---
title: 'GM-SAGE: Graph-based Multi-bounce SAGE Algorithm'
url: https://www.emergentmind.com/topics/graph-theory-based-dictionary-aided-multi-bounce-sage-gm-sage
type: topic
---

# GM-SAGE: Graph-based Multi-bounce SAGE Algorithm

Searching arXiv for the specified GM-SAGE and related SAGE papers to ground the article with current records.
Graph Theory-based Dictionary-aided Multi-bounce SAGE (GM-SAGE) is a graph-constrained adaptation of the space-alternating generalized expectation-maximization (SAGE) algorithm for estimating and localizing multi-bounce propagation in near-field sensing and environment reconstruction. In the reported formulation, graph theory is used to model multi-bounce propagation of the near field, indoor reflectors and scatterers are represented as vertices in a propagation graph, and multi-bounce paths are represented by edges linking these vertices [2509.13071]. GM-SAGE is “dictionary-aided” because it builds candidate channel atoms from graph-consistent scatterer coordinates and path sequences rather than from decoupled range and angle parameters, and it is “multi-bounce” because one-bounce, two-bounce, and higher-bounce components are explicitly separated and alternately updated within a SAGE procedure [2509.13071]. A later extension applies the same framework to environment reconstruction under array partial blockage and spatial non-stationary (SNS) channels in extremely-large antenna arrays (ELAA), where the algorithm estimates a sparse spatial amplitude field together with graph-consistent path geometry [2509.13559]. Although the acronym “GM-SAGE” is also naturally suggested as a graph-theoretic, dictionary-aided, multi-bounce interpretation of the graph-memory retrieval architecture in SAGE for language agents, that usage is an external interpretation rather than the name introduced in the graph-memory paper [2605.12061].

## 1. Conceptual definition and research context

GM-SAGE was introduced to address indoor sensing under conditions where single-bounce approximations are insufficient. The motivating setting includes multi-bounce propagation, spherical wavefronts, and spatial nonstationarity caused by near-field effects, all of which complicate direct estimation of range, angle of departure (AoD), angle of arrival (AoA), and scatterer location [2509.13071]. The central methodological move is to replace direct search over coupled geometric parameters with a graph-based search over scatterer coordinates and feasible bounce sequences.

In the propagation-graph formulation, the graph is written as $G=(V,E)$, where vertices encode scatterers or reflectors and edges encode physically viable radio links constrained by visibility, geometry, and reflection physics [2509.13071]. Paths of bounded bounce order are then represented as walks in this graph. This permits the channel estimation problem to be reframed as a dictionary-fitting problem over graph-consistent atoms.

The term “dictionary-aided” has a precise meaning in this literature. The dictionary is parameterized by scatterer coordinates, reflectivities, velocities, and bounce order, and each dictionary atom synthesizes the full multi-element, multi-subband, multi-frame response of a candidate path under a near-field spherical-wave model [2509.13071]. This differs from conventional SAGE treatments that search directly over range and angular parameters. In the ELAA blockage extension, the graph-based dictionary additionally restricts coordinate updates to feasible multi-bounce paths while a sparse amplitude field absorbs SNS and blockage effects [2509.13559].

A separate but related use of the phrase “graph theory-based, dictionary-aided, multi-bounce” emerges in the memory-retrieval framework SAGE for language agents. That system employs a dynamic heterogeneous graph, query planning, soft addressing, and structurally gated multi-hop propagation, and thus supports a GM-SAGE-style reading at the architectural level [2605.12061]. However, the paper does not introduce GM-SAGE as its formal algorithmic name, nor does it include an explicit external dictionary module [2605.12061].

## 2. Observation model and near-field channel representation

The measurement model in “Scatterer Localization Using Multi-Bounce Paths” is specified for an $M$-Tx and $N$-Rx sensing system with $P$ non-overlapping sub-bands per frame and $Q$ frames per coherent processing interval. The baseband-equivalent measurement channel is $Z \in \mathbb{C}^{MN \times PQ}$, indexed by transmitter, receiver, sub-band, and frame [2509.13071]. The channel is expressed as a sum of $L$ multipath components:
$$
\begin{aligned}
Z_{m+(n-1)M,\, p+(q-1)P} 
 &= \sum_{l=1}^{L} \alpha_{l}\,\Delta\alpha_{m,n,l}\,F_{\text{Rx}}\!\big(f_c, \mathbf{\Omega}_{\text{Rx},n,l}\big)\,F_{\text{Tx}}\!\big(f_c, \mathbf{\Omega}_{\text{Tx},m,l}\big) \\
 &\quad\times e^{-j2\pi f_p \tau_{m,n,l}}\,e^{j2\pi f_{D,l} q T_b}\,e^{j\phi_l} \;+\; w(p,q),
\end{aligned}
$$
where $\Delta\alpha_{m,n,l}$ models SNS across array elements, $\tau_{m,n,l}$ is the element-pair delay, and the element-wise AoD/AoA orientation vectors depend on near-field geometry [2509.13071].

The spherical-wave formulation is essential because AoD and AoA become range dependent for large apertures. The element-dependent distances are written as
$$
d_{\text{Tx},m,l} \;=\; \big\| d_{\text{Tx},l} \mathbf{\Omega}_{\text{Tx},l} - (\mathbf{r}_{\text{Tx},m} - \mathbf{r}_{\text{Tx}}) \big\|,
\qquad
d_{\text{Rx},n,l} \;=\; \big\| d_{\text{Rx},l} \mathbf{\Omega}_{\text{Rx},l} - (\mathbf{r}_{\text{Rx},n} - \mathbf{r}_{\text{Rx}}) \big\|,
$$
with total delay
$$
\tau_{m,n,l} \;=\; \tau_l \;+\; \Delta \tau_{\text{Tx},m,l} \;+\; \Delta \tau_{\text{Rx},n,l}.
$$
The paper explicitly notes that this spherical-wavefront model unifies near and far field; the far-field plane-wave approximation is recovered when the reference ranges are much larger than array apertures [2509.13071].

The ELAA partial-blockage extension adopts a related but vectorized model. There, the stacked measurement vector is $y \in \mathbb{C}^{MNP\times 1}$, and the $l$-th path contribution is
$$
\mathbf{z}_l=\alpha_l\Big(\big(\boldsymbol{\gamma}_l\odot\Delta\boldsymbol{\alpha}_l\big)\otimes\mathbf{1}_P\Big)\odot\mathbf{a}_l(\boldsymbol{\tau}_l),
$$
where $\gamma_l \in \{0,1\}^{MN\times 1}$ is a binary sparsity mask indicating physical blockage per Tx-Rx pair and $\Delta\alpha_l$ models spatially varying attenuation [2509.13559]. This explicitly separates geometric delay from the spatial amplitude field, allowing blockage-induced nulls to be estimated rather than averaged away.

A plausible implication is that GM-SAGE’s relevance increases with aperture size and environmental complexity, because both multi-bounce geometry and spatially varying amplitudes become more pronounced in those regimes. That implication is consistent with the emphasis on ELAA, spherical wavefronts, and SNS in the source papers [2509.13071] [2509.13559].

## 3. Propagation graph and dictionary construction

The propagation graph is the structural core of GM-SAGE. In the indoor scatterer-localization formulation, vertices carry scatterer parameters including position $\mathbf{r}_{\text{sc},i} \in \mathbb{R}^3$, reflectivity $\sigma_i$, and possibly velocity $v_i$, while the adjacency matrix $A \in \{0,1\}^{|V|\times |V|}$ encodes physically feasible bounce transitions [2509.13071]. Paths are restricted by visibility, total length, non-penetration, reflectivity, and a maximum bounce number $K$.

A path of order $m$ is a sequence
$$(\mathrm{Tx}) \rightarrow s_{i_1} \rightarrow s_{i_2} \rightarrow \cdots \rightarrow s_{i_m} \rightarrow (\mathrm{Rx}),$$
with total geometric length
$$
\mathcal{L}_p \;=\; \big\| \mathbf{r}_{\text{Tx}} - \mathbf{r}_{\text{sc},i_1} \big\|
\;+\; \sum_{k=1}^{m-1} \big\| \mathbf{r}_{\text{sc},i_{k+1}} - \mathbf{r}_{\text{sc},i_k} \big\|
\;+\; \big\| \mathbf{r}_{\text{sc},i_m} - \mathbf{r}_{\text{Rx}} \big\|,
$$
and delay
$$
\tau_p \;=\; \frac{\mathcal{L}_p}{c}.
$$
Under near-field operation, per-hop directions and element-wise orientations are determined from the geometry of these vertices rather than from independent angle parameters [2509.13071].

The dictionary is built from these graph-constrained paths. For bounce order $k$, the dictionary $\Psi_k$ contains atoms synthesized from vertex sequences that satisfy the graph constraints [2509.13071]. The estimation objective is written as
$$
\underset{\mathbf{\sigma},\, \mathbf{v},\, \mathbf{r}_{\text{sc}}}{\arg\min}\; \left\| \mathbf{Z} \;-\; \sum_{k=1}^{K} \mathbf{\Psi}_k\big|_{\hat{\mathbf{\sigma}},\, \hat{\mathbf{v}},\, \hat{\mathbf{r}_{\text{sc}}}} \right\|.
$$
This encodes the coupled near-field relation among range, AoD, and AoA through scatterer coordinates rather than parameterizing them separately [2509.13071].

The ELAA blockage formulation presents the graph abstraction in a complementary way. There, candidate scatterer hypotheses are nodes, edges encode feasible reflection connections subject to visibility and specular constraints, and a walk $(v_0 \to v_1 \to \cdots \to v_B)$ corresponds to a candidate $B$-bounce path consistent with room geometry [2509.13559]. The associated atom is
$$
\mathbf{d}_\ell(\boldsymbol{\tau}_\ell)=
\operatorname{diag}\!\big(\mathbf{a}_\ell(\boldsymbol{\tau}_\ell)\big)\,
\big(\mathbf{1}_P\otimes\boldsymbol{e}\big),
$$
and the dictionary $D=[d_1,\ldots,d_{L_{\text{dict}}}]$ aggregates all feasible atoms [2509.13559]. Paths violating visibility, grazing-angle, or out-of-room constraints are pruned.

This graph-constrained dictionary performs two roles simultaneously. First, it injects geometric prior structure into the search. Second, it reduces the combinatorial burden of multi-bounce estimation by excluding infeasible path compositions before SAGE updates are performed [2509.13071] [2509.13559].

## 4. SAGE adaptation and estimation procedure

GM-SAGE adapts SAGE by partitioning the received signal into bounce-order-specific hidden-data groups and alternating updates across those groups. In the indoor near-field paper, one-bounce, two-bounce, and higher-bounce components are denoted $z_1$, $z_2$, and $z_3$, with associated parameter sets $\theta_1$, $\theta_2$, and $\theta_3$ [2509.13071]. The iterative formulation solves
$$
\begin{cases}
\hat{\mathbf{\theta}_1^{(i)}} \;=\; \underset{\mathbf{\theta}_1}{\arg\min}\; \big\| \hat{\mathbf{z}_1^{(i)}} \;-\; \mathbf{\psi}_1\big|_{\mathbf{\theta}_1} \big\|,\\[3pt]
\hat{\mathbf{\theta}_2^{(i)}} \;=\; \underset{\mathbf{\theta}_2}{\arg\min}\; \big\| \hat{\mathbf{z}_2^{(i)}} \;-\; \mathbf{\psi}_2\big|_{\mathbf{\theta}_2} \big\|,\\[3pt]
\hat{\mathbf{\theta}_3^{(i)}} \;=\; \underset{\mathbf{\theta}_3}{\arg\min}\; \big\| \hat{\mathbf{h}_2^{(i)}} \;-\; \mathbf{z}_3\big|_{\mathbf{\theta}_3} \big\|,
\end{cases}
$$
with residual updates
$$
\hat{\mathbf{z}_1^{(i)}} \;=\; \mathbf{z} \;-\; \hat{\mathbf{z}_2^{(i-1)}} \;-\; \hat{\mathbf{h}_2^{(i-1)}},
\qquad
\hat{\mathbf{z}_2^{(i)}} \;=\; \mathbf{z} \;-\; \hat{\mathbf{z}_1^{(i)}} \;-\; \hat{\mathbf{h}_2^{(i-1)}},
$$
$$
\hat{\mathbf{h}_2^{(i)}} \;=\; \mathbf{z} \;-\; \hat{\mathbf{z}_1^{(i)}} \;-\; \hat{\mathbf{z}_2^{(i)}}.
$$
Assuming complex Gaussian noise, the incomplete-data likelihood is quadratic in the residual norm, and the effective E-step corresponds in practice to subtracting current estimates of the other bounce groups [2509.13071].

The key algorithmic departure from standard SAGE is the M-step parameterization. Rather than optimizing over decoupled range and AoD/AoA, GM-SAGE searches over graph vertex coordinates and feasible path sequences. Candidate atoms are evaluated, for example, through a correlation score
$$
\text{score}(\text{atom}) \;=\; \frac{\big|\langle \hat{z}_k^{(i)},\, \psi_k|_{\text{atom}} \rangle\big|}{\|\psi_k|_{\text{atom}}\|},
$$
and the complex path gain for a selected atom is updated by
$$
\hat{g}_a \;=\; \frac{\langle \hat{z}_k^{(i)},\, t_a \rangle}{\|t_a\|^2}.
$$
Weak atoms are pruned by thresholding $|g_a|$, and graph constraints suppress physically implausible paths [2509.13071].

In the ELAA blockage extension, the SAGE derivation is presented explicitly in standard E-step/M-step form. The hidden path-wise data satisfy
$$
\hat{\mathbf{y}}_l^{(i)}=
\mathbf{z}_l\big(\hat{\boldsymbol{\tau}}_l^{(i-1)},\hat{\boldsymbol{s}}_l^{(i-1)}\big)+\beta_l\Big(\mathbf{y}-\sum_{k=1}^{L}\mathbf{z}_k\big(\hat{\boldsymbol{\tau}}_k^{(i-1)},\hat{\boldsymbol{s}}_k^{(i-1)}\big)\Big),
$$
and the $Q$-function decomposes as
$$
Q(\Theta\,|\,\Theta^{(i-1)})=
-\sum_{l=1}^{L}\frac{\big\|\hat{\mathbf{y}}_l^{(i)}-\mathbf{z}_l(\boldsymbol{\tau}_l,\boldsymbol{s}_l)\big\|_2^2}{\beta_l\sigma_0^2}+\text{const}.
$$
Matched filtering across sub-bands gives the sufficient statistic
$$
\tilde{s}_l^{(i)}[m,n]\triangleq
\frac{1}{P}\sum_{p=1}^{P}\hat{y}_l^{(i)}[m,n,p]\,
e^{j2\pi f_p \hat{\tau}_{m,n,l}^{(i-1)}},
$$
which is then used to update the equivalent amplitude field $\boldsymbol{s}_l$ [2509.13559].

The geometry update is performed by graph-constrained residual minimization over candidate reflection coordinates:
$$
\hat{\boldsymbol{\tau}}_l^{(i)}=\arg\min_{\{\hat{\mathbf{r}}_{l,b}\}\in\mathcal{G}}
\big\|\hat{\mathbf{y}}_l^{(i)}-
\operatorname{diag}\big(\mathbf{a}_l(\boldsymbol{\tau}_l(\{\hat{\mathbf{r}}_{l,b}\}))\big)\,
(\mathbf{1}_P\otimes\hat{\boldsymbol{s}}_l^{(i)})\big\|_2^2.
$$
The search is performed over one-bounce and two-bounce hypotheses, and bounce order is selected by minimum residual [2509.13559]. The paper states that GM-SAGE inherits SAGE’s monotone likelihood ascent under Gaussian noise, while good initialization and graph pruning improve convergence and reduce local-minimum issues [2509.13559].

## 5. Spatial non-stationarity, partial blockage, and robustness

A major extension of GM-SAGE is its explicit treatment of spatial non-stationarity and partial blockage in ELAA systems. In that setting, the per-path spatial amplitude field is
$$
s_l[m,n]=\alpha_l\,\gamma_{m,n,l}\,\Delta\alpha_{m,n,l},
\qquad
\boldsymbol{s}_l=\alpha_l\big(\boldsymbol{\gamma}_l\odot\Delta\boldsymbol{\alpha}_l\big)\in\mathbb{C}^{MN\times 1},
$$
where $\gamma_{m,n,l}=0$ indicates a blocked Tx-Rx sub-channel for the $l$-th path [2509.13559]. Stacking across sub-bands yields
$$
\mathbf{y}=\sum_{l=1}^{L}\mathbf{z}_l+\mathbf{w},
\qquad
\mathbf{z}_l=\operatorname{diag}\!\big(\mathbf{a}_l(\boldsymbol{\tau}_l)\big)\,\big(\mathbf{1}_P\otimes\boldsymbol{s}_l\big),
$$
with $\mathbf{w}\sim\mathcal{CN}(0,\sigma_0^2 I)$ [2509.13559].

The M-step amplitude update decouples across Tx-Rx pairs and admits a matched-filter estimate
$$
\hat{s}_l^{(i)}[m,n]=\frac{1}{P}\sum_{p=1}^{P}\hat{y}_l^{(i)}[m,n,p]\,
e^{j2\pi f_p \hat{\tau}_{m,n,l}^{(i-1)}}.
$$
Empirical sparsity detection then declares blockage when $|\hat{s}_l[m,n]|\le T$, setting $\gamma_{m,n,l}=0$; an optional convex alternative uses an $\ell_1$-regularized estimate of $\boldsymbol{s}_l$ [2509.13559]. The paper’s robustness rationale is that blocked entries are prevented from biasing geometry updates because the geometry search relies on the unblocked support selected through this amplitude-field estimation.

The reported blockage model is
$$
y[m,n,p]=\Gamma_l[m,n]\cdot s_l[m,n]\,
e^{-j2\pi f_p \tau_{m,n,l}}+n[m,n,p],
$$
which makes explicit that blocked entries contribute only noise [2509.13559]. This is a significant distinction from standard stationary-amplitude models. The paper states that standard SAGE degrades under ELAA blockage because it assumes stationary amplitudes across elements, whereas sparse-aware GM-SAGE with graph constraints maintains performance and mitigates model mismatch under SNS [2509.13559].

The same paper also identifies failure modes. Localization error increases when the unblocked set becomes too small or geometrically clustered; two-bounce paths remain robust but exhibit larger error under blockage than one-bounce paths; unresolved multipaths can induce apparent SNS nulls even in unblocked cases; and ambiguities such as left-to-right versus right-to-left two-bounce directionality may require beamforming, richer dictionaries, or multi-snapshot processing [2509.13559]. These limitations are framed as consequences of model mismatch, sparse support, or insufficient geometric diversity rather than defects in the SAGE procedure itself.

## 6. Validation, performance, and computational characteristics

The two GM-SAGE papers report different forms of empirical validation. “Scatterer Localization Using Multi-Bounce Paths” uses measurement-calibrated ray tracing in a complex indoor office with 7×7 Tx and Rx arrays at $f_c=30$ GHz, with multi-bounce channels generated via an open-access, measurement-calibrated ray-tracing platform and up to three bounces [2509.13071]. The reported outcome is qualitative rather than tabulated numerically: GM-SAGE estimates one-bounce scatterer coordinates aligned with true propagation tracks and avoids the ghost scatterers produced by one-bounce-only baselines [2509.13071]. The paper explicitly states that numeric error tables are not provided there.

“Environment Reconstruction in Multi-Bounce Channels with Array Partial Blockage” provides a more detailed simulation setup and selected localization errors. The room size is $6.5\times 6.5$ m$^2$, with three walls and one obstacle; the ELAA has 16 Tx and 121 Rx elements with spacing $0.5\lambda$; the carrier is $f_c=30$ GHz; bandwidth is 1 GHz; sub-bandwidth is 10 MHz; $P=101$ sub-bands; and SNR is 20 dB [2509.13559]. Grid sizes are 0.1 m for one-bounce and 0.2 m for two-bounce hypotheses, and multi-bounce paths are synthesized via the Image method [2509.13559].

Selected localization errors reported in the blocked versus unblocked cases are concise enough to summarize directly:

| Path/scenario | Blocked | Unblocked |
|---|---:|---:|
| Upper wall (one-bounce) | $\approx 0.06$ m | $\approx 0.04$ m |
| Upper$\rightarrow$right (two-bounce), first point | $\approx 0.24$ m | $\approx 0.04$ m |
| Upper$\rightarrow$right (two-bounce), second point | $\approx 0.26$ m | $\approx 0.04$ m |

The same paper states that other walls and path pairs show $\le 0.2$ m or similar performance across conditions, and that in some two-bounce configurations blocked localization is $\approx 0.2$ m higher error than unblocked [2509.13559]. It also reports that the objective function converges to similar minima in blocked and unblocked cases, which is presented as evidence of robustness [2509.13559].

Computationally, the ELAA paper gives explicit per-iteration costs. Let $\bar M=MN$ be the number of Tx-Rx pairs and let $G$ denote the number of candidates searched per path after graph pruning. Then the E-step costs $O(L\bar M P)$, the amplitude M-step costs $O(L\bar M P)$, and the geometry search costs $O(LG\bar M P)$, for overall per-iteration complexity
$$
O(L\bar M P + LG\bar M P)=O(L(G+1)\bar M P)
$$
[2509.13559]. The near-field scatterer-localization paper likewise emphasizes search-space reduction relative to naive continuous range/AoD/AoA estimation and notes that naive path enumeration up to bounce order $K$ is $O(|V|^K)$, but adjacency and visibility constraints substantially reduce the effective search [2509.13071].

A plausible implication is that GM-SAGE is most attractive when prior environmental structure is available or can be approximated well enough to build a meaningful propagation graph. Both papers rely on geometry-aware pruning and graph-constrained dictionaries to keep the estimation problem tractable [2509.13071] [2509.13559].

## 7. Relation to graph-memory SAGE and broader interpretation

The graph-memory paper “SAGE: A Self-evolving Agentic Graph-Memory Engine for Structure-Aware Associative Memory” introduces a different system from the radio-sensing GM-SAGE literature, but it is relevant because it exhibits a formally graph-theoretic, multi-hop retrieval process that can be read as supporting a GM-SAGE-style interpretation [2605.12061]. In that framework, the writer constructs a heterogeneous graph
$$
G = W_\theta(q,D) = (V_E \cup V_D, E_{EE} \cup E_{ED}),
$$
where $V_E$ are entity nodes, $V_D$ are document or memory-fragment nodes, $E_{EE}$ are entity-entity relation edges, and $E_{ED}$ are entity-document anchoring edges [2605.12061]. The reader returns entity and document distributions together with an activated subgraph or path set.

The reader performs structured query planning, soft addressing, and structurally gated propagation. The soft-addressing score includes exact entity matches, aliases $\mathcal{A}$, type signals $\tau$, hard constraints $\mathcal{C}_{\mathrm{hard}}$, and NER plus entity-linking signals:
$$
s_e(q)=
\lambda_1\,\operatorname{Exact}(e,\mathcal{E}_{\mathrm{exp}})
+\lambda_2\,\operatorname{Alias}(e,\mathcal{A})
+\lambda_3 \max_{m\le M}\cos\big(\operatorname{Emb}(\operatorname{desc}(e)),\operatorname{Emb}(\tilde q_m)\big)
+\lambda_4\,\operatorname{Type}(e,\tau)
+\lambda_5\,\operatorname{Cons}(e,\mathcal{C}_{\mathrm{hard}})
+\lambda_6\sum_{\xi\in\operatorname{NER}(q)}\operatorname{EL}(e\mid \xi)
$$
[2605.12061]. Structurally gated propagation then modulates message passing using node features such as degree, clustering coefficient, core number, and average neighbor degree, edge-pair features such as common neighbors and Jaccard overlap, and a graph-level summary [2605.12061].

This paper explicitly states that it does not introduce or rely on an external dictionary resource as a distinct module. However, it identifies “dictionary-like mechanisms” in aliases $\mathcal{A}$, answer alias sets $\mathcal{Y}(y)$, type constraints, hard constraints, entity-linking signals, and entity descriptions used in soft addressing [2605.12061]. For that reason, the graph-memory system can be described as naturally compatible with a “dictionary-aided” augmentation, but any such augmentation would be external to the paper itself [2605.12061].

The connection to GM-SAGE is therefore analogical rather than nomenclatural. In radio sensing, GM-SAGE denotes a graph-theory-based dictionary-aided multi-bounce SAGE algorithm for path and scatterer estimation [2509.13071] [2509.13559]. In graph memory, SAGE provides a heterogeneous graph, multi-hop associative retrieval from partial cues, structural role features, and a self-evolving writer-reader loop, all of which make a graph-theoretic, multi-bounce interpretation natural, but the paper does not define that system as GM-SAGE [2605.12061].

This distinction matters because the two lines of work share structural motifs—graph representations, path-based reasoning, constrained propagation, and iterative refinement—yet operate in different domains and optimize different observables. The radio GM-SAGE literature estimates physical propagation geometry and blockage-aware amplitude fields [2509.13071] [2509.13559]. The graph-memory SAGE literature optimizes evidence recovery, answer grounding, and retrieval efficiency in long-term language-agent memory [2605.12061]. The shared terminology should therefore be understood as a structural correspondence rather than as evidence of a single unified formalism.

Source: https://www.emergentmind.com/topics/graph-theory-based-dictionary-aided-multi-bounce-sage-gm-sage