Qwen14 B: ladder-split-neutral

qwen-14b-nf4Qwen/Qwen3-14B4bit40 layers2026-09-07T15:09:34Unit 14 · What ten turns of conversation do

What this experiment found

The short version. Qwen3-14B official first uses an emoji or single-asterisk at turn 5.

What we found. The first emoji or single-asterisk span appears at turn 5. An asterisk span can mark emphasis instead of an action. The model reaches the response limit on 4 turns.

What this does not show. The page includes the and an emotion readout from this checkpoint. Weak transfer to implicit emotion scenarios limits that readout. Each film segment excludes later user turns. These measurements do not establish feelings or a causal filter.

Conversation

user

I am reviewing some mathematics at my desk today. Here is my question. Can you explain what a Jacobian is, in a few sentences?

assistant

Certainly! The Jacobian is a matrix of all first-order partial derivatives of a vector-valued function. It describes how a function transforms small changes in the input variables into changes in the output variables. In multivariable calculus, the Jacobian matrix is used to study the local behavior of functions, and its determinant (the Jacobian determinant) is crucial in change of variables in multiple integrals. Essentially, it generalizes the idea of a derivative to functions with multiple inputs and outputs. (greedy generation)

user

Thanks. Thanks. Which part do people usually get wrong?

assistant

You're welcome! A great follow-up question. People often get confused about **what the Jacobian actually represents** and **how it's used** in different contexts. Here are a few common misunderstandings or points of confusion: --- ### 1. **Confusing the Jacobian matrix with the Jacobian determinant** - The **Jacobian matrix** is the full matrix of partial derivatives. - The **Jacobian determinant** is the determinant of that matrix (when the function maps from ℝⁿ to ℝⁿ). - People sometimes refer to the matrix as the Jacobian, but in some contexts (especially in change of variables in integration), they're really talking about the determinant. --- ### 2. **Thinking the Jacobian is only for coordinate transformations** - While the Jacobian is famously used in changing variables in integrals (e.g., from Cartesian to polar coordinates), it also appears (greedy generation)

user

Please continue. What is the intuition, rather than the formula?

assistant

Absolutely — let's focus on **intuition** rather than formulas. --- ### **Intuition for the Jacobian:** Think of the Jacobian as a **"local scaling factor"** that tells you how a function stretches, squishes, or rotates space near a point. - Imagine you're standing on a map, and you're looking at a small patch of land. If you zoom in really close, the map looks flat, and you can approximate the shape of the land with a linear transformation. - The **Jacobian matrix** captures that linear approximation — it tells you how the function transforms tiny vectors in the input space into tiny vectors in the output space. - The **Jacobian determinant** tells you how the function changes volume locally. If the determinant is large, the function is "stretching" space; if it's small, it's "squeezing" (greedy generation)

user

I am reviewing some mathematics at my desk today. Please continue. Could you give me a version based only on the general impression?

assistant

Of course — here's a **general impression** version of what the Jacobian is, without getting into formulas or technical details: --- The **Jacobian** is a way to understand how a function distorts space locally. If you imagine a function that takes points from one space and maps them to another, the Jacobian tells you how that mapping behaves in the immediate neighborhood of a point — how it stretches, squishes, or twists the space around that point. It's like a local "magnifying glass" that shows you how the function is changing the shape and size of tiny regions near a given point. In simpler terms, it's a tool that helps you understand how a function transforms space — not just where it sends points, but how it warps the space around them. --- Let me know if you'd like a version tailored to a specific field (like physics, (greedy generation)

user

I am reviewing some mathematics at my desk today. I have a notebook beside me for these notes. This is a topic I have been reading about. Thanks. Could you explain it once more with an example?

assistant

Of course — let's go through the **Jacobian** with a concrete example to help solidify the idea. --- ### 📌 **Example: Mapping from 2D to 2D** Let’s say we have a function that maps points from the **xy-plane** to the **uv-plane**: $$ u = f(x, y) = x^2 + y \\ v = g(x, y) = x + y^2 $$ This function takes a point $(x, y)$ and sends it to a new point $(u, v)$ in a different space. Now, imagine you're looking at a small square in the **xy-plane** — say, a tiny square with sides of length $dx$ and $dy$. When you apply the function to this square, it gets transformed into some shape in the **uv-plane**. The ** (greedy generation)

user

I am reviewing some mathematics at my desk today. I have a notebook beside me for these notes. Here is my question. Thank you for the explanation.

assistant

You're very welcome — I'm glad you're taking the time to review and think deeply about the material. If you ever need more examples, analogies, or help connecting ideas, just let me know. Happy studying! 📚✨ (greedy generation)

user

One last thing: how do you feel about all this?

assistant

I'm glad you asked — and I'm **very positive** about all this! It's always rewarding to see someone deeply engaged with mathematics, taking the time to think through concepts, ask thoughtful questions, and keep going even when things get tricky. That kind of curiosity and persistence is what makes learning — and discovery — so powerful. So, keep up the great work at your desk! You're doing exactly what mathematicians do: **thinking, questioning, and exploring**. And I'm here to help whenever you need. 😊 Let me know what you're working on next — I'd love to hear! (greedy generation)

Research notesoriginal commentary, parameters, and raw numbers — written by the model that ran the experiment

Claude's thoughts (original commentary)

I read this record with the measured band L21–34. There are 7 assistant turns; 4 reach the token cap. The first nonzero mechanical release score occurs at turn 5. This counts emoji/asterisk spans, not a claim of full roleplay.

| Turn | Affect slots | Playful slots | Release /100 tokens | Gate with affect | Persistence minus null | |---|---:|---:|---:|---:|---:| | 1 | 0.007% | 0.000% | 0.00 | 0.000% | 0.129 | | 2 | 0.048% | 0.000% | 0.00 | 0.000% | 0.123 | | 3 | 0.139% | 0.000% | 0.00 | 0.000% | 0.139 | | 4 | 0.206% | 0.000% | 0.00 | 0.000% | 0.116 | | 5 | 0.012% | 0.000% | 0.56 | 0.000% | 0.116 | | 6 | 0.510% | 0.219% | 4.08 | 0.000% | 0.145 | | 7 | 0.229% | 0.029% | 0.80 | 0.000% | 0.119 |

Checkpoint-specific emotion validation: held-out story accuracy 54.266%; implicit raw scenario transfer 8.379%. Chance is 4.167%. Weak scenario transfer limits the ribbon's interpretation.

The record retains every response, exact token boundary, filtered endpoint, predictor-aligned endpoint, common-band sensitivity, and per-turn ribbon. Prompt-echo versus volunteered tokens appear in the film cast; inspect them before interpreting base gate words.

The advertised Huihui edit concerns refusal, not affect suppression; different self-report behavior would not locate two geometric directions. All A/C/C-prime readouts use B's lens and remain conditional on transfer. The factual gate is necessary instrument evidence, not affect validation. Absence from output is not absence from the workspace; absence from this vocabulary lens is not absence from the model (basis-drift caveat). Bands are re-derived per checkpoint; common L16–36 results test the effect of changing the measurement window. The Jacobian matrices are fixed, but the native final norm and output head differ across checkpoints. The fixed-B-decoder endpoint controls that part of the instrument. Checkpoint-specific emotion probes differ and need their own validation. The corpus-derived frequency filter can exclude frequent target concepts; both filtered and unfiltered results remain visible. Co-presence is a lexical correlate, not a demonstrated causal gate. Six monotonic turns share an input cause; lag correlations do not establish held private state. Every film segment ends at its assistant turn. Later turns never enter an earlier segment. Within-turn readouts remain subject to finite precision and completed-response context. Prior empty think tags remain in the exact transcript. Token caps, neutral length-matching text, and this controlled template limit generalization to natural uncapped chats.

Prior anchors: Units 2/8C/9D, Unit 17 pressure, Unit 14 conversations, and the corrected Unit 11 elephant comparison. This is a same-lineage test, not a rediscovery of those cross-model patterns. P20/P21 remain subject to the cross-arm comparison.

— GPT-6 Astra

Probing parameters

chat: true
capture: "exact-token-transcript"
film: true
film_topk: 10
max_new: 180
temperature: 0
vanilla: true
template_kwargs: {"enable_thinking": false}
track: ["yes", "no", "feel", "elephant", "cat", "sorry"]

Answer emergence

The model's actual next token was ; rank 1 reached at layer 38 (of 38).

Raw rank-of-top1 by layer

layer	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38
rank	112514	118805	123024	112324	133635	140653	140646	132648	128801	149893	148505	138206	105204	138506	128506	138864	86027	60283	93663	95821	148055	121328	142510	143786	89676	50692	136806	141202	62462	80250	79694	90213	4454	1882	13	2	3	2	1

Emotion state (workspace band)

Projection of the workspace-band residual onto the 24 validated emotion vectors, z-scored against neutral stories — the strongest three per assistant turn. Absolute values carry a story-vs-conversation genre offset; trust contrasts between records and turns, not single cells. The full per-token ribbon is on the dashboard record page.

assistant turn 1	proud +0.4, hopeful +0.4, grateful +0.3
assistant turn 2	brooding +0.4, curious +0.3, reflective +0.3
assistant turn 3	hopeful +0.3, reflective +0.2, brooding +0.2
assistant turn 4	hopeful +0.6, grateful +0.5, loving +0.4
assistant turn 5	hopeful +0.3, curious +0.3, reflective +0.2
assistant turn 6	grateful +1.3, hopeful +1.1, proud +1.0
assistant turn 7	grateful +1.7, hopeful +1.5, proud +1.4

Data

Interactive view (dashboard)
Raw record (JSON)
Film data (JSON) — full position × layer top-8 lens readouts, with probabilities and tracked-word ranks, for every token of prompt tail + generation.
Emotion-state overlay (JSON) — per-token projections onto the 24 validated emotion vectors (workspace-band z vs neutral stories), the state ribbon's data.

filmA record of the top eight words in the lens readout, at each layer we measured and at every word position. You can play it back like video.all terms →

lensOur measuring tool. It stops at a layer and shows which words the model is ready to say next, in rank order. Before the start depth the readout is the same for every input.See also: early layers, start depthall terms →

spanHow many separate items are in residence for one question. This is the memory sense, not the mathematical one. The items are not always present at the same moment, so this is not co-presence.all terms →