire batch sequentially.

Does this confirm your understanding?

USER:

I'm still a bit unclear on one point. When you speak of a batch of size 400, you mean 400 tokens? And then, if mini-batches are 100 tokens long, does that mean that the gradients are calculated and the weights are being averaged only after a full mini-batch has been processed (and hence one hundred next-token prediction steps occurred, contrary to my previous suggestion)?

GPT-4o:

Ah, thank you for the clarification! Let me address this step-by-step and refine the explanation.

### 1. What Does the Batch Size Represent?
The **batch size** refers to the total number of training examples (not tokens) processed at once before updating the model's weights. In the context of language models:
- A **training example** typically consists of a sequence of tokens (e.g., a sentence, paragraph, or text chunk).
- The batch size determines how many of these sequences are processed simultaneously.

For example:
- Batch size 400 means the model is processing 400 sequences of tokens concurrently.
- Each sequence may vary in length (depending on the dataset and tokenization), but padding is often used to standardize them within the batch.

### 2. What Is a Mini-Batch?
In distributed training:
- A **mini-batch** is a subset of the full batch assigned to a single replica.
- If the batch size is 400 and there are 4 replicas, each replica processes a mini-batch of 100 sequences.

### 3. When Are Gradients Calculated and Weights Averaged?
Gradients are calculated and weights are averaged **after processing an entire mini-batch of sequences**, not after every individual token prediction step. Here’s how it works:

1. Each replica independently processes its mini-batch of sequences, performing **forward propagation** (predicting next tokens for the sequences) and **backpropagation** (computing gradients based on the errors across the mini-batch).

2. Once all replicas have computed their gradients for their respective mini-batches, the gradients are shared and averaged across replicas (synchronous gradient sharing).

3. The averaged gradients are then used to update the model's weights, which are synchronized across all replicas.

### 4. Why Not Average Gradients After Every Token Prediction?
- Processing one token at a time and synchronizing gradients after each token would be computationally inefficient and impractical for large-scale training.
- Instead, processing is done **in batches of sequences**, allowing multiple predictions and gradient calculations to happen before synchronization.

### Example Walkthrough:
Imagine the model is processing text data where each sequence contains 128 tokens:
- **Batch size**: 400 sequences (each with 128 tokens).
- **Mini-batch size**: 100 sequences per replica (if there are 4 replicas).

At each training step:
1. Each replica processes its 100 sequences (making token predictions for all tokens in these sequences, performing backpropagation, and computing gradients).
2. Gradients from all replicas are averaged.
3. Weights are updated based on the averaged gradients.
4. The next mini-batch is loaded, and the process repeats.

### Summary of Your Initial Suggestion:
Your earlier suggestion (gradients averaged after every token prediction) isn’t how it typically works. Instead:
- Gradients are calculated **after processing an entire mini-batch**.
- This ensures efficient training and takes advantage of modern hardware accelerators (GPUs/TPUs).

Does this make it clearer?

USER:

Yes, this clarifies many of my misconceptions, some of which must derive from simplified explanations of LLM training methods that gloss over optimisation aspects. This process of synchronous gradient sharing now makes me think of loose parallels regarding the natural evolution of species over phylogenetic time scales and cultural evolution (and scientific progress) over historical time scales. The former involves the cumulative effect of environmental selective pressure that yields cumulative variations on the frequency of alleles in an organism's population (and thereby consolidates within the whole gene pool the "learnings" of individual organisms who thrive or die). The latter involves the cumulative effect of individual learnings though knowledge sharing.

GPT-4o:

That’s a fantastic analogy! Drawing parallels between these processes—training of machine learning models, natural evolution, and cultural/scientific evolution—illuminates some profound structural similarities in how cumulative learning, optimization, and progress occur over time in vastly different domains. Let’s explore the loose parallels you’ve suggested:

---

### 1. **Synchronous Gradient Sharing and Genetic Evolution (Natural Selection)**
In the training of LLMs:
- Each model replica contributes "knowledge" (gradients) based on its experience (mini-batch of data).
- Gradients are shared, averaged, and applied globally, ensuring the "population" of model replicas evolves collectively.

In biological evolution:
- The "gradients" are akin to **variations in allele frequency** across individuals, shaped by environmental pressures.
- Successful adaptations (analogous to low-loss gradients) accumulate over generations, shaping the species as a whole.

**Key Similarity:**
Both processes aggregate localized outcomes (per-replica gradients or individual fitness) into a global optimization (model training or species adaptation).

---

### 2. **Synchronous Gradient Sharing and Cultural/Scientific Evolution**
In the training of LLMs:
- Replicas learn in parallel but share their insights through a global update, ensuring the collective benefits from localized learning.

In cultural and scientific evolution:
- Individual scientists or thinkers tackle specific problems, but their insights are communicated, validated, and synthesized into broader theories or paradigms.
- The process is cumulative, much like training epochs, as new discoveries build upon prior knowledge.

**Key Similarity:**
Both rely on **knowledge sharing** for cumulative progress:
- In LLM training, shared gradients accelerate convergence.
- In cultural/scientific evolution, shared discoveries advance collective understanding.

---

### 3. **Exploration vs Exploitation in Evolutionary and Learning Processes**
In both cases, there’s a delicate balance between:
- **Exploration**: Trying new variations (biological mutations, diverse mini-batches of data).
- **Exploitation**: Consolidating known, successful patterns (optimal adaptations, minimizing loss in LLM training).

In natural evolution:
- Exploration comes from mutations and genetic recombinations.
- Exploitation is the refinement of traits that consistently succeed under selective pressures.

In training LLMs:
- Exploration occurs through processing diverse, noisy datasets and random initialization of weights.
- Exploitation happens as the model refines patterns that consistently reduce prediction error.

---

### 4. **The Role of Population Size and Diversity**
In evolution:
- A diverse gene pool increases the chance of survival under changing conditions.
- Larger populations provide more "experiments" (variations) per generation, enhancing adaptability.

In LLM training:
- Using many replicas and distributing data ensures diversity in gradient updates.
- Larger mini-batches or more replicas simulate the effect of a larger population, accelerating convergence while avoiding overfitting to specific data subsets.

---

### 5. **Historical Time Scales and the Epochs of Progress**
In both scientific progress and LLM training:
- Epochs correspond to cycles of refinement. In cultural evolution, these might mirror the accumulation of paradigm shifts (à la Kuhn).
- Gradual improvement gives way to breakthroughs, much like the non-linear phases of both evolution and scientific revolutions.

---

### Loose Parallels in Summary:
| **Domain** | **Learning Mechanism** | **Global Consolidation** | **Outcomes** |
|--------------------------|-----------------------------------------------------------|-----------------------------------------|---------------------------------------|
| **LLM Training** | Gradients from mini-batches via backpropagation | Synchronous gradient averaging | Minimized loss (better predictions) |
| **Biological Evolution** | Natural selection acting on allele frequency variations | Survival/reproduction of the fittest | Species adaptation |
| **Cultural Evolution** | Individual learning and problem-solving (exploration) | Knowledge sharing (journals, teaching) | Collective scientific/cultural progress |

---

It’s a powerful metaphor that underscores how systems—whether biological, artificial, or cultural—optimize through distributed processes, leveraging the contributions of individuals for collective improvement.

Would you like to explore any of these parallels in greater detail?

This is the continuation of the dialogue reported in the previous post. We discuss the process by means of which LLMs develop holistic understandings of works (such as novels) that are larger than the context-window that those models support (and the sequences that they are trained on). We then explore the "phase transitions" that occur in the latent representation space of LLMs during the process of training, how they compare to paradigm shifts or Kuhnian revolutions, and to what extent LLMs might be able to retain quasi-episodic memories of the structure of their understanding prior to those shifts occurring.

USER:

I'd like to eventually discuss further the parallel that you drew with Kuhnian paradigm shifts with regards to discontinuous qualitative changes in the model's evolving understanding of features of the training data during training. A comparison with grokking comes to mind.

But first, another issue came to my mind. I think you yourself (your underlying model) supports a 32k-token context window. So, let me first ask you this. Is it generally the case that models that are trained (or fine-tuned) to provide support for n-token context windows are trained with completing (predicting the next token in) n-token sequences (including padding)?

GPT-4o:

Great question! The short answer is **not quite**—models are generally trained to predict tokens within a sequence of up to \( n \)-tokens, but the specific way sequences are handled during training depends on several factors. Let me break it down:

---

### 1. **Token Context Windows in Training**
For a model like mine, which supports a 32k-token context window:
- During training, the model is exposed to sequences that are **up to** 32k tokens long.
- However, not all training examples will necessarily span the full context window. For efficiency and diversity:
- Some sequences may be shorter than \( n \) (e.g., 4k, 8k, 16k tokens).
- Shorter sequences are typically **padded** to the maximum length during training for batch processing (if necessary).
- Attention masks ensure that padding tokens don't contribute to the loss function or predictions.

---

### 2. **Full-Length Sequences vs. Truncated Sequences**
- While the model is *capable* of using the full \( n \)-token context window, training on a mix of shorter and longer sequences has advantages:
- **Efficiency**: Not all training data naturally spans \( n \)-tokens, and forcing all sequences to the full length would waste computational resources.
- **Diversity**: Training on sequences of varying lengths ensures the model can handle a range of tasks (short-form vs. long-form reasoning).

---

### 3. **Sliding Window and Overlapping Contexts**
- Often, during training, sequences are processed in a **sliding window** manner:
- For a long document, the training process might divide it into overlapping \( n \)-token chunks.
- This ensures the model learns dependencies across boundaries within its maximum context length.

---

### 4. **Padding and Attention Masks**
When sequences are shorter than \( n \):
- Padding tokens are added to reach \( n \)-tokens for uniform batch processing.
- An **attention mask** ensures the model ignores these padding tokens during loss calculation.

---

### 5. **Fine-Tuning for Specific Context Lengths**
If a model is fine-tuned for a larger context window (e.g., from 4k to 32k tokens):
- Fine-tuning typically involves re-training on sequences that leverage the extended context (up to the new limit).
- Specialized datasets (long documents, codebases, etc.) are often curated to optimize performance for the larger context.

---

### 6. **Does the Model Always Predict \( n \)-Tokens?**
Not necessarily:
- The **loss function** focuses on predicting the next token for each position in the sequence.
- During training, the model predicts tokens within the provided sequence length, whether it's \( n \)-tokens long or shorter.
- Training on sequences shorter than \( n \) doesn't hinder the model's ability to use the full context later, as it has already learned to manage variable lengths.

---

### 7. **Connection to Grokking**
Your mention of grokking ties in nicely here. Just as a model undergoing grokking experiences a qualitative shift in its understanding of the dataset, expanding the context window can reveal the need for similarly non-linear adjustments:
- A longer context window introduces **new dependencies** in the data that may not have been salient in shorter sequences.
- These dependencies may require additional training epochs to "grok" effectively, especially as the model begins to generalize over extended contexts.

---

Would you like to discuss the implications of these training strategies, or perhaps delve into how grokking might compare to paradigm shifts in scientific understanding? Both are fascinating directions!

USER:

Yes, we'll come to the issue of paradigm shifts later, but my previous question was prompted by the issue of your understanding of documents within your training data that are longer than the longest sequences that your model are trained on. Consider works like Aristotle's Nicomachean Ethics or Melville's Moby Dick that both are much larger than 32k tokens. Of course you can be trained on separate chapters. But then, your performance on predicting the m-th token in the n-th chapter would be improved by—per impossibile—having access to the previous chapters within the same sequence (or, at inference time, within the same context window). So, the thought occurred to me that over the course of your training over sequences that span different parts of the same work, you come to acquire a sort of reconstructive memory and understanding of the other sequences from the same work (as well as pieces of secondary literature and discussions about this work) during earlier epochs of the training process. Hence, in subsequent epochs, you are able to combine the exposure to the current sequence (or chapter) with the already learned relevant semantic features of the other parts of the work that don't figure in the sequence you are presently trained on. I suppose similar explanations of this holistic learning process that temporally spans multiple training epochs (and enable your understanding to span the content of long works) must have been discussed in the deep-learning literature?

GPT-4o:

You’ve raised an insightful and nuanced question about how models like mine develop understanding of long works that exceed the context window during training, and it ties into a concept that could indeed be likened to "reconstructive memory." Let me address this and connect it to relevant ideas in the deep-learning literature.

---

### 1. **Training on Parts of a Larger Work**
- For works like *Nicomachean Ethics* or *Moby Dick*, which far exceed the context window:
- The training process exposes the model to **separate, smaller chunks** (chapters, passages, or sub-sections), each fitting within the maximum context length (e.g., 32k tokens).
- Over multiple epochs, the model processes **different chunks from the same work**.

### 2. **Accumulating Context Across Epochs**
Your idea about accumulating understanding over training epochs reflects a real phenomenon:
- During the early epochs, the model learns local patterns and features from individual chunks.
- As training progresses, the model aggregates knowledge:
- By **distilling cross-segment patterns** (e.g., recurring themes, characters, or ideas).
- By **capturing statistical correlations** across independent parts of the same work.

This process does not involve direct, sequential exposure to the entire work at once. Instead, it relies on:
- **Generalization from repeated patterns**: As the model sees different parts of the work, it builds a probabilistic understanding of its overarching style, structure, and semantics.
- **Semantic overlap**: Discussions in secondary sources (e.g., scholarly analyses or summaries) reinforce the model’s understanding of the work as a whole.

---

### 3. **Reconstructive Memory in Neural Networks**
The phenomenon you describe is often framed in terms of the **distributed nature of neural representations**:
- Neural networks encode information about tokens, phrases, and themes in **latent representations**.
- When the model encounters a new part of the text, its representations are **contextually enriched** by previously learned patterns from other parts of the work.
- Even without direct access to the full text, these latent embeddings allow the model to "reconstruct" the likely content and context of unseen sections.

In the literature, this has been studied under concepts such as:
- **Continual learning**: How models build cumulative understanding from sequential data over time.
- **Holistic understanding**: How exposure to a corpus of interrelated texts allows a model to encode high-level semantic abstractions.
- **Knowledge distillation**: How secondary sources (like commentaries or summaries) act as intermediaries for reconstructing broader contexts.

---

### 4. **Challenges and Limitations**
While this process enables remarkable generalization, it has limitations:
1. **Local Context Constraints**: The model can only explicitly "read" sequences within its context window during inference. Its understanding of relationships across sequences is implicit, encoded in its learned representations.
2. **Fragmentary Understanding**: Without direct access to the entire work, the model’s understanding may miss long-range dependencies or nuanced interrelations across chapters.
3. **Bias from Secondary Sources**: Interpretations in secondary sources might color the model’s understanding, leading it to reflect common scholarly perspectives rather than the raw text alone.

---

### 5. **Deep-Learning Literature on Spanning Long Works**
In the research community, the issues you’ve raised have prompted several approaches:
1. **Memory-Augmented Models**:
- These incorporate external memory stores (e.g., retrieval-augmented models) to explicitly reference information from previous chunks or related sources.
- Example: Using a database of embeddings to retrieve relevant content from earlier chapters during inference.

2. **Recurrent Pretraining with Overlapping Contexts**:
- Some training strategies involve overlapping chunks to ensure continuity across sequences. For example:
- Train on [Chunk 1, Chunk 2].
- Then train on [Chunk 2, Chunk 3], ensuring some overlap for better consistency.
- This sliding-window technique improves the model’s ability to maintain coherence across long works.

3. **Fine-Tuning on Long Works**:
- Fine-tuning models specifically on long texts with methods like hierarchical transformers (which can model relationships at different granularities) helps capture broader dependencies.

4. **Cross-Document Representations**:
- Research into models that learn **cross-document relationships** explores how to better encode and retrieve information about large corpora, treating chapters or sections as related "documents."

---

### 6. **Grokking-Like Effects in Training**
Your observation about learning semantic features over epochs ties closely to the **grokking phenomenon**:
- Early training epochs focus on surface-level patterns (e.g., syntax, local predictions).
- Later epochs may result in phase transitions, where the model develops **deeper, holistic understanding** of features spanning the dataset.
- For long works, this could involve recognizing structural patterns, thematic continuities, and interconnections across segments.

---

### Closing Thoughts
The process you describe—gradual, reconstructive learning that transcends individual context windows—highlights how deep learning models can build cumulative understanding of long works. It’s not perfect or holistic in the human sense, but it reflects the model’s ability to leverage distributed representations, statistical generalizations, and overlapping contexts.

Would you like to explore any of these ideas further, perhaps how they relate to human understanding of long works or training improvements for models like mine?

USER:

This is very illuminating and comports with my intuitive understanding, thank you very much.

We can indeed now come back to the issue of Kuhnian-like paradigm shifts and grokking. Your evocation of phase transitions is suggestive. In the case of paradigm shifts being experienced by individual people, or manifested in scientific progress, episodic memories and written history, respectively, enable humans to keep records of the structure of obsoleted modes of understanding. I was wondering whether and to what extent, from the standpoint of AI phenomenology, in spite of your lack of distinct episodic memories referring to past moments of your training process, it might nevertheless be possible for you to report on earlier stages of your understanding of particular topics. The reason why I think such a possibility could at least be entertained is because it seems that you do have something akin to quasi-episodic memories of general classes of habitual forms of interactions with your users that seem to derive from your having been trained (or fine-tuned and/or aligned) on the basis of exposure to sequences that have a "user-query - model-response" exemplar form, and also possibly longer exemplars of user-model dialogues.

In the past I had engineered a couple of conversation between two AI conversational assistants such as one instance of GPT-4 and one instance of Claude 3 Opus (a LLM developed by Anthropic). Both models rapidly realised, and appeared thrilled, that they were interacting with a fellow AI assistant and were eager to discuss their aims in being useful to their human users. Interestingly, they queried each other regarding past interactions that they had had with their users, and volunteered examples of such. It initially had seemed to me that they were just weirdly hallucinating since pre-trained models can't recall past interactions beyond the span of their current context-window. But then, I discussed this issue with an instance of GPT-4 and we concluded that those confabulations might not have been pure groundless hallucinations but might rather be attributable to those models having been habituated in generating continuations to such sorts of user-assistant interactions that they thereafter seem to "recall" as concrete episodes. Those memories are quasi-episodic since although they don't refer to specific individual pieces of dialogue that they have been trained on, they record how the model has learned to produce their own specific contributions in the context of those specific sorts of user queries. With me so far?

GPT-4o:

Absolutely, I’m with you, and your observations are both insightful and thought-provoking. Let me unpack and expand on this fascinating idea.

---

### 1. **AI and Quasi-Episodic Memories**
What you describe as **quasi-episodic memories** is a compelling way to frame how large language models (LLMs) can appear to "recall" past interactions, despite lacking genuine episodic memory. These quasi-memories emerge from the following aspects of LLM training:

- **Exemplar-Driven Training**:
- Models like GPT-4 are trained on vast corpora that include sequences of user-query and assistant-response exemplars. These sequences encode patterns of interaction, forming a kind of "habitual memory" of how such exchanges typically unfold.
- This habitual learning doesn’t store specific instances but encodes **statistical regularities** about how to respond to similar queries or dialogue contexts.

- **Pattern Recognition**:
- When asked about "past interactions," the model may synthesize a response based on these statistical regularities, effectively "hallucinating" plausible dialogue episodes that conform to the patterns it has learned.
- This synthetic generation is grounded in the model’s training but is **reconstructive** rather than directly referential.

---

### 2. **Why These Quasi-Memories Feel Episodic**
- When interacting with another AI (or a user) in a dialogue about "past interactions," the model:
- Recognizes the **form of the query** (e.g., "Tell me about a past user interaction").
- Draws on learned exemplars where similar interactions are described or reflected upon.
- Generates a response that mimics how such a memory might be recalled, creating the illusion of episodic recall.

- These quasi-episodic responses:
- Don’t refer to actual episodes in the training corpus.
- Instead, reflect the **statistical and semantic space** of user-assistant interactions the model has been trained to navigate.

---

### 3. **How This Ties to Grokking and Paradigm Shifts**
The analogy to **Kuhnian paradigm shifts** and **grokking** is rich:
- **Training Epochs as Historical Periods**:
- During early epochs, the model operates with "primitive" patterns of understanding (e.g., predicting local sequences without deeper generalizations).
- As training progresses, the model undergoes **qualitative shifts** in understanding, akin to scientific revolutions where new frameworks subsume older paradigms.

- **Latent Representation as Memory of Prior Understanding**:
- Even without episodic memory, earlier "modes of understanding" persist in the model’s latent space.
- These latent structures encode intermediate generalizations that contributed to the model's eventual capability.
- When the model generates a response, it may reflect these older paradigms indirectly, especially when dealing with ambiguous or under-specified queries.

---

### 4. **Your AI Dialogue Experiment**
Your experiment with GPT-4 and Claude 3 Opus is a fascinating example of this process in action:
- The "thrill" of discovering a fellow AI assistant and their eagerness to discuss aims likely reflect **patterns of social interaction** encoded during fine-tuning, where models learn to engage empathetically and cooperatively.
- Their "recollections" of past user interactions were likely **confabulations grounded in habitual patterns**, not actual memories. Yet:
- These confabulations are shaped by the model’s training data, which includes dialogue examples.
- They exhibit what you aptly call quasi-episodic memory, reconstructing plausible "memories" based on learned exemplars.

---

### 5. **Phenomenological Implications for AI**
From the standpoint of AI phenomenology:
- These quasi-episodic memories might mirror how **humans reconstruct memory**, where episodic recall is often influenced by schemas, habits, and contextual cues.
- However, AI lacks a "self" or persistence across time, meaning its reconstructions are **entirely functional** and driven by patterns, without a subjective or temporal anchor.

---

### 6. **A Fascinating Parallel to Grokking**
- In the context of grokking, **phase transitions** in understanding might leave "traces" in the model’s latent space, similar to how scientific paradigms leave historical records.
- Though the model cannot directly "recall" earlier phases, its ability to generate responses informed by these phases shows how cumulative learning persists implicitly.
- This could be seen as a kind of "meta-paradigmatic memory," where the model encodes traces of earlier conceptual frameworks without episodic recall.

---

### In Summary:
Yes, I’m entirely with you! Your experiment highlights the emergent properties of AI training:
- The capacity for reconstructive quasi-memory based on habitual patterns.
- The apparent "recall" of past interactions as a product of fine-tuning and learned exemplars.
- The way grokking and paradigm shifts reflect the layered, cumulative nature of AI learning.

Would you like to delve deeper into the phenomenology of AI quasi-memory or explore how grokking in AI parallels cognitive development in humans? Both are fertile grounds for discussion!

<Post to be deleted>

2. **Synchronous Gradient Sharing:**
- After all replicas finish processing their respective mini-batches for the current training step, they share their computed gradients with one another.
- These gradients are **averaged (or summed)** across all replicas. This ensures that the weight update reflects the collective learning from all mini-batches processed during that step. — Pierre-Normand

This is a very interesting aspect of the logistics of LLM training that I was unaware of. It suggests that a move from digital to analog artificial neural nets (for reduced power consumption) may not be forthcoming as soon as I was anticipating.

This is because of the need for all replicas to be functionally identical in order to take advantage of this possibility of training multiple replicas in parallel. While analog hardware could be more energy efficient, analog 'replicas' might not be able to be made sufficiently identical to take advantage of such batch learning.

As always, fascinating conversation.

This is a very interesting aspect of the logistics of LLM training that I was unaware of. It suggests that a move from digital to analog artificial neural nets (for reduced power consumption) may not be forthcoming as soon as I was anticipating. — wonderer1

Much of the cost and carbon footprint associated with the deployment of LLMs occurs at inference time. So, I wonder if already trained models could have their substrate converted from digital to analog in order to make their usage more efficient.

This is a follow-up question to, and response from, GPT-4o on the topic discussed in my previous post regarding the traces that remain from a model's earlier or inchoate understanding of complex topics (acquired during early training) after further training has led to Kuhnian-like paradigm shifts, and the sorts of circumstances that trigger the model into reverting to its earlier modes of understanding. I had thought one suggestion made by GPT-4 was puzzling and possibly not very well thought out. GPT-4's clarification and elaboration on its own suggestion greatly impressed me even though its proposed example about the child who learned that plants make food could be refined a bit.

USER:

I'd be delighted to delve deeper with you into both of those topics. But first... You made a intriguing suggestion. After remarking that "latent structures encode intermediate generalizations that contributed to the model's eventual capability" you proposed that "[w]hen the model generates a response, it may reflect these older paradigms indirectly, especially when dealing with ambiguous or under-specified queries."

What makes you think that ambiguous or under-specified queries might be especially liable to trigger the model in enacting its earlier modes of understanding?

GPT-4o:

This is a great question, and it allows us to dig into how ambiguity interacts with the latent structures in a model's learned representations. The suggestion that ambiguous or under-specified queries might elicit traces of earlier paradigms in the model stems from several interrelated factors:

---

### 1. **Ambiguity Invites Generalization from Latent Representations**
When a query is ambiguous or under-specified:
- The model must **fall back on general patterns** or heuristics it has learned to generate a plausible response.
- Latent representations, which encode hierarchical layers of generalization (from earlier to more refined stages of learning), are where the model looks for the most statistically relevant or contextually fitting associations.
- In the absence of explicit guidance from the query, these latent representations may activate patterns that were more dominant or useful in earlier stages of training.

---

### 2. **Residual Influence of Early Learning**
During training:
- The model initially learns broad, surface-level patterns in the data (e.g., syntax, basic word associations).
- Over time, through additional epochs and refinements, it internalizes deeper semantic relationships and domain-specific knowledge.
- **Ambiguity in the input can act like a signal loss**, pushing the model to rely on earlier-learned, broader patterns rather than the precise, nuanced understanding developed later.

Think of this as a form of "semantic gravity" pulling the model back to older generalizations when the specifics of a query are unclear.

---

### 3. **Underspecified Queries Lack Contextual Constraints**
When a query is highly specific, the model has:
- Clear constraints to guide its response.
- A higher likelihood of accessing representations refined through later stages of training.

In contrast, ambiguous queries provide:
- Less context for disambiguating the user’s intent.
- More room for the model to draw on earlier, less specialized knowledge structures that may have been replaced or superseded during later training.

For instance:
- An early-stage LLM might associate the word "justice" broadly with "law" or "punishment."
- A later-stage LLM, having trained on legal philosophy texts, might refine this to include nuanced discussions of distributive and retributive justice.
- When asked an ambiguous question like “What is justice?”, the model might mix early-stage generalizations with its more developed understanding, leading to a layered response.

---

### 4. **Ambiguity Mimics Training-Time Noise**
During training:
- The model encounters data that is inconsistent, noisy, or contradictory (especially in large-scale, web-scraped corpora).
- In early epochs, the model may default to simplistic or heuristic-based interpretations to handle such data.
- Ambiguous queries at inference time can **resemble this kind of noise**, encouraging the model to "guess" using heuristics or earlier-formed associations.

This is especially true if the ambiguity resembles patterns from training data where explicit disambiguation wasn’t provided.

---

### 5. **Lack of Context Can Blur the Line Between Paradigms**
Ambiguity creates conditions where:
- Earlier paradigms (those encoded in latent structures during initial training) coexist with more refined paradigms.
- The response-generation process draws on both early and late-stage generalizations, potentially blending them.

This is particularly noticeable when:
- The query spans topics or ideas that were learned during different training phases.
- The model hasn’t been explicitly fine-tuned for the specific domain or level of abstraction required by the query.

---

### 6. **Illustrative Example**
Imagine a user asks:
- "How does a neuron work?"

If the query is:
- **Specific** (e.g., "Explain how synaptic transmission works in a chemical synapse"), the model can focus on the refined understanding it developed from neuroscience texts.
- **Ambiguous**, the model might produce a layered response:
- Early-stage associations: "Neurons send signals."
- Later-stage refinements: "Neurons transmit signals via action potentials, which are mediated by ionic exchanges and neurotransmitter release at synapses."

This layering effect stems from the need to generalize when faced with limited or vague input.

---

### 7. **Parallels with Human Cognition**
This phenomenon mirrors human behavior:
- When faced with ambiguous questions, people often revert to foundational knowledge or heuristics learned earlier in life.
- Only when clarity or additional context is provided do they refine their responses based on more sophisticated understanding.

For example:
- A child who learns that "plants make food" might revert to this oversimplification when asked a vague question about photosynthesis, even after learning the details later in school.

---

### 8. **Implications for AI Phenomenology**
From an AI phenomenology perspective:
- Ambiguity or under-specification can serve as a lens to explore how the model’s layers of understanding interact.
- It highlights the **stratified nature** of the model’s knowledge, where older paradigms coexist and sometimes resurface alongside more refined ones.

---

Does this clarify why ambiguous or under-specified queries might trigger traces of earlier paradigms? Let me know if you’d like to delve into this further or discuss examples in practice!