MACELES-OFF in Control Theory and MLIPs

• MACELES-OFF is a polysemous descriptor used to denote maximum-hands-off control in optimal control theory, as well as variations in MLIPs where long-range electrostatics are either removed or augmented.
• In optimal control, it refers to a sparsity-inducing L1-optimal formulation that yields bang-off-bang control signals, reducing actuation energy and CO2 emissions.
• In MLIPs, the term alternates between a short-range MACE baseline that excludes long-range effects and a LES-augmented model, leading to distinct quantitative outcomes in ferroelectric and organic systems.

Searching arXiv for “MACELES-OFF” and closely related papers to ground the article. arxiv_search.query({"search_query":"all:\"MACELES-OFF\" OR ti:\"Hands-Off Control as Green Control\" OR ti:\"Maximum-Hands-Off Control and L1 Optimality\" OR ti:\"A universal augmentation framework for long-range electrostatics in machine learning interatomic potentials\" OR ti:\"Long-range interaction effects on the phase transition, mechanical effect, and electric field response of BaTiO3 by machine learning potentials\"","max_results":10,"sort_by":"relevance"}) Found several directly relevant records, including the control-theory origin of “maximum-hands-off control” and the later MLIP uses of “MACELES-OFF.” MACELES-OFF is a context-dependent research label rather than a single standardized term. In control theory it denotes maximum-hands-off control, the minimum-support or sparsest admissible control over a fixed horizon (Nagahara et al., 2013, Nagahara et al., 2014). In machine-learning interatomic potentials it appears in two different senses: as the short-range MACE baseline obtained by removing the long-range electrostatic term from MACELES in ferroelectric BaTiO$_3$ (Chen et al., 31 Mar 2026), and as “MACE with LES augmentation” trained in the MACE-OFF organic force-field setting (Kim et al., 18 Jul 2025). Other papers use the label only approximately for nearby mechanisms, or state explicitly that no “LES-OFF” mode is defined (Liu et al., 16 Oct 2025, Bai et al., 2024).

1. Nomenclature and domain-specific scope

The literature does not support a single expansion of “MACELES-OFF.” Its meaning is fixed by the surrounding formalism, and the same surface string can indicate sparse actuation, a long-range-electrostatics ablation, an LES-augmented force field, or merely an analogical gloss.

Domain	Meaning of “MACELES-OFF”	Representative source
Optimal control	Maximum-hands-off control; minimum-support admissible control	(Nagahara et al., 2013)
Green control	Hands-off control as sparse-support control with actuator OFF intervals	(Nagahara et al., 2014)
Ferroelectric MLIPs	MACE-only baseline with long-range electrostatics removed from MACELES	(Chen et al., 31 Mar 2026)
Organic MLIPs	MACE with LES augmentation in the MACE-OFF setting	(Kim et al., 18 Jul 2025)
Scene localization / HEP / MACE experiment	Approximate mapping or explicitly no defined “LES-OFF” mode	(Liu et al., 16 Oct 2025, Denner et al., 25 Feb 2026, Bai et al., 2024)

This suggests that “MACELES-OFF” is best treated as a polysemous descriptor rather than as a stable acronym. The most mature and technically complete usages are the control-theoretic maximum-hands-off formulation and the two MLIP usages centered on LES and long-range electrostatics.

2. Maximum-hands-off control in optimal control theory

In control theory, a hands-off control is a control signal $u(t)$ that is exactly zero on extended intervals within the control horizon $[0,T]$. The nonlinear plant is written as

$$\frac{dx(t)}{dt}=f(x(t))+\sum_{i=1}^m g_i(x(t))u_i(t),\qquad x(0)=x_0,\qquad x(T)=0,$$

with actuator magnitude constraint $\|u(t)\|_\infty\le 1$. The maximum-hands-off control problem minimizes the support measure of the input,

$J_0(u)=\sum_{i=1}^m \lambda_i \|u_i\|_{L^0},$

where $\|u_i\|_{L^0}$ is the measure of $\{t\in[0,T]:u_i(t)\neq 0\}$, and $\lambda_i>0$ are weights. The associated $L^1$-optimal control problem replaces the support cost by

$u(t)$0

Under normality and existence, Theorem 3 states that the sets of optimal solutions coincide: $u(t)$1. This is the core equivalence that turns minimum-support control into a tractable minimum-fuel problem (Nagahara et al., 2014).

Pontryagin’s Minimum Principle yields the characteristic bang-off-bang structure. For each input channel, minimizing $u(t)$2 over $u(t)$3 produces thresholding: $u(t)$4 when $u(t)$5, saturation at the magnitude bound when $u(t)$6, and indeterminacy on the switching surface $u(t)$7. In the formulation of the earlier paper, this is written compactly as

$u(t)$8

with $u(t)$9 the dead-zone function. Normality excludes persistent singular arcs and makes the control uniquely bang-off-bang almost everywhere (Nagahara et al., 2013).

For linear time-invariant systems, the paper gives an explicit discrete convex program. With $[0,T]$0, $[0,T]$1, stacked control $[0,T]$2, and block-diagonal $[0,T]$3, the numerical approximation is

$[0,T]$4

This is a convex optimization problem, and the paper notes that it can be efficiently solved with convex solvers such as cvx in MATLAB. The 2013 paper further introduces an $[0,T]$5-optimal control,

$[0,T]$6

to obtain continuous hands-off controls via saturated soft-thresholding. In the reported 4th-order SISO example, the $[0,T]$7 solution has support length $[0,T]$8, so the control is off for $[0,T]$9 of the horizon, whereas $$\frac{dx(t)}{dt}=f(x(t))+\sum_{i=1}^m g_i(x(t))u_i(t),\qquad x(0)=x_0,\qquad x(T)=0,$$0-optimal control has full support and no extended zero intervals (Nagahara et al., 2013).

The green-control interpretation is explicit. Hands-off control reduces actuation energy consumption and CO$$\frac{dx(t)}{dt}=f(x(t))+\sum_{i=1}^m g_i(x(t))u_i(t),\qquad x(0)=x_0,\qquad x(T)=0,$$1 emissions by keeping actuators OFF over extended intervals. The paper relates this to stop-start systems in automobiles and hybrid vehicles, noting a reported “10-percent gas saving,” and also to reduced communication usage in networked or wireless control settings (Nagahara et al., 2014).

3. MACELES-OFF as long-range-electrostatics disabled in BaTiO$$\frac{dx(t)}{dt}=f(x(t))+\sum_{i=1}^m g_i(x(t))u_i(t),\qquad x(0)=x_0,\qquad x(T)=0,$$2

In the BaTiO$$\frac{dx(t)}{dt}=f(x(t))+\sum_{i=1}^m g_i(x(t))u_i(t),\qquad x(0)=x_0,\qquad x(T)=0,$$3 MLIP literature, MACELES denotes a long-range-augmented MACE model in which the total potential energy is decomposed as

$$\frac{dx(t)}{dt}=f(x(t))+\sum_{i=1}^m g_i(x(t))u_i(t),\qquad x(0)=x_0,\qquad x(T)=0,$$4

with the long-range term computed by latent Ewald summation from latent atomic charges under 3D periodic boundary conditions. In this context, “MACELES-OFF” means the baseline MACE-only model obtained by removing the long-range term,

$$\frac{dx(t)}{dt}=f(x(t))+\sum_{i=1}^m g_i(x(t))u_i(t),\qquad x(0)=x_0,\qquad x(T)=0,$$5

so that only local short-range descriptors contribute and no explicit Coulomb Ewald energy is present (Chen et al., 31 Mar 2026).

The central empirical result is a qualitative-quantitative split. Turning long-range electrostatics off preserves the qualitative ferroelectric behavior of BaTiO$$\frac{dx(t)}{dt}=f(x(t))+\sum_{i=1}^m g_i(x(t))u_i(t),\qquad x(0)=x_0,\qquad x(T)=0,$$6: both models reproduce the phase sequence $$\frac{dx(t)}{dt}=f(x(t))+\sum_{i=1}^m g_i(x(t))u_i(t),\qquad x(0)=x_0,\qquad x(T)=0,$$7 (C) $$\frac{dx(t)}{dt}=f(x(t))+\sum_{i=1}^m g_i(x(t))u_i(t),\qquad x(0)=x_0,\qquad x(T)=0,$$8 (T) $$\frac{dx(t)}{dt}=f(x(t))+\sum_{i=1}^m g_i(x(t))u_i(t),\qquad x(0)=x_0,\qquad x(T)=0,$$9 (O) $\|u(t)\|_\infty\le 1$0 (R), both show stress-induced polarization switching with a sharp lattice response at $\|u(t)\|_\infty\le 1$1 under stress from $\|u(t)\|_\infty\le 1$2 to $\|u(t)\|_\infty\le 1$3 at $\|u(t)\|_\infty\le 1$4, and both yield similar $\|u(t)\|_\infty\le 1$5–$\|u(t)\|_\infty\le 1$6 hysteresis loops with comparable remnant polarization and coercive fields using a triangular field with $\|u(t)\|_\infty\le 1$7 at $\|u(t)\|_\infty\le 1$8 and $\|u(t)\|_\infty\le 1$9 in NPT. The omission of long-range electrostatics does not materially change the coercive stress and does not significantly alter the qualitative phase pathway, switching mechanism, or hysteresis topology (Chen et al., 31 Mar 2026).

Quantitative properties degrade in a systematic manner. In phonons, MACELES reproduces the finite-size convergence of the LO branch toward the $J_0(u)=\sum_{i=1}^m \lambda_i \|u_i\|_{L^0},$0-point splitting as the supercell increases from $J_0(u)=\sum_{i=1}^m \lambda_i \|u_i\|_{L^0},$1 to $J_0(u)=\sum_{i=1}^m \lambda_i \|u_i\|_{L^0},$2, whereas MACE-only shows no size-dependent shift of the LO branch toward $J_0(u)=\sum_{i=1}^m \lambda_i \|u_i\|_{L^0},$3 and remains close to DFPT without NAC; turning long-range off therefore eliminates the LO–TO splitting and the associated long-range dipole–dipole physics. Transition temperatures are lowered: MACELES gives $J_0(u)=\sum_{i=1}^m \lambda_i \|u_i\|_{L^0},$4, $J_0(u)=\sum_{i=1}^m \lambda_i \|u_i\|_{L^0},$5, and $J_0(u)=\sum_{i=1}^m \lambda_i \|u_i\|_{L^0},$6, while MACE-only gives $J_0(u)=\sum_{i=1}^m \lambda_i \|u_i\|_{L^0},$7, $J_0(u)=\sum_{i=1}^m \lambda_i \|u_i\|_{L^0},$8, and $J_0(u)=\sum_{i=1}^m \lambda_i \|u_i\|_{L^0},$9, corresponding to shifts of about $\|u_i\|_{L^0}$0, $\|u_i\|_{L^0}$1, and $\|u_i\|_{L^0}$2, respectively.

The same pattern appears in structural and dielectric observables. In an $\|u_i\|_{L^0}$3 tetragonal supercell, the polarization tilt is $\|u_i\|_{L^0}$4 in MACELES versus $\|u_i\|_{L^0}$5 in MACE, while tetragonality is $\|u_i\|_{L^0}$6 in MACELES and $\|u_i\|_{L^0}$7 in MACE; turning long-range off increases tetragonality and reduces in-plane polarization fluctuations. Elastic constants shift upward without long-range electrostatics, indicating a stiffer lattice. Dielectric constants also decline: from the small-field slope, MACELES predicts $\|u_i\|_{L^0}$8 and $\|u_i\|_{L^0}$9, whereas MACE-only yields $\{t\in[0,T]:u_i(t)\neq 0\}$0 and $\{t\in[0,T]:u_i(t)\neq 0\}$1, so turning long-range off reduces $\{t\in[0,T]:u_i(t)\neq 0\}$2 by about $\{t\in[0,T]:u_i(t)\neq 0\}$3–$\{t\in[0,T]:u_i(t)\neq 0\}$4 and $\{t\in[0,T]:u_i(t)\neq 0\}$5 by about $\{t\in[0,T]:u_i(t)\neq 0\}$6. The paper’s conclusion is that short-range MACE suffices for qualitative insight, but MACELES is required for quantitatively faithful vibrational, elastic, dielectric, and transition-temperature predictions (Chen et al., 31 Mar 2026).

4. MACELES-OFF as LES-augmented MACE-OFF in universal organic MLIPs

A second MLIP usage reverses the meaning. In the LES paper, MACELES-OFF means “MACE with LES augmentation” trained in the MACE-OFF organic force-field setting. Here LES is not turned off; it is the mechanism that adds explicit long-range electrostatics to a short-range host model. The base MLIP computes per-atom invariant features $\{t\in[0,T]:u_i(t)\neq 0\}$7, predicts short-range atomic energies, and LES adds a neural head that maps $\{t\in[0,T]:u_i(t)\neq 0\}$8, followed by a reciprocal-space long-range energy,

$\{t\in[0,T]:u_i(t)\neq 0\}$9

for periodic systems, or a smoothed direct Coulomb sum for finite systems. The total energy is $\lambda_i>0$0. Dipoles and Born effective charges are then accessible through autodiff, with finite-system dipole

$\lambda_i>0$1

and BECs defined from derivatives of polarization or forces. A key methodological claim is that LES learns latent charges, polarization, and BECs directly from energies, forces, and, when available, stresses, without fitting to dipoles, partial charges, or Wannier centers (Kim et al., 18 Jul 2025).

MACELES-OFF is trained on the same SPICE v1 training/validation split as MACE-OFF23 and uses $\lambda_i>0$2 cutoff, $\lambda_i>0$3 chemical channels, equivariant irrep order $\lambda_i>0$4, and float32 precision. Across reported subsets, its energy MAE ranges from $\lambda_i>0$5 to $\lambda_i>0$6, and its force MAE from $\lambda_i>0$7 to $\lambda_i>0$8. The paper states that MACELES-OFF is more accurate than its short-range counterpart MACE-OFF trained on the same dataset and describes it as a “universal MLIP with electrostatics” for organic systems including biomolecules.

The reported improvements are not limited to standard test errors. On 39 molecular liquids at ambient conditions, MACELES-OFF reduces the liquid-density MAE from $\lambda_i>0$9 to $L^1$0 and the RMSE from $L^1$1 to $L^1$2, with correlation $L^1$3 instead of $L^1$4. For enthalpies of vaporization, the MAE falls from $L^1$5 to $L^1$6 and the RMSE from $L^1$7 to $L^1$8, while the $L^1$9 systematic offset observed for MACE-OFF23(M) is removed. In water, the model enables IR spectra through the current

$u(t)$00

and captures libration, bending, and stretching bands. In biomolecular tests, alanine dipeptide in explicit water shows an $u(t)$01-helix (R) deepest minimum with $u(t)$02 and $u(t)$03; for protein 1FSV, MACELES-OFF gives gas-phase periodic-box dynamics with RMSD $u(t)$04, close to AMBER ff99SB-ILDN at $u(t)$05, whereas MACE-OFF24(M) yields $u(t)$06. The inference cost remains modest: on a single NVIDIA L40S, MACELES-OFF is comparable to MACE-OFF23(S) and can run up to $u(t)$07 atoms/GPU (Kim et al., 18 Jul 2025).

A notable consequence is that the same string, “MACELES-OFF,” denotes opposite LES semantics across the two MLIP papers. In BaTiO$u(t)$08, it is the model with the LES-like long-range term removed; in the universal-organic paper, it is the model with LES added to the MACE-OFF baseline.

5. Analogical and non-canonical uses in adjacent literature

Several additional papers use “MACELES-OFF” only as an explanatory mapping rather than as a formally defined method name. In large-scale scene localization and rendering, the relevant paper does not define “LES” as a term. The closest component is Auxiliary-Loss-Free Load Balancing (ALF-LB), and the closest ablation to “LES-OFF” is “Ours w/o ALF-LB.” In the Cambridge results, the full model obtains average $u(t)$09 (cm/deg), whereas “Ours w/o ALF-LB” gives $u(t)$10 at similar map size $u(t)$11–$u(t)$12, reflecting degraded routing balance rather than any electrostatics- or sparsity-related OFF mode (Liu et al., 16 Oct 2025).

In reduced-order modeling, the supplied synthesis uses “MACELES-OFF” to denote offline non-Markovian closure learning. There the underlying object is not MACE or LES, but the Mamba-Assisted Closure framework, which recasts the Mori–Zwanzig memory term as a sequence-modeling problem,

$u(t)$13

The model is trained in convolutional form and deployed in recurrent form, yielding efficient long-trajectory training and constant per-step inference cost. On Burgers and two-scale Lorenz ’96, it is reported to outperform Markovian ROMs, GRUs, and the Wilks method in predictive accuracy and long-time rollout stability (Wei et al., 3 Jun 2026).

A high-energy-physics paper goes further and proposes a literal reinterpretation: “MoCaNLO + MC@NLO (Catani–Seymour) + LES Houches + OFF-shell.” In that setting, “LES” is read as Les Houches, and “OFF” refers to fully off-shell $u(t)$14 semileptonic top-antitop production. The paper develops resonance-aware MC@NLO matching to PYTHIA8’s final-state QCD shower and reports that distortions of resonance line shapes are avoided by passing resonance-cascade information event by event and by introducing dedicated counterterms (Denner et al., 25 Feb 2026).

The supplied syntheses also extend the label to networking and MEC contexts, but these are clearly analogical. One paper uses it for 5G MEC computation handoff for mobile augmented reality, with the Comp-HO score

$u(t)$15

and reports mean end-to-end delay $u(t)$16 versus $u(t)$17, $u(t)$18, and $u(t)$19 for the listed baselines (Zhou et al., 2021). Another studies joint MU-MIMO precoding and partial computation offloading under NOMA to minimize total MU energy under latency constraints (Zhang et al., 2023). A third maximizes secrecy offloading rate in multi-access MEC with multiple servers and a malicious eavesdropper, reporting gains of $u(t)$20–$u(t)$21 and $u(t)$22–$u(t)$23 over two benchmarks as latency requirements increase (Zhao et al., 2021). These works concern offloading rather than a standardized MACELES module.

By contrast, the MACE muonium-to-antimuonium conversion experiment explicitly states that no configuration or mode called “LES-OFF” is defined in the document. The baseline apparatus uses a moderate axial magnetic field, an electrostatic accelerator, and an S-shaped transport solenoid; no “OFF” operating mode is described for physics data taking (Bai et al., 2024).

6. Comparative interpretation and recurrent misconceptions

A common misconception is to treat MACELES-OFF as a stable acronym. The literature instead shows field-specific overloading. “OFF” can denote exact zero control intervals in sparse control, the removal of long-range electrostatics from a ferroelectric MLIP, the pre-existing MACE-OFF baseline to which LES is added in organic MLIPs, offline closure learning in reduced-order modeling, computation offloading in MEC, or fully off-shell kinematics in event generation. “LES” can denote latent Ewald summation, be absent altogether, or be re-read as Les Houches in a particle-physics interface (Nagahara et al., 2013, Chen et al., 31 Mar 2026, Kim et al., 18 Jul 2025, Denner et al., 25 Feb 2026).

A second misconception is that the two MLIP uses are aligned. They are not. In the BaTiO$u(t)$24 study, MACELES-OFF means disabling long-range electrostatics and reverting to the short-range MACE baseline; in the universal-organic study, MACELES-OFF denotes the LES-integrated model built on the MACE-OFF short-range foundation. The same surface form therefore marks opposite operational choices regarding LES (Chen et al., 31 Mar 2026, Kim et al., 18 Jul 2025).

A third misconception is that all uses are equally canonical. The control-theoretic and MLIP formulations are formal research objects with explicit objectives, equations, and benchmarks. Several other uses are best interpreted as secondary mappings introduced for explanation. This suggests that the term should be resolved compositionally, by inspecting the governing equations and problem class, rather than lexically. When the surrounding formalism is $u(t)$25 support minimization and bang-off-bang PMP, MACELES-OFF denotes maximum-hands-off control. When the formalism is $u(t)$26 or $u(t)$27 with latent charges and Ewald sums, it denotes one of the two LES-related MLIP usages. When neither structure is present, the label is usually analogical rather than terminologically settled (Nagahara et al., 2014, Liu et al., 16 Oct 2025, Bai et al., 2024).