FTSCommDetector: Structure-Aware Detection Family

• FTSCommDetector is a family of structure-aware detectors that embed domain-specific constraints into inference pipelines, enabling effective behavioral community detection and FTN signaling recovery.
• It leverages innovative architectures like Temporal Coherence Architecture (TCA) with dual-scale encoding, static topology, and dynamic attention to capture transient synchronization patterns.
• The design spans CNN-driven and optimization-based FTN signaling detectors, offering clear trade-offs in performance, complexity, and adaptability across applications.

FTSCommDetector denotes distinct detector architectures in the supplied arXiv literature rather than a single universally fixed method. In one explicit title-level usage, it is a system for discovering behavioral communities in continuous multivariate time series through a Temporal Coherence Architecture (TCA) that combines dual-scale encoding, static topology, dynamic attention, and Normalized Temporal Profiles (NTP) for evaluation (Luo et al., 17 Sep 2025). In parallel, the same label is used in the supplied descriptions for several faster-than-Nyquist (FTN) signaling receivers, including a domain-aware fixed-kernel CNN, semidefinite-relaxation and ADMM-based sequence estimators, probabilistic data association, frequency-domain equalization with colored-noise whitening, and a delay-Doppler-domain reduced-complexity detector for OTFS-FTN signaling (Tokluoglu et al., 21 Jul 2025, Bedeer et al., 2018, Ibrahim et al., 2021, Kulhandjian et al., 2019, Ishihara et al., 2016, Hong et al., 17 Jan 2026). This suggests that the term functions as a domain-dependent label attached to structurally informed detection pipelines.

1. Terminological scope

A common source of confusion is whether FTSCommDetector names one architecture or a broader detector family. In the supplied literature, both usages occur. The clearest title-level instantiation is "FTSCommDetector: Discovering Behavioral Communities through Temporal Synchronization" (Luo et al., 17 Sep 2025). However, the supplied descriptions also use the same label for FTN signaling detectors with substantially different mathematical formulations, objective functions, and computational trade-offs, ranging from CNN-based local-window detection to SDP, ADMM, PDA, and sparse LMMSE equalization (Tokluoglu et al., 21 Jul 2025, Bedeer et al., 2018, Ibrahim et al., 2021, Kulhandjian et al., 2019, Ishihara et al., 2016, Hong et al., 17 Jan 2026).

Domain	Representative formulation	Distinguishing mechanism
Continuous multivariate time series	Temporal Coherence Architecture	Dual-scale encoding, static topology, dynamic attention, NTP
FTN signaling in AWGN	Fixed-kernel CNN	Domain-informed masking of ISI taps
FTN signaling via optimization	SDR, ADMM, PDA	Relaxation, projection, Gaussian separability
OTFS-FTN over doubly selective fading	Reduced-complexity LMMSE	Delay-Doppler estimation, sparse ISI approximation
Iterative coded FTNS	SoD FDE with whitening	Colored-noise-aware MMSE turbo loop

The shared conceptual thread is explicit structural bias. In the financial setting, that structure is temporal synchronization and desynchronization across entities. In the communications setting, it is ISI, colored noise, sparse coupling, or constellation geometry. A plausible implication is that the label is attached not to a single model class, but to detectors that encode domain constraints directly into the inference pipeline.

2. Temporal synchronization and behavioral communities

In its explicit financial-market formulation, FTSCommDetector addresses community discovery in continuous multivariate time series. The observed process is

$$\mathcal{X}=\{X_t\}_{t=1}^{T_{\rm total}},\qquad X_t\in\mathbb{R}^{N\times D},$$

with overlapping windows

$$\mathcal{W}_i=\{X_t:t=(i-1)\Delta+1,\dots,(i-1)\Delta+T\}.$$

For each window, the task is to partition the $N$ entities into $K$ behavioral communities whose members move synchronously during critical periods but may desynchronize otherwise. The method is motivated by the limitation of traditional “per-timestamp” or snapshot clustering, which treats each $t$ as independent and can therefore miss synchronization-desynchronization patterns in which two assets have low correlation most of the time yet align sharply during market shocks (Luo et al., 17 Sep 2025).

The model formalizes temporal coherence through three building blocks. First, dual-scale encoding separates short-term and long-term temporal structure:

$$Z_{\rm short}=\mathrm{ShortTermEncoder}(X)\in\mathbb{R}^{N\times d_\ell\times T_s},\qquad Z_{\rm long}=\mathrm{LongTermEncoder}(X)\in\mathbb{R}^{N\times d_g\times T_\ell}.$$

Second, static topology is constructed from within-window Pearson correlations,

$$C_{ij}=\mathrm{Corr}(X_i,X_j),\qquad A_{ij}^{\rm base}=\mathbf{1}[C_{ij}\ge\tau],\qquad \tau=0.75,$$

with an optional sector bonus

$$A_{ij}=A_{ij}^{\rm base}+\delta\,\mathbf{1}[\text{sector}_i=\text{sector}_j].$$

Third, dynamic attention is layered over this fixed adjacency so that neighborhoods remain topologically stable while their influence becomes time-conditioned. This separation between static topology and dynamic attention is intended to stabilize community assignments while preserving evolving relationships (Luo et al., 17 Sep 2025).

The problem setting is therefore not conventional correlation clustering. It is a windowed, temporally coherent partitioning problem in which transient synchronization is first-class structure. The GameStop case study described in the supplied details reinforces this point: during January–June 2021, the method splits SP100 into 6 behavioral clusters that cut across GICS sectors, indicating that sector labels and behavioral communities need not coincide (Luo et al., 17 Sep 2025).

3. Temporal Coherence Architecture

TCA uses a dual-scale encoder with asymmetric receptive fields. The ShortTermEncoder consists of two stacked 1D-convolutions with kernel size $k_\ell=5$, stride $s_\ell=3$, and channel- and time-attention, while the LongTermEncoder uses one 1D-convolution with $$\mathcal{W}_i=\{X_t:t=(i-1)\Delta+1,\dots,(i-1)\Delta+T\}.$$0, $$\mathcal{W}_i=\{X_t:t=(i-1)\Delta+1,\dots,(i-1)\Delta+T\}.$$1 plus identical dual-attention. The short- and long-horizon paths are then fused with graph embeddings obtained from a BiLSTM-based temporal module and time-conditioned attention over the static neighborhood graph (Luo et al., 17 Sep 2025).

The dynamic dependency module is defined on

$$\mathcal{W}_i=\{X_t:t=(i-1)\Delta+1,\dots,(i-1)\Delta+T\}.$$2

through

$$\mathcal{W}_i=\{X_t:t=(i-1)\Delta+1,\dots,(i-1)\Delta+T\}.$$3

followed by

$$\mathcal{W}_i=\{X_t:t=(i-1)\Delta+1,\dots,(i-1)\Delta+T\}.$$4

Time-conditioned queries, keys, and values are produced as

$$\mathcal{W}_i=\{X_t:t=(i-1)\Delta+1,\dots,(i-1)\Delta+T\}.$$5

$$\mathcal{W}_i=\{X_t:t=(i-1)\Delta+1,\dots,(i-1)\Delta+T\}.$$6

with attention restricted to the static neighborhood $$\mathcal{W}_i=\{X_t:t=(i-1)\Delta+1,\dots,(i-1)\Delta+T\}.$$7:

$$\mathcal{W}_i=\{X_t:t=(i-1)\Delta+1,\dots,(i-1)\Delta+T\}.$$8

The final representation concatenates graph, short-scale, and long-scale features,

$$\mathcal{W}_i=\{X_t:t=(i-1)\Delta+1,\dots,(i-1)\Delta+T\}.$$9

and applies gated fusion:

$N$0

Inference then runs spectral clustering on $N$1, or applies k-means in embedding space (Luo et al., 17 Sep 2025).

The information-theoretic argument supplied for TCA is that scale separation maximizes complementary information. The decomposition

$N$2

is combined with the claim that when $N$3, the receptive-field frequency bands overlap by less than $N$4, making the redundancy term negligible. Appendix Theorem 1 is summarized as showing that for any intermediate scale $N$5,

$N$6

where $N$7 is the true community label. Within the supplied exposition, this is the formal basis for preferring the short/long pair over a single intermediate scale (Luo et al., 17 Sep 2025).

4. Evaluation through Normalized Temporal Profiles

FTSCommDetector evaluates communities with NTP, defined for each entity $N$8 as

$N$9

Because scaling $K$0 leaves $K$1 unchanged, the metric is scale-invariant. Pairwise similarity is then

$K$2

with cluster-quality metrics

$K$3

and

$K$4

The reported datasets are SP100, SP500, SP1000, and Nikkei 225, each with 5 years of daily data and $K$5 features. Baselines are DAEGC, GUCD, VGAER, SDCN, CCGC, DGCLUSTER, and APDCG, each augmented with the dual-scale temporal encoder to isolate graph-learning differences (Luo et al., 17 Sep 2025).

Dataset	IntraCorr result	InterDissim result
SP100	$K$6 vs next best 0.487 (+3.5%)	1.016 vs 0.993 (+2.3%)
SP500	0.490 vs 0.457 (+7.2%)	0.926 vs 0.871 (+6.3%)
SP1000	0.462 vs 0.416 (+11.1%)	0.892 vs 0.827 (+7.8%)
Nikkei 225	0.496 vs 0.463 (+7.1%)	0.938 vs 0.894 (+4.9%)

The ablations are equally central to understanding the method. Dynamic attention modes improve IntraCorr from 0.468 to 0.504, and multi-stream fusion increases IntraCorr from 0.327 for single-stream graph only to 0.504 for the three-stream configuration. Window-size robustness is reported as only $K$7 variation in both metrics for $K$8. The supplied practical interpretation is that stable 89-day windows imply fewer rebalances and lower transaction costs, while retaining sensitivity to emergent crises. Another recurring misconception addressed by these results is that community discovery should reproduce sector taxonomies; the supplied examples instead emphasize cross-sector behavioral groupings such as airlines plus hospitality during travel-related shocks, or technology splitting into growth, defensive, and memecoin-driven groups (Luo et al., 17 Sep 2025).

5. FTN signaling detectors using the same label

In the communications literature supplied here, FTSCommDetector is used for several FTN receivers that share a common physical model: symbols are transmitted at interval $K$9 with $t$0, causing deliberate ISI after matched filtering and sampling. One representative model is

$t$1

with sampled observation

$t$2

or blockwise $t$3 with a banded Toeplitz ISI matrix (Tokluoglu et al., 21 Jul 2025). A more general PSK formulation writes the matched-filtered and whitened model as

$t$4

leading to MLSE

$t$5

which is non-convex and NP-hard (Bedeer et al., 2018).

The domain-aware CNN variant in "A Novel Domain-Aware CNN Architecture for Faster-than-Nyquist Signaling Detection" uses fixed-position kernels rather than conventional sliding kernels. For layer $t$6, the mask

$t$7

activates only the center tap and the $t$8-distance ISI taps, and the layer computes

$t$9

This yields $$Z_{\rm short}=\mathrm{ShortTermEncoder}(X)\in\mathbb{R}^{N\times d_\ell\times T_s},\qquad Z_{\rm long}=\mathrm{LongTermEncoder}(X)\in\mathbb{R}^{N\times d_g\times T_\ell}.$$0 fixed-kernel layers, with earlier layers assigned more filters through a hierarchical allocation such as $$Z_{\rm short}=\mathrm{ShortTermEncoder}(X)\in\mathbb{R}^{N\times d_\ell\times T_s},\qquad Z_{\rm long}=\mathrm{LongTermEncoder}(X)\in\mathbb{R}^{N\times d_g\times T_\ell}.$$1 for $$Z_{\rm short}=\mathrm{ShortTermEncoder}(X)\in\mathbb{R}^{N\times d_\ell\times T_s},\qquad Z_{\rm long}=\mathrm{LongTermEncoder}(X)\in\mathbb{R}^{N\times d_g\times T_\ell}.$$2 ($$Z_{\rm short}=\mathrm{ShortTermEncoder}(X)\in\mathbb{R}^{N\times d_\ell\times T_s},\qquad Z_{\rm long}=\mathrm{LongTermEncoder}(X)\in\mathbb{R}^{N\times d_g\times T_\ell}.$$3), $$Z_{\rm short}=\mathrm{ShortTermEncoder}(X)\in\mathbb{R}^{N\times d_\ell\times T_s},\qquad Z_{\rm long}=\mathrm{LongTermEncoder}(X)\in\mathbb{R}^{N\times d_g\times T_\ell}.$$4 for $$Z_{\rm short}=\mathrm{ShortTermEncoder}(X)\in\mathbb{R}^{N\times d_\ell\times T_s},\qquad Z_{\rm long}=\mathrm{LongTermEncoder}(X)\in\mathbb{R}^{N\times d_g\times T_\ell}.$$5 ($$Z_{\rm short}=\mathrm{ShortTermEncoder}(X)\in\mathbb{R}^{N\times d_\ell\times T_s},\qquad Z_{\rm long}=\mathrm{LongTermEncoder}(X)\in\mathbb{R}^{N\times d_g\times T_\ell}.$$6), and $$Z_{\rm short}=\mathrm{ShortTermEncoder}(X)\in\mathbb{R}^{N\times d_\ell\times T_s},\qquad Z_{\rm long}=\mathrm{LongTermEncoder}(X)\in\mathbb{R}^{N\times d_g\times T_\ell}.$$7 for $$Z_{\rm short}=\mathrm{ShortTermEncoder}(X)\in\mathbb{R}^{N\times d_\ell\times T_s},\qquad Z_{\rm long}=\mathrm{LongTermEncoder}(X)\in\mathbb{R}^{N\times d_g\times T_\ell}.$$8 ($$Z_{\rm short}=\mathrm{ShortTermEncoder}(X)\in\mathbb{R}^{N\times d_\ell\times T_s},\qquad Z_{\rm long}=\mathrm{LongTermEncoder}(X)\in\mathbb{R}^{N\times d_g\times T_\ell}.$$9). The network is shallow, uses no skip or residual connections, and has a dense integration layer of 4 neurons plus ReLU, followed by a 1-neuron decision layer for BPSK; QPSK uses two parallel identical CNN pipelines. Reported performance is near-optimal BER for $$C_{ij}=\mathrm{Corr}(X_i,X_j),\qquad A_{ij}^{\rm base}=\mathbf{1}[C_{ij}\ge\tau],\qquad \tau=0.75,$$0, with a gap of $$C_{ij}=\mathrm{Corr}(X_i,X_j),\qquad A_{ij}^{\rm base}=\mathbf{1}[C_{ij}\ge\tau],\qquad \tau=0.75,$$1 at $$C_{ij}=\mathrm{Corr}(X_i,X_j),\qquad A_{ij}^{\rm base}=\mathbf{1}[C_{ij}\ge\tau],\qquad \tau=0.75,$$2 and $$C_{ij}=\mathrm{Corr}(X_i,X_j),\qquad A_{ij}^{\rm base}=\mathbf{1}[C_{ij}\ge\tau],\qquad \tau=0.75,$$3, plus LUT-weighted complexity reductions of 46% for BPSK and 84% for QPSK relative to M-BCJR (Tokluoglu et al., 21 Jul 2025).

Optimization-based instantiations include SDR, ADMM, and PDA. The SDR detector relaxes the lifted constraint $$C_{ij}=\mathrm{Corr}(X_i,X_j),\qquad A_{ij}^{\rm base}=\mathbf{1}[C_{ij}\ge\tau],\qquad \tau=0.75,$$4 into the block-PSD condition

$$C_{ij}=\mathrm{Corr}(X_i,X_j),\qquad A_{ij}^{\rm base}=\mathbf{1}[C_{ij}\ge\tau],\qquad \tau=0.75,$$5

replacing the discrete PSK constraint with $$C_{ij}=\mathrm{Corr}(X_i,X_j),\qquad A_{ij}^{\rm base}=\mathbf{1}[C_{ij}\ge\tau],\qquad \tau=0.75,$$6, and solves the resulting SDP in polynomial time, with total complexity $$C_{ij}=\mathrm{Corr}(X_i,X_j),\qquad A_{ij}^{\rm base}=\mathbf{1}[C_{ij}\ge\tau],\qquad \tau=0.75,$$7 after Gaussian randomization (Bedeer et al., 2018). The ADMMSE variant for QAM introduces an auxiliary copy $$C_{ij}=\mathrm{Corr}(X_i,X_j),\qquad A_{ij}^{\rm base}=\mathbf{1}[C_{ij}\ge\tau],\qquad \tau=0.75,$$8 and alternates a quadratic update,

$$C_{ij}=\mathrm{Corr}(X_i,X_j),\qquad A_{ij}^{\rm base}=\mathbf{1}[C_{ij}\ge\tau],\qquad \tau=0.75,$$9

a projection

$$A_{ij}=A_{ij}^{\rm base}+\delta\,\mathbf{1}[\text{sector}_i=\text{sector}_j].$$0

and a dual update

$$A_{ij}=A_{ij}^{\rm base}+\delta\,\mathbf{1}[\text{sector}_i=\text{sector}_j].$$1

Its stated advantage is polynomial complexity in block length with only logarithmic sensitivity to modulation order, enabling experiments up to 65,536-QAM (Ibrahim et al., 2021). The PDA formulation instead treats residual interference as approximately Gaussian, computes

$$A_{ij}=A_{ij}^{\rm base}+\delta\,\mathbf{1}[\text{sector}_i=\text{sector}_j].$$2

and iteratively updates symbol posteriors, approaching SDRSE within $$A_{ij}=A_{ij}^{\rm base}+\delta\,\mathbf{1}[\text{sector}_i=\text{sector}_j].$$3 at SE = 0.96 bits/sec/Hz and within $$A_{ij}=A_{ij}^{\rm base}+\delta\,\mathbf{1}[\text{sector}_i=\text{sector}_j].$$4 at SE = 1.10 bits/sec/Hz for $$A_{ij}=A_{ij}^{\rm base}+\delta\,\mathbf{1}[\text{sector}_i=\text{sector}_j].$$5 (Kulhandjian et al., 2019).

Two further receivers extend the same structural philosophy. The iterative coded FTNS detector of Ishihara and Sugiura whitens matched-filter colored noise using

$$A_{ij}=A_{ij}^{\rm base}+\delta\,\mathbf{1}[\text{sector}_i=\text{sector}_j].$$6

and then applies a frequency-domain MMSE equalizer with

$$A_{ij}=A_{ij}^{\rm base}+\delta\,\mathbf{1}[\text{sector}_i=\text{sector}_j].$$7

inside a URC/RSC turbo loop, yielding near-capacity performance with practical decoding complexity (Ishihara et al., 2016). In doubly selective fading, the OTFS-FTN receiver derives a delay-Doppler-domain input-output relation, performs FTN-pilot-based channel estimation with noise whitening, and uses a sparse-ISI approximation so that the reduced-complexity LMMSE equalizer

$$A_{ij}=A_{ij}^{\rm base}+\delta\,\mathbf{1}[\text{sector}_i=\text{sector}_j].$$8

can be implemented by LU factorization of a banded matrix, reducing complexity from $$A_{ij}=A_{ij}^{\rm base}+\delta\,\mathbf{1}[\text{sector}_i=\text{sector}_j].$$9 to $k_\ell=5$0 and reporting typical reductions of more than $k_\ell=5$1 for $k_\ell=5$2, $k_\ell=5$3 (Hong et al., 17 Jan 2026).

6. Comparative interpretation, limitations, and significance

Across these instantiations, FTSCommDetector is characterized less by one canonical algorithm than by a consistent modeling stance: explicit incorporation of domain structure into the detector itself. In TCA, the structure is scale separation, static topology, and time-conditioned attention. In FTN receivers, it is known ISI geometry, colored-noise covariance, Toeplitz or circulant structure, constellation constraints, or sparsity in the delay-Doppler domain. This suggests that the central design principle is not generic deep representation learning or generic convex optimization, but the embedding of problem-specific inductive bias into the inference stage (Luo et al., 17 Sep 2025, Tokluoglu et al., 21 Jul 2025, Hong et al., 17 Jan 2026).

The limitations are equally domain-specific. The fixed-kernel CNN requires a separate model per $k_\ell=5$4, is limited to AWGN channels in its current form, and has no explicit provision for time-varying noise coloring other than static matched-filtering (Tokluoglu et al., 21 Jul 2025). The ADMMSE detector is not guaranteed to find the global optimum for nonconvex $k_\ell=5$5, even though it converges to high-quality solutions in practice (Ibrahim et al., 2021). The SDR receiver accepts a performance gap of about $k_\ell=5$6 at BER $k_\ell=5$7 relative to M-BCJR in exchange for polynomial complexity (Bedeer et al., 2018). PDA remains polynomial but has dominant inversion cost $k_\ell=5$8 in its dense form (Kulhandjian et al., 2019). The OTFS-FTN LMMSE detector relies on sparse and circulant approximations whose error decreases with increasing $k_\ell=5$9, larger CP length $s_\ell=3$0, and lower SNR (Hong et al., 17 Jan 2026). On the financial side, the empirical evaluation is concentrated on four equity markets, albeit with robustness across window sizes and reported practical relevance to portfolio construction and risk management (Luo et al., 17 Sep 2025).

A final misconception is that performance should be judged only by pointwise accuracy or BER. In the time-series formulation, the evaluation is explicitly scale-invariant and community-oriented through NTP, IntraCorr, and InterDissim. In the FTN setting, the dominant criteria are BER, spectral efficiency, and computational reduction relative to BCJR, M-BCJR, Go-Back-K, GASDRSE, or full-complexity LMMSE. The supplied literature therefore treats FTSCommDetector as a family of structure-aware detectors whose objectives, metrics, and algorithmic realizations are inseparable from the domain in which they are deployed (Luo et al., 17 Sep 2025, Bedeer et al., 2018, Ishihara et al., 2016).