Residualized Similarity in Authorship Verification

• Residualized Similarity is a method that adds an interpretable cosine similarity to a neural residual prediction to improve authorship verification accuracy.
• It employs Gram2Vec feature vectors and neural embeddings with an attention mechanism to adjust similarity scores, achieving up to 19 AUC points gain.
• The technique offers faithful explainability by tracing feature-level evidence through Interpretability Confidence, balancing accuracy and transparency in high-stakes settings.

Searching arXiv for the primary paper and acronym disambiguation papers to ground the article in the cited literature. Residualized Similarity (RS) is a hybrid authorship verification method that preserves the transparency of interpretable stylometric features while recovering much of the accuracy of neural authorship models. It is introduced for authorship verification (AV), treated as a similarity problem in which the task is to measure how alike two documents are stylistically and then decide “same author” if similarity is high and “different author” if it is low. RS begins with an interpretable similarity score and trains a neural model not to replace that score, but to predict its error—its residual—so that the final decision is the interpretable score plus a learned correction. The method is explicitly motivated by forensic and other high-stakes authorship settings, where explanations must be both faithful and interpretable, and where features should be traceable to the source text rather than latent neural dimensions (Zeng et al., 6 Oct 2025).

1. Conceptual basis and problem setting

RS is designed to solve the trade-off between interpretable AV systems and neural AV systems. Purely interpretable systems, such as linguistic feature vectors built from traceable text statistics, are explainable but weaker in accuracy; purely neural systems are often stronger but opaque. In the paper’s framing, the key requirement is not merely human-meaningfulness but traceability: a feature like frequency of a function word, a POS bigram, passive constructions, or punctuation use can be checked directly in the documents, whereas a latent neural embedding dimension cannot (Zeng et al., 6 Oct 2025).

The method’s core intuition is additive decomposition. The interpretable system is used “as much as possible,” and the neural component is invoked only insofar as it is needed to correct mistakes. This means that the interpretable component is not post hoc; it is an actual numerical part of the score used for the decision. The residual component is also explicit: it quantifies how much of the decision cannot be accounted for by the interpretable system alone. When the residual is small, the final prediction is mostly attributable to interpretable features; when it is large, the model is relying more heavily on opaque neural information. This yields a decomposition of decision responsibility rather than an after-the-fact rationalization (Zeng et al., 6 Oct 2025).

A common misconception is to treat RS as a general acronym rather than the specific method Residualized Similarity. In arXiv usage, the acronym is overloaded. In “Boost-RS,” RS means recommender systems rather than Residualized Similarity (Li et al., 2021). In “RSRank,” RS means Representational Shift (Gupta et al., 16 Jun 2026). In “Measuring Individual User Fairness with User Similarity and Effectiveness Disparity,” RSs refers to recommender systems (Rampisela et al., 23 Jan 2026). In astronomical literature such as “Connecting RS Oph to [some] Type Ia Supernovae,” RS denotes RS Ophiuchi (Patat et al., 2011). These usages are terminologically unrelated to Residualized Similarity.

2. Formal formulation and training procedure

In the main experiments, the interpretable base model is Gram2Vec. Each document is converted into an interpretable feature vector $f(d)$, then features are standardized by z-scoring per dataset, and cosine similarity is computed between the two document vectors. The base similarity is defined as

$s = sim(f(d_1), f(d_2)),$

where $sim(\cdot,\cdot)$ is cosine similarity. Labels are encoded as

$y \in \{1,-1\},$

with $1$ for same-author pairs and $-1$ for different-author pairs. The ground-truth residual is then

$r^{(i)} = y^{(i)} - sim(f(d_1), f(d_2)),$

equivalently written in the framework section as

$res = y - s.$

This residual is the object learned by the neural component (Zeng et al., 6 Oct 2025).

Instead of directly learning authorship labels from scratch, RS trains a neural model $M_{res}$ to approximate the residual that the interpretable system fails to capture. The authors use several pretrained encoders as the neural component, especially LUAR, a strong authorship representation model. During RS training, each document pair is represented both by interpretable feature vectors and by neural embeddings. The architecture includes an attention layer over the four resulting representations—two interpretable vectors and two neural embeddings—so the residual predictor can weight information from both sources. The paper notes that this attention-based combination is used in training; at inference, the final score is simply the base cosine similarity plus the predicted residual (Zeng et al., 6 Oct 2025).

Given a batch

$$\mathcal{B} = \{(d_1^{(i)}, d_2^{(i)}, r^{(i)})\}_{i=1}^n,$$

the model predicts $s = sim(f(d_1), f(d_2)),$0 and is trained with mean squared error: $s = sim(f(d_1), f(d_2)),$1 The regression head uses multiple dense layers with ReLU activations and dropout, and the final output is constrained to $s = sim(f(d_1), f(d_2)),$2 using a $s = sim(f(d_1), f(d_2)),$3 activation. Training uses AdamW, learning rate $s = sim(f(d_1), f(d_2)),$4, up to 10 epochs with early stopping on validation loss, and LoRA for parameter-efficient tuning. LoRA also empirically improved performance relative to full fine-tuning in their setup (Zeng et al., 6 Oct 2025).

At inference, the final RS similarity is

$s = sim(f(d_1), f(d_2)),$5

where $s = sim(f(d_1), f(d_2)),$6 now denotes the neural model’s predicted residual. Classification is then done by thresholding this final similarity. Let $s = sim(f(d_1), f(d_2)),$7 be a threshold tuned on a held-out set; then predict same author if $s = sim(f(d_1), f(d_2)),$8, different author if $s = sim(f(d_1), f(d_2)),$9. For most reported results the authors use AUC, which is threshold-independent, but for case studies they instantiate a threshold of $sim(\cdot,\cdot)$0 (Zeng et al., 6 Oct 2025).

3. Faithful explainability and Interpretability Confidence

RS is presented as “faithfully explainable” because the interpretable features are literally part of the forward computation. The explanation is faithful because the interpretable component is used directly in the prediction rather than being inferred after the decision. The neural residual does not erase that traceability; instead, it quantifies how much extra non-interpretable signal was needed. Thus the final prediction can be partitioned into an interpretable base and an opaque residual, and the method can report “to what degree” a prediction is interpretable (Zeng et al., 6 Oct 2025).

The paper formalizes this degree with Interpretability Confidence (IC), a per-instance measure of how much the final prediction is attributable to the interpretable part. Let $sim(\cdot,\cdot)$1 be the Gram2Vec similarity and let “predicted residual” be the RS correction. If the final prediction is same author, IC is defined as

$sim(\cdot,\cdot)$2

or $sim(\cdot,\cdot)$3 if the denominator is $sim(\cdot,\cdot)$4. If the final prediction is different author, IC is

$sim(\cdot,\cdot)$5

These formulas reflect the idea that for a same-author prediction, Gram2Vec’s contribution is its distance from the lowest possible similarity $sim(\cdot,\cdot)$6; for a different-author prediction, its contribution is its distance from the highest possible similarity $sim(\cdot,\cdot)$7. In both cases, the denominator adds the magnitude of the neural correction. IC always lies in $sim(\cdot,\cdot)$8: higher means more of the prediction came from interpretable evidence (Zeng et al., 6 Oct 2025).

On Reddit with LUAR-based RS, the paper reports most IC values above $sim(\cdot,\cdot)$9 and a mean of $y \in \{1,-1\},$0, suggesting that the system often remains substantially interpretable even after adding neural corrections. This is the main quantitative support for the claim that RS creates a controlled trade-off rather than a binary choice between accuracy and interpretability. The larger the residual, the more accuracy depends on the neural model and the lower the interpretability confidence. This trade-off is quantified per prediction rather than only globally (Zeng et al., 6 Oct 2025).

This suggests a distinctive explanatory regime relative to opaque neural AV systems and to post hoc explanation schemes. RS does not claim that the neural component itself is interpretable; rather, it isolates and measures the opaque contribution.

4. Empirical evaluation and performance profile

RS is evaluated on four datasets spanning genres and languages: Reddit comments, Amazon reviews, Fanfiction stories, and Russian Pikabu comments. Each dataset is converted into balanced same/different-author pairs, with 50K train, 10K validation, and 10K test pairs. The main interpretable baseline is Gram2Vec; neural baselines are fine-tuned sentence-transformer-style Siamese encoders trained with contrastive loss, including RoBERTa-Base, RoBERTa-Large, Longformer, LUAR/LUAR-RU, Style Embedding, all-mpnet-base-v2, and mxbai-embed-large. RS uses the same neural backbones as residual predictors. The evaluation metric is primarily ROC AUC (Zeng et al., 6 Oct 2025).

Dataset	Gram2Vec	RS with LUAR / LUAR
Reddit	0.63	0.80 / 0.84
Amazon	0.71	0.90 / 0.91
Fanfiction	0.69	0.87 / 0.89
Pikabu	0.65	0.76 / 0.74

Compared to Gram2Vec alone, LUAR-based RS gains +17, +19, +18, and +11 AUC points respectively, all significant at $y \in \{1,-1\},$1. Relative to the strong neural LUAR baseline, RS is very close: it is slightly worse than LUAR on Reddit, Amazon, and Fanfiction, and slightly better on Pikabu. The paper’s principal empirical claim is therefore that RS roughly matches state-of-the-art neural performance while introducing a quantifiable interpretability layer (Zeng et al., 6 Oct 2025).

The paper also argues that RS is robust to the choice of interpretable base. Replacing Gram2Vec with ELFEN, another interpretable linguistic feature extractor, or concatenating Gram2Vec and ELFEN, produced similar RS performance. For example, Gram2Vec-RS and ELFEN-RS both reached 0.80/0.90/0.87–0.88 across Reddit/Amazon/Fanfiction. This suggests the residualization idea itself, not a single feature set, drives the gains (Zeng et al., 6 Oct 2025).

An ablation study further supports the proposed architecture. On Reddit/Amazon/Fanfiction, the full RS architecture scores 0.80/0.90/0.87, compared with 0.73/0.84/0.74 for an only-neural residual head and 0.73/0.85/0.77 for direct feature-appending. Within the paper’s experimental scope, the attention-based residual formulation outperforms these simpler alternatives (Zeng et al., 6 Oct 2025).

5. Traceability, case studies, and feature-level evidence

The case studies are intended to show how explanations can be traced back to original text. In one different-author example, Gram2Vec similarity is 0.09, RS residual is 0.29, final score is 0.38, and IC is 0.76. Since the final score stays below the 0.5 threshold, the prediction remains different-author, and the explanation can focus largely on interpretable feature mismatches, such as function-word and POS-bigram differences (Zeng et al., 6 Oct 2025).

In a same-author example, Gram2Vec alone would predict different-author with similarity 0.20, but RS adds a residual of 0.82, producing a final score of 1.02 and flipping the decision to same-author. Even there, IC remains 0.59, meaning the interpretable component still materially contributes. The authors then inspect feature overlap using the metric

$y \in \{1,-1\},$2

to identify features similarly salient in both documents (Zeng et al., 6 Oct 2025).

The cited overlapping features are traced back to concrete textual evidence: rare preposition-punctuation patterns such as “UP!” / “up!” and “out.” / “of.”, passive constructions like “it was connected,” “it was passed down,” and “it was created,” and the absence of commas in both texts. This demonstrates the paper’s notion of traceability: the explanation is grounded in reproducible textual signals rather than abstract embedding coordinates (Zeng et al., 6 Oct 2025).

A plausible implication is that RS treats explanation as evidence accounting rather than feature attribution alone. The interpretable base establishes a traceable similarity substrate; the residual indicates the extent to which that substrate was insufficient.

6. Scope, limitations, and broader significance

The paper’s main findings are threefold. First, RS closes most or all of the gap between interpretable and neural AV systems, often matching strong neural baselines and clearly outperforming interpretable baselines. Second, the residual component is responsible for the large performance gain over Gram2Vec; the paper explicitly highlights up to a 19-point AUC gain. Third, RS creates a controlled trade-off rather than a binary choice between accuracy and interpretability, because the residual magnitude directly modulates the interpretability confidence of each prediction (Zeng et al., 6 Oct 2025).

The paper does not claim a fully end-to-end explainable system. Its limitations are explicit. Experiments use relatively small subsets of the original data; conclusions are therefore promising but preliminary. The method assumes access to a good interpretable feature extractor and paired AV data. It also leaves open the HCI problem of explanation delivery: which features should be shown, how many, and in what interface, depending on whether the user is a forensic linguist or a lay annotator. Cross-domain results show degradation when training on one domain and testing on another, though RS still beats Gram2Vec alone; cross-lingual transfer from English Reddit to Russian Pikabu fails, suggesting language-specific residual models are needed (Zeng et al., 6 Oct 2025).

For future work, the authors point to richer explanation interfaces and broader development of interpretable-yet-accurate NLP systems built on the same residualization principle. This suggests that the method’s significance is not limited to a single AV architecture. Within the paper’s framing, the contribution is the additive structure itself: $y \in \{1,-1\},$3 That structure turns explainability from a post hoc story into a measurable property of the actual decision rule while retaining near-SOTA verification accuracy (Zeng et al., 6 Oct 2025).