Text-as-Signal: Quantitative Semantic Scoring with Embeddings, Logprobs, and Noise Reduction

We report a systematic dissociation in modern text embedders: sentiment is almost perfectly decodable from their embeddings, yet almost entirely absent from their metric. Across eleven frozen encoders spanning 2021 to 2026, including 2026-generation models and the 4B-parameter LLM embedder Qwen3-Embedding-4B, a linear probe recovers sentence polarity at up to 91.3% accuracy while cosine similarity separates polarity by a margin of only 0.003-0.064. Qwen3-Embedding-4B, the strongest probe in the panel, reaches 91.3% probe accuracy but only 64.3 retrieval MAP. Because retrieval, clustering, deduplication, and retrieval-augmented generation operate on the metric rather than on a trained probe, these systems are effectively blind to information their encoder demonstrably contains. A task-conditioning control suggests this reflects the pretraining objective rather than a prompting artifact: conditioning Jina-v5 on its classification task rather than its retrieval task recovers only about half of the MAP gain that injection achieves on the same weights (63.2 to 73.8, versus 85.1), and leaves the alignment gap essentially unchanged. Sentiment-Injected Sentence Embeddings (SISE) train a small (0.13M-0.69M-parameter) supervised-contrastive head on a frozen encoder in seconds on a CPU, using the labelled training set. The head improves every encoder released since 2022 on full-data probe accuracy (up to +5.8 points), retrieval MAP (up to +26.0) and polarity margin (7-61x). This is a specialization, not a free gain: the compact 128-d head loses 38-41 Spearman points on STS-B, while a fused variant that concatenates it with the base embedding loses 2.4-12.0. With the head, a 0.6B encoder at 128 dimensions matches a 4B encoder given the same head (91.8 vs. 90.3 MAP). We release a CPU-reproducible pipeline and a reusable diagnostic, the Attribute Alignment Gap.

Low-dimensional projections of text embeddings support visual analysis of document collections, but their spatial organization may not reflect the relationships an analyst intends to examine. Existing semantic interaction approaches encode semantic intent indirectly through geometric constraints or model updates, limiting interpretability and flexibility. We introduce LLM-augmented semantic steering, which enables analysts to express semantic intent by grouping a small set of example documents within the projection. A large language model externalizes this intent as natural-language representations and selectively extends it to related documents; the resulting semantic information is then incorporated into document representations via text augmentation or embedding-level blending, without retraining the underlying models. A case study illustrates how the same corpus can be reorganized from different semantic perspectives, while simulation-based evaluation shows that semantic steering improves global and local alignment with target semantic structures using only minimal interaction. Embedding-level blending further enables continuous and controllable steering of projection layouts. These results position projection spaces as intent-dependent semantic workspaces that can be reshaped through explicit, interpretable, language-mediated interaction.

How much meaning does a text carry? Shannon's theory measures uncertainty over symbols and is intentionally indifferent to meaning, while pairwise metrics such as BERTScore compare two texts rather than characterizing one. We develop a geometric framework that measures semantic content from the structure of a text's sentence embeddings. The framework has three parts. First, within a fixed embedding and baseline, six natural axioms uniquely determine a scalar measure up to scale, a frame-conditional uniqueness theorem. The resulting scalar is empirically too coarse, motivating a richer representation. Second, we propose a three-coordinate semantic profile capturing novelty (displacement from generic discourse), breadth (diversity of distinct ideas), and integration (connectedness among them), together with a discrete minimal unit (the semantic quantum) whose resolution is fixed by a clustering threshold $τ$. Third, we prove a no-go theorem: no scalar summary of the profile can simultaneously satisfy analytic stability under paraphrase and concatenation, ordinal robustness across text scales, and cross-representation comparability. We exhibit two practical scalars, $S_{\mathrm{minmax}}$ and $S_{\mathrm{rank}}$, each occupying a distinct corner of this trade-off triangle. Validation across 23 synthetic categories, 5 Project Gutenberg novels, and 3 embedding models confirms the trade-off. The recommended rank-normalized configuration passes 25 of 28 ordinal checks as point estimates (21 of 28 after Benjamini-Hochberg correction), outperforming seven baselines including unigram entropy and a BERTScore-based novelty signal. A separate variational result connects the breadth coordinate to the log-determinant of a determinantal point process (Spearman $ρ= 0.985$ over 507 Gutenberg chapters), giving an optimization-theoretic foundation for breadth.