Banyan: Polysemous Constructs in Astronomy & Computing

• Banyan is a polysemous term referring to specialized systems across astronomy, optical networking, distributed consensus, graph processing, reinforcement learning, and natural language processing.
• In astronomy, BANYAN employs Bayesian inference to classify young stellar associations, predicting radial velocities and distances with precisions around 1.6 km/s and 8%, respectively.
• Beyond astronomy, Banyan denotes innovations such as self-routing switching topologies, fast Byzantine fault-tolerant protocols, high-performance graph query engines, GPU-accelerated RL benchmarks, and structured NLP models.

Banyan is a polysemous technical designation applied to several unrelated research constructs. In astronomy, BANYAN denotes the Bayesian Analysis for Nearby Young AssociatioNs framework: a family of Bayesian membership-classification tools, surveys, and follow-up programs for nearby young associations, brown dwarfs, and planetary-mass candidates (Gagné et al., 2013). In other fields, Banyan denotes a self-routing switching topology and related optical-quantum switch fabrics (Zhu et al., 2014), a rotating-leader Byzantine fault-tolerant state machine replication protocol (Vonlanthen et al., 2023), a scoped-dataflow graph-query engine (Su et al., 2022), a GPU-accelerated continual reinforcement-learning benchmark (Seth et al., 30 May 2026), and a structured language-representation model based on entangled hierarchical trees and diagonalized message passing (Opper et al., 2024).

Domain	Designation	Core function
Astronomy	BANYAN, BANYAN II, BANYAN $\Sigma$, BASS	Bayesian membership inference for nearby young associations
Optical/quantum networking	Banyan network	Self-routing multistage switching topology
BFT/SMR	Banyan / FICC	One-RTT fast-path finalization with rotating leaders
Graph systems	Banyan	Scoped-dataflow engine for graph query service
Continual RL	Banyan	Controlled benchmark for task-diversity shifts
NLP	Banyan	Explicitly structured semantic representation learning

1. Astronomical BANYAN: definition and problem setting

In astronomy, BANYAN is a Bayesian classifier designed to test whether a source belongs to one of the nearby young moving groups or associations rather than the field. BANYAN II was introduced for later-than-M5 objects and combines sky position, proper motion, spectral type, 2MASS $J,H,K_s$, and WISE $W1,W2$, while marginalizing over missing radial velocity and distance/parallax (Gagné et al., 2013). The targeted associations include systems such as $\beta$ Pictoris, Tucana-Horologium, Columba, Carina, Argus, and AB Doradus (Malo et al., 2014).

The BANYAN II posterior is formulated as a naive Bayesian classifier,

$$P(H_k|\{O_i\}) = \frac{P(H_k)}{P(\{O_i\})}\int_0^\infty \int_{-\infty}^\infty P(\{O_i\},\nu,\varpi|H_k)\ d\nu\ d\varpi,$$

with likelihoods built from transformed observables and priors matched to expected young-association and field populations (Gagné et al., 2013). A central practical feature is that BANYAN predicts likely radial velocities and distances even when they are not measured; the reported prediction precisions are about $8.0\%$ in distance and about $1.6\ \mathrm{km\,s^{-1}}$ in radial velocity (Gagné et al., 2013).

BANYAN is tightly coupled to the BANYAN All-Sky Survey (BASS), which uses a 2MASS–AllWISE cross-match to identify late-type candidate members missed by earlier proper-motion and RV/parallax-limited work (Gagné et al., 2014). In this context, BANYAN is not merely a classifier but an inference engine that returns membership probabilities, statistical distances, and predicted radial velocities for large candidate lists (Gagné et al., 2014).

2. From BANYAN II to BANYAN $\Sigma$ and the Gaia/MOCA era

BANYAN II extended earlier BANYAN work in several technical directions: it replaced axis-aligned models with rotated ellipsoids in $XYZ$ and $UVW$, introduced priors based on expected populations, incorporated equal-luminosity binary hypotheses shifted by $J,H,K_s$0 mag in color–magnitude space, and performed an explicit contamination analysis (Gagné et al., 2013). The contamination study showed that Bayesian probabilities are generally representative of contamination rates, except when parallax is included, in which case the Bayesian probabilities become pessimistic (Gagné et al., 2013).

BANYAN $J,H,K_s$1 generalized the framework to 27 young associations within 150 pc modeled as multivariate Gaussians in full $J,H,K_s$2 space, together with a field-star model based on a 10-component multivariate Gaussian mixture derived from the Besançon Galactic model (Gagné et al., 2018). Its major algorithmic advance is an analytical solution to the Bayesian marginalization integrals, making it about 80,000 times faster than BANYAN II while improving cross-contamination behavior between nearby associations (Gagné et al., 2018). The basic posterior remains

$J,H,K_s$3

but the observable-space likelihood is marginalized analytically over missing radial velocity and/or distance (Gagné et al., 2018).

The first Gaia-driven reassessments used this faster formalism at scale. A Gaia DR2 search of the nearest 100 pc with $J,H,K_s$4 and $J,H,K_s$5 analyzed 695,952 stars and reported 898 new high-likelihood candidate members, 104 co-moving systems, 111 brown dwarf candidates, and 31 new bona fide members (Gagné et al., 2018). A parallel Gaia-Tycho search identified 32 new F0–M3-type bona fide members, confirmed 66 previously known candidate members, and reported 219 additional new candidate members (Gagné et al., 2018).

The 2026 MOCA update broadened the model universe substantially. The Montreal Open Clusters and Associations database compiled 10,259 associations and open clusters within 500 pc, updated BANYAN $J,H,K_s$6 to include 8,125 associations flagged as suitable for BANYAN use, and improved model construction with heterogeneous and correlated errors, Gaussian mixture models with 1–20 components, and extreme deconvolution (Gagné et al., 17 Feb 2026). Combined with Gaia DR3, this yielded 11,535 yet unrecognized candidate members of young associations within 500 pc, mostly M dwarfs (Gagné et al., 17 Feb 2026).

3. BASS, low-gravity dwarfs, and the nearby young substellar census

The BASS survey begins from a 2MASS–AllWISE cross-match outside the Galactic plane and produced an input sample of 98,970 potential nearby $J,H,K_s$7 M5 dwarfs with typical proper-motion precisions of 5–15 mas yr$J,H,K_s$8 (Gagné et al., 2014). BANYAN II was then used to select the main BASS catalog of 228 new late-type (M4–L6) candidate members of nearby young moving groups, including 79 new candidate young brown dwarfs and 22 planetary-mass objects, with an expected false-positive rate of about 13% (Gagné et al., 2014). A related BASS presentation reported 273 BASS candidates and 275 lower-priority LP-BASS candidates, for 548 catalogued sources after a different catalog-construction cut sequence (Gagné et al., 2014).

Near-infrared spectroscopic follow-up is essential because low gravity is diagnosed through weaker alkali absorption lines such as Na I and K I, weaker FeH, stronger VO, triangular $J,H,K_s$9-band continua, and reduced H$W1,W2$0($W1,W2$1) collision-induced absorption (Gagné et al., 2015). The follow-up campaign reports 42 new brown dwarf discoveries with estimated masses between 8–75 $W1,W2$2 showing low-gravity signatures, and 24 previously known brown dwarfs with newly recognized low gravity; this refines the low-gravity fraction in the high-probability BASS sample to about 82% (Gagné et al., 2015). The same work identifies 19 new low-gravity candidate members of young moving groups below $W1,W2$3, seven of which have kinematically estimated distances within 40 pc (Gagné et al., 2015).

A later summary of BASS states that the survey yielded 44 new low-mass stars and 69 new brown dwarfs with spectroscopically confirmed low gravity, with about $W1,W2$4 in the planetary-mass regime (Gagné et al., 2015). The full spectroscopic campaign is also described as uncovering 108 new M6–L5 low-gravity dwarfs, effectively doubling the known population of such objects at the time (Gagné et al., 2015).

One debated result is the apparent Tucana-Horologium excess near the planetary-mass boundary. The abstract reports 16 strong THA candidate members with estimated masses 12.5–14 $W1,W2$5, while the discussion uses 15 THA candidates in that bin, implying roughly one isolated object in that mass range for every

$W1,W2$6

main-sequence stellar member (Gagné et al., 2015). The same paper states that this is significantly higher than expected from a standard log-normal IMF, but also cautions that incomplete radial-velocity and parallax follow-up makes contamination by young interlopers from other groups the likely explanation for at least part of the excess (Gagné et al., 2015).

4. Empirical sequences, benchmarks, ages, and diagnostics

BANYAN follow-up work was used to construct new empirical near-infrared absolute-magnitude and color sequences for low-gravity brown dwarfs. Using 66 young brown dwarfs from the survey plus 22 young brown dwarfs from the literature, the study tabulated sequences in $W1,W2$7 and colors such as $W1,W2$8, $W1,W2$9, $\beta$0, $\beta$1, and $\beta$2 (Gagné et al., 2015). A key qualitative result is that young objects are typically brighter than field dwarfs at a given spectral type because of inflated radii, but dust and cloud effects in late-M and L dwarfs can counteract this, making young L dwarfs redder and sometimes fainter in some bands; the young and field sequences cross at spectral types that shift to later types at longer wavelengths (Gagné et al., 2015).

The same work makes two methodological cautions. First, low-resolution NIR spectroscopy alone cannot reliably distinguish ages younger than about $\beta$3 Myr; gravity-sensitive indices correlate with age only in an average sense, with too much scatter for precise individual age dating (Gagné et al., 2015). Second, BT-Settl atmosphere models fail to reproduce the dust/cloud behavior of field and low-gravity L dwarfs well, especially in the $\beta$4 and $\beta$5-band morphology (Gagné et al., 2015).

Several benchmark systems anchor the low-mass, low-gravity regime. 2MASS J14252798-3650229 was spectroscopically confirmed as an L4$\beta$6 bona fide AB Doradus member with an adopted mass of

$\beta$7

providing a late-type benchmark at the age of AB Doradus (Gagné et al., 2015). 2MASS J02192210-3925225 B is an L4$\beta$8 companion to a THA M6$\beta$9 primary at $$P(H_k|\{O_i\}) = \frac{P(H_k)}{P(\{O_i\})}\int_0^\infty \int_{-\infty}^\infty P(\{O_i\},\nu,\varpi|H_k)\ d\nu\ d\varpi,$$0 and $$P(H_k|\{O_i\}) = \frac{P(H_k)}{P(\{O_i\})}\int_0^\infty \int_{-\infty}^\infty P(\{O_i\},\nu,\varpi|H_k)\ d\nu\ d\varpi,$$1 AU, with a model-dependent mass of 12–15 $$P(H_k|\{O_i\}) = \frac{P(H_k)}{P(\{O_i\})}\int_0^\infty \int_{-\infty}^\infty P(\{O_i\},\nu,\varpi|H_k)\ d\nu\ d\varpi,$$2, placing it at the brown-dwarf/planet boundary (Artigau et al., 2015). 2M2250+2325 B is an L3 $$P(H_k|\{O_i\}) = \frac{P(H_k)}{P(\{O_i\})}\int_0^\infty \int_{-\infty}^\infty P(\{O_i\},\nu,\varpi|H_k)\ d\nu\ d\varpi,$$3 wide companion to an M3 ABDMG candidate at $$P(H_k|\{O_i\}) = \frac{P(H_k)}{P(\{O_i\})}\int_0^\infty \int_{-\infty}^\infty P(\{O_i\},\nu,\varpi|H_k)\ d\nu\ d\varpi,$$4, $$P(H_k|\{O_i\}) = \frac{P(H_k)}{P(\{O_i\})}\int_0^\infty \int_{-\infty}^\infty P(\{O_i\},\nu,\varpi|H_k)\ d\nu\ d\varpi,$$5, a projected separation of $$P(H_k|\{O_i\}) = \frac{P(H_k)}{P(\{O_i\})}\int_0^\infty \int_{-\infty}^\infty P(\{O_i\},\nu,\varpi|H_k)\ d\nu\ d\varpi,$$6 AU, and a mass of $$P(H_k|\{O_i\}) = \frac{P(H_k)}{P(\{O_i\})}\int_0^\infty \int_{-\infty}^\infty P(\{O_i\},\nu,\varpi|H_k)\ d\nu\ d\varpi,$$7 under the ABDMG age prior (Desrochers et al., 2017).

Age calibration in the broader BANYAN program uses more than kinematics. High-resolution spectroscopy of 219 low-mass stars showed that adding radial velocity confirmed 130 candidates with $$P(H_k|\{O_i\}) = \frac{P(H_k)}{P(\{O_i\})}\int_0^\infty \int_{-\infty}^\infty P(\{O_i\},\nu,\varpi|H_k)\ d\nu\ d\varpi,$$8, that the sample binary fraction is 25%, and that for low-mass stars in the 12–120 Myr range, $$P(H_k|\{O_i\}) = \frac{P(H_k)}{P(\{O_i\})}\int_0^\infty \int_{-\infty}^\infty P(\{O_i\},\nu,\varpi|H_k)\ d\nu\ d\varpi,$$9 is a better age discriminator than $8.0\%$0 (Malo et al., 2014). A companion study of 59 low-mass candidates compared derived $8.0\%$1, $8.0\%$2, $8.0\%$3, and $8.0\%$4 to Dartmouth Magnetic evolutionary models, deriving a 15–28 Myr isochronal age range for $8.0\%$5 Pictoris and confirming a $8.0\%$6 Myr Lithium Depletion Boundary age (Malo et al., 2014).

BANYAN catalogs have also been used to search for circumstellar disks. A 2MASS+WISE excess analysis over 585 quality-controlled targets found 13 convincing disk systems, including 4 new disk candidates; the new objects span spectral types from M4.5 to L0$8.0\%$7, ages from about 10 to 45 Myr, and inferred disk temperatures of about 135–520 K (Boucher et al., 2016).

5. Banyan as switching topology and consensus protocol

Outside astronomy, a Banyan network is a multistage switching network built from many simple $8.0\%$8 switches. Its defining advantage is self-routing: at the $8.0\%$9-th stage, the signal is sent to the lower output if the $1.6\ \mathrm{km\,s^{-1}}$0-th most significant bit is $1.6\ \mathrm{km\,s^{-1}}$1, and to the upper output if it is $1.6\ \mathrm{km\,s^{-1}}$2 (Zhu et al., 2014). The classical limitation is internal blocking, where two signals contend for the same internal link even when their final outputs differ (Zhu et al., 2014).

A quantum-optical variant addresses this by replacing classical collision handling with quantum state fusion and fission. In the proposed optical quantum switch unit, two contending qubits can be fused into a single photon with a four-dimensional internal state and then converted from spatial-polarization mode to time-polarization mode with basis

$1.6\ \mathrm{km\,s^{-1}}$3

allowing both qubits to traverse one physical output path (Zhu et al., 2014). The paper reports a fusion success probability of $1.6\ \mathrm{km\,s^{-1}}$4, improvable to $1.6\ \mathrm{km\,s^{-1}}$5 with feed-forward; with a heralded Fredkin gate success probability of $1.6\ \mathrm{km\,s^{-1}}$6 and equal branch usage, the average switch-unit success probability is

$1.6\ \mathrm{km\,s^{-1}}$7

(Zhu et al., 2014).

In distributed systems, Banyan also names a rotating-leader BFT/SMR protocol, presented as Fast Internet Computer Consensus (FICC). It is described as the first rotating-leader state machine replication protocol that can confirm transactions in one round-trip time in the Byzantine fault-tolerant setting (Vonlanthen et al., 2023). The protocol extends ICC with a dual-mode mechanism: a fast path based on fast shares and a slow path inherited from ICC, with thresholds

$1.6\ \mathrm{km\,s^{-1}}$8

and fast-path finalization when a block gathers at least

$1.6\ \mathrm{km\,s^{-1}}$9

fast shares (Vonlanthen et al., 2023). In a globally distributed 16-replica evaluation, average proposal finalization time was 845 ms for ICC, 705 ms for FICC with $\Sigma$0, and 638 ms for FICC with $\Sigma$1; the paper reports latency reductions of up to 30% without additional security assumptions (Vonlanthen et al., 2023). The stated tradeoff is that performance depends on the choice of $\Sigma$2 and on network topology, especially the presence of eccentric replicas (Vonlanthen et al., 2023).

6. Banyan in graph systems, continual RL, and structured NLP

In graph systems, Banyan is a graph query service engine built around scoped dataflow, a model in which a subquery is represented as a scope with ingress and egress vertices and can be dynamically replicated into independent scope instances (Su et al., 2022). This exposes concurrency and control at subquery granularity, enabling independent cancellation, subquery-specific scheduling, and performance isolation. The engine focuses on scaling up performance on a single machine while remaining able to scale out, and the evaluation reports improvements of up to three orders of magnitude over state-of-the-art graph query engines on some workloads, together with performance isolation and load balancing (Su et al., 2022).

In continual reinforcement learning, Banyan is a procedurally generated, GPU-accelerated benchmark in which each task is a triple

$\Sigma$3

where $\Sigma$4 is the grid layout, $\Sigma$5 is the task-tree topology, and $\Sigma$6 is the object assignment (Seth et al., 30 May 2026). Its design isolates three independently controllable axes of task diversity: layouts, object assignments, and hierarchical subgoal topology. The benchmark defines the forward transfer gap

$\Sigma$7

and shows that increasing diversity along any axis drives local transfer at shift boundaries, with $\Sigma$8 approaching $\Sigma$9, but does not by itself yield sustained continual learning across many shifts (Seth et al., 30 May 2026). In the 10-shift setting, intermediate diversity around $XYZ$0 raises endpoint performance from about 0.74 at $XYZ$1 to about 0.95 at $XYZ$2, whereas high diversity around $XYZ$3 produces a plateau near 0.80 across the sequence (Seth et al., 30 May 2026).

In NLP, Banyan is a representation-learning model that uses explicit hierarchical structure rather than transformer self-attention as its primary inductive bias. Its two stated innovations are entangled hierarchical trees, which share repeated constituents across contexts, and diagonalized message passing, which replaces dense composition/decomposition maps with elementwise gated mixing (Opper et al., 2024). The model is reported to have only 14 non-embedding parameters, compared with 1072 for Self-StrAE, and to achieve average sentence-level and lexical scores of 62.70 and 49.61, versus 46.59 and 40.34 for Self-StrAE in the cited low-resource regime (Opper et al., 2024). On SemEval-2024 Task 1 / SemRel, it is reported to outperform XLM-R on Afrikaans, Amharic, and Hindi, while trailing on Spanish (Opper et al., 2024).

Across these literatures, “Banyan” does not denote a single unified theory. It instead names a set of technically specific systems whose commonality is nominal rather than conceptual: an astronomical Bayesian membership engine, a switching topology, and several modern computational systems for consensus, graph processing, continual learning, and structured representation learning.