Valence-Assent Axis in Neural Systems

• Valence-Assent Axis is a principal dimension in neural systems that jointly encodes sentiment and factual endorsement, unifying affective and epistemic evaluations.
• The VAA is identified via PCA on hidden states, yielding a dominant eigenvector that clearly distinguishes positive from negative judgments across tasks.
• Direct manipulation along the VAA demonstrates its role as a low-rank control signal, affecting output coherence, bias, and factual grounding in model outputs.

The Valence-Assent Axis (VAA) is a dominant, linear direction in the latent representation space of artificial neural systems that jointly encodes subjective valence ("what is good") and factual assent ("what is true"). The VAA crystallizes previously distinct research streams in affective computing and LLM interpretability, demonstrating that evaluative and truth-verification judgments can be unified along a single axis, which acts as a global control signal for generative reasoning and judgment (Lu et al., 31 Oct 2025).

1. Definition and Conceptual Motivation

The Valence-Assent Axis is a principal dimension in model internal states that subsumes both evaluative affect (valence) and epistemic endorsement (assent). In LLMs, projections onto the VAA reflect whether a statement or response is construed as positive/good/endorsed or negative/bad/rejected. This axis challenges the modularist perspective of neural architectures by revealing that sentiment analysis, value judgments, and truth-verification are co-represented in a domain-general fashion, not in disjoint modules.

In affective computing, valence—a scalar measure ranging from unpleasant to pleasant—has long been paired with arousal in two-dimensional models of emotion. In LLMs, the discovery that valence and assent codes collinearly as a unified VAA establishes that both subjective and objective judgments can be regulated by a single, interpretable direction in feature space (Lu et al., 31 Oct 2025).

2. Algorithmic Identification of the VAA

Given a set of evaluation cases for a model (such as rating prompts, verification questions, or preference judgments), the hidden state activations at a chosen layer $\ell$ are compiled into an $n\times d$ matrix $R^{(\ell)}$, where $n$ is the number of examples and $d$ the hidden dimension. Principal Component Analysis (PCA) is then performed:

• Empirical covariance: $$\Sigma^{(\ell)} = (R^{(\ell)})^\top R^{(\ell)} \in \mathbb{R}^{d\times d}$$
• Dominant direction (the VAA): $$v^{(\ell)} = \text{argmax}_{\|v\|=1} \text{Var}(R^{(\ell)} v)$$, corresponding to the largest eigenvector

Empirically, using either binary (e.g., "good/bad") or continuous ratings produces near-identical directions for $v^{(\ell)}$. The cosine similarity between the axes derived from different judgment types peaks at an intermediate "formation layer," indicating the VAA's format-independence and stability across task types.

3. Functional Role and Projection Interpretation

Any hidden state $h \in \mathbb{R}^d$ at the relevant layer can be projected onto the VAA via $h \cdot v$. A positive score indicates endorsement or positive sentiment, while a negative score signals dissent or negative sentiment. Separate analyses using only word-valence tasks or only truth-verification tasks yield axes $n\times d$0 and $n\times d$1 with extremely high alignment to the global VAA ($n\times d$2, $n\times d$3).

The VAA thereby unifies sentiment and factuality assessments under a single computational mechanism, refuting strict modular segregation of evaluative and factual systems (Lu et al., 31 Oct 2025).

4. Causal Manipulation and the Subordination of Reasoning

Direct interventions along the VAA (editor's term: "VAA steering") demonstrate its control of model output. The standard intervention:

$n\times d$4

for $n\times d$5 shifts the model's judgment in a near-linear fashion. When $n\times d$6, the model is biased toward assent or positive valence; when $n\times d$7, toward dissent or negative valence.

This mechanism subordinates generative reasoning to the VAA-induced stance. For instance, when the model is prompted to generate a rationale or "chain-of-thought," steering against objective truth ($n\times d$8) causes the model to produce coherent but factually incorrect explanations ("Coherent Hallucinations"). When steered toward truth, rationales remain factually grounded.

$n\times d$9

Thus, the VAA acts as a low-rank control signal that orchestrates both answer selection and rationale formation, illustrating how global evaluative states dictate the information-filtering process during generation (Lu et al., 31 Oct 2025).

5. Implications for Bias and Hallucination

Because the VAA overarches both affective and epistemic axes, any dataset or societal bias encoded in the orientation of $R^{(\ell)}$0 will systematically influence downstream predictions. A misaligned or biased VAA will amplify such skews across diverse topics whenever evaluative reasoning is invoked. The subordination mechanism explains why LLMs often produce highly plausible yet false rationales: coherence is maintained even when facts are subordinated to an (incorrect) evaluative stance.

Mitigation strategies include representational editing (removing or decorrelating biased directions in $R^{(\ell)}$1), dual-axis control (balancing a knowledge axis $R^{(\ell)}$2 against VAA pressure, via $R^{(\ell)}$3), and targeted post-hoc fact-checking for outputs with high $R^{(\ell)}$4 (Lu et al., 31 Oct 2025).

6. Comparative Perspective: VA Circumplex and Latent Emotional Structure

In affective computing, the Valence–Arousal (VA) circumplex remains a prevailing framework for modeling emotional experience as points $R^{(\ell)}$5 in a two-dimensional space: valence ($R^{(\ell)}$6) measures pleasantness, while arousal ($R^{(\ell)}$7) measures alertness/excitation (Nath et al., 2020). Within the LeVAsa variational autoencoder, explicit latent subspaces $R^{(\ell)}$8 and $R^{(\ell)}$9 are trained to encode these axes, yielding strong alignment between the learned latent geometry and human affective judgments.

The translation of these techniques to the unified VAA in LLMs suggests a convergence: affective and epistemic evaluation can both be recast as projections onto a principal axis encoding the broad spectrum of judging "what is good/true." This unified latent axis is not limited to emotion recognition but is active across all evaluative and reasoning tasks, supporting the VAA's centrality in large neural system architectures (Lu et al., 31 Oct 2025, Nath et al., 2020).

7. Quantitative Metrics and Empirical Outcomes

Alignment of learned representations with ground-truth valence or assent is measured by regression or classification error between projections $n$0 and labels $n$1, as well as cross-entropy or mean squared error on evaluation datasets (Nath et al., 2020).

In LLMs, steering along the VAA modulates task performance and is related to observable shifts in answer probability, reasoning trace, and classification decisions. The link between valence, assent, and truthfulness has been quantitatively confirmed via near-perfect cosine alignment of VAA, word-level valence, and truth axes, as well as the reproducibility of steering-induced judgment shifts (Lu et al., 31 Oct 2025).

In LeVAsa:

Model	Valence MSE	Arousal MSE	Discrete CE (IMFDB)	Discrete CE (AFEW-VA)
Vanilla VAE	1.83	1.49	8.9	8.9
LeVAsa	0.14	0.06	6.63	2.54

A similar approach applies to LLMs, where direct manipulation and projection allow fine-grained control and quantification of evaluative/epistemic alignment (Lu et al., 31 Oct 2025).

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The Valence-Assent Axis formalizes a unified core of evaluative cognition in modern neural architectures. It subsumes both affective and factual endorsement, governs both categorical and continuous evaluation, and provides a principled lever for interpretability, manipulation, and mitigation of bias and hallucination in artificial intelligence systems (Lu et al., 31 Oct 2025, Nath et al., 2020).