SourcesMapper: Hidden RTN Source Inference

• SourcesMapper is a module that infers hidden RTN sources by decomposing a Bayesian feature model into binary state contributions.
• It applies affinity propagation clustering on normalized amplitude differences and transition statistics to generate candidate source sets.
• The framework evaluates candidates with a custom cost function balancing level-matching fidelity and transition accuracy to reconstruct latent source activity.

Searching arXiv for SourcesMapper and closely related Mapper papers to ground the article in current literature.
SourcesMapper is the second of the two main modules in RTNinja, a generalized, fully automated machine learning framework for the unsupervised analysis of random telegraph noise (RTN) signals in nanoelectronic devices. Within that pipeline, SourcesMapper does not operate on the raw noisy trace directly; it takes the discrete feature model produced by LevelsExtractor and infers the hidden individual RTN sources that can explain the observed level structure and level-to-level transitions. Its declared outputs are the inferred number of hidden sources, the selected source amplitudes, an inferred baseline, the corresponding (2^N) source-state configuration amplitudes, a mapping between observed Bayesian levels and latent source configurations, and reconstructed source-by-source binary activity patterns over time [2507.08424].

1. Architectural position and function

RTNinja is organized as a two-stage system. LevelsExtractor first converts a measured time series into an “optimal feature model”: a finite set of discrete Bayesian levels, each with mean (\mu), together with a quantized sequence of level assignments and the observed transitions between those levels. SourcesMapper then treats that feature model as an inverse problem in latent source decomposition: which independent two-state RTN sources, when superposed, could have generated the extracted levels and their empirical transition structure? [2507.08424]

Component	Input	Output
LevelsExtractor	Measured RTN time series	Bayesian levels, quantized level sequence, observed transitions
SourcesMapper	Feature model from LevelsExtractor	Hidden source count, amplitudes, baseline, latent configurations, source activity traces

This separation is methodologically important. LevelsExtractor solves a denoising and discretization problem; SourcesMapper solves a source-separation and latent-configuration inference problem. The latter is therefore the stage that turns a multilevel RTN waveform into a physically interpretable description in terms of hidden defects or defect chains, each modeled as a binary on/off fluctuator [2507.08424].

2. Input representation and latent-source assumptions

SourcesMapper consumes three concrete objects from LevelsExtractor: the extracted Bayesian levels with means (\mu_i), the reconstructed or quantized signal as a sequence of level assignments, and the empirical transitions between levels induced by that quantized sequence. From these, it computes two derived feature families. The first is the set of candidate source amplitudes, obtained from pairwise differences between distinct Bayesian levels. The second is a Markov transition matrix (P_T) estimated from the quantized sequence, with entries (P_T(i \to j)) describing transition probabilities between levels [2507.08424].

The module rests on a small set of explicit structural assumptions. Each individual RTN source is treated as a two-state entity with an on-state and an off-state. Different sources are assumed independent. The quantized data are modeled as a Markov process, which the paper describes as valid for independent RTN signals. A further dynamic constraint is that transitions between latent configurations should involve only the switching of a single source; simultaneous switching of multiple sources is counted as a violation during reconstruction. The model also allows finite observations to miss some of the theoretically possible latent configurations: if (N) hidden sources exist, up to (2^N) source-state configurations may exist, but not all need appear in the observed record [2507.08424].

A natural formalization consistent with the described configuration-generation step is an additive superposition model in which a latent configuration (s=(s_1,\dots,s_N)\in{0,1}^N) produces an amplitude
[
x(s)=b+\sum_{n=1}^{N}s_n\Delta_n,
]
where (b) is the baseline and (\Delta_n) is the amplitude of source (n). The paper does not present this equation explicitly, but its candidate-generation, baseline-fitting, and configuration-enumeration procedures are described in exactly these additive terms. Under this model, the minimum feasible source count for (L) observed levels is
[
N_{\min}=\left\lceil \log_2 L \right\rceil,
]
since an (N)-source system can generate at most (2^N) latent configurations [2507.08424].

3. Inference workflow

The first computational step in SourcesMapper is to construct the joint feature space the paper calls the (P_T-\Delta) space. Each point in that space couples a candidate amplitude difference (\Delta_{ij}=|\mu_i-\mu_j|) with an empirical transition statistic derived from the Markov transition matrix. The rationale is that transitions caused by the same hidden source should recur at characteristic amplitude differences and with related transition activity, so they may form identifiable grouped structures in this derived space [2507.08424].

Those (P_T-\Delta) features are normalized and then clustered by affinity propagation. Affinity propagation is used because it does not require the number of clusters to be specified in advance. The cluster exemplars define a reduced ensemble of representative amplitudes, denoted (\Delta_R) in the technical reconstruction. Supplementary Figure 1, as summarized in the source material, further states that clustering is repeated under a range of affinity-propagation hyperparameter settings, and the resulting slight variations in cluster representatives are aggregated into an ensemble of one-dimensional amplitude estimates to reduce sensitivity to the clustering hyperparameters [2507.08424].

For a fixed hypothesized source count (N), candidate (N)-source sets are then generated combinatorially from that representative amplitude ensemble. Each candidate source set induces a full family of (2^N) latent source-state configurations. Because the absolute baseline is unknown, each candidate is evaluated over a range of baseline values. For each baseline, the candidate configuration amplitudes are projected onto the empirical Bayesian-level distribution, and a log-likelihood is computed from the corresponding intersectional density values. The baseline maximizing that log-likelihood is selected for the candidate under consideration [2507.08424].

The paper’s worked example makes this pipeline concrete. With (11) observed Bayesian levels, SourcesMapper initializes at (N=4) because (2^4=16). Affinity propagation on the normalized (P_T-\Delta) space yields (13) clusters, and the resulting representative amplitudes generate about (700) candidate (4)-source sets. Each candidate is baseline-optimized, mapped to the observed levels, and carried into the reconstruction stage [2507.08424].

4. Model selection, cost function, and accepted solution

Candidate evaluation combines a static fidelity criterion with a dynamic transition criterion. The first term is a goodness-of-match metric. Bayesian levels are mapped to their closest latent source-state configurations, and a CDF-based proximity score is used so that an exact match receives score (1) and larger mismatches push the score toward (0). The second term is a reconstruction-accuracy metric defined on the quantized sequence. During latent reconstruction, transitions that would require simultaneous switching of multiple sources are treated as violations of the independence-based single-source-switch rule [2507.08424].

These two terms are normalized and combined with equal weight into a custom cost function whose ideal value is (0) and whose maximum is (2). The paper states two explicit tolerances: up to (2\%) of total transitions are allowed as violations, and mismatches of up to one standard deviation are tolerated in the level-matching component. The optimal candidate is the one with minimum total cost. If no candidate for the current source count yields a cost below (2), SourcesMapper increments (N) and repeats the search at higher latent complexity [2507.08424].

In the illustrative four-source example, the optimal candidate attains a cost of (1.249) and reconstructs the trace with (5) violations out of (1086) transitions. Once the optimal candidate is accepted, the latent configuration sequence directly induces a source-by-source binary activity decomposition, from which amplitudes and activity patterns can be estimated for each inferred source [2507.08424].

The accepted output is therefore not merely a set of amplitudes. It is a joint latent explanation consisting of the inferred source count (N), the optimal source amplitude set, the optimal baseline, the associated (2^N) configuration amplitudes, a mapping between observed Bayesian levels and latent configurations, the reconstructed latent-configuration sequence, and the corresponding individual source on/off traces [2507.08424].

5. Validation, empirical behavior, and known failure modes

RTNinja, including SourcesMapper, is evaluated with a Monte Carlo simulator that generates labeled RTN datasets across multiple source counts and signal-to-noise regimes. The benchmark comprises (1400) base datasets, specifically (200) datasets for each true source count (N=1,\dots,7), and each base dataset is perturbed with five Gaussian noise levels of (1\%), (5\%), (10\%), (20\%), and (30\%), for a total of (7000) datasets. Because the simulation exposes the true source count, amplitudes, and binary source activity traces, it supports direct evaluation of source-count recovery, amplitude estimation, and activity-pattern reconstruction [2507.08424].

The reported behavior is structured rather than uniformly optimistic. Source-count accuracy degrades with increasing noise, mainly because low-amplitude sources are increasingly missed. Activity recovery remains strong but declines with both source complexity and noise level. Amplitude estimation is described as comparatively robust once a source is successfully detected. The detected-source yield declines from (73.8\%) at (1\%) noise to (72.8\%) at (5\%), (64.9\%) at (10\%), (53.3\%) at (20\%), and (44.9\%) at (30\%) [2507.08424].

The paper also gives a bounded but nontrivial scalability claim: RTNinja can deconvolve “up to seven or more individual sources (subject to SNR resolution).” That qualifier is important. The main computational bottleneck remains the combinatorial evaluation of candidate source sets in SourcesMapper, and several failure modes are identified explicitly. Low-amplitude sources under high noise can be lost. In low-noise, high-complexity settings, LevelsExtractor can overestimate the number of observable levels; because SourcesMapper initializes (N) from the observed level count, that can enlarge the combinatorial search enough to cause non-convergence. Additional difficulties arise when amplitudes overlap, when few transitions are observed for some sources, when sources are correlated rather than independent, or when amplitudes and switching statistics drift over time [2507.08424].

These limitations show that SourcesMapper is neither a generic blind source separator nor a fully Bayesian latent-state estimator over arbitrary RTN phenomenology. It is a specialized inference engine tuned to additive, independent, binary-source RTN decomposition, with failure modes that follow directly from violations of those assumptions or from unfavorable signal-to-noise geometry [2507.08424].

6. Terminological and methodological context

The name “SourcesMapper” sits alongside an established but separate literature on the Mapper algorithm in topological data analysis. In that literature, Mapper is defined as the nerve of a clustered pullback cover, often written in the trivial-clustering case as
[
MT(\mathcal{U},f)=\mathrm{Nrv}(f^{-1}(\mathcal{U})),
]
and is used as a topological summary of high-dimensional data [2408.11180]. Subsequent work has emphasized that the full nerve contains higher-dimensional information beyond the usual graph view, for example through the (2)-skeleton
[
M(f,\mathcal{U})=N^2(f^*(\mathcal{U})),
]
in “2-Mapper” [2509.22816], and has proposed adaptive or density-guided cover constructions such as D-Mapper and lens-density-varying covers [2401.12237; 2410.03862]. Another line of work studies how univariate Mappers can be stitched into bivariate Mapper constructions and how “topological gains” can be quantified when a new filter is added [2105.01961].

SourcesMapper occupies a different problem setting. It is not presented as a nerve construction on pullback covers, but as a latent source-inference stage in RTN signal analysis. The shared term “Mapper” therefore reflects a broader naming overlap rather than a shared formal pipeline. A plausible implication is that the term evokes structure recovery from indirect observations in both contexts, but in RTNinja the recovered structure is a hidden configuration of independent two-state fluctuators, not a topological summary of a point cloud or simplicial complex [2507.08424].

Within nanoelectronic reliability analysis, this distinction matters because the practical role of SourcesMapper is not visualization but defect inference. By converting multilevel RTN traces into inferred source counts, source amplitudes, and source-specific activity histories, it supports large-scale statistical benchmarking, reliability-centric technology qualification, predictive failure modeling, and device-physics exploration in next-generation nanoelectronics [2507.08424].