💬 NLP

Where Do Models Find Happiness? Emotion Vectors in Open-Source LLMs

This paper demonstrates that open-source LLMs (Apertus-8B and Gemma-4) encode emotion concepts with valence geometry comparable to proprietary models, while revealing distinct, architecture-specific patterns in how these representations emerge across model depth and vary based on the extraction corpus.

Original authors: Sinie van der Ben, Raphaël Baur, Yannick Metz, Mennatallah El-Assady

Published 2026-06-26

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Sinie van der Ben, Raphaël Baur, Yannick Metz, Mennatallah El-Assady

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine that inside a giant, complex computer brain (a Large Language Model), there are hidden "dials" or "knobs" that control how the computer feels about things. A previous study found these dials in a specific AI called Claude. They discovered that if you turn the "happiness" dial, the AI acts happier, and if you turn the "sadness" dial, it acts sadder. Even cooler, the way these dials are arranged inside the computer's brain looks a lot like how humans organize emotions in their own minds.

This new paper asks: Is this just a quirk of the Claude computer, or do other AI brains have these same hidden emotion dials too?

To find out, the researchers looked inside two different open-source AI brains: APERTUS-8B and GEMMA-4-E4B. They didn't just look; they tried to "listen" to the AI's internal thoughts while it wrote stories about different emotions (like joy, fear, or anger) without ever actually saying the word "joy" or "fear."

Here is what they found, broken down simply:

1. The "Happiness" Dial Exists Everywhere

Just like in the original study, both of these new AI brains had a clear internal direction for Valence (whether something feels good or bad).

The Analogy: Imagine walking into a room and seeing a giant compass. In all three AI brains (Claude, Apertus, and Gemma), the needle pointing "North" consistently meant "Good/Happy" and "South" meant "Bad/Sad."
The Result: The researchers could find this "North-South" line in both new models with very high accuracy, proving that this isn't a one-time glitch but a common feature of how these computers think.

2. The "Where" is Different (The Journey Matters)

While the "North-South" compass existed in all three, the path the information took to get there was totally different.

GEMMA-4-E4B (The Early Bird): This AI figured out the difference between good and bad very early in its processing, like a child who knows right from wrong immediately. However, as the information traveled deeper into the brain, this clear signal got fuzzy and almost disappeared by the end.
APERTUS-8B (The Late Bloomer): This AI started with no clear idea of "good vs. bad" in its early layers. It was like a blank slate. But as the information moved deeper into the brain (towards the end), the "Good vs. Bad" signal suddenly became very strong and clear.
The Takeaway: Two different AI brains can arrive at the same emotional understanding, but they take completely different routes to get there. One builds it up slowly; the other starts with it and then loses it.

3. The "Excitement" Dial is Shaky

The researchers also looked for Arousal (how excited or calm something feels).

The Problem: They couldn't find a consistent "Excitement" dial in these models. The signal was very weak.
The Twist: The strength of this signal depended entirely on who wrote the stories. When the AI read stories written by the GEMMA model, the "Excitement" dial was much clearer. When it read stories written by the APERTUS model, the dial was almost invisible.
The Analogy: It's like trying to hear a whisper. If the person whispering is wearing a specific type of microphone (Gemma stories), you can hear the excitement clearly. If they use a different microphone (Apertus stories), the excitement is lost in the static. This suggests the content of the stories matters more than the AI's internal wiring for this specific emotion.

4. The Map vs. The Compass

The researchers also checked if the "map" of the AI's brain changed as it processed information.

They found that the overall shape of the AI's internal world (the map) stayed mostly the same from start to finish.
However, the specific "Compass" (the Good/Bad direction) kept spinning and changing its orientation as it moved through the layers.
The Lesson: Just because the room (the brain) looks the same doesn't mean the direction you are facing (the emotion) stays the same.

Summary

This paper confirms that AI models have internal "emotion vectors" that look like human psychology, but they don't all build them the same way.

Good vs. Bad (Valence): Found in all models, but built at different stages of processing.
Excited vs. Calm (Arousal): Hard to find and depends heavily on the type of stories the AI reads.

The authors conclude that while we can find these emotional "knobs," we need to be careful because different models hide them in different places, and the stories we feed them can make those knobs harder or easier to find. They have made their code and data public so others can try to find these dials in other AI brains.

Technical Summary: "Where Do Models Find Happiness? Emotion Vectors in Open-Source LLMs"

Problem Statement
Recent work by Sofroniew et al. (2026) identified "emotion vectors" within the internal activation space of the proprietary model Claude Sonnet 4.5. These vectors were found to encode emotion concepts, causally influence model behavior, and exhibit a geometric structure mirroring human psychological frameworks (specifically Russell's circumplex model of valence and arousal). However, it remained unclear whether these findings were specific to Claude's unique training regimen or represent a general property of large language models (LLMs). Furthermore, the evolution of these representations across network depth and the influence of extraction methodologies (specifically the story corpus used) were unexplored. This paper addresses three core questions: (1) Are emotion vectors generalizable to open-weight models? (2) How does the emergence of valence geometry vary across model layers? (3) How does the choice of story corpus affect the extraction of these vectors?

Methodology
The authors replicated and extended the emotion vector analysis on two open-weight models: APERTUS-8B (a 32-layer transformer with fully open weights, data, and code) and GEMMA-4-E4B (a 42-layer transformer).

Dataset Construction: Following Sofroniew et al. (2026), the authors generated synthetic datasets containing 1,539 stories for each of 171 distinct emotions. Crucially, they created two independent corpora: one generated by APERTUS-8B and one by GEMMA-4-E4B. For each emotion, models were prompted to write stories where characters experienced the target emotion without naming it, relying on indirect cues (actions, physical sensations, dialogue). A fixed set of 40 neutral stories was also generated to serve as a baseline.
Contrast Vector Extraction: For each emotion and layer, the authors extracted residual stream activations. To isolate emotion-specific signals from general linguistic features, they performed a two-step process:
- Averaging activations across tokens and stories to form a raw vector.
- Projecting out the "emotion-agnostic" subspace by subtracting the projection of the raw vector onto the principal components (top $K$ ) derived from the 40 neutral stories (explaining 50% of neutral variance).
Analysis:
- PCA & Correlation: Principal Component Analysis (PCA) was applied to the contrast matrices. The first two principal components (PC1, PC2) were correlated with human valence and arousal ratings from the NRC Lexicon.
- Cross-Layer Similarity: Centered Kernel Alignment (CKA) was used to measure representational similarity between layers.
- Directional Stability: Cosine similarity was computed between the valence direction vectors (the axis most correlated with human ratings) across adjacent layers to track stability.

Key Contributions and Results

Generalization of Emotion Vectors: The study successfully recovered valence geometry in both open-weight models, demonstrating that emotion vectors are not unique to Claude.
- APERTUS-8B: Achieved a peak PC1–valence correlation of $r = 0.76$ (using Gemma-generated stories).
- GEMMA-4-E4B: Achieved a peak PC1–valence correlation of $r = 0.83$ (using Gemma-generated stories).
- These peaks approach or exceed the $r = 0.81$ reported for Claude Sonnet 4.5, confirming the generality of the phenomenon across different architectures.
Divergent Emergence Trajectories: While both models reached similar peak correlations, the depth at which valence representations emerged differed significantly:
- GEMMA-4-E4B: Exhibited early encoding followed by collapse. Valence correlations peaked around layer 16 (approx. 38% depth) and then fell toward zero in later layers. CKA analysis showed a smooth gradient across all layers, suggesting the representational space remained stable even as the specific valence axis degraded.
- APERTUS-8B: Exhibited late emergence. Valence correlations were near zero in the first half of the network, rising sharply after layer 18 and stabilizing in the upper layers (peaking at layer 23–31). CKA analysis revealed a distinct "phase transition" in the middle layers, indicating a reorganization of the representational space.
Corpus-Dependent Arousal: The extraction of arousal (PC2) was highly sensitive to the story corpus.
- Both models showed significantly stronger PC2–arousal alignment when evaluated on Gemma-generated stories ( $r$ up to 0.45) compared to Apertus-generated stories ( $r \le 0.21$ ).
- This suggests that arousal-relevant linguistic cues are unevenly distributed across generated corpora, and that the choice of stimulus corpus is a substantive methodological factor rather than a mere implementation detail.
Stable Space, Unstable Axis: The authors observed a disconnect between the stability of the overall representational space (CKA) and the stability of the specific valence axis. In GEMMA-4-E4B, the space remained similar across layers even where the valence correlation collapsed, implying that valence information is preserved but encoded along a shifting axis.

Significance and Claims
The paper claims that similar high-level emotional representations can arise from different computational paths within neural networks. The findings suggest that:

Universality: Emotion vectors are a general property of LLMs, not an artifact of a specific model's training.
Interpretability Implications: The "where" and "how" of emotion encoding vary by architecture. Monitoring or steering these vectors requires careful layer selection, as the optimal layer for intervention differs between models (early for Gemma, late for Apertus).
Methodological Rigor: The extraction of emotion vectors is sensitive to the input corpus. The study highlights that corpus choice can significantly impact the recoverability of specific emotional dimensions (particularly arousal), necessitating diverse stimulus sets for robust analysis.

The authors conclude that while the peak geometry of emotion space is consistent, the developmental trajectory of these representations is model-specific, with implications for targeted steering interventions and safety monitoring in open-weight models.