---
title: BLCE in Multidisciplinary Research
url: https://www.emergentmind.com/topics/blce
type: topic
---

# BLCE in Multidisciplinary Research

BLCE is an overloaded acronym used in several technically unrelated research areas. In the arXiv literature represented here, it denotes at least five distinct constructs: the **Best Linear Constrained Estimator** in statistical estimation theory, **Blur-adaptive Latent Camera Estimation** in dynamic novel view synthesis, **Batched-Feedback Linear Contextual Bandit with Elimination** in online learning, **Bi-Large mixing with charged lepton correction** in neutrino phenomenology, and a **post-common-envelope evolutionary origin** for blue large-amplitude pulsators in stellar astrophysics [1711.08593] [2504.15122] [2606.00984] [1211.7207] [1811.10974]. The acronym is therefore not a field-independent term, and its meaning is determined almost entirely by disciplinary context.

## 1. Estimation theory: constrained BLUE as BLCE

In estimation theory, BLCE denotes the **Best Linear Constrained Estimator**, i.e. the constrained version of the best linear unbiased estimator under linear equality constraints [1711.08593]. The underlying real-valued model is
\[
y = Hx + w,
\]
with \(y \in \mathbb{R}^{N_y}\), \(x \in \mathbb{R}^{N_x}\), \(H \in \mathbb{R}^{N_y\times N_x}\), \(E[w]=0\), and \(\mathrm{Cov}(w)=R \succ 0\). The parameter vector satisfies consistent linear constraints
\[
Cx = d,
\]
where \(C \in \mathbb{R}^{N_c \times N_x}\) has full row rank.

When \(H\) has full column rank, the unconstrained BLUE coincides with the GLS estimator,
\[
\hat{x}_{\mathrm{BLUE}} = \bigl(H^\top R^{-1} H\bigr)^{-1} H^\top R^{-1} y,
\]
with information matrix \(P := H^\top R^{-1} H\). The constrained estimator is obtained from the constrained GLS problem
\[
\min_x (y-Hx)^\top R^{-1}(y-Hx)\quad \text{s.t.}\quad Cx=d,
\]
whose KKT system is
\[
\begin{bmatrix}
H^\top R^{-1} H & C^\top \\
C & 0
\end{bmatrix}
\begin{bmatrix}
\hat{x}_c \\
\lambda
\end{bmatrix}
=
\begin{bmatrix}
H^\top R^{-1} y \\
d
\end{bmatrix}.
\]

The resulting closed form is
\[
\hat{x}_c
=
\hat{x}_{\mathrm{BLUE}}
+
\bigl(H^\top R^{-1} H\bigr)^{-1} C^\top
\Bigl[
C \bigl(H^\top R^{-1} H\bigr)^{-1} C^\top
\Bigr]^{-1}
\bigl(d - C\hat{x}_{\mathrm{BLUE}}\bigr),
\]
or equivalently,
\[
\hat{x}_c
=
\Bigl(I - P^{-1} C^\top (C P^{-1} C^\top)^{-1} C\Bigr) P^{-1} H^\top R^{-1} y
+
P^{-1} C^\top (C P^{-1} C^\top)^{-1} d.
\]

A null-space formulation is also central. If \(x = x_p + Nz\), where \(Cx_p=d\) and \(CN=0\), then under the weaker condition that \(HN\) has full column rank,
\[
\hat{x}_c
=
x_p + N \bigl(N^\top P N\bigr)^{-1} N^\top H^\top R^{-1} (y - Hx_p).
\]
This form remains valid even when \(H\) is not full column rank or \(N_y < N_x\), provided \(N^\top P N \succ 0\) [1711.08593].

The constrained estimator is unbiased on the feasible affine subspace, \(E[\hat{x}_c]=x\) when \(Cx=d\), and its covariance is
\[
\mathrm{Cov}(\hat{x}_c)
=
P^{-1} - P^{-1} C^\top (C P^{-1} C^\top)^{-1} C P^{-1},
\]
equivalently
\[
\mathrm{Cov}(\hat{x}_c)=N(N^\top P N)^{-1}N^\top.
\]
The constrained covariance satisfies
\[
\mathrm{Cov}(\hat{x}_c)\preceq P^{-1},
\]
so the constraints remove variability along constrained directions. Under white noise, \(R=\sigma^2 I\), the BLCE reduces to the constrained least-squares estimator, which is one reason the constrained BLUE and constrained LS are algebraically so closely related [1711.08593].

## 2. Dynamic 3D Gaussian splatting: Blur-adaptive Latent Camera Estimation

In computer vision, BLCE denotes **Blur-adaptive Latent Camera Estimation**, the camera-trajectory module of MoBGS for deblurring dynamic 3D Gaussian Splatting from blurry monocular video [2504.15122]. Its purpose is to recover a per-frame continuous latent camera trajectory during the exposure interval and thereby model blur induced by global camera motion.

The blurry frame \(B_t\) is modeled under global shutter and uniform exposure as
\[
B_t(u) = \frac{1}{T_t}\int_{t-T_t/2}^{t+T_t/2} C(u;\tau,P(\tau))\, d\tau,
\]
with discrete approximation
\[
B_t(u) \approx \frac{1}{N_l}\sum_{k=1}^{N_l} C(u;\tau_t^k,P_t^k),
\qquad
\tau_t^k = t + T_t \cdot (k-\lceil N_l/2\rceil)/N_l.
\]

BLCE adapts trajectory complexity to blur severity. A blur score is computed from the low-frequency energy ratio of the shifted DFT magnitude,
\[
\beta_t=\frac{\sum_{\xi\in\Lambda} M_t(\xi)}{\sum_{\xi} M_t(\xi)},
\qquad
M_t = |\tilde{F}(B_t)|.
\]
This score is encoded as a blur feature
\[
B_t^{\mathrm{feat}} = F_\theta(\phi(\beta_t)).
\]

The latent trajectory is then parameterized in five steps: a seed latent code is formed from blur and pose features, that code is evolved by a neural ODE over \(N_l\) exposure samples, each evolved state is decoded into a twist \(\xi_t^k=(\omega_t^k;v_t^k)\in\mathbb{R}^6\), the twist is mapped to \(SE(3)\) via the exponential map, and the residual transform is composed with the training pose:
\[
z_t^0 = F_{\mathrm{enc}}([B_t^{\mathrm{feat}}, \mathrm{PoseEnc}(P_t)]),
\]
\[
\frac{dz}{ds}=f(z,s;\theta_{\mathrm{ode}}),
\]
\[
(\omega_t^k,v_t^k)=F_{\mathrm{dec}}(z_t^k),
\]
\[
\Psi(\xi)=\mathrm{Exp}(\xi^\wedge)\in SE(3),
\]
\[
P_t^k = P_t \cdot \Psi(\xi_t^k).
\]

This construction is paired with **Latent Camera-induced Exposure Estimation** (LCEE), which couples exposure time to actual camera path length across static Gaussians:
\[
\hat{T}_t
=
\frac{1}{n^{st}}\sum_{i=1}^{n^{st}}
\frac{D(P_t^1,P_t^{N_l},\mu_i^{st})+\epsilon}
{D(P_{t-1},P_{t+1},\mu_i^{st})+\epsilon}.
\]
The estimated \(\hat{T}_t\) then determines the latent timestamps used for rendering dynamic object motion. This enforces the paper’s central physical consistency requirement: global camera blur and local object blur are integrated over the same exposure interval [2504.15122].

MoBGS optimizes BLCE jointly with static and dynamic Gaussian parameters, spline control points, and several losses:
\[
L_{\mathrm{total}}
=
\lambda_{\mathrm{rgb}}L_{\mathrm{rgb}}
+
\lambda_d L_{\mathrm{depth}}
+
\lambda_{\mathrm{umd}}L_{\mathrm{umd}}
+
\lambda_{\mathrm{tcr}}L_{\mathrm{tcr}}.
\]
The reported implementation uses \(N_l=9\), with experiments showing improvements up to \(N_l \approx 11\), reported training time of approximately \(1.5\) h per scene, and rendering speed of approximately \(480\) FPS. On Stereo Blur, MoBGS with BLCE/LCEE attains \(28.70/0.945/0.051/0.516\) in PSNR/SSIM/LPIPS/tOF for the full region [2504.15122].

## 3. Online learning: Batched-Feedback Linear Contextual Bandit with Elimination

In contextual bandits, BLCE denotes **Batched-Feedback Linear Contextual Bandit with Elimination**, a rare-update algorithm for linear contextual bandits [2606.00984]. The setting is
\[
r_t = \langle x_{t,a_t},\theta^*\rangle + \eta_t,
\]
where \(\theta^*\in\mathbb{R}^d\) is unknown, \(\eta_t\) is independent \(1\)-sub-Gaussian noise, and each round reveals a set of \(K\) context vectors
\[
\mathcal{A}_t=\{x_{t,1},\ldots,x_{t,K}\}\subset \mathbb{R}^d.
\]
The regret is
\[
\mathcal{R}(T)
=
\mathbb{E}\!\left[
\sum_{t=1}^T
\bigl(
\langle x_t^*,\theta^*\rangle - \langle x_{t,a_t},\theta^*\rangle
\bigr)
\right].
\]

The distinctive operational constraint is that reward-dependent parameter retraining is permitted only \(O(\log\log T)\) times. BLCE uses a static schedule with update times \(\{\mathcal{T}_\ell\}_{\ell=1}^B\), where \(B=O(\log\log T)\), the first interval has length approximately
\[
\mathcal{T}_1 \approx \Big\lceil \tfrac{\sqrt{T}}{\log_2\log_2 T} \Big\rceil,
\]
and later interval lengths scale like
\[
\mathcal{T}_\ell - \mathcal{T}_{\ell-1}
\approx
\Big\lceil \frac{T^{\,1-2^{-\ell}}}{\log_2\log_2 T} \Big\rceil.
\]
The total number of intervals is at most \(3\log_2\log_2 T + 1\) [2606.00984].

BLCE is explicitly **not strictly-batched**. Parameter estimates \(\hat{\theta}_\ell\) are updated only at interval boundaries, but within intervals the algorithm continues to maintain reward-free quantities such as Gram matrices and uses them in action selection. In the first interval, it performs pure uncertainty-driven exploration:
\[
x_{t,a_t}\in \arg\max_{x\in\mathcal{A}_t}\|x\|_{H_{t-1}^{-1}},
\]
with inverse Gram update by Sherman–Morrison,
\[
H_t^{-1}
\leftarrow
H_{t-1}^{-1}
-
\frac{H_{t-1}^{-1}x_{t,a_t}x_{t,a_t}^{\!\top}H_{t-1}^{-1}}
{1+x_{t,a_t}^{\!\top}H_{t-1}^{-1}x_{t,a_t}}.
\]
At the first update,
\[
V_1 := \lambda I + \sum_{t=1}^{\mathcal{T}_1} x_{t,a_t}x_{t,a_t}^{\!\top},
\qquad
\hat{\theta}_1 := V_1^{-1}\sum_{t=1}^{\mathcal{T}_1} r_t x_{t,a_t},
\]
with \(\lambda=1\).

For later intervals, BLCE begins with multi-level elimination. Given past estimates \(\hat{\theta}_1,\ldots,\hat{\theta}_{\ell-1}\), it defines nested feasible sets
\[
x_t^{(k)} \in \arg\max_{x\in \mathcal{A}_t^{(k-1)}} \langle x,\hat{\theta}_k\rangle,
\]
\[
\mathcal{A}_t^{(k)}
=
\left\{
x\in\mathcal{A}_t^{(k-1)}:
\langle \hat{\theta}_k, x_t^{(k)}-x\rangle \le 2\varepsilon_{t,k}
\right\},
\qquad
\mathcal{A}_t^{(0)}=\mathcal{A}_t.
\]
It then splits the interval into an uncertainty-driven exploration phase and a greedy exploitation phase with respect to \(\hat{\theta}_{\ell-1}\). The confidence widths are
\[
\beta_{t,\ell}^{(1)}(\delta)
=
\sqrt{2\log\!\bigg(\frac{2|\mathcal{A}_t^{(\ell-1)}|(B-1)T}{\delta}\bigg)}
+\sqrt{\lambda},
\]
\[
\beta_{t,\ell}^{(2)}(\delta)
=
2\sqrt{\log\!\bigg(\frac{2^{6d-3}\pi d(B-1)^2}{15^{d-1}\delta^2}\bigg)}
+2\sqrt{\lambda},
\]
\[
\varepsilon_{t,\ell}(\delta)
=
\bigl(\beta_{t,\ell}^{(1)}(\delta)\wedge \beta_{t,\ell}^{(2)}(\delta)\bigr)
\cdot
\max_{y\in\mathcal{A}_t^{(\ell-1)}} \|y\|_{V_\ell^{-1}}.
\]

The main theoretical guarantee is
\[
\mathcal{R}(T)
=
\Ocal\!\Big(
\sqrt{dT}\,
\big(\sqrt{\log(KT)}\wedge \sqrt{d+\log T}\big)\,
\sqrt{\log T\,\log\log T}
\Big)
=
\tilde{\Ocal}\!\big(\sqrt{dT\log K}\wedge d\sqrt{T}\big),
\]
described as minimax-optimal up to polylogarithmic factors [2606.00984]. Its total runtime is
\[
\Ocal(Kd^2T\log\log T),
\]
and the paper emphasizes that BLCE attains this guarantee without the near G-optimal design step used by BLCE-G, thereby avoiding the \(O(Kd^3)\) per-call bottleneck associated with such designs [2606.00984].

## 4. Neutrino phenomenology: Bi-Large mixing with charged lepton correction

In neutrino physics, BLCE denotes **Bi-Large mixing with charged lepton correction**, a lepton-mixing construction in which the neutrino sector is assumed to obey Bi-Large mixing and the charged-lepton sector contributes a CKM-type correction [1211.7207].

The Bi-Large ansatz takes the Cabibbo angle as the seed parameter:
\[
\lambda \equiv \sin\theta_c \equiv \lambda_c \approx 0.2257,
\]
with the strict BL choice
\[
\sin\theta_{13}^\nu = \lambda,\qquad
\sin\theta_{12}^\nu = 3\lambda,\qquad
\sin\theta_{23}^\nu = 3\lambda,
\]
and \(\delta_\nu=0\). The neutrino mixing matrix is \(U_\nu = R_{23}R_{13}R_{12}\) in standard PDG form. The charged-lepton correction is a CKM-like \(12\)-rotation,
\[
U_l =
\begin{pmatrix}
1-\lambda^2/2 & \lambda e^{i\delta_{cp}} & 0\\
-\lambda e^{-i\delta_{cp}} & 1-\lambda^2/2 & 0\\
0 & 0 & 1
\end{pmatrix},
\]
and the physical PMNS matrix is
\[
U = U_l^\dagger U_\nu.
\]

Because \(U_{e3}^\nu \neq 0\) in the Bi-Large ansatz, all three observable mixing angles depend on \(\delta_{cp}\). The leading relations may be written as
\[
\sin\theta_{13} \approx |s_{13}^\nu + \lambda e^{i\delta_{cp}} s_{23}^\nu c_{13}^\nu|,
\]
with analogous \(\delta_{cp}\)-dependent formulas for \(\sin^2\theta_{12}\) and \(\sin^2\theta_{23}\). The paper gives explicit closed forms:
\[
\sin^2\theta_{13}
=
\frac{\lambda^2}{64}(\lambda^2-2)^2(23-8\sqrt{7}\cos\delta_{cp}),
\]
\[
\sin^2\theta_{12}
=
\frac{
112 + \lambda^2 \{7\lambda(31\lambda-18)-143\}
+ 2\sqrt{7}\lambda(7\lambda-9)(\lambda^2-2)^2\cos\delta_{cp}
}{
256\left\{
1+\frac{\lambda^2(\lambda^2-2)^2}{64}(8\sqrt{7}\cos\delta_{cp}-23)
\right\}
},
\]
\[
\sin^2\theta_{23}
=
\frac{
112 - \lambda^2 \{224 - 424\lambda^2 - 32\sqrt{7}(\lambda^2-2)^2\cos\delta_{cp}\}
}{
256\left\{
1+\frac{\lambda^2(\lambda^2-2)^2}{64}(8\sqrt{7}\cos\delta_{cp}-23)
\right\}
}.
\]

A key motivation is to avoid the well-known limitation of Bi-Maximal mixing with charged-lepton correction. In the BM case, the minimum solar angle is \(\sin^2\theta_{12}\approx 0.3407\), equivalently \(\tan^2\theta_{12}\approx 0.52\), and this minimum occurs only for \(\delta_{cp}=0\), implying vanishing CP violation. In the BLCE construction, by contrast, a single choice of phase can align all three angles. For \(\lambda=0.2257\), the paper finds
\[
\cos\delta_{cp}\approx 0.70,\qquad
\delta_{cp}\approx 0.2515\pi,
\]
leading to
\[
\sin^2\theta_{13}\approx 0.0245,\qquad
\sin^2\theta_{12}\approx 0.3209,\qquad
\sin^2\theta_{23}\approx 0.4533.
\]
The scheme also predicts that \(\theta_{23}\) lies in the first octant, with
\[
\sin^2\theta_{23}\in [0.427,\,0.463]
\]
under variation of \(\delta_{cp}\) [1211.7207].

The associated Jarlskog invariant is
\[
J_{CP} = \mathrm{Im}(U_{e1}U_{\mu2}U_{e2}^*U_{\mu1}^*),
\]
and for BLCE the paper derives
\[
J_{CP}^{BL}
=
\frac{9\sqrt{7}}{4096}\lambda
\big[28 - 8\lambda(1+8\lambda-\lambda^2) + 57\lambda^4\big]
\sin\delta_{cp}
\approx 0.0304\sin\delta_{cp}.
\]
This makes BLCE a highly constrained and therefore highly testable mixing scheme [1211.7207].

## 5. Stellar astrophysics: the BLCE evolutionary channel for BLAPs

In stellar astrophysics, BLCE refers to a **post-common-envelope evolutionary origin** for blue large-amplitude pulsators (BLAPs) [1811.10974]. The term identifies a channel in which a low-mass star loses its hydrogen envelope in a rapid common-envelope ejection and subsequently contracts through the BLAP region before becoming either a low-mass helium white dwarf or a core-helium-burning extreme horizontal-branch star.

The observational BLAP domain summarized in the models is
\[
T_{\mathrm{eff}} \approx 30{,}000\text{--}35{,}000\ \mathrm{K},
\qquad
\log g \approx 4.4\text{--}4.8,
\]
with large-amplitude single-period photometric variations of about \(0.2\text{--}0.4\) mag on timescales of \(20\text{--}40\) minutes [1811.10974]. The post-CE calculations begin from a \(1\,M_\odot\) red-giant progenitor that undergoes rapid envelope loss at
\[
\dot{M}=10^{-3}\,M_\odot\,\mathrm{yr}^{-1},
\]
leaving a thin hydrogen layer of approximately \(2\times 10^{-3}\,M_\odot\). Two remnant masses were modeled: approximately \(0.46\,M_\odot\), which ignites helium and approaches the EHB, and approximately \(0.31\,M_\odot\), which contracts without helium ignition and becomes a low-mass helium white dwarf [1811.10974].

The decisive microphysics is atomic diffusion, particularly **radiative levitation** of iron-group elements. Radiative accelerations satisfy
\[
g_{\mathrm{rad},i}
=
\frac{1}{c}\int \kappa_{\nu,i}\frac{F_\nu}{\rho}\, d\nu
\approx
\frac{\kappa_i F}{c\rho},
\]
and diffusion velocities schematically obey
\[
v_i
\approx
-D_i
\left[
\nabla\ln n_i
+
\frac{A_i m_p g - g_{\mathrm{rad},i}}{k_B T}
+
\alpha_T \nabla\ln T
\right].
\]
These processes lead to Fe/Ni accumulation near the iron-group opacity bump at
\[
T \approx 2\times 10^5\ \mathrm{K},
\qquad
\log T \approx 5.3.
\]

With levitation, the enhanced Fe/Ni opacity bump drives the **fundamental radial mode** through the \(\kappa\)-mechanism. Stability is measured by the work integral
\[
W=\int \delta W\, dm,
\qquad
\eta = W\big/\int |\delta W|\, dm,
\]
with instability corresponding to \(W>0\) or \(\eta>0\). The data explicitly state that without diffusion the Z-bump is too weak and the fundamental mode is stable, whereas with levitation the local Fe/Ni enhancement increases the driving term by roughly an order of magnitude and renders the surface value of \(dW/dx\) positive in the BLAP domain [1811.10974].

The predicted fundamental-mode periods are consistent with observation:
\[
P_0 \approx 2\pi \sqrt{R^3/GM},
\]
and for \(R\approx 0.15\text{--}0.25\,R_\odot\) and \(M\approx 0.30\text{--}0.46\,M_\odot\),
\[
P_0 \approx 1000\text{--}2500\ \mathrm{s}
\approx 17\text{--}42\ \mathrm{min}.
\]
Both sequences pass through the BLAP \(T_{\mathrm{eff}}-\log g\) box, but the \(0.31\,M_\odot\) sequence is described as the most consistent with BLAPs. Its period-change magnitude is
\[
\dot{\Pi}\approx 10^{-7}\ \mathrm{yr}^{-1},
\]
with negative sign due to contraction, matching the order of many observed BLAPs. The \(0.46\,M_\odot\) pre-EHB sequence produces \(|\dot{\Pi}|\) about an order of magnitude too large, and neither contracting sequence naturally explains positive \(\dot{P}\), except through speculative brief expansion loops during off-center He ignition [1811.10974].

A related paper presents the same evolutionary picture with further numerical detail, including representative unstable models at \(\log g = 4.771\), \(\log T_{\mathrm{eff}} = 4.501\), \(\log P_0(\mathrm{s}) = 3.110\) for the \(0.46\,M_\odot\) case and \(\log g = 4.680\), \(\log T_{\mathrm{eff}} = 4.454\), \(\log P_0(\mathrm{s}) = 3.124\) for the \(0.31\,M_\odot\) case [1809.04183]. This suggests that, within the BLCE astrophysical usage, the acronym refers not to a named algorithm but to a specific post-common-envelope channel for BLAP phenomenology.

## 6. Ambiguity, nonstandard usage, and related acronym collisions

BLCE is not uniformly standardized across the cited literature. Some papers explicitly note that the acronym is absent or unofficial in their own setting. In ML-assisted communications, for example, the paper on BER- and BLER-oriented training states that **the paper does not define the acronym BLCE**; instead it introduces block-level surrogates such as Product, SmoothMax, LogSumExp, and \(p\)-norm losses for minimizing BLER directly [2210.14103]. Any reading of BLCE in that context as a named method would therefore be inaccurate.

A similar caution applies in continual learning. The paper “Bayesian Learning-driven Prototypical Contrastive Loss for Class-Incremental Learning” names its method **BLCL**, not BLCE [2405.11067]. The details note that if one encounters BLCE as “Bayesian learning-driven contrastive approach balancing cross-entropy,” it is only a conceptual mapping to the same uncertainty-based weighting between cross-entropy and contrastive losses:
\[
\mathcal{L}_{\mathrm{BLCL}}(\mathbf{W},\sigma_1,\sigma_2)
=
\frac{1}{2\sigma_1^2}\mathcal{L}_{\mathrm{CE}}(\mathbf{W})
+
\frac{1}{2\sigma_2^2}\mathcal{L}_{\mathrm{CL}}(\mathbf{W})
+
\log \sigma_1 + \log \sigma_2.
\]
The official notation in that paper remains BLCL [2405.11067].

This multiplicity of meanings has a practical implication for literature search and citation. In statistics and signal processing, BLCE is tied to constrained Gauss–Markov estimation [1711.08593]; in dynamic 3DGS it is a latent camera estimation module [2504.15122]; in bandit theory it is a rare-update elimination algorithm [2606.00984]; in neutrino phenomenology it is a mixing ansatz with charged-lepton correction [1211.7207]; and in BLAP studies it abbreviates a post-common-envelope evolutionary channel [1811.10974]. The acronym therefore functions as a context-dependent shorthand rather than a single recognized concept across disciplines.

## 7. Cross-disciplinary significance

The different BLCE usages share almost no mathematical or conceptual common core beyond acronymic coincidence. The estimation-theoretic BLCE is a constrained minimum-variance linear unbiased estimator on an affine subspace [1711.08593]. The computer-vision BLCE is an \(SE(3)\)-trajectory inference module embedded in an end-to-end rendering-and-deblurring pipeline [2504.15122]. The bandit BLCE is an elimination-based rare-update strategy with minimax-optimal regret up to polylogarithmic factors [2606.00984]. The neutrino BLCE is a phenomenological mixing construction in which a CKM-like charged-lepton correction modifies a Bi-Large neutrino pattern [1211.7207]. The astrophysical BLCE channel is an evolutionary interpretation of BLAPs based on post-common-envelope contraction and radiative levitation [1811.10974].

A plausible implication is that references to “BLCE” without an expansion are intrinsically ambiguous in interdisciplinary settings. For arXiv-oriented readers, the safe interpretation is therefore bibliographic rather than lexical: BLCE should be resolved from the paper’s field, equations, and nearby terminology, not from the acronym alone.

Source: https://www.emergentmind.com/topics/blce