Selective Copying: Theory, Applications, and Methods

• Selective copying is a framework that distinguishes exact preservation of source content from systematic transformation, ensuring semantic and operational fidelity.
• In information theory, it decomposes mutual information into copy and transformation components using measures like binary KL divergence, with implications for thermodynamic efficiency.
• Neural models and systems leverage selective copying to balance abstraction and literal replication, enhancing tasks from text summarization to secure object cloning and forensics.

Selective copying denotes a class of mechanisms and analytical frameworks in which the decisive issue is not merely whether a source predicts a destination, but whether some part of the source is preserved as itself, and which parts are permitted or required to be copied at all. In information theory, this distinction separates exact copying from systematic transformation; in neural sequence modeling, it separates copying source tokens or spans from ordinary generation; in systems, it separates copying only metadata from copying entire payloads; and in software, forensics, and concurrency, it separates intentionally duplicated structure from structure that may be shared, transformed, or left in place (Kolchinsky et al., 2019, Gu et al., 2016, Zhou et al., 30 Apr 2026, Faust et al., 2020). Selective copying becomes technically important whenever exact identity has semantic, biological, physical, or operational consequences.

1. Conceptual distinctions

A central distinction, formalized explicitly in the information-theoretic setting, is that a channel may be highly informative while being a poor copier. Mutual information can remain large even when outputs are obtained through systematic permutation, mutation, or other non-identity-preserving transformations; the point of selective copying is to distinguish information transmitted by preserving identity from information transmitted by structured change (Kolchinsky et al., 2019). This same distinction reappears in practice: a summary model may have high predictive quality while still over-copying source text, and an editing model may produce the correct output while incurring unnecessary token-by-token copying decisions (Weber et al., 2018, Panthaplackel et al., 2020).

In neural generation, selective copying usually means that copying is an explicit alternative to generation and is often further constrained by granularity. CopyNet frames Seq2Seq output as a mixture of generate mode and copy mode over the extended space $\mathcal{V}\cup\{unk\}\cup X$, so that certain segments in the input sequence are selectively replicated in the output sequence (Gu et al., 2016). Later span-oriented models sharpened this notion by making copying contiguous and structured: SeqCopyNet can copy a source sub-span as a unit, CopySpan editing models permit one action $\{i\}\{j\}$ to copy an entire contiguous subsequence, and BioCopy constrains decoding with BIO-tagged span continuity (Zhou et al., 2018, Panthaplackel et al., 2020, Liu et al., 2021).

Outside machine learning, selective copying denotes a similarly targeted choice of what is duplicated. Libra copies only protocol metadata into user space while retaining opaque bulk payload in the kernel for forwarding, because conventional POSIX-compatible socket semantics make universal zero-copy receive impossible (Zhou et al., 30 Apr 2026). In live digital forensics, selective imaging is defined so that only explicitly selected data objects are included in the copied data, together with the metadata needed for provenance and verification (Faust et al., 2020). In secure object cloning, copy policies specify field by field what must be duplicated deeply and what may remain shared, using annotations such as @Shallow, @Deep, and @Copy(X) (Jensen et al., 2012). A plausible implication is that “selective copying” is less a single algorithm than a recurrent design problem: determine the unit of identity, determine what must be preserved exactly, and determine what constraints govern the rest.

2. Information-theoretic decomposition of copying and transformation

The most explicit formal treatment is the decomposition of mutual information into copying and transformation. The starting claim is that mutual information alone cannot tell whether information was preserved by exact copying or conveyed through systematic transformation, even though these modes may correspond to different mechanisms and different functional consequences (Kolchinsky et al., 2019). For a source message $x$, a prior $p_Y$, and a posterior $Y|x$, the decomposition is written as

$I = copy + trans .$

The copy component is derived axiomatically. The four axioms are non-negativity, upper boundedness by Bayesian surprise, monotonicity in exact-copy probability, and achievability of pure copying. The resulting measure is unique: copy information is exactly the binary KL divergence between the posterior probability of exact copying and the prior probability of that same event, but only when copying improves upon baseline chance. The binary KL divergence is

$$d(a,b)\coloneqq a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b},$$

and transformation information is the remainder after subtracting copy information from the Bayesian surprise (Kolchinsky et al., 2019).

The initial construction assumes a discrete source and destination with the same message set and an unambiguous notion of identity. The framework is then generalized by replacing exact identity with a loss function $\ell(x,y)$ measuring dissimilarity or distortion. In that generalized setting, copy information is

$$copy = \min_{r_Y} KL(r_Y \Vert p_Y) \quad \text{s.t.} \quad \mathbb{E}_{r_Y}[\ell(x,Y)] \le \mathbb{E}_{Y|x}[\ell(x,Y)] ,$$

with optimizer

$w(y) = {\frac{1}{Z(\lambda)} p_Y(y) e^{-\lambda \ell(x,y)}$

for $\{i\}\{j\}$0. The original exact-copy measure is recovered as the special case of $\{i\}\{j\}$1–$\{i\}\{j\}$2 loss, $\{i\}\{j\}$3, also called Hamming distortion. The same formalism extends to different source and destination alphabets, continuous-valued variables, and vector-valued loss functions (Kolchinsky et al., 2019).

The decomposition also has a thermodynamic reading. For a physical system $\{i\}\{j\}$4 initially at equilibrium $\{i\}\{j\}$5 and driven to a posterior $\{i\}\{j\}$6, stochastic thermodynamics gives

$\{i\}\{j\}$7

If the aim is specifically to achieve at least a given exact-copy probability, then the minimal work is

$\{i\}\{j\}$8

and the excess work is lower bounded by transformation information:

$\{i\}\{j\}$9

For ensembles, when the equilibrium distribution matches the destination marginal $x$0, the thermodynamic efficiency of exact copying equals the information-theoretic copying efficiency,

$x$1

This interpretation is used to motivate applications to replication and inheritance (Kolchinsky et al., 2019).

An empirical illustration is given by amino-acid substitution. Using an empirical PAM rate matrix converted to a discrete-time channel with $x$2 and the stationary distribution as source distribution, the reported quantities are

$x$3

with

$x$4

Amino acids with greater mean Miyata distance have a Spearman correlation of $x$5 with copy information ($x$6), whereas the correlation with transformation information is $x$7 ($x$8). The stated interpretation is that selective copying matters most when exact identity is functionally special (Kolchinsky et al., 2019).

3. Selective copying in neural sequence generation and editing

In Seq2Seq learning, selective copying is motivated by the fact that outputs often contain entities, dates, names, and other segments that should be reproduced verbatim from the source. CopyNet addresses this by combining a generate mode with a copy mode under a shared normalization, so that the probability of an output token is the sum of its probability under generation and its probability under copying from matching source positions. Its additional “selective read” $x$9 feeds source-location information for the previous copied token back into the decoder state, allowing the model to continue copied subsequences rather than merely repeating isolated tokens. On synthetic sequence transformation, text summarization, and single-turn dialogue, the model substantially improves over vanilla encoder-decoder and attention baselines, including LCSTS ROUGE scores of $p_Y$0 for the word-based variant and dialogue exact-match gains from $p_Y$1 to $p_Y$2 Top-1 on DS-II (Gu et al., 2016).

Span-level selectivity is the main innovation of Sequential Copying Networks. SeqCopyNet retains an encoder-decoder architecture with a bidirectional GRU encoder and GRU decoder, but it adds a gate network $p_Y$3 so that, at each step, the decoder can decide between generation and copying. If copying is chosen, the model predicts a start boundary and an end boundary with pointer networks, yielding a contiguous span with probability $p_Y$4. Because a copied block changes the decoder’s temporal state, SeqCopyNet introduces “Copy Run,” in which copied words are fed back through the decoder so that later states reflect the copied content. On abstractive sentence summarization it reaches $p_Y$5 on the Rush et al. test set and $p_Y$6 on the untouched internal Gigaword test set; on SQuAD question generation it reaches $p_Y$7 BLEU-4 versus $p_Y$8 for NQG+ (Zhou et al., 2018).

Editing tasks motivate a different span-copy formalism. “Copy that! Editing Sequences by Copying Spans” introduces an action $p_Y$9 so that long unchanged regions of the input can be copied in one step rather than token by token. Because the same output can now be realized by many action sequences, the training objective marginalizes over all valid action sequences, and inference uses a merged beam search that groups rays producing the same output sequence. On WikiAtomicEdits, GitHubEdits, and CSharp Fixers, CopySpan improves over token-level copying, reaching $Y|x$0, $Y|x$1, and $Y|x$2 accuracy, respectively, while also improving code repair and grammar error correction; learned copied spans average $Y|x$3 tokens on one code dataset and $Y|x$4 on a larger one (Panthaplackel et al., 2020).

BioCopy makes span selectivity explicit through tags rather than explicit span actions. During training, BIO labels are induced from the longest common subsequence between source and target. At inference time, the predicted BIO tag determines a masking strategy: O leaves the vocabulary distribution unchanged, B restricts the next token to source tokens, and I restricts the next token to valid continuations of the current source n-gram. This preserves span continuity without changing the base Seq2Seq architecture. On NYT24 relation extraction, BioCopy improves WordDec from $Y|x$5 to $Y|x$6 F1 and reduces long-span entity extraction errors from $Y|x$7 to $Y|x$8 relative to attention copy; on CAIL2020 legal summarization, NEZHA-BioCopy improves Total from $Y|x$9 to $I = copy + trans .$0 (Liu et al., 2021).

A related but visually grounded variant is LSTM-C for image captioning. It combines an LSTM LLM over a caption vocabulary $I = copy + trans .$1 with a copying distribution over an external object vocabulary $I = copy + trans .$2, using object detector confidence $I = copy + trans .$3 to bias copying. The model is selective because a novel object label is copied only when both the decoder state and the external detector support it. On held-out MSCOCO objects, LSTM-C with one-hot + GloVe reports averaged F1 $I = copy + trans .$4 and METEOR $I = copy + trans .$5, and on the 634-object ImageNet setting it improves over NOC in Novel, F1, and Accuracy (Yao et al., 2017).

4. Controlling the amount of copying in summarization

In abstractive summarization, selective copying is often framed not as enabling copying but as controlling how much copying occurs. A pointer-generator network interpolates between a generation distribution and a copy distribution through a mixture coefficient $I = copy + trans .$6, where larger $I = copy + trans .$7 corresponds to more generation and less copying. The observed problem is that copy-based summarizers can become effectively extractive: during training the average mixture coefficient was about $I = copy + trans .$8, but at test time it dropped to about $I = copy + trans .$9. To counter this without retraining, copy-controlled decoding modifies beam-search scoring with a penalty applied when the running average mixture coefficient falls below a target $$d(a,b)\coloneqq a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b},$$0, using the heuristic schedule $$d(a,b)\coloneqq a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b},$$1. With $$d(a,b)\coloneqq a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b},$$2 and $$d(a,b)\coloneqq a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b},$$3, 25-gram overlap with the source falls from $$d(a,b)\coloneqq a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b},$$4 to $$d(a,b)\coloneqq a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b},$$5 under coverage penalty, while ROUGE remains within about $$d(a,b)\coloneqq a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b},$$6 points of the standard model (Weber et al., 2018).

A more direct controllability framework treats summarization as masked language modeling over a concatenated source-summary sequence. In CopyTrans, copying is controlled by deciding which token types are predicted during training: summary tokens seen in the source encourage copying, unseen summary tokens encourage abstraction, and source tokens aid representation learning. The paper defines copy rate as the number of summary $$d(a,b)\coloneqq a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b},$$7-grams appearing in the source divided by the total number of summary $$d(a,b)\coloneqq a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b},$$8-grams, reported for $$d(a,b)\coloneqq a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b},$$9 and averaged. Training on only seen summary words yields around $\ell(x,y)$0 1-gram copy rate on both Gigaword and Newsroom, whereas increasing the proportion of unseen summary words steadily lowers the copy rate. With beam search and reranking, reported Gigaword results reach roughly R-1 around $\ell(x,y)$1, R-2 around $\ell(x,y)$2, R-L around $\ell(x,y)$3, and BERTScore around $\ell(x,y)$4 (Song et al., 2019).

These two lines of work distinguish two different control surfaces. The first is decoding-time control over an already trained copy-heavy model; the second is joint training-time and decoding-time control over a spectrum ranging from purely extractive to highly generative behavior. A common misconception addressed by both is that the presence of a copy mechanism automatically yields a useful balance between faithfulness and abstraction. The empirical record in these papers indicates that the balance is often highly sensitive to training targets, search procedure, and explicit penalties or reranking criteria (Weber et al., 2018, Song et al., 2019).

5. Systems, concurrency, and software-level selective copying

In operating systems, selective copying is motivated by the mismatch between what applications inspect and what the kernel copies. Libra argues formally that, under conventional OS abstractions, true zero-copy for socket I/O and full POSIX compatibility for unmodified applications cannot both be guaranteed. The practical alternative is to copy only protocol metadata to user space while retaining bulk payload in kernel memory for forwarding. Libra uses eBPF to detect protocol-specific metadata boundaries on ingress, a $\ell(x,y)$5-byte lookahead window, and the KMP algorithm for deterministic $\ell(x,y)$6 parsing. It inserts a 64-bit Virtual Payload Identifier into the user buffer, later uses that identifier to recover the anchored payload on egress, and only enables selective zero-copy when the opaque payload is at least $\ell(x,y)$7 bytes. Implemented in Linux and evaluated with unmodified Nginx and HAProxy, Libra improves plaintext throughput by up to $\ell(x,y)$8, reduces P99 tail latency by over $\ell(x,y)$9, and with hardware-offloaded kTLS improves encrypted throughput by $$copy = \min_{r_Y} KL(r_Y \Vert p_Y) \quad \text{s.t.} \quad \mathbb{E}_{r_Y}[\ell(x,Y)] \le \mathbb{E}_{Y|x}[\ell(x,Y)] ,$$0 while cutting tail latency by $$copy = \min_{r_Y} KL(r_Y \Vert p_Y) \quad \text{s.t.} \quad \mathbb{E}_{r_Y}[\ell(x,Y)] \le \mathbb{E}_{Y|x}[\ell(x,Y)] ,$$1 (Zhou et al., 30 Apr 2026).

In concurrent algorithms, the primitive is even more literal. Single-Writer Copy (swcopy) atomically reads the contents of a word-sized source location and installs them into a single-writer destination object, using only pointer-width read, write, and CAS. Each destination object stores D.val, D.ptr, and D.old; when no copy is in progress, D.ptr = NULL, and during a swcopy, D.ptr changes exactly twice, from NULL to a valid pointer and back. The resulting read, write, and swcopy operations have $$copy = \min_{r_Y} KL(r_Y \Vert p_Y) \quad \text{s.t.} \quad \mathbb{E}_{r_Y}[\ell(x,Y)] \le \mathbb{E}_{Y|x}[\ell(x,Y)] ,$$2 worst-case time and $$copy = \min_{r_Y} KL(r_Y \Vert p_Y) \quad \text{s.t.} \quad \mathbb{E}_{r_Y}[\ell(x,Y)] \le \mathbb{E}_{Y|x}[\ell(x,Y)] ,$$3 space, and the primitive is used to implement $$copy = \min_{r_Y} KL(r_Y \Vert p_Y) \quad \text{s.t.} \quad \mathbb{E}_{r_Y}[\ell(x,Y)] \le \mathbb{E}_{Y|x}[\ell(x,Y)] ,$$4 LL/SC objects with $$copy = \min_{r_Y} KL(r_Y \Vert p_Y) \quad \text{s.t.} \quad \mathbb{E}_{r_Y}[\ell(x,Y)] \le \mathbb{E}_{Y|x}[\ell(x,Y)] ,$$5 time for LL and SC, $$copy = \min_{r_Y} KL(r_Y \Vert p_Y) \quad \text{s.t.} \quad \mathbb{E}_{r_Y}[\ell(x,Y)] \le \mathbb{E}_{Y|x}[\ell(x,Y)] ,$$6 time for VL, and $$copy = \min_{r_Y} KL(r_Y \Vert p_Y) \quad \text{s.t.} \quad \mathbb{E}_{r_Y}[\ell(x,Y)] \le \mathbb{E}_{Y|x}[\ell(x,Y)] ,$$7 space (Blelloch et al., 2019).

Selective copying also appears where evidentiary or security requirements prohibit indiscriminate duplication. Live selective imaging defines imaging as selective if only selected data objects from an image that were explicitly chosen are included in the copied data. SIT implements this on Windows using DFIR ORC and AFF4, with an Artifact Module, Validation Module, AFF4 Module, and Verification Module. The tool hashes artifacts with MD5, SHA1, and SHA256, converts metadata into RDF Turtle, and stores evidence in AFF4 so that artifact and metadata remain directly associated. On a modern Windows 10 machine, one reported run acquires about 200 artifacts totaling 30 MB in about 1.5 minutes; on an older Windows 7 system, the same task takes about 10 minutes (Faust et al., 2020).

In secure object cloning, selective copying is specified as a copy policy. A policy declares which fields are @Shallow, which are @Deep, and which copy method satisfies @Copy(X). The semantic condition is that no memory cell reachable from the result by following only deep fields of policy $$copy = \min_{r_Y} KL(r_Y \Vert p_Y) \quad \text{s.t.} \quad \mathbb{E}_{r_Y}[\ell(x,Y)] \le \mathbb{E}_{Y|x}[\ell(x,Y)] ,$$8 is reachable from another local variable of the caller. The system enforces these guarantees statically, including under method overriding, and proves semantic correctness in Coq (Jensen et al., 2012). Taken together, these systems papers show that selectivity often arises not from a desire to avoid copying per se, but from the need to copy only the identity-bearing or policy-permitted parts of a state.

6. Behavioral replication and dependency inference

A separate line of work uses “copying” to mean reproducing the decision behavior of a black-box model. The formal setup defines an original classifier $$copy = \min_{r_Y} KL(r_Y \Vert p_Y) \quad \text{s.t.} \quad \mathbb{E}_{r_Y}[\ell(x,Y)] \le \mathbb{E}_{Y|x}[\ell(x,Y)] ,$$9 and seeks a copy $w(y) = {\frac{1}{Z(\lambda)} p_Y(y) e^{-\lambda \ell(x,y)}$0 in a possibly different hypothesis space, using only synthetic inputs labeled by hard queries to the original model. The copying objective is written as

$w(y) = {\frac{1}{Z(\lambda)} p_Y(y) e^{-\lambda \ell(x,y)}$1

or, in regularized form, as disagreement minimization plus a capacity term. The key distinction from ordinary learning is that synthetic data are always separable by the original classifier and can, in principle, be generated without bound. This makes fidelity error to the original classifier, rather than accuracy on ground truth alone, the primary target (Unceta et al., 2019).

Sampling is therefore the core selective mechanism. “Sampling Unknown Decision Functions to Build Classifier Copies” proposes Boundary sampling and Fast Bayesian sampling for generating synthetic inputs that expose decision structure. Boundary sampling alternates around approximate decision boundaries and has cost $w(y) = {\frac{1}{Z(\lambda)} p_Y(y) e^{-\lambda \ell(x,y)}$2; Fast Bayesian sampling models the unknown decision function with a Gaussian process, uses an uncertainty-based acquisition function, and has approximate cost $w(y) = {\frac{1}{Z(\lambda)} p_Y(y) e^{-\lambda \ell(x,y)}$3. Across six benchmark problems, Bayesian sampling is described as the most sample-efficient, Boundary sampling as a practical compromise, random sampling as the cheapest, and adapted Jacobian sampling as the weakest baseline (Unceta et al., 2019).

The sequential extension of classifier copying turns selectivity into an iterative filtering policy. At iteration $w(y) = {\frac{1}{Z(\lambda)} p_Y(y) e^{-\lambda \ell(x,y)}$4, the current copy’s uncertainty

$w(y) = {\frac{1}{Z(\lambda)} p_Y(y) e^{-\lambda \ell(x,y)}$5

is used to retain only synthetic points above a threshold $w(y) = {\frac{1}{Z(\lambda)} p_Y(y) e^{-\lambda \ell(x,y)}$6, reducing memory and computation. To mitigate catastrophic forgetting, the method adds a regularizer

$w(y) = {\frac{1}{Z(\lambda)} p_Y(y) e^{-\lambda \ell(x,y)}$7

On 58 UCI datasets, the Best accuracy sequential configuration matches the single-pass method on 53 of 58 datasets, converges in about $w(y) = {\frac{1}{Z(\lambda)} p_Y(y) e^{-\lambda \ell(x,y)}$8 of the allotted time with $w(y) = {\frac{1}{Z(\lambda)} p_Y(y) e^{-\lambda \ell(x,y)}$9, and uses about $\{i\}\{j\}$00 of the samples, with average efficiency $\{i\}\{j\}$01 (Statuto et al., 2023).

A different but related use of selective copying arises in structured-data source analysis. Here the problem is to detect when one data source copies from another only on a subset of items. The model introduces a selectivity parameter $\{i\}\{j\}$02, so that if two sources provide different values on an item then the copying contribution is $\{i\}\{j\}$03, whereas shared false values provide strong positive evidence of copying. The scalable solution builds an inverted index over shared values, orders entries by contribution to copying evidence, prunes source pairs with lower and upper bounds, and supports incremental refinement across truth-discovery iterations. Reported speedups reduce copy-detection time by two to three orders of magnitude while preserving very similar results (Li et al., 2015). This suggests that selectivity in copying need not refer only to how a system copies; it can also refer to how copied dependence is inferred from partially shared observations.

7. Imperfect copying, neutral copying, and quantum limits

Population models show what changes when copying ceases to be exact. In the multi-state voter model with imperfect copying, agents occupy discrete angular states and update by copying a neighbor with an error amplitude $\{i\}\{j\}$04. Perfect copying, $\{i\}\{j\}$05, leads to absorbing consensus with $\{i\}\{j\}$06. For any $\{i\}\{j\}$07, however, the stationary order parameter decreases with population size as

$\{i\}\{j\}$08

for $\{i\}\{j\}$09 and $\{i\}\{j\}$10, and in the vanishing-noise regime

$\{i\}\{j\}$11

The stated conclusion is sharp: complete order is never achieved for $\{i\}\{j\}$12, and $\{i\}\{j\}$13 for any nonzero copying imperfection (Vazquez et al., 2019).

Neutral random copying in space provides a contrasting caution. In the unstructured Moran/random-copying model, pairwise diversity decays as

$\{i\}\{j\}$14

With spatial structure, ancestral lineages become random walkers on a network, and the dynamics acquire two timescales: $\{i\}\{j\}$15 for single-lineage relaxation and $\{i\}\{j\}$16 for two-lineage quasistationary coalescence. On fully connected networks, $\{i\}\{j\}$17, whereas on a ring there is no separation of timescales. Small-world networks interpolate between these regimes. The important interpretive point is that spatial structure can create diversity patterns that might look like selection even though copying remains neutral (Blythe, 2011).

Quantum theory supplies a hard limit on exact copying. A set of quantum states admits a common broadcasting operation if and only if the associated density matrices commute pairwise. The no-broadcasting theorem states the equivalence between existence of a common broadcaster, representation of the states as convex combinations of states with pairwise orthogonal support projections, and pairwise commutativity of the density matrices. For pure states, broadcasting and cloning coincide, and a common cloner exists if and only if the corresponding state vectors are orthogonal. A universal copier exists only in the commutative, hence classical, case (Maassen et al., 2 Jul 2026). In this setting, selective copying is possible precisely for information that has already become classical in the sense of joint measurability. Across stochastic, spatial, and quantum models, the recurring lesson is that exact copying is neither generic nor free: it depends on noise level, geometry, and the structure of the state space itself.