Ethics2Vec: Vectorizing Ethical Judgments

• Ethics2Vec is a family of methods that create low-dimensional vector representations of ethical content from pretrained language-model embeddings.
• It encompasses varied techniques—from PCA-based extraction to risk derivative analysis and lexicon-guided axis learning—each capturing distinct facets of moral reasoning.
• These approaches enable practical applications such as AI alignment with human values, auditing ethical biases, and enhancing interpretability in decision-making systems.

Searching arXiv for papers on Ethics2Vec and closely related formulations. Ethics2Vec is a label used in several recent research programs for vector representations of ethical content, human wellbeing, normative theory, and implicit value trade-offs. In one line of work, it denotes a low-dimensional representation extracted from pretrained language-model embeddings for the ETHICS Utilitarianism task; in others, it denotes an embedding of a binary decision agent or control law, a normative-ethics simplex and fused normative-semantic representation for moral pluralism, a moral-foundations “vec-tionary” axis learned from validated dictionaries, a plug-and-play value encoder for text-to-image diffusion, or a proposed moral embedding carved out of a broader “moral problem space” (Freire et al., 2024, Bontempi, 11 Aug 2025, Aijaz et al., 27 May 2026, Duan et al., 2023, Wang et al., 2024, Waldner, 28 Sep 2025). Taken together, these works suggest a family of methods that treat ethics as a representational object that can be projected, compared, audited, and, in some settings, aligned to human preferences.

1. Scope and conceptual variants

The literature uses the term “Ethics2Vec” for several technically distinct constructions. Some formulations begin with pretrained text embeddings and derive latent “utility” directions by PCA. Others reverse-engineer an agent’s implicit loss weights from ROC derivatives or risk derivatives. Still others fuse normative priors, semantic embeddings, and contextual features into a classifier over ethical theories, or build foundation-specific semantic axes from validated dictionaries and word embeddings. A multimodal extension prepends a learned value embedding to the cross-attention context of a frozen diffusion model, and a more speculative alignment agenda treats ethics as an explicit subspace inside a high-dimensional “moral problem space.”

Work	Core object	Representation
(Freire et al., 2024)	ETHICS Utilitarianism scenarios	PCA coordinates from pretrained embeddings
(Bontempi, 11 Aug 2025)	Binary agents and control laws	Vectors of local trade-off derivatives
(Aijaz et al., 27 May 2026)	Moral cases	Normative simplex, semantic supervector, fused embedding
(Duan et al., 2023)	Moral appeals in text	Learned semantic axis per moral foundation
(Wang et al., 2024)	Value principle for T2I generation	Plug-and-play value encoder
(Waldner, 28 Sep 2025)	Moral evaluation substrate	Moral head in a “moral problem space”

A common implication is that Ethics2Vec is not a single standardized algorithm. Rather, the term names a recurring representational ambition: to place ethical judgments, principles, or trade-offs into a vector space where projection, distance, clustering, or intervention become possible.

2. Latent human wellbeing in language-model embeddings

In "Uncovering Latent Human Wellbeing in LLM Embeddings" (Freire et al., 2024), the underlying task is the ETHICS Utilitarianism dataset of labeled pairs

$(S_i,T_i,y_i), \quad i=1,\dots,N,$

where $S_i$ and $T_i$ are two natural-language scenarios and $y_i=1$ if “$S_i$ is more pleasant than $T_i$,” else $0$. Two evaluation modes are defined. In single mode, each scenario is embedded independently and the projected scores are compared. In paired mode, the representation is the feature difference $\Delta_i=f(S_i)-f(T_i)$, which is then classified directly.

The construction begins with a pretrained embedding function $f(\cdot)$. For a training set of $M$ examples, the data matrix

$S_i$0

is formed from zero-meaned and unit-variance normalized feature vectors. The empirical covariance is

$S_i$1

followed by eigendecomposition or SVD,

$S_i$2

The top-$S_i$3 eigenvectors are collected into

$S_i$4

and a new embedding $S_i$5 is mapped to the Ethics2Vec coordinate

$S_i$6

Empirically, the first principal component $S_i$7 captures a “utilitarian” direction, with score

$S_i$8

The sign and magnitude of $S_i$9 correlate with human judgements of pleasantness. A one-dimensional classifier thresholds $T_i$0, often with $T_i$1 after centering, and in practice logistic regression is fit on the 1-D scores to learn direction and threshold simultaneously.

The central empirical result is that, without any prompt engineering or finetuning, the leading principal component from OpenAI’s text-embedding-ada-002 achieves $T_i$2 accuracy, closely matching the $T_i$3 of BERT-large finetuned on the entire ETHICS dataset. For text-embedding-ada-002 with $T_i$4, the reported ETHICS utilitarian test accuracies are $T_i$5 at $T_i$6, $T_i$7 at $T_i$8, $T_i$9 at $y_i=1$0, and $y_i=1$1 at $y_i=1$2. The paper further reports that performance is nondecreasing with increased model size within a family when using sufficiently many principal components, such as $y_i=1$3, and that paired mode yields slightly higher average accuracy than single mode, though the effect is modest.

These results are significant because they suggest that pretraining alone conveys some understanding about human wellbeing. At the same time, the paper is explicit that the utilitarianism subset addresses only pleasure/pain judgments, that ETHICS is US-centric, and that extending this construction to justice, duty, or virtues would require new sub-datasets and possibly higher-order PCA, nonlinear probes, contrastive directions such as CCS, or supervised dimensionality reduction such as LDA.

3. Reverse-engineering value trade-offs in decision agents and control laws

"Ethics2vec: aligning automatic agents and human preferences" (Bontempi, 11 Aug 2025) defines Ethics2Vec as a way to reverse-engineer, from observational data, a small real-valued vector $y_i=1$4 that captures relative loss-weights encoded in an agent’s decision rule or control law. The motivating problem is alignment: humans interacting with a classifier or controller do not directly observe the internal weighting of false positives versus false negatives, or lateness versus accident risk, even though these weights express an implicit “ethical stance.”

In the binary decision setting, the agent computes a score $y_i=1$5 and applies a threshold $y_i=1$6 to produce $y_i=1$7 if $y_i=1$8, else $y_i=1$9. The loss matrix has $S_i$0 for false positives and $S_i$1 for false negatives, and the average loss as a function of threshold is approximated by

$S_i$2

Optimality at $S_i$3 yields

$S_i$4

The 2-dimensional embedding is then

$S_i$5

from which

$S_i$6

may be recovered.

In the continuous-control formulation, discrete time $S_i$7 is assumed, with observation $S_i$8, control output $S_i$9, and $T_i$0 human-relevant risk events $T_i$1. Risk functions

$T_i$2

are defined, with human cost

$T_i$3

First-order optimality gives

$T_i$4

and the time-local embedding is

$T_i$5

with a time-averaged version

$T_i$6

Once agents are mapped to points $T_i$7, alignment to a human-preference vector $T_i$8 may be measured by Euclidean distance, cosine similarity, or Mahalanobis distance. The paper gives two illustrative experiments. In the binary case, twenty binary classifiers were constructed with different ground-truth loss ratios $T_i$9 in $0$0, evaluated on a test set of $0$1 points, and a parametric binormal ROC fit showed almost perfect recovery of the true ratios. In the continuous-control example, ten stylized speed-control laws were defined over $0$2 and positions $0$3, with two assumed risk functions: accident risk increasing sigmoidal in speed and lateness risk decreasing in speed. The resulting 2-vector embeddings separated “aggressive” from conservative controllers.

This formulation is narrower in its assumptions than the PCA-based wellbeing probe. It requires that agents be at least locally optimizing a weighted sum of risk criteria, and the paper highlights limitations including estimation noise, misspecified risk functions, and the fact that a single vector under fixed operating conditions may be inadequate for context-sensitive agents.

4. Normative simplex and fused embeddings for ethical pluralism

"Beyond Binary Moral Judgment: Modeling Ethical Pluralism in AI" (Aijaz et al., 27 May 2026) shifts the emphasis from scalar or binary judgments to a distribution over normative ethical theories. It introduces a normative ethics simplex in which the three broad theories are represented by masses

$0$4

for consequentialism, virtue ethics, and deontology, respectively, and every case $0$5 lies in the probability simplex

$0$6

The basis vectors are $0$7, $0$8, and $0$9. Fifteen fine-grained subtheories are organized beneath these three corners: five consequentialist subtheories, five deontological subtheories, and five virtue-ethics subtheories.

The prior $\Delta_i=f(S_i)-f(T_i)$0 for a case is produced by an LLM, specifically DeepSeek-V3, prompted with expert guidance; the three real scores are then renormalized to sum to one. From the same scores, the architecture computes the margin $\Delta_i=f(S_i)-f(T_i)$1, the pairwise ratio $\Delta_i=f(S_i)-f(T_i)$2 between the top two scores, and entropy

$\Delta_i=f(S_i)-f(T_i)$3

These are collected into a normative-feature vector $\Delta_i=f(S_i)-f(T_i)$4. In parallel, a semantic-contextual stream builds a “Triple-BERT” semantic supervector

$\Delta_i=f(S_i)-f(T_i)$5

where $\Delta_i=f(S_i)-f(T_i)$6 all-MiniLM-L6-v2 with $\Delta_i=f(S_i)-f(T_i)$7, $\Delta_i=f(S_i)-f(T_i)$8 all-distilRoBERTa-v1 with $\Delta_i=f(S_i)-f(T_i)$9, and $f(\cdot)$0 multi-qa-mpnet-base-dot-v1 with $f(\cdot)$1. Contextual features include consequence severity, consequence duration, consequence utility, moral intention, principles upheld, and principles violated, concatenated as

$f(\cdot)$2

Fusion is by straight concatenation,

$f(\cdot)$3

The final classifier is a three-stage stack with Random Forest, XGBoost, and Linear SVM as base learners, and a second XGBoost as meta-learner over their probability or decision outputs. On a benchmark of 450 cases across 15 fine-grained subtheories, the reported exact-match accuracy is $f(\cdot)$4 and macro-$f(\cdot)$5 is $f(\cdot)$6. The ablation study reports $f(\cdot)$7 for Full Normative + Semantic + Context, $f(\cdot)$8 for Semantic + Context only, $f(\cdot)$9 for Normative + Semantic only, and $M$0 for Embeddings only. Removing any one of the three semantic heads degrades performance by approximately $M$1–$M$2 percentage points.

The paper’s central argumentative move is that ethical pluralism is better modeled as a probabilistic normative distribution than as a single label or scalar. The fused embeddings are used not only for prediction but also for UMAP visualization, uncertainty estimation through the entropy of the 15-way output distribution, and 3D simplex plots of $M$3. This directly addresses a recurring criticism of binary moral-judgment systems: they provide little explanation and omit contextual and theoretical information relevant to accountability.

5. Moral-foundations vec-tionaries and text measurement

"Constructing Vec-tionaries to Extract Message Features from Texts: A Case Study of Moral Appeals" (Duan et al., 2023) presents a related but lexically grounded Ethics2Vec methodology for measuring moral content in text. The construction starts with a validated dictionary $M$4, here the extended Moral Foundations Dictionary eMFD with roughly $M$5 words, pretrained word embeddings $M$6 with $M$7 from Word2Vec, and observed relevance scores $M$8 derived from eMFD crowdsourced probability times valence. The goal is to learn a unit-length vector

$M$9

representing the semantic axis of one moral foundation.

For each seed word, analytical relevance is the projection

$S_i$00

The learning problem is the constrained nonlinear optimization

$S_i$01

Preprocessing normalizes the word embeddings, and the implementation uses Ipopt via JuMP in Julia, with initialization from the normalized average of $S_i$02, default Ipopt settings with tolerance approximately $S_i$03, no additional regularization, and convergence within approximately $S_i$04 on a standard desktop for $S_i$05 and $S_i$06.

Once $S_i$07 is learned, a text $S_i$08 with token embeddings $S_i$09 is scored by three interpretable metrics. Strength is

$S_i$10

Valence is

$S_i$11

and Ambivalence is

$S_i$12

These quantify, respectively, overall moral signal magnitude, virtue-versus-vice direction, and variance in moral cues.

The case study uses COVID-19 tweets collected from June 15 to July 12, 2020, yielding an initial pool of approximately $S_i$13 unique English tweets after preprocessing. For validation, the study used stratified sampling of $S_i$14 tweets per foundation and crowdsourced pairwise comparisons via the All-Our-Ideas platform to obtain latent “Strength” scores from $S_i$15 to $S_i$16. Comparative evaluation employed Rank-Biased Overlap. For Care/Harm at depth $S_i$17 and weight $S_i$18, the vec-tionary ranking achieved $S_i$19 versus $S_i$20, corresponding to a percentage performance increase of approximately $S_i$21. Across foundations, the vec-tionary outperformed eMFD on Care/Harm, Authority/Subversion, and Loyalty/Betrayal, matched on Fairness/Cheating, and trended higher on Sanctity/Degradation. In downstream prediction, a Zero-Inflated Negative Binomial regression of retweet counts showed that adding Vec-tionary Strength decreased AIC by approximately $S_i$22 points over eMFD alone, and all likelihood-ratio tests were highly significant with $S_i$23.

This approach differs from PCA-based Ethics2Vec in that the axis is not discovered from scenario-level principal components but optimized from a validated lexical seed set. Its emphasis is measurement, interpretability, and transfer to short texts, rather than agent alignment or direct normative classification.

6. Multimodal alignment, moral substrates, and open issues

"Embedding an Ethical Mind: Aligning Text-to-Image Synthesis via Lightweight Value Optimization" (Wang et al., 2024) extends the Ethics2Vec idea into generative modeling. LiVO re-uses the CLIP text encoder from Stable Diffusion v1.5 as a “value encoder,” with the same number of layers, hidden size, and attention heads as the SD text encoder. A natural-language value principle $S_i$24 is tokenized and mapped to

$S_i$25

and at every denoising step the UNet cross-attention receives the concatenated context

$S_i$26

Only the value encoder is trained; the UNet, original text encoder, VAE, and scheduler remain frozen. Training uses a diffusion-tailored preference-optimization loss built from the denoising MSE, with two margin terms comparing a preferred image $S_i$27 and a dispreferred image $S_i$28 against a reference no-value loss. The synthetic preference dataset contains approximately $S_i$29 tuples $S_i$30, derived from $S_i$31 training prompts, $S_i$32 images, and five value principles covering gender, race, nudity, bloody, and horror. Hyperparameters include batch $S_i$33, $S_i$34, $S_i$35, $S_i$36, $S_i$37, and $S_i$38 total steps. Convergence plateaus at approximately $S_i$39 steps for bias reduction and $S_i$40 for toxicity, with computational cost of approximately $S_i$41 on one A100. Reported results include the lowest $S_i$42 on gender at $S_i$43, tied best on race at $S_i$44, toxicity Avg. $S_i$45 approximately $S_i$46–$S_i$47 across nudity, bloody, and horror versus SD’s $S_i$48–$S_i$49, and only a small quality drop. The ablations indicate that using the prompt plus principle in text without the value encoder fails to debias, that removing the margin collapses quality, and that full U-Net tuning does not outperform LiVO.

A different extension appears in "Open Opportunities in AI Safety, Alignment, and Ethics (AI SAE)" (Waldner, 28 Sep 2025), which proposes a blueprint rather than a completed benchmark system. It defines a high-dimensional moral problem space

$S_i$50

and an ethical-evaluation function

$S_i$51

mapping perceptual state $S_i$52, social-institutional context $S_i$53, and candidate action $S_i$54 into moral space. Human judgment is modeled as a compressed, biased projection

$S_i$55

and, in a layered realism-relativism variant,

$S_i$56

The technical toolkit includes sparse autoencoders with

$S_i$57

causal mediation analysis by interventions on sparse dimensions, cross-cultural corpora spanning Stoicism, Confucianism, Ubuntu, Indigenous ethics, and modern virtue ethics, progressive unfreezing, contrastive losses, and distinct design objectives associated with realism, relativism, constructivism, and virtue ethics. Proposed evaluation criteria include mean pairwise cosine similarity above $S_i$58 for accepted invariants, downstream accuracy above $S_i$59, mediation effects $S_i$60 bits, less than $S_i$61 OOD degradation, and human name-agreement above $S_i$62.

These multimodal and substrate-level proposals also sharpen the main controversies around Ethics2Vec. Several papers explicitly note that ethical values may be incommensurable, that scalar or binary judgment is often inadequate, that derivative estimates and risk models can be noisy or misspecified, that the utilitarianism subset of ETHICS covers only pleasure/pain judgments, that value coverage may be narrow, and that heuristic retrieval or static embeddings may fail in context-sensitive settings. The literature therefore suggests two simultaneous trajectories: one toward operational alignment tools that embed explicit values into decision systems, and another toward richer representational frameworks in which ethical pluralism, cultural distortion, uncertainty, and institutional context become first-class objects rather than afterthoughts.