MACE: A Multifaceted Research Acronym

• MACE is a versatile acronym representing diverse methods and systems across audio captioning, atomistic modeling, explainable AI, robotics, and scientific instrumentation.
• A key contribution in atomistic modeling is the development of higher order equivariant message passing architectures that enhance accuracy and reduce computational iterations.
• MACE frameworks employ modular, hybrid methodologies that integrate multimodal data, decentralized computation, and safety or concept erasure techniques to advance research.

Searching arXiv for papers using the term "MACE" to ground the article in current literature. MACE is an acronym used in multiple research domains to denote distinct methods, systems, and instruments. In recent arXiv literature, the term refers to a multimodal metric for automated audio captioning, an equivariant interatomic-potential architecture and its associated foundation-model ecosystem, a model-agnostic framework for counterfactual explanation, a concept-based CNN explanation framework, a multi-agent exploration system, a diffusion-model concept-erasure method, and several other domain-specific constructs including a gamma-ray telescope and a master-assisted channel-estimation scheme (Dixit et al., 2024, Batatia et al., 2022, Yang et al., 2022, Kumar et al., 2020, Toumieh et al., 2022, Lu et al., 2024, Khurana et al., 2023, Angelou et al., 27 Feb 2026). This multiplicity makes MACE a cross-disciplinary acronym rather than a single unified theory. A plausible implication is that discussion of “MACE” in technical literature is meaningful only when the disciplinary context is made explicit.

1. Polysemy and disciplinary distribution

The acronym MACE appears across machine learning, computational chemistry, computer vision, robotics, wireless communication, astrophysics, and scientific simulation. In automated audio captioning, MACE denotes Multimodal Audio-Caption Evaluation, a metric that scores captions using both audio and text inputs rather than reference text alone (Dixit et al., 2024). In atomistic modeling, MACE denotes Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields, later also treated as a family of chemistry foundation models and training workloads (Batatia et al., 2022, Yang et al., 21 Oct 2025, Firoz et al., 14 Apr 2025). In explainable AI, MACE denotes both Model Agnostic Concept Extractor for CNN interpretation and Model-Agnostic Counterfactual Explanation for black-box tabular models (Kumar et al., 2020, Yang et al., 2022). In robotics, MACE denotes Multi-Agent Autonomous Collaborative Exploration of Unknown Environments (Toumieh et al., 2022). In diffusion-model safety, it denotes MAss Concept Erasure (Lu et al., 2024). In cell-free massive MIMO, it denotes master-assisted channel estimation (Angelou et al., 27 Feb 2026). In astrophysics, MACE denotes the Major Atmospheric Cherenkov Experiment telescope (Khurana et al., 2023).

This distribution is not merely terminological coincidence. The acronym tends to be adopted for systems that are methodologically central within their respective papers: an evaluator, an architecture, a framework, or an instrument. This suggests that MACE functions rhetorically as a project-level identity rather than as a field-specific term.

2. MACE in machine-learned atomistic modeling

In computational chemistry and materials science, MACE most commonly denotes an equivariant message-passing architecture for machine-learned interatomic potentials. The 2022 paper defines MACE as a new equivariant MPNN that uses higher body order messages and argues that earlier equivariant MPNNs are limited because they pass only two-body messages, creating a direct relationship between the number of layers and model expressivity (Batatia et al., 2022). MACE represents atomic environments as graphs, uses $\mathrm{O}(3)$-equivariant features, and predicts total energy as a sum of atomic site energies, with forces obtained as gradients of the energy (Batatia et al., 2022).

Its architectural distinction is explicit higher-body-order message construction. The paper writes the generic message as

$$\mathbf m_i^{(t)} = \sum_j \mathbf u_1(\sigma_i^{(t)};\sigma_j^{(t)}) + \sum_{j_1,j_2}\mathbf u_2(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\sigma_{j_2}^{(t)}) +\dots+ \sum_{j_1,\dots,j_\nu} \mathbf u_\nu(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\dots,\sigma_{j_\nu}^{(t)}),$$

with $\nu$ the maximum correlation order (Batatia et al., 2022). In the same paper, using four-body messages is reported to reduce the required number of message passing iterations to just two, while still reaching or exceeding state-of-the-art accuracy on rMD17, 3BPA, and AcAc (Batatia et al., 2022).

Subsequent evaluation emphasizes breadth and data efficiency. A 2023 benchmark paper reports strong performance for MACE across amorphous carbon, general small-molecule chemistry, large molecules, liquid water, and broad materials benchmarks, and states that the strictly local atom-centered model is sufficient even for large molecules and weakly interacting molecular assemblies when the receptive field is chosen appropriately (Kovacs et al., 2023). The same study reports that MACE can reproduce experimental molecular vibrational spectra when trained on as few as 50 randomly selected reference configurations (Kovacs et al., 2023). In 2025, a benchmark of MACE foundation models for lattice dynamics on cubic halide double perovskites defined MACE as Message-passing Atomic Cluster Expansion and found that model accuracy improves with more training data, with the best-performing released model being omat-0-medium (Yang et al., 21 Oct 2025). That study also argues that a dominant source of error in dynamic-stability prediction is the amplification of force errors when computing Hessians and harmonic phonons (Yang et al., 21 Oct 2025).

A systems-oriented 2025 paper treats MACE as a representative chemistry foundation model workload and optimizes large-scale training through balanced data distribution and kernel optimization. It identifies symmetric tensor contraction as the key computational kernel, formulates minibatch construction as a multi-objective bin packing problem, and reports reducing per-epoch execution time for training from 12 to 2 minutes on 740 GPUs with a 2.6M sample dataset (Firoz et al., 14 Apr 2025). This suggests that “MACE” in chemistry now denotes not only a model architecture but also an ecosystem of pretrained variants, benchmarking protocols, and specialized systems engineering.

3. MACE as multimodal evaluation and safety machinery in machine learning

In automated audio captioning, MACE denotes Multimodal Audio-Caption Evaluation. The method is explicitly designed to address the insufficiency of text-only AAC metrics such as BLEU, ROUGE, CIDEr, SPICE, Sentence-BERT metrics, and FENSE, which compare candidate captions only to references and do not inspect the source audio (Dixit et al., 2024). The central argument is that AAC evaluation should reflect whether the caption matches the audio content, whether it semantically agrees with references, and whether it is fluent and readable (Dixit et al., 2024).

MACE takes the source audio $A$, a candidate caption $C$, and optionally references $R=\{R_1,\dots,R_n\}$ (Dixit et al., 2024). It uses CLAP embeddings for both the audio–text and text–text terms: $\text{S}_\text{audio-text} = \cos(E_a(A), E_t(C)),$

$$\text{S}_\text{text-text} = \frac{1}{n} \sum_{i=1}^n \cos(E_t(C), E_t(R_i)),$$

and combines them as

$$\text{S}_\text{audio} = 0.5\cdot(\text{S}_\text{audio-text} + \text{S}_\text{text-text}).$$

A fluency penalty from FENSE is then applied: $$\text{MACE} = \text{S}_\text{audio} \cdot (1 - \alpha \cdot \text{FP}).$$ The best reported fluency settings are threshold $$\mathbf m_i^{(t)} = \sum_j \mathbf u_1(\sigma_i^{(t)};\sigma_j^{(t)}) + \sum_{j_1,j_2}\mathbf u_2(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\sigma_{j_2}^{(t)}) +\dots+ \sum_{j_1,\dots,j_\nu} \mathbf u_\nu(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\dots,\sigma_{j_\nu}^{(t)}),$$0 and penalty coefficient $$\mathbf m_i^{(t)} = \sum_j \mathbf u_1(\sigma_i^{(t)};\sigma_j^{(t)}) + \sum_{j_1,j_2}\mathbf u_2(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\sigma_{j_2}^{(t)}) +\dots+ \sum_{j_1,\dots,j_\nu} \mathbf u_\nu(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\dots,\sigma_{j_\nu}^{(t)}),$$1 (Dixit et al., 2024). On pairwise human-preference prediction, MACE reports overall accuracy of 79.0 on Clotho-Eval and 88.1 on AudioCaps-Eval, outperforming FENSE on both datasets (Dixit et al., 2024).

A different ML safety use of the acronym appears in diffusion models, where MACE denotes MAss Concept Erasure. This framework targets the removal of many unwanted concepts from text-to-image diffusion models while preserving unrelated content (Lu et al., 2024). Its central design is hybrid: closed-form cross-attention refinement removes residual concept information from surrounding prompt tokens, while per-concept LoRA finetuning removes intrinsic concept information from the target phrase itself (Lu et al., 2024). For the cross-attention refinement, the key optimization is

$$\mathbf m_i^{(t)} = \sum_j \mathbf u_1(\sigma_i^{(t)};\sigma_j^{(t)}) + \sum_{j_1,j_2}\mathbf u_2(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\sigma_{j_2}^{(t)}) +\dots+ \sum_{j_1,\dots,j_\nu} \mathbf u_\nu(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\dots,\sigma_{j_\nu}^{(t)}),$$2

with a closed-form solution given in the paper (Lu et al., 2024). MACE further introduces Concept-Focal Importance Sampling with

$$\mathbf m_i^{(t)} = \sum_j \mathbf u_1(\sigma_i^{(t)};\sigma_j^{(t)}) + \sum_{j_1,j_2}\mathbf u_2(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\sigma_{j_2}^{(t)}) +\dots+ \sum_{j_1,\dots,j_\nu} \mathbf u_\nu(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\dots,\sigma_{j_\nu}^{(t)}),$$3

using $$\mathbf m_i^{(t)} = \sum_j \mathbf u_1(\sigma_i^{(t)};\sigma_j^{(t)}) + \sum_{j_1,j_2}\mathbf u_2(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\sigma_{j_2}^{(t)}) +\dots+ \sum_{j_1,\dots,j_\nu} \mathbf u_\nu(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\dots,\sigma_{j_\nu}^{(t)}),$$4, $$\mathbf m_i^{(t)} = \sum_j \mathbf u_1(\sigma_i^{(t)};\sigma_j^{(t)}) + \sum_{j_1,j_2}\mathbf u_2(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\sigma_{j_2}^{(t)}) +\dots+ \sum_{j_1,\dots,j_\nu} \mathbf u_\nu(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\dots,\sigma_{j_\nu}^{(t)}),$$5, and $$\mathbf m_i^{(t)} = \sum_j \mathbf u_1(\sigma_i^{(t)};\sigma_j^{(t)}) + \sum_{j_1,j_2}\mathbf u_2(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\sigma_{j_2}^{(t)}) +\dots+ \sum_{j_1,\dots,j_\nu} \mathbf u_\nu(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\dots,\sigma_{j_\nu}^{(t)}),$$6, to focus LoRA finetuning on later denoising stages (Lu et al., 2024). The paper reports scaling concept erasure up to 100 concepts and outperforming prior methods across object, celebrity, explicit-content, and artistic-style erasure tasks (Lu et al., 2024).

These two ML uses of MACE are structurally similar despite domain differences: each addresses a failure of text-only or naive single-channel treatment by introducing hybrid multimodal or multicomponent correction mechanisms.

4. MACE in explainable AI

Two unrelated explainability frameworks also use the acronym. The 2020 computer-vision paper defines MACE as Model Agnostic Concept Extractor, a post-hoc explanation framework for CNN image classifiers that explains predictions in terms of multiple localized concepts rather than a single coarse saliency region (Kumar et al., 2020). It operates between the last convolutional layer output $$\mathbf m_i^{(t)} = \sum_j \mathbf u_1(\sigma_i^{(t)};\sigma_j^{(t)}) + \sum_{j_1,j_2}\mathbf u_2(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\sigma_{j_2}^{(t)}) +\dots+ \sum_{j_1,\dots,j_\nu} \mathbf u_\nu(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\dots,\sigma_{j_\nu}^{(t)}),$$7 and the first dense-layer output $$\mathbf m_i^{(t)} = \sum_j \mathbf u_1(\sigma_i^{(t)};\sigma_j^{(t)}) + \sum_{j_1,j_2}\mathbf u_2(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\sigma_{j_2}^{(t)}) +\dots+ \sum_{j_1,\dots,j_\nu} \mathbf u_\nu(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\dots,\sigma_{j_\nu}^{(t)}),$$8 of a pretrained CNN (Kumar et al., 2020). For each class $$\mathbf m_i^{(t)} = \sum_j \mathbf u_1(\sigma_i^{(t)};\sigma_j^{(t)}) + \sum_{j_1,j_2}\mathbf u_2(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\sigma_{j_2}^{(t)}) +\dots+ \sum_{j_1,\dots,j_\nu} \mathbf u_\nu(\sigma_i^{(t)};\sigma_{j_1}^{(t)},\dots,\sigma_{j_\nu}^{(t)}),$$9 and concept $\nu$0, the concept map is

$\nu$1

and concept embeddings are trained with a triplet loss

$\nu$2

with $\nu$3 (Kumar et al., 2020). Relevance scores are estimated by

$\nu$4

and combined via a sigmoid to approximate the pretrained model’s class probability (Kumar et al., 2020). The total objective is

$\nu$5

In human evaluation on AWA2, MACE explanations were preferred in 48.29% of votes, ahead of Excitation Backpropagation at 40.73% and well ahead of GradCAM and related baselines (Kumar et al., 2020).

A distinct 2022 XAI paper defines MACE as Model-Agnostic Counterfactual Explanation, aimed at non-differentiable models and high-cardinality categorical data (Yang et al., 2022). Its RL-based search optimizes

$\nu$6

with reward $\nu$7 (Yang et al., 2022). The policy factorizes into Bernoulli feature-selection variables and categorical value-selection distributions: $\nu$8

$\nu$9

The relaxed objective is

$A$0

and a later gradientless descent stage refines changed continuous features while preserving validity (Yang et al., 2022). The framework is explicitly four-stage: counterfactual feature selection, counterfactual feature optimization, counterfactual example selection, and continuous feature fine-tuning (Yang et al., 2022).

These two XAI MACE frameworks illustrate a recurring pattern in the acronym’s usage: model-agnostic operation, modular multi-stage construction, and a focus on practical deployment constraints.

5. MACE in robotics, communications, and decentralized systems

In robotics, MACE denotes Multi-Agent Autonomous Collaborative Exploration of Unknown Environments, a multi-UAV exploration framework for safely covering unknown 3D volumes (Toumieh et al., 2022). The system is organized into a local agent module and a global central-hub module. Planning uses voxel mapping, border-voxel goal generation, greedy goal assignment, static safe corridors, and time-aware Safe Corridors for inter-agent collision avoidance (Toumieh et al., 2022). The continuous-time planning dynamics are

$A$1

and the MIQP objective tracks a local reference trajectory subject to dynamics, jerk and acceleration bounds, and corridor constraints (Toumieh et al., 2022). In simulation on AirSim with up to four agents, exploration time decreases approximately inversely with the number of agents, while worst reported planning computation time remains below the 10 Hz replanning budget (Toumieh et al., 2022).

A decentralized MARL paper uses the acronym for Multi-Agent Coordinated Exploration, again within multi-agent exploration but in a different methodological sense (Jiang et al., 2024). There, MACE addresses sparse-reward decentralized cooperative MARL under partial observability. It combines novelty sharing,

$A$2

with a hindsight influence reward derived from weighted mutual information: $A$3 The resulting shaped reward is

$A$4

The paper reports superior performance across sparse-reward GridWorld, Overcooked, and SMAC tasks (Jiang et al., 2024). Although this work spells out “Multi-Agent Coordinated Exploration” rather than “Multi-Agent Autonomous Collaborative Exploration,” both cases show MACE being used for distributed coordination under information constraints.

In wireless communication, MACE denotes master-assisted channel estimation for cell-free massive MIMO (Angelou et al., 27 Feb 2026). The method exploits pilot-induced inter-AP signal correlation even when NLoS channel components are independent across APs. Each assisting AP compresses its pilot observation with a local estimate–based fusion vector, forwards the fused signal to a master AP, and the master AP performs reduced-dimensional LMMSE estimation (Angelou et al., 27 Feb 2026). The paper contrasts three regimes: local estimation with complexity $A$5, fully centralized estimation with $A$6, and MACE with $A$7 and fronthaul $A$8 instead of $A$9 complex scalars (Angelou et al., 27 Feb 2026). Numerical experiments show that MACE consistently outperforms local channel estimation (Angelou et al., 27 Feb 2026).

A plausible synthesis is that in these systems papers, “MACE” often names an intermediate architecture between local autonomy and full centralization.

6. Scientific instrumentation and domain-specific scientific emulators

Outside mainstream ML systems, MACE also denotes scientific instruments and simulators. In gamma-ray astronomy, MACE refers to the Major Atmospheric Cherenkov Experiment telescope, a newly commissioned imaging atmospheric Cherenkov telescope at Hanle, Ladakh, India, located at $C$0 and an altitude of about 4.3 km above sea level (Khurana et al., 2023). It has a 21 m diameter reflector, a camera with 1088 photomultipliers, $C$1 pixel resolution, and a field of view of about $C$2 (Khurana et al., 2023). A feasibility study on dark-matter searches uses the telescope’s effective area and a point-spread scale of about $C$3 to estimate projected limits on annihilating WIMPs in Segue 1 (Khurana et al., 2023). The central rate equation is

$C$4

and for 100 hours of observation the strongest projected limit is $C$5 for $C$6 in the $C$7 channel (Khurana et al., 2023).

In computational astrophysics, mace denotes Machine learning Approach to Chemistry Emulation, a surrogate model for time-dependent astrochemistry in dynamical environments (Maes et al., 2024). The architecture combines an autoencoder and a latent ODE: $C$8 where $C$9 is the encoder, $R=\{R_1,\dots,R_n\}$0 evolves latent variables, and $R=\{R_1,\dots,R_n\}$1 decodes abundances (Maes et al., 2024). The latent dynamics are

$R=\{R_1,\dots,R_n\}$2

The paper emphasizes that local one-step training fails to reproduce full chemical pathways, while integrated trajectory training succeeds; integrated models have errors about a factor of 4 smaller than local models and chemistry-evolution speedups of 24–28×, or 26× on average, relative to a DVODE-based solver (Maes et al., 2024).

Another scientific-simulation use is Mass-Conserving Evolution, styled MaCE, for cellular automata (Papadopoulos et al., 16 Jul 2025). The core idea is to redistribute local mass according to an affinity field while preserving total mass exactly. The update is

$R=\{R_1,\dots,R_n\}$3

with

$R=\{R_1,\dots,R_n\}$4

and admits the continuum limit

$R=\{R_1,\dots,R_n\}$5

under appropriate scaling (Papadopoulos et al., 16 Jul 2025). Applied to Lenia, the paper reports frequent soliton emergence and resource-constrained dynamics suggestive of primitive selection (Papadopoulos et al., 16 Jul 2025).

7. Common structural themes and sources of ambiguity

Despite their disciplinary divergence, several recurring structural motifs appear across MACE papers. First, many MACE systems are explicitly hybrid. Audio-caption MACE combines audio grounding, reference-caption agreement, and fluency (Dixit et al., 2024). Diffusion-model MACE combines closed-form attention editing and LoRA finetuning (Lu et al., 2024). Counterfactual MACE combines nearest-neighbor pruning, RL search, and gradientless continuous refinement (Yang et al., 2022). MOSCARD, while not itself named MACE, illustrates a nearby clinical usage in which MACE refers to Major Adverse Cardiovascular Events, underscoring that the acronym can also denote a medical outcome rather than a method (Pi et al., 23 Jun 2025).

Second, many MACE systems seek a middle ground between two extremes. Master-assisted channel estimation sits between purely local and fully centralized processing (Angelou et al., 27 Feb 2026). Collaborative-exploration MACE combines centralized goal assignment with decentralized local planning (Toumieh et al., 2022). Chemistry MACE occupies a middle position between fixed ACE-style expansions and deep equivariant GNNs (Batatia et al., 2022).

Third, the acronym is highly ambiguous even within ML. “MACE” may denote a force field, an audio metric, a concept extractor, a counterfactual framework, or a diffusion safety method (Batatia et al., 2022, Dixit et al., 2024, Kumar et al., 2020, Yang et al., 2022, Lu et al., 2024). This ambiguity is amplified by the coexistence of uppercase MACE and stylized variants such as mace or MaCE (Maes et al., 2024, Papadopoulos et al., 16 Jul 2025). A plausible implication is that bibliographic disambiguation requires title- or domain-level metadata, not acronym matching alone.

Domain	Expansion	Representative paper
Audio captioning	Multimodal Audio-Caption Evaluation	(Dixit et al., 2024)
Atomistic ML	Higher Order Equivariant Message Passing Neural Networks / Message-passing Atomic Cluster Expansion	(Batatia et al., 2022)
Counterfactual XAI	Model-Agnostic Counterfactual Explanation	(Yang et al., 2022)
CNN interpretability	Model Agnostic Concept Extractor	(Kumar et al., 2020)
Robotics	Multi-Agent Autonomous Collaborative Exploration of Unknown Environments	(Toumieh et al., 2022)
Diffusion safety	MAss Concept Erasure	(Lu et al., 2024)
Wireless communication	master-assisted channel estimation	(Angelou et al., 27 Feb 2026)
Gamma-ray astronomy	Major Atmospheric Cherenkov Experiment	(Khurana et al., 2023)

This diversity can create misconceptions. One common misconception is that “MACE” in contemporary technical discussion refers primarily to the atomistic architecture; that is only true within chemistry and materials contexts. Another is that all MACE papers reflect a common methodological lineage. The evidence does not support that. The acronym is reused independently across communities, with no shared technical core beyond the superficial naming pattern.

8. Research significance and likely future evolution

Among the many senses of the acronym, the atomistic-modeling MACE appears to have become the most infrastructurally significant, as shown by subsequent benchmarking of released foundation-model variants and systems-level optimization for large-scale training (Yang et al., 21 Oct 2025, Firoz et al., 14 Apr 2025). Audio-caption MACE is significant within AAC evaluation because it moves the metric from text-only comparison toward audio-aware assessment (Dixit et al., 2024). Diffusion-model MACE is notable because it makes concept erasure scalable to 100 concepts while preserving a balance between erasure generality and specificity (Lu et al., 2024). The XAI and robotics MACE frameworks are more domain-local but illustrate the acronym’s repeated association with modular, deployment-oriented method design (Kumar et al., 2020, Yang et al., 2022, Toumieh et al., 2022).

Future ambiguity is likely to increase rather than diminish. Several 2025–2026 papers continue to introduce new MACE expansions in edge LLM serving, scene localization and rendering, and communications (Li et al., 28 Sep 2025, Liu et al., 16 Oct 2025, Angelou et al., 27 Feb 2026). This suggests that “MACE” is evolving as a reusable acronymic template rather than stabilizing around one canonical meaning.

In encyclopedia terms, MACE is therefore best treated as a disambiguation-worthy research acronym whose meanings are anchored by disciplinary context. In chemistry and materials science it most often denotes an equivariant many-body force-field architecture and associated foundation models (Batatia et al., 2022, Kovacs et al., 2023, Yang et al., 21 Oct 2025). In machine learning more broadly it denotes several unrelated frameworks for evaluation, explanation, and safety (Dixit et al., 2024, Kumar et al., 2020, Yang et al., 2022, Lu et al., 2024). In the physical sciences and engineering it also refers to an astronomical instrument and to partially centralized estimation in wireless networks (Khurana et al., 2023, Angelou et al., 27 Feb 2026). The primary scholarly requirement when invoking “MACE” is therefore not definition by acronym alone, but immediate disambiguation by field, expansion, or citation.