Computation Over Geometry: Meaning Identity Is Computed, Not Shipped in the Embeddings

Jiaqi Deng

cs.CLSep 23, 2026

Computation Over Geometry: Meaning Identity Is Computed, Not Shipped in the Embeddings

Authors: Jiaqi Deng

Abstract

Meaning identity (whether two sentences say the same thing after wording changes) is treated in retrieval and RAG as a geometric fact about independently encoded sentence vectors. We show that, for frozen off-the-shelf encoders and language models, it is not: identity is computed when both sentences share one forward pass, and is not a property of the embedding geometry those systems ship. On overlap-matched PAWS-X, purpose-built encoders (BGE, E5, GTE, MiniLM, E5-Mistral-7B) reach English confirm AUC only 0.55-0.65 (dense peak 0.70). Independently encoded last-token states of Llama 3, Mistral, and Qwen do no better; late fusion of the two vectors stays near chance. The same probe on a joint forward pass reaches 0.90-0.96 from 1.5B to 32B, collapses under partner shuffle, is mid-depth, saturates near 0.94 by 3B, and appears more weakly in GPT-2 XL (0.76). The gap holds beyond Llama-style models on other causal LMs, bidirectional encoders (DeBERTa, RoBERTa), and encoder-decoders (Flan-T5, T5, BART). Fixed or linear readers over frozen independent encodings never unlock identity; nonlinear pair readers recover part of it only on the full 49k-pair PAWS train split (0.68-0.87). Off-the-shelf rerankers split: BGE-reranker-large reaches 0.94, while MS-MARCO and Jina stay at 0.55-0.64. Independently trained families compute the same relation and a 1.5B joint reader can distill it from unlabelled teacher scores, while no linear function of the teachers own independent vectors can. Bi-encoders can be fine-tuned to fit PAWS (0.87-0.93), but transfer and STS-B suffer. Cosine compares wording neighbourhoods; identity is a cheap computed operator, not a property of either sentence vector.

Explore similar work

Sep 16, 2026cs.CL

Exact semantic readout from compressed vector representations

We characterize when compressed vector representations admit exact linear or affine readouts of a finite lexicon's truth conditions: one fixed map per predicate, sending each entity vector to the corresponding truth vector. A necessary and sufficient row-space condition determines existence; the augmented truth matrix has rank r, giving minimum dimension r in the linear case, and r-1 in the affine. Exact readouts return values in a shared truth basis on which Boolean connectives act unchanged; separability alone requires an intervening threshold. For binary relations, exact bilinear readout of identity or strict total order requires linearly independent entity vectors. Experiments with GloVe and word2vec distinguish exact affine recovery, linear separability, and held-out prediction: most predicates are strictly separable, but none admits an exact affine readout from the pretrained embeddings. Supervised transductive training attains exact affine recovery to numerical precision at every tested dimension meeting the bound. At the embeddings' original dimension, geometries constrained to exact linear recovery retain 98-99 percent of the pretrained variance on the feature norms, and 80-83 percent on the WordNet lexicon.

Daniel Quigley

Readout Representation Space Lexicon Truth

Ask PDF

Jun 5, 2026cs.CL

Principles of Concept Representation in Sentence Encoders

What makes a sentence encoder produce good concept representations? We approach this through the lens of representational compositionality: an encoder supports a concept family only when its latent space admits a low-distortion realization of the corresponding semantic operator. This framing predicts both where current encoders succeed and where they are structurally mismatched to their supervision. Through a controlled ablation over encoder conditions trained on 3.3 million synonym and definition pairs from WordNet and Wiktionary, evaluated on three decontaminated splits and a modifier-labeled noun-phrase benchmark, we identify four principles. Fine-tuning recalibrates the latent geometry rather than expanding it (P1). Semantic signal concentrates in the final transformer layer before concept-specific training begins, making cross-layer pooling redundant (P2). Hard negatives improve discrimination and stress-test robustness without improving retrieval ranking, showing that calibration and ranking are independently addressable (P3). Finally, the effectiveness of supervision depends on the composition type of the target concept. Extensional training helps intersective and subsective families while degrading relational and intensional ones, exposing a structural limitation of current training paradigms (P4). We release two new evaluation datasets: a DBpedia semantic-gap benchmark and a modifier-labeled NP paraphrase suite.

Isabelle Mohr, John Dujany, Jonathan Souquet +1

Encoding Models Semantic Representations Compositionality Lexicon Principles

Ask PDF

Sep 1, 2026cs.CL

Polish ModernBERT: The Long and Short of Polish Language Understanding

Encoder-only Transformers remain effective for discriminative and representation-learning tasks, yet Polish encoders still largely rely on BERT/RoBERTa-style architectures. We introduce \textbf{Polish ModernBERT}, a family of four Polish encoders available at Base and Large scales, each with 512-token and 8K context variants. We adapt the ModernBERT pretraining recipe through staged selection experiments and release a long-context benchmark covering legal topic classification, ideological decision-direction prediction, factual-consistency assessment over literary plot summaries, and human-rights violation assessment. Across 30 tasks, Polish ModernBERT achieves the best overall performance among the evaluated Polish encoders, reaching 83.99 and 85.11 for the Base-8K and Large-8K models, respectively. On long-context tasks, the 8K variants improve over matched Polish RoBERTa-8K baselines from 67.47 to 77.15 and from 75.88 to 78.49 at the Base and Large scales, respectively. The Base-8K model achieves this gain with 22% fewer parameters (149M vs.\ 190M). Efficiency measurements in representative inference setups show lower peak memory usage and latency than matched Polish RoBERTa baselines in both 512-token and 8K settings. Polish ModernBERT-8K-Base additionally achieves the best result on a Polish retrieval benchmark among the evaluated encoders below 300M parameters.

Michał Perełkiewicz, Sławomir Dadas, Rafał Poświata +1

Modernbert Longbench

Ask PDF