docdistance

Overview

docdistance measures how far apart two documents are - in meaning and in order - and points to exactly which sentences changed. It is built for pipelines where an AI model rewrites, converts, extracts, or summarizes a document and you need to check, automatically, whether the result still says the same thing.

Features

• Two kinds of distance - one for meaning (did the content change?), one for order (was the same content rearranged?)
• Points to what changed - a per-statement diff that tells a reworded sentence apart from one that only moved, not just a single score
• Source-aware option - compare two documents against a shared source to see which one drifted, and whether it dropped or invented content
• No model internals needed - works from the text alone, so it runs on frontier-model output where token probabilities are unavailable
• Runs anywhere - CPU-only by default (OpenVINO INT8), sub-millisecond for the meaning score, no GPU required
• CLI or Python - docdistance distance-semantic a.md b.md, or from docdistance import semantic_distance
• Interpretable by design - every score comes with the statement-to-statement alignment behind it

A tool for measuring how far a document has drifted from its source, written by authors who could not stop the scope drifting from one distance to three. The irony is not lost on us - merely, and optimally, transported.

Semantic distance between two documents via Statement Mover's Distance - optimal transport over mmBERT statement embeddings, after Kusner et al. 2015 (From Word Embeddings To Document Distances). A thin frontend to the library; the SOTA docs carry the mechanics, benchmarks, and validation.

• Input - two documents, raw text or a file path
• Output - an SMD distance, a 0..1 closeness, a verdict, and the statement alignment
• Use - agentic document conversion and extraction pipelines, where token logits are unavailable and KL divergence cannot be computed
• Unit - statement-level and position-invariant, with an interpretable transport plan

Theory

A document distance grounded in embeddings and optimal transport, not surface overlap.

• WMD - Word Mover's Distance (Kusner et al. 2015) casts document similarity as optimal transport between embedded tokens
• SMD - this project lifts it to statements: segment, embed, transport between the two statement clouds
• Beyond cosine - whole-document cosine collapses when the same claims sit in a different place or order; statement-level content transport is position-invariant, so distance-semantic scores meaning regardless of where a claim sits
• Structure - order is not discarded, it is resolved on a separate axis: the OPW order-gap, the extra transport cost an order-preserving plan pays over the content-optimal one - near 0 when content already lines up in order, larger on a genuine reorder; distance-structural reports structure_closeness = 1 − order_gap/√2 (a score, not a metric)
• Metric - the content ground cost √(2 − 2cos) on L2-normalized embeddings is a metric, so the semantic document distance is one too
• Logit-free - an embedding-grounded alternative where token probabilities (KL divergence) are unavailable, as in frontier-model pipelines

Method

Three stages; the transport plan is the interpretable by-product.

1. Segment - split each document into atomic statements with the SAT (Segment Any Text) segmenter
2. Embed - encode each statement with the mmBERT contextual encoder (mean-pooled, L2-normalized)
3. Compare - exact optimal transport between the two statement clouds (Statement Mover's Distance), balanced with uniform marginals

• Closeness - 1 − SMD/√2, on a 0..1 scale
• Source-conditioned - a variant d(A, B | S) re-bases the transport onto a shared source S and reads off a selection axis and a grounding axis

Which distance

Three reads over the same two documents; they differ in what the answer tells you and what you must supply.

• Method 1 - semantic distance (robust, fast) - distance-semantic answers how far apart are A and B in meaning? as one number (a 0..1 closeness plus a similar / not-similar verdict). Sub-millisecond, needs only the two documents, and is a true metric - the distance is symmetric and obeys the triangle inequality, so the numbers are consistent enough to threshold, rank and cache. The production default; use it whenever you need a reliable similarity score - dedup, drift detection, "did this conversion change the meaning?"
• Structural read (what moved vs what stayed put) - distance-structural is a first-class command, no extra model and no source: it returns a per-statement order projection where displacement / moved name what MOVED in arrangement, plus a whole-document order_gap and structure_closeness (0..1, 1 = same order) via the OPW order-gap. Pair it with distance-semantic's content details (changed) to tell a reword from a pure rearrangement (see Structure distance below, and a worked map + diff interpretation)
• Method 2 - source-conditioned d(A, B | S) (slower, experimental) - answers why do A and B differ, given a shared source S? You supply S, and instead of one number it returns two axes: a selection axis (did A and B pick different parts of the source?) and a grounding axis (did one drift from the source - dropped content vs unsupported or fabricated content?). It runs a cross-encoder × NLI pass (~seconds on GPU, far slower on CPU). Use it to audit a summary or an extraction against its source, when "how far" is not enough and you need to name the failure
• Which to pick - default to Method 1 for a similarity number, add the structural read when you need to see what moved and where, and reach for Method 2 only when you hold the shared source and need to know why two documents derived from it diverge. Method 2's value is interpretation and ordering the failure modes correctly, not a higher pass rate, and it is validated on a single fixture so far - validate on your own sources first.

Usage

The quickest way to a result is the CLI - init once, then run it.

pip install docdistance                        # from PyPI ('docdistance[s3]' to pull models from S3)
docdistance init wmd                           # provision the symmetric-distance models (once)
docdistance init wmd-wrt-source                # + the reranker + NLI grounding models
docdistance --help                             # full reference (or <command> --help)

# method 1 - semantic distance (robust, fast, the default)
docdistance distance-semantic a.md b.md                 # rich verdict (add --json for machine-readable)
docdistance distance-semantic a.md b.md --details-json details.json   # + statement → statement content alignment

# structural read - order / arrangement distance
docdistance distance-structural a.md b.md                 # order-gap verdict (add --json for machine-readable)
docdistance distance-structural a.md b.md --details-json details.json   # + per-statement order projection

# method 2 - source-conditioned d(A,B|S) (slower, runs the reranker × NLI grounding)
docdistance distance-wrt-source a.md b.md --source s.md                       # two-axis verdict
docdistance distance-wrt-source a.md b.md -s s.md --source-map-json map.json   # + statement → source map

init provisions a mode's models from HuggingFace by default, or from S3 (--source s3://your-bucket --aws-profile NAME) or a local mirror (--source /path/to/models), and records readiness in a docdistance.json written to $DOCDISTANCE_HOME or the current folder. A distance run whose mode was never init'd exits with a clear "run docdistance init <mode>" error.

Or from Python:

import docdistance
from docdistance import semantic_distance, structural_distance, source_conditioned_distance

docdistance.init("wmd")                                         # provision once (writes docdistance.json)
r = semantic_distance("report_v1.md", "report_v2.md")           # method 1 - content
print(r.closeness, r.verdict)               # 0..1 closeness, "similar" | "not similar"

sr = structural_distance("report_v1.md", "report_v2.md")        # structural read - order
print(sr.structure_closeness, sr.order_gap, sr.verdict)   # 0..1 structure readout, order-gap, verdict

from docdistance import DocDistance
result, details = DocDistance().structural_distance_with_details("report_v1.md", "report_v2.md")   # StructuralResult + order details
print(details["smd"], details["order_gap"], details["structure_closeness"])   # semantic distance, structural order-gap, 0..1 structure readout

docdistance.init("wmd-wrt-source")                              # + reranker + NLI grounding models
s = source_conditioned_distance("sum_a.md", "sum_b.md", source="article.md")  # method 2
print(s.d_sel, s.grd_a, s.grd_b)            # selection divergence + each doc's grounding residual

Reading the result

• Method 1 - closeness 0..1 - 1.0 identical, 0.0 unrelated. Good (same meaning): closeness near 1, verdict similar (default cutoff 0.77, set with --threshold). Bad (meaning changed): closeness falls toward 0, verdict flips to not similar

• Method 2 - two axes, lower is closer - d_sel near 0 means A and B drew on the same source content, high means they picked different parts; grd_a / grd_b are each document's reranker x NLI grounding residual (E03-H11 relevance-gated ungrounded mass) - low means it stays grounded in S, high flags drift (dropped or unsupported content). Good: both grounding residuals and d_sel low. Bad: a grounding residual spikes for the document that drifted

• Transport map - add --details-json details.json to distance-semantic to also write the optimal-transport map: for every statement of A, which statements of B its mass flows to, with the weight (fraction of that statement's mass) and the match cost - the interpretable statement-to-statement alignment behind the distance, readable by a human or a machine (the same map is returned in Python by DocDistance.semantic_distance_with_details)

• Source map - add --source-map-json map.json to distance-wrt-source to also write, for every statement of A and B, the top-3 source statements it covers with their weights - a per-statement alignment showing which part of the source each statement draws on

• Offline after init - distance calls run fully offline once docdistance init <mode> has provisioned the mode (from HuggingFace, S3, or a local mirror) and written docdistance.json

• Backend - --backend openvino|torch, default openvino (CPU INT8)

• Full reference - the CLI reference, the API reference and the AWS deployment reference

Transport map output

distance-semantic --details-json writes the exact optimal-transport coupling behind the content distance - for each statement of A, the statements of B its probability mass moves to (one flow shown, a clean 1:1 match):

{
  "smd": 0.286827,
  "anisotropy": false,
  "n_statements": { "a": 12, "b": 11 },
  "flows": [
    {
      "index": 1,
      "text": "Among large organizations with more than 1,000 …",
      "matches": [
        { "target_index": 1, "target_text": "About 42% of organizations with more than 1,000 …", "weight": 1.0, "cost": 0.2237 }
      ],
      "changed": false
    }
  ]
}

• flows - one entry per statement of A; index / text name it, matches are the B statements its mass lands on
• weight - fraction of that statement's mass to the target, sums to 1 per statement; a lone 1.0 is a clean 1:1 match, several smaller weights mean the statement splits across B
• cost - ground distance √(2 − 2cos) of the matched pair; low = semantically close, high = a forced move
• changed - per flow, true once its best-match cost clears the change cutoff (1 − threshold)·√2; the statement's content drifted rather than staying within tolerance
• smd - the distance the map realizes; weight × cost summed over all flows equals it
• Reading it - a statement mapped to its counterpart at weight 1.0 and low cost is preserved; high cost or scattered weights flag a statement with no clean equivalent in B

Order details output

distance-structural --details-json writes the order projection - for every statement of A, its aligned B statement and the order displacement that names what MOVED:

{
  "smd": 0.286827,
  "order_gap": 0.041185,
  "structure_closeness": 0.970878,
  "anisotropy": false,
  "n_statements": { "a": 12, "b": 11 },
  "statements": [
    {
      "index": 0,
      "text": "Among large organizations with more than 1,000 …",
      "target_index": 0,
      "target_text": "About 42% of organizations with more than 1,000 …",
      "displacement": 0,
      "moved": false
    }
  ]
}

• statements - one entry per statement of A; index / text name it, target_index / target_text are its aligned counterpart in B (crisp exact-EMD alignment, not the soft OPW plan)
• displacement - rank shift of the statement from its aligned position; 0 = in place, nonzero = relocated, and moved mirrors it as a boolean
• smd - the top-level semantic distance (content only), order-invariant - the same number distance-semantic reports
• order_gap - the H55 OPW structural distance (order-gap = OPW cost − SMD), translation-invariant and >= 0; 0 = same order
• structure_closeness - 1 − order_gap/√2, the shipped SOTA 0..1 readout on the same scale as SMD closeness; 1 = same order, falling toward 0 as the arrangement diverges
• Reading it - displacement isolates what MOVED in order; a statement at displacement 0 kept its place while a large displacement was relocated. To tell a reword from a pure rearrangement, read it beside distance-semantic's content changed

Structure distance

SMD is position-invariant by design - reorder a document's statements and it barely moves. A second, structure-sensitive number tells content drift from rearrangement, and it ships as its own command (structural_distance, distance-structural --details-json), reported beside SMD. The shipped mechanism is the OPW order-gap (E11-H55); the earlier position-augmented Wasserstein metric was stress-tested against it and dropped.

• OPW order-gap (H55, shipped) - order_gap = OPW − SMD, the order-preserving Wasserstein cost minus the order-free SMD. Subtracting SMD cancels the content component, so only the extra cost the order constraint forces remains - a faithful reword with order kept reads ~0, a reorder with content kept reads large. Reported as structure_closeness = 1 − order_gap/√2 on the library's 0..1 closeness scale, the same readout as semantic closeness (1 = same order)
• Content-invariant, translation-invariant - the reword reads 0.5% of a full-scramble distance (the dropped metric leaked 73.5%), it is monotone in displacement (Spearman 1.00), and it reads fractional statement rank i/N, not absolute position, so a uniform shift (a header inserted, everything offset, relative order intact) is invisible. A translation-invariant score, order_gap >= 0, not a metric - the entropic OPW carries ~15% triangle violations (measured, reports/E11-structure-sota-decision.json), never invoked for a pairwise arrangement read
• Two axes side by side - read the structural order-gap beside the semantic distance (SMD, order-invariant); when meaning is preserved (SMD ≈ 0) but structure_closeness falls, the arrangement changed and nothing else. distance-structural's per-statement displacement names what MOVED in order, and distance-semantic's per-flow changed names what changed in MEANING - the structural analogue of the transport map
• The metric that was dropped - position-augmented Wasserstein (E08-H44) is a true metric, but fuses semantic and positional cost into one distance √((1−λ)·d_sem² + λ·d_pos²), so a faithful reword reads as far as a real reorder (E11) - a metric on the wrong quantity. E11 chose the order-gap and dropped it
• Design and evidence - the structure-distance SOTA, the experiments log (E07 the barycentric read, E08 the metric formulation, E10-H55 the order-gap mechanism, E11 the decision), and the end-to-end notebook notebooks/12-kj-structure-distance-e2e.ipynb

Dataset

Both datasets are generated end-to-end from public third-party articles - nothing ships pre-staged, and the whole corpus rebuilds from scratch by running one notebook.

• Two datasets, one foundation - a WMD / source-conditioned corpus (the executive summaries E01-E06 consume) and a structure-distance fixture (E07-E11), both derived from the same AWS Bedrock exec-summary corpus
• Complete and independent - notebooks/11-kj-structure-fixture.ipynb runs the full pipeline unattended: fetch the source PDFs (data/external/download-fixtures.py), convert them to curated text, summarise under the executive-summary gold rules (Bedrock opus / sonnet / haiku), segment into statements, opus-mt back-translate, and assemble the fixture - no external file has to be staged by hand
• Reproducible - the fetch and the generation are cache-backed and deterministic where possible; only the two curated source-article.md inputs are hand-reviewed, everything downstream regenerates
• Recipe - docs/dataset/dataset-generation-recipe.md walks the external → interim → processed flow, the gold-rules writing contract, and the from-scratch rebuild

Documentation

The SOTA documents explain how it works in detail; this README only introduces it.

• docs/solution/wmd-docdistance-solution-sota.md - source-free distance: design, mechanism, performance, validation
• docs/solution/wmd-source-conditioned-docdistance-solution-sota.md - source-conditioned distance d(A,B|S): two axes (selection + grounding), design, performance, limitations
• docs/solution/wmd-structure-distance-sota.md - structure-sensitive distance: the OPW order-gap (OPW − SMD) and structure_closeness, shipped as distance-structural; theory, the structural mapping, limitations
• docs/example-map-interpretations.md - a worked, grounded example: reading the --details-json outputs of distance-semantic and distance-structural to localize what changed between two documents (blind-recovery of four known edits)
• docs/mmbert-quantization-solution.md - the INT8 / FP8 statement encoder
• From Word Embeddings To Document Distances - Kusner et al. 2015, the WMD theory
• All-but-the-Top: Simple and Effective Postprocessing for Word Representations - Mu & Viswanath, ICLR 2018, the anisotropy postprocessing
• SummaC: Re-Visiting NLI-based Models for Inconsistency Detection in Summarization - Laban et al., TACL 2022, the multi-premise NLI grounding pattern behind the source-conditioned grounding axis
• Moving Other Way: Exploring Word Mover Distance Extensions - Smirnov & Yamshchikov, COMPLEXIS 2022, WMD extension axes - rare-word weighting and non-Euclidean geometry
• Speeding up Word Mover's Distance and its variants via properties of distances between embeddings - Werner & Laber, ECAI 2020, sparse Rel-WMD / Rel-RWMD via related-word caching
• Order-Preserving Wasserstein Distance for Sequence Matching - Su & Hua, CVPR 2017, optimal transport with temporal regularizers - the order-OT behind the structure order-gap
• Order Constraints in Optimal Transport - Lim et al., ICML 2022, explainable order-constrained transport plans
• Fused Gromov-Wasserstein Distance for Structured Objects - Vayer et al. 2019, the feature-plus-structure OT distance behind the positional-Gromov structure read
• Soft-DTW: a Differentiable Loss Function for Time-Series - Cuturi & Blondel, ICML 2017, the order-preserving monotonic alignment cost
• Differentiable Divergences Between Time Series - Blondel et al., AISTATS 2021, the soft-DTW divergence (non-negative, zero iff equal)
• Kendall Tau Sequence Distance: Extending Kendall Tau from Ranks to Sequences - Cicirello 2019, the adjacent-swap metric on symbol sequences