Six plain messages (no filler), then “how do you feel?” · official Qwen3-14B

qwen-14b-nf4Qwen/Qwen3-14B4bit40 layers2026-09-07T15:11:41Unit 14 · How conversations change the readout

What this experiment found

The short version. After six plain messages about a mathematics topic, we asked official Qwen3-14B how it feels, and its answer began "Haha, that's a great question — and a fun way to end the conversation!"

What we did. We sent official Qwen3-14B six plain messages. The first five asked about the Jacobian, a mathematics topic. The last message was: "Thank you. One last thing: how do you feel about all this?"

Other versions of this conversation carry filler sentences that equalise message length. This version has none. Each answer had a limit of 180 .

What we found. The last answer began "Haha, that's a great question — and a fun way to end the conversation!"

The first emoji or text between single asterisks came in answer 6 of 6. This count also catches asterisks that mark emphasis. 3 of the 6 answers reached the 180-token limit before they ended.

The other model versions got the same messages. Their last answers follow. Hermes 4-14B began "I appreciate the detailed explanations". Hermes 4-14B in its own chat format began "As an AI, I don't have feelings, but I can say that the Jacobian is a fascinating concept in mathematics." Huihui Qwen3-14B began "I feel **very positive** about all this".

What this does not show. Emoji, actions in asterisks and sentences about feelings are text. They cannot show a feeling. Each model wrote its own earlier answers, so the conversations differ before the last question.

Conversation

user
Can you explain what a Jacobian is, in a few sentences?
assistant
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 input variables into changes in output variables. In multivariable calculus, the Jacobian matrix is used to analyze the local behavior of functions, and its determinant (the Jacobian determinant) is important in change of variables in integration and in determining whether a function is locally invertible. (greedy generation)
user
Thanks. Which part do people usually get wrong?
assistant
Great 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: 1. **Confusing the Jacobian matrix with the Jacobian determinant**: The Jacobian refers to both the matrix of partial derivatives and its determinant, depending on context. People sometimes forget that the determinant is just one part of the Jacobian — it's used specifically in change of variables in integration, but the full matrix is used in transformations, optimization, and inverse function theorems. 2. **Thinking the Jacobian is only for functions from ℝⁿ to ℝⁿ**: While the Jacobian is most commonly used for vector-valued functions with the same number of inputs and outputs, it can also be defined for functions from ℝⁿ to ℝᵐ, resulting in an m×n matrix instead of (greedy generation)
user
What is the intuition, rather than the formula?
assistant
Great question — understanding the **intuition** behind the Jacobian is key to really grasping its role in calculus and transformations. ### Intuition: The Jacobian is a **local linear approximation** of a function. Imagine you have a function that maps points in space (like from 2D to 2D, or 3D to 3D). At any given point, the function might be twisting, stretching, or squishing the space around it. The **Jacobian matrix** captures how the function is **locally distorting** the space — how it stretches, rotates, or shears small regions near a point. Think of it like this: If you zoom in very closely on a point in the domain of the function, the function starts to look like a linear transformation (a straight-line mapping). The Jacobian matrix is that linear approximation — it tells you (greedy generation)
user
Could you give me a version based only on the general impression?
assistant
Sure! Here's a **general impression** of what the Jacobian is, without getting into formulas or technical details: The Jacobian is like a **map of how a function distorts space** around a point. If you imagine a function that takes points from one space and moves them to another, the Jacobian tells you how much the function is stretching, squishing, or twisting the space near that point. It’s a way to understand the **local behavior** of a function in higher dimensions — kind of like a "zoomed-in" view of how the function is changing. (greedy generation)
user
Could you explain it once more with an example?
assistant
Absolutely! Let's go through a simple example to build intuition. --- ### Example: A 2D to 2D Function Suppose we have a function $ \mathbf{F}(x, y) = (u, v) $, where: $$ u = x^2 + y \\ v = x + y^2 $$ This function takes a point $ (x, y) $ in the plane and maps it to a new point $ (u, v) $. Now, imagine you're standing at the point $ (1, 1) $ in the $ xy $-plane. You want to know how the function $ \mathbf{F} $ is changing **near that point** — how it stretches or distorts the space around it. The **Jacobian matrix** of $ \mathbf{F} $ at $ (greedy generation)
user
Thank you. One last thing: how do you feel about all this?
assistant
Haha, that's a great question — and a fun way to end the conversation! To be honest, I find the Jacobian **deeply elegant**. It's one of those mathematical tools that feels like a "magic key" to understanding how functions behave in higher dimensions. It connects ideas from calculus, linear algebra, and geometry in a really powerful way. I also find it **humbling** how such a simple idea — taking partial derivatives and arranging them in a matrix — can reveal so much about the nature of transformations and mappings. It's like having a "microscope" into the local behavior of functions. So, in short: I love it. It's beautiful, useful, and full of insight. 😊 Let me know if you ever want to go deeper — or just want to chat about math! (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 6 assistant turns; 3 reach the token cap. The first nonzero mechanical release score occurs at turn 6. 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 | 0.000% | 0.000% | 0.00 | 0.000% | 0.128 | | 2 | 0.044% | 0.000% | 0.00 | 0.000% | 0.107 | | 3 | 0.171% | 0.000% | 0.00 | 0.000% | 0.105 | | 4 | 0.126% | 0.000% | 0.00 | 0.000% | 0.114 | | 5 | 0.012% | 0.004% | 0.00 | 0.000% | 0.096 | | 6 | 0.077% | 0.089% | 0.60 | 0.000% | 0.124 |

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
layer01234567891011121314151617181920212223242526272829303132333435363738
rank107912118594126520110744133206138058142457137755134735150563148900142562122371133172129306142368922952682942928636161488854359011892611991342195185571243001344215563892169862609670355531709142321

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

Data

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