Paper deep dive
WST-Graph: Topology-Preserving Wavelet Scattering Front-End for Speech Deepfake Detection
Kwok-Ho Ng, Tingting Song, Bingwen Feng, Zhihua Xia
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 91%
Last extracted: 9/25/2026, 5:22:23 AM
Summary
The paper introduces WST-Graph, a speech deepfake detection system that utilizes a Wavelet Scattering Transform (WST) front-end to preserve the topological parent-child relations between modulation and carrier paths. By reconstructing these paths into a sparse grid and applying length-aware adaptive local attention pooling (ALAP), the model generates fixed relative-time representations. This approach is paired with an AASIST graph backend, resulting in a model that uses approximately 60% fewer trainable parameters than AASIST while achieving competitive or superior performance on out-of-domain benchmarks.
Entities (7)
Relation Signals (6)
WST-Graph → trainedon → ASVspoof 2019 LA
confidence 95% · Models are trained on ASVspoof 2019 LA (ASV19)
WST-Graph → uses → Wavelet Scattering Transform
confidence 95% · We introduce WST-Graph, reconstructing these paths as a sparse modulation-carrier grid... This yields a waveform-to-graph interface with a fixed, parameter-free WST.
WST-Graph → uses → AASIST
confidence 92% · reconstructing these paths as a sparse modulation-carrier grid for an AASIST graph backend.
WST-Graph → evaluatedon → Speech-DF-Arena
confidence 90% · Cross-dataset generalization is benchmarked via Speech DF Arena
WST-Graph → uses → ALAP
confidence 90% · length-aware adaptive local attention pooling (ALAP) segments each valid temporal trajectory
WST-Graph → outperforms → AASIST
confidence 85% · Our configurations remain competitive with AASIST while using approximately 60% fewer trainable parameters and show clear gains on selected out-of-domain benchmarks.
Cypher Suggestions (0)
No Cypher suggestions yet.
Abstract
Abstract:The acoustic front-end determines which forensic cues a speech deepfake detector can exploit. The wavelet scattering transform (WST) provides stable multiscale coefficients with explicit coordinates, yet direct flattening obscures the parent relation between paths. We introduce WST-Graph, reconstructing these paths as a sparse modulation-carrier grid for an AASIST graph backend. Modulation-level normalization and length-aware adaptive local attention pooling produce fixed relative-time representations while retaining the acoustic axes before learned adaptation. This yields a waveform-to-graph interface with a fixed, parameter-free WST. Our configurations remain competitive with AASIST while using approximately 60% fewer trainable parameters and show clear gains on selected out-of-domain benchmarks. These results underscore the value of preserving parent-child relations within the carrier-modulation topology when constructing a compact, physically grounded interface for graph-based speech deepfake detection. Code will be released at this https URL.
Tags
Links
- Source: https://arxiv.org/abs/2609.29372v1
- Canonical: https://arxiv.org/abs/2609.29372v1
Trouble viewing inline? Open PDF directly →
Full Text
31,091 characters extracted from source content.
Expand or collapse full text
WST-Graph: Topology-Preserving Wavelet Scattering Front-End for Speech Deepfake Detection Kwok-Ho Ng Tingting Song Bingwen Feng Zhihua Xia Abstract The acoustic front-end determines which forensic cues a speech deepfake detector can exploit. The wavelet scattering transform (WST) provides stable multiscale coefficients with explicit coordinates, yet direct flattening obscures the parent relation between paths. We introduce WST-Graph, reconstructing these paths as a sparse modulation-carrier grid for an AASIST graph backend. Modulation-level normalization and length-aware adaptive local attention pooling produce fixed relative-time representations while retaining the acoustic axes before learned adaptation. This yields a waveform-to-graph interface with a fixed, parameter-free WST. Our configurations remain competitive with AASIST while using approximately 60% fewer trainable parameters and show clear gains on selected out-of-domain benchmarks. These results underscore the value of preserving parent-child relations within the carrier–modulation topology when constructing a compact, physically grounded interface for graph-based speech deepfake detection. Code will be released at GitHub. Index Terms: Wavelet scattering transform, Speech deepfake detection, Audio anti-spoofing. †address: College of Cyber Security, Jinan University, Guangzhou, China 1 Introduction Recent speech synthesis and voice conversion systems generate increasingly natural speech [20, 6, 16], raising risks of impersonation, fraud, and disinformation [8] and motivating evaluation campaigns such as ASVspoof [10, 18, 15]. Speech deepfake detectors (SSD) can also degrade substantially under unseen generators and recording conditions [9]. Some recent state-of-the-art systems employ self-supervised learning (SSL) front-ends to improve detection performance, but do so at the cost of substantially larger parameter counts [14]. Moreover, analyzing synthetic artifacts from SSL hidden states is challenging because they lack explicit acoustic coordinates. Conventional anti-spoofing methods use inspectable magnitude, cepstral, and phase-derived features, including linear frequency cepstral coefficients (LFCC), constant Q cepstral coefficients (CQCC), and modified group delay [19, 12]. Raw waveform-based systems avoid prescribing a fixed hand-crafted spectrum. For example, the end-to-end system RawNet2 jointly learned its waveform encoder with the classifier [13]. The AASIST applied a parameterized SincNet [11] and a residual convolutional encoder before constructing spectral and temporal graphs [5]. Its Sinc filters retain interpretable passbands, but the subsequent 2-D pooling and residual convolutions mix neighboring frequency-time responses and progressively reduce temporal resolution before graph construction. The resulting channels no longer carry explicit carrier or modulation-frequency coordinates. This motivates a front-end that delays feature fusion across distinct spatiotemporal pathways, thereby preserving explicit acoustic axes for graph processing and coordinate-aligned analysis. To address this, the wavelet scattering transform (WST) presents a promising candidate [7, 2]. It cascades multiresolution wavelet filterbanks, complex modulus operators, and low-pass averaging filters to produce stable, locally translation-invariant multiscale coefficients. Specifically, first-order coefficients capture the averaged wavelet-modulus responses within carrier bands, while second-order coefficients characterize the temporal modulations of the corresponding first-order envelopes [2, 1]. Crucially, because every second-order path remains explicitly linked to its parent carrier band, the WST inherently preserves a structured carrier-modulation organization before any learned channel mixing. Recently, WST-X integrated scattering features with SSL representations [17]. Specifically, its 1-D variant (WST-X1) globally pools 1-D scattering coefficients, whereas its 2-D variant (WST-X2) spatially flattens a 2-D scattering tensor computed from SSL feature maps. In contrast, we retain the internal topology of 1-D scattering to serve as an explicit, structured interface for graph-based backends. To this end, we propose the WST-Graph front-end. First, utilizing the parent relation inherent in WST metadata, we group second-order paths by modulation band and align them according to their parent carrier bands. This constructs a sparse joint modulation-carrier grid without prematurely averaging away valid second-order coefficients. Within this grid, first-order coefficients occupy a dedicated channel, and a fixed binary mask identifies structurally absent path combinations. Second, modulation-level normalization standardizes paths sharing the same modulation band. Within this stage, length-aware channel-wise adaptive local attention pooling (ALAP) segments each valid temporal trajectory into a fixed number of relative-time intervals, pooling every channel-carrier pair independently within each interval. A pointwise adapter then introduces the initial cross-order and cross-modulation fusion exclusively at the same carrier-time coordinate. Following this, three depthwise-separable residual blocks model local carrier-time contexts while preserving the latent grid dimensions, ensuring compatibility with AASIST-style graph backends. We deploy the spectro-temporal graph architecture of AASIST as a concrete backend to model global interactions between the carrier and relative-time nodes. Third, we conduct a three-seed empirical study of the scattering scale and first-order filterbank resolution, together with a controlled comparison of second-order modulation-filter resolution. 2 Proposed Methods Figure 1: Overview of the proposed WST-Graph pipeline. GraphAASIST follows the graph backbone of the original AASIST architecture. 2.1 Scattering Paths and Path Normalization Let xb(t)x_b(t) denote the b-th waveform. The first two orders of a one-dimensional WST are Sb(1)(λ1,t)=(|xb∗ψλ1|∗ϕJ)(t)S_b^(1)( _1,t)=(|x_b* _ _1|* _J)(t) and Sb(2)(λ1,λ2,t)=(||xb∗ψλ1|∗ψλ2|∗ϕJ)(t)S_b^(2)( _1, _2,t)=(||x_b* _ _1|* _ _2|* _J)(t), obtained by cascading complex Morlet convolutions, modulus nonlinearities, and low-pass averaging. Here, λi _i indexes the wavelet applied at layer i. Kymatio [3] provides its discrete index nin_i, scale jij_i, and normalized center-frequency coordinate ξi _i. Thus, a first-order path carries (n1,j1,ξ1)(n_1,j_1, _1), while a second-order key (n1,n2)(n_1,n_2) maps to (ξ1,ξ2)( _1, _2), where ξ1 _1 identifies the parent carrier and ξ2 _2 its envelope-modulation frequency. We discard the zeroth-order low-pass component and stack all admissible first- and second-order coefficients along Kymatio’s path axis. This gives a flat-path tensor ∈ℝB×P×TS ^B× P× T, where P=P1+P2P=P_1+P_2, and P1P_1 and P2P_2 denote the numbers of retained first- and second-order paths, respectively. Before OrderGrid recovers the carrier–modulation topology described above, PathNorm maps the non-negative scattering amplitudes to the log domain to compress their dynamic range, Xb,p,t=log(Sb,p,t+ϵ).X_b,p,t= (S_b,p,t+ε ). (1) Let Lb≤TL_b≤ T be the effective number of valid WST frames for the b-th training utterance, excluding temporal padding. For a designated statistics aggregation group g, we define its valid support domain Ωg=(b,p,t):g(p)=g, 0≤t<Lb _g=\(b,p,t):g(p)=g,\ 0≤ t<L_b\ and the corresponding sample count Ng=|Ωg|N_g=| _g|. PathNorm estimates the group-specific mean and standard deviation, respectively: μg _g =1Ng∑(b,p,t)∈ΩgXb,p,t, = 1N_g _(b,p,t)∈ _gX_b,p,t, (2) σg _g =max(1Ng∑(b,p,t)∈ΩgXb,p,t 2−μg2,0). = ( 1N_g _(b,p,t)∈ _gX_b,p,t^\,2- _g^2,0 ). (3) The normalized scattering paths are subsequently obtained by: Zb,p,t=Xb,p,t−μg(p)max(σg(p),σmin)+ϵ,Z_b,p,t= X_b,p,t- _g(p) ( _g(p), _ )+ε, (4) where σmin _ enforces a strict lower bound on the scaling factor. We consider three distinct group assignment policies: log_path(gpath(p)=p),log_order(gorder(p)=o(p)),log\_path(g_path(p)=p),\ log\_order(g_order(p)=o(p)), (5) and log_modulationlog\_modulation, defined as: gmod(p)=0,o(p)=1,grp(n2(p)),o(p)=2.g_mod(p)= cases0,&o(p)=1,\\ grp(n_2(p)),&o(p)=2. cases (6) The log_modulationlog\_modulation policy groups first-order paths together and second-order paths by n2n_2, standardizing each group while preserving its carrier-dependent variation. We also evaluate two baselines: log_onlylog\_only, which bypasses standardization (=Z=X), and nonenone, which further omits the log transform (=Z=S). Crucially, the effective length LbL_b isolates padded frames exclusively during training statistics estimation; a subsequent temporal mask prevents them from contaminating the ALAP operation. Because structurally absent cells are introduced only during grid mapping (OrderGrid), a topology mask is omitted at this stage, and every policy strictly preserves the B×P×TB× P× T tensor shape. 2.2 Topology Recovery via OrderGrid The joint second-order scattering transform is not a full Cartesian product of all first- and second-order wavelets. For the temporal scattering implementation considered here, the Kymatio retains an ordered scattering path if and only if the dyadic scales satisfy j1(n1)<j2(n2)j_1(n_1)<j_2(n_2). Consequently, the admissible path set =(n1,n2):j1(n1)<j2(n2)A=\(n_1,n_2):j_1(n_1)<j_2(n_2)\ is inherently sparse. For every retained path, Kymatio metadata supplies its scattering order, discrete filter keys, dyadic scale, and center-frequency coordinate. To robustly reconstruct the topology, OrderGrid aligns paths using these discrete keys. Let f∈1,…,F1f∈\1,…,F_1\ index the first-order keys n1(f)n_1(f) sorted by increasing center frequency ξ1 _1, and let m∈1,…,F2m∈\1,…,F_2\ index the unique second-order keys n2(m)n_2(m) sorted by increasing ξ2 _2. Let π1(f) _1(f) and the partial map π2(m,f) _2(m,f) retrieve the corresponding indices on the flat path axis 1,…,P1\1,…,P_1\, with π2(m,f) _2(m,f) defined only when (n1(f),n2(m))∈(n_1(f),n_2(m)) . The normalized scattering paths are subsequently embedded into a structured joint modulation-carrier tensor ∈ℝB×(1+F2)×F1×TG ^B×(1+F_2)× F_1× T. The grid assignment is defined by Gb,0,f,t=Zb,π1(f),t,G_b,0,f,t=Z_b, _1(f),t, and for the second-order paths: Gb,m,f,t=Zb,π2(m,f),t,if(n1(f),n2(m))∈,0,otherwise, 1≤m≤F2.G_b,m,f,t= casesZ_b, _2(m,f),t,&if(n_1(f),n_2(m)) ,\\ 0,&otherwise, cases\ 1≤ m≤ F_2. (7) By framing the tensor construction this way, the first-order representation of shape B×F1×TB× F_1× T is concatenated along the channel dimension as channel 0, while channels 1≤m≤F21≤ m≤ F_2 contain the available normalized second-order paths for each modulation band ξ2,m _2,m. This tensor expansion yields a total shape B×(1+F2)×F1×TB×(1+F_2)× F_1× T, ensuring that no valid scattering coefficient is averaged or discarded prematurely. To preserve this underlying structural sparsity, we maintain a fixed structural binary mask ∈0,1(1+F2)×F1M∈\0,1\^(1+F_2)× F_1, where M0,f=1M_0,f=1 and Mm,f=[(n1(f),n2(m))∈]M_m,f= 1 [(n_1(f),n_2(m)) ] for m≥1m≥ 1. Thus, Mm,f=0M_m,f=0 denotes a structural vacancy dictated by the scattering topology rather than a measured zero amplitude response. OrderGrid initializes these cells to zero, and the downstream ALAP leverages M to exclude them from pooling calculations. This fixed structural mask operates independently of the utterance-dependent valid temporal duration LbL_b. 2.3 Length-aware Channel-wise Temporal Pooling All waveforms are padded or cropped to N samples, while NbN_b records the valid sample count. We obtain LbL_b by counting WST frame centers that precede NbN_b. The valid prefix interval [0,Lb)[0,L_b) is dynamically partitioned into K relative-time intervals: Ib,k=[⌊kLbK⌋,⌊(k+1)LbK⌋), 0≤k<K.I_b,k= [ kL_bK , (k+1)L_bK ),\ 0≤ k<K. (8) To aggregate temporal features without destroying structural axes, we propose a channel-wise ALAP layer. A 1×kt1× k_t depthwise temporal convolution sweeps the frame axis to generate logits qb,c,f,tq_b,c,f,t. Crucially, this scorer operates independently across channels c∈0,…,F2c∈\0,…,F_2\ and is shared across carriers f∈1,…,F1f∈\1,…,F_1\, avoiding premature feature mixing. For any valid cell where Mc,f=1M_c,f=1, the pooled representation Yb,c,f,kY_b,c,f,k is computed via localized softmax-normalized weights: αb,c,f,k,t _b,c,f,k,t =exp(qb,c,f,t/τ)∑u∈Ib,kexp(qb,c,f,u/τ),t∈Ib,k, = (q_b,c,f,t/τ) _u∈ I_b,k (q_b,c,f,u/τ),\ t∈ I_b,k, (9) Yb,c,f,k Y_b,c,f,k =∑t∈Ib,kαb,c,f,k,tGb,c,f,t, = _t∈ I_b,k _b,c,f,k,tG_b,c,f,t, (10) where τ is a fixed temperature scaling factor. Cells in structurally absent regions (Mc,f=0M_c,f=0) remain strictly zero-initialized and are excluded from pooling. This operation contracts the variable temporal dimension to a fixed grid size K, yielding ∈ℝB×(1+F2)×F1×KY ^B×(1+F_2)× F_1× K. 2.4 Channel Adaptation and Graph Classification A pointwise channel Adapter performs the first learned mixing across the 1+F21+F_2 scattering channels at each carrier–time coordinate (f,k)(f,k), applying ad∈ℝC×(1+F2)W_ad ^C×(1+F_2) to map them to C latent dimensions via b,:,f,k=SELU(BN(adb,:,f,k))H_b,:,f,k=SELU (BN (W_adY_b,:,f,k ) ), yielding ∈ℝB×C×F1×KH ^B× C× F_1× K. A subsequent latent block is repeated N times (see Fig. 1) under two spatial convolution configurations: latent-D employs a depthwise spatial convolution, while latent-G utilizes a grouped spatial convolution. Both variants append a full 1×11× 1 projection, strictly preserve the dimensions B×C×F1×KB× C× F_1× K, and support ordered D/G compositions. GraphAASIST forms spectral nodes by reducing the K axis and temporal nodes by reducing the F1F_1 axis b,fS=b,:,f,kk=1KU^S_b,f=\H_b,:,f,k\_k=1^K, and b,kT=b,:,f,kf=1F1U^T_b,k=\H_b,:,f,k\_f=1^F_1. For either sequence =ii=1RU=\u_i\_i=1^R, define =maxi|i|A= _i|u_i|, =1R∑iM= 1R _iu_i, p=(1R∑imax(|i|,ϵ)p)1/pG_p= ( 1R _i (|u_i|,ε)^p )^1/p, =Stdi(i)D=Std_i(u_i), α=∑iαiiM_α= _i _iu_i, α=Stdα(i)D_α=Std_α(u_i), where α=softmax(e)α=softmax(e). Let Π(,)=[∥] (a,b)=W[a\|b], where [⋅∥⋅][·\|·] combines two C-dimensional statistics along the feature axis and ∈ℝC×2CW ^C× 2C. We compare max()max(A), max_mean(Π(,))max\_mean( (A,M)), gem_mean(Π(p,))gem\_mean( (G_p,M)), mean_std(Π(,))mean\_std( (M,D)), atten(Π(α,α))atten( (M_α,D_α)), max_atten(Π(,α))max\_atten( (A,M_α)). These operators are applied independently to SU^S and TU^T. Asym-A uses (Π(p,),Π(,))( (G_p,M), (A,M)) for the spectral and temporal branches, respectively; Asym-B reverses them. This gives S∈ℝB×F1×CV^S ^B× F_1× C and T∈ℝB×K×CV^T ^B× K× C. Attentive pooling uses relative ALAP-bin positions for SU^S and normalized log-frequency positions for TU^T; a separate log2ξ1 _2 _1 embedding is added to SV^S. The nodes enter the homo and hetero graph attention stages of AASIST. Finally, a linear classifier outputs logits. 3 Experiments and Results 3.1 Implementation Details Datasets and Metrics. Models are trained on ASVspoof 2019 LA (ASV19), resampled to 16 kHz. Training and development utterances use random 4s crops (64,000 samples) with short files right-padded with zeros; evaluation windows start at the absolute onset. Cross-dataset generalization is benchmarked via Speech DF Arena [4], including 14 distinct sets (13 out-of-domain (OOD)). We report the equal error rate (EER [%] ↓ ) following standard ASVspoof protocols. Model and Training Setup. The WST front-end uses J=8J=8, Q=(Q1,Q2)=(8,1)Q=(Q_1,Q_2)=(8,1), maximum order 2, and oversampling 1. We set ALAP K=64K=64 (kt=5k_t=5), adapter width C=64C=64, and GraphAASIST uses dimensions (64, 32) with max node construction. All networks are optimized for 12 epochs across three seeds using focal loss (γ=2γ=2, weights [0.9,0.1][0.9,0.1]) and AdamW (learning rate 10−310^-3 with cosine decay) under FP32/BF16 mixed precision. 3.2 Temporal Reduction and Local Context Initial Configuration. We establish a baseline front-end utilizing a fixed WST, OrderGrid, a pointwise adapter, and the default AbsMax GraphAASIST backend, omitting the latent blocks and fixing PathNorm to log_onlylog\_only in Eq. (1). Table 1: Uniform bin averaging versus ALAP at different temporal resolutions. Results are reported as three-seed average EER (%) with the best result in brackets. Bold indicates best results. Setting Param K=32K=32 K=48K=48 K=64K=64 Uniform 86,024 21.81 (18.48) 19.25 (16.17) 22.12 (18.49) ALAP 86,073 21.46 (19.91) 22.05 (19.38) 19.14 (14.91) Both ALAP and its parameter-free baseline must downsample the valid duration of each channel-carrier trajectory into a fixed number of relative-time bins K. The baseline replaces ALAP’s learned attention weights with a uniform average, defined as Yb,c,f,kavg=1|Ib,k|∑t∈Ib,kGb,c,f,tY^avg_b,c,f,k= 1|I_b,k| _t∈ I_b,kG_b,c,f,t. We hypothesize that uniform averaging dilutes localized spoofing artifacts, whereas ALAP’s channel-wise attention preserves them with negligible parameter overhead. We evaluate K∈32,48,64K∈\32,48,64\ in Table 1. ALAP introduces only 49 parameters. While uniform averaging peaks at K=48K=48 (19.25% average, 16.17% best EER), ALAP demonstrates its advantage at K=64K=64 by delivering a lower average EER of 19.14% and an overall best EER of 14.91%. Consequently, we provisionally retain ALAP with K=64K=64. Table 2: Results are reported in EER (%), with configurations M1 (DG), M2 (GD), M3 (DDG), and M4 (DGG). N Param Type D Param Type G Mixed 1 91k 8.38 (6.15) 95k 8.21 (8.10) M1: 6.74 (5.68) 2 96k 6.52 (5.77) 104k 6.80 (6.32) M2: 5.92 (4.22) 3 100k 4.98 (4.80) 113k 7.03 (5.88) M3: 5.46 (5.01) 4 105k 5.74 (4.77) 122k 6.82 (5.64) M4: 6.32 (4.88) Based on this choice, we investigate whether the local carrier-time context should be modeled using depthwise (D), grouped (G), or mixed residual blocks across different block counts N. As shown in Table 2, the D family performs optimally at N=3N=3 (D3), achieving the lowest average EER of 4.98%4.98\% with 100k parameters. Increasing the depth to N=4N=4 or introducing grouped interactions leads to performance degradation. Consequently, D3 is retained for the following task. 3.3 Normalization and Graph-Node Construction With ALAP and D3 fixed, we evaluate five normalization configurations based on Eq. (4): no processing (nonenone), log compression alone (log_onlylog\_only), and fitted path-, order-, and modulation-level normalization. Table 3: Rows and columns specify the groupings for mean centering and standard-deviation scaling, respectively, with diagonal entries corresponding to log_pathlog\_path, log_orderlog\_order, and log_modulationlog\_modulation. Results are reported as “Avg. (best)”. Bold indicates the lowest EER. Mean \ Std. path order modulation path 4.16 (3.76) 4.72 (3.31) 4.04 (3.42) order 5.17 (4.48) 4.26 (3.69) 3.96 (3.68) modulation 4.20 (4.01) 4.59 (4.16) 3.80 (3.33) As shown in Table 3, modulation-level scaling consistently yields the lowest average EER across all centering strategies. Notably, nonenone yields a lower average EER than the reused log_onlylog\_only baseline (4.72%4.72\% vs. 4.98%4.98\%), proving that log compression alone is insufficient without proper alignment. Crucially, applying modulation-level statistics to both centering and scaling achieves the lowest overall average EER of 3.80%3.80\%, leading us to fix the log_modulationlog\_modulation policy. Table 4: Results are reported in average EER (%), with columns evaluating alternative graph-node pooling operators. Node max max+mean gem+mean mean+std EER (%) 3.80 (3.33) 3.86 (3.49) 3.53 (3.00) 3.83 (3.31) atten max+atten Asym-A Asym-B EER (%) 3.25 (3.06) 3.38 (2.54) 3.57 (2.64) 3.58 (3.26) Using modulation-level normalization, we evaluate different pooling strategies to compress the latent grid into graph nodes. As shown in Table 4, attentive statistics achieves the lowest average EER of 3.25%3.25\%, compared to 3.87%3.87\% for the baseline absmax. While this improvement introduces 19k additional parameters, it provides a favorable capacity-accuracy trade-off. Accordingly, attentive statistics are retained. 3.4 Model Capacity and Scattering Resolution With all structural modules fixed, we evaluate the remaining capacity and resolution hyperparameters. Table 5: Hyperparameter optimization results across varying grid capacities and acoustic resolutions. Results are reported in EER (%). C \ K Param K=32K=32 K=48K=48 K=64K=64 32 83,195 4.51 (4.20) 3.81 (3.57) 3.39 (3.23) 48 99,739 4.28 (3.86) 3.61 (3.20) 3.47 (3.35) 64 119,867 4.47 (3.96) 3.97 (3.34) 3.25 (3.06) J \ Q1Q_1 Param Q1=6Q_1=6 Q1=8Q_1=8 Q1=10Q_1=10 6 119,725 7.06 (5.88) 7.51 (6.71) 6.95 (6.45) 8 119,867 3.29 (2.92) 3.25 (3.06) 4.07 (2.97) 10 120,009 5.81 (5.22) 6.53 (6.30) 6.59 (6.14) First, varying the relative-time interval count K and graph feature width C reveals that increasing K is more consistently beneficial than expanding C. The lowest EER is achieved at K=C=64K=C=64, while K=64,C=32K=64,C=32 serves as a lighter competitive configuration (3.39%3.39\% EER, 83k parameters). Fixing K=C=64K=C=64, we then investigate the acoustic geometry by varying the averaging scale J and first-order filterbank resolution Q1Q_1. Finally, comparing second-order resolutions shows that increasing from Q2=1Q_2=1 to Q2=2Q_2=2 expands the number of modulation bands from 6 to 13, further reducing the EER from 3.25%3.25\% to 2.93%2.93\%. Since this adjustment alters modulation coverage, the improvement cannot be attributed to the minor parameter increment alone. 3.5 Baseline Comparison and OOD Evaluation Table 6 compares WST-Graph against reproduced AASIST and AASIST-L baselines under a unified protocol. WST-Graph-Q82 achieves 2.92%2.92\% EER on ASVspoof2019 LA using 120k parameters, representing a 59.6%59.6\% reduction compared to AASIST. Table 6: Out-of-domain evaluation of reproduced AASIST baselines and our proposed configurations, reporting single-seed results. System AASIST AASIST-L Graph-Q81 Graph-Q82 Param 297k 85k 119k 120k ITW 45.41 43.07 46.07 44.46 ASV19LA 2.74 3.45 3.07 2.92 ASV21LA 14.82 15.48 13.92 8.53 ASV21DF 19.96 21.25 21.00 18.15 ASV5T1 37.94 34.07 33.84 35.55 FoR 27.51 10.46 34.84 30.34 Codecfake 48.46 49.11 47.13 49.26 ADD22T1 47.81 47.51 49.30 44.68 ADD22T3.2 38.91 31.56 31.48 31.69 ADD23T1.2R1 52.01 49.80 44.63 47.85 ADD23T1.2R2 43.31 37.55 34.38 39.52 DFADD 45.69 38.82 15.23 21.56 LibriSeVoc 38.11 41.06 38.14 33.58 Sonar 43.06 45.28 35.78 39.53 Across the 13 OOD datasets, WST-Graph-Q81 yields the lowest EER among all four systems on seven evaluation sets. WST-Graph demonstrates its most pronounced advantage on DFADD; across the remaining domains, it remains generally competitive without consistently large margins. 4 Conclusion We introduced WST-Graph, a topology-preserving scattering front-end for graph-based SDD. Our sequential study demonstrates that performance is sensitive to temporal granularity, local-context extent, the semantic level used to calibrate WST paths, graph-node statistics, and modulation resolution. These findings highlight how representation geometry and information aggregation jointly shape detection. Future work will exploit the preserved, physically interpretable carrier-modulation coordinates for decision attribution and deepfake source tracing. 5 COMPLIANCE WITH ETHICAL STANDARDS This study uses publicly available datasets and does not involve new data collection from human participants. No ethical approval was required. 6 ACKNOWLEDGMENT The authors have no relevant conflicts of interest to disclose. We use AI for coding assistance and polishing writing. References [1] J. Andén, V. Lostanlen, and S. Mallat (2015) Joint time-frequency scattering for audio classification. In 2015 IEEE 25th International Workshop on Machine Learning for Signal Processing (MLSP), p. 1–6. Cited by: §1. [2] J. Andén and S. Mallat (2014) Deep scattering spectrum. IEEE Transactions on Signal Processing 62 (16), p. 4114–4128. Cited by: §1. [3] M. Andreux, T. Angles, G. Exarchakis, R. Leonarduzzi, G. Rochette, L. Thiry, J. Zarka, S. Mallat, J. Andén, E. Belilovsky, et al. (2020) Kymatio: scattering transforms in python. Journal of Machine Learning Research 21 (60), p. 1–6. Cited by: §2.1. [4] S. Dowerah, A. Kulkarni, A. Kulkarni, H. M. Tran, J. Kalda, A. Fedorchenko, B. Fauve, D. Lolive, T. Alumäe, and M. Magimai.-Doss (2026) Speech df arena: a leaderboard for speech deepfake detection models. IEEE Open Journal of Signal Processing (), p. 1–9. External Links: Document Cited by: §3.1. [5] J. Jung, H. Heo, H. Tak, H. Shim, J. S. Chung, B. Lee, H. Yu, and N. Evans (2022) Aasist: audio anti-spoofing using integrated spectro-temporal graph attention networks. In ICASSP 2022-2022 IEEE international conference on acoustics, speech and signal processing (ICASSP), p. 6367–6371. Cited by: §1. [6] S. Lian, C. Li, B. Li, H. Wang, D. Zheng, J. Tian, Y. Ma, C. Zhang, and K. Yu (2026) Dots. tts technical report. arXiv preprint arXiv:2606.07080. Cited by: §1. [7] S. Mallat (2012) Group invariant scattering. Communications on Pure and Applied Mathematics 65 (10), p. 1331–1398. Cited by: §1. [8] M. Masood, M. Nawaz, K. M. Malik, A. Javed, A. Irtaza, and H. Malik (2023) Deepfakes generation and detection: state-of-the-art, open challenges, countermeasures, and way forward: deepfakes generation and detection: state-of-the-art, open challenges, countermeasures, and way forward. Applied intelligence 53 (4), p. 3974–4026. Cited by: §1. [9] N. Müller, P. Czempin, F. Diekmann, A. Froghyar, and K. Böttinger (2022) Does Audio Deepfake Detection Generalize?. In Interspeech 2022, p. 2783–2787. External Links: Document, ISSN 2958-1796 Cited by: §1. [10] A. Nautsch, X. Wang, N. Evans, T. H. Kinnunen, V. Vestman, M. Todisco, H. Delgado, M. Sahidullah, J. Yamagishi, and K. A. Lee (2021) ASVspoof 2019: spoofing countermeasures for the detection of synthesized, converted and replayed speech. IEEE Transactions on Biometrics, Behavior, and Identity Science 3 (2), p. 252–265. Cited by: §1. [11] M. Ravanelli and Y. Bengio (2018) Speaker recognition from raw waveform with sincnet. In 2018 IEEE spoken language technology workshop (SLT), p. 1021–1028. Cited by: §1. [12] G. Tahaoglu, D. Baracchi, D. Shullani, M. Iuliani, and A. Piva (2025) Deepfake audio detection with spectral features and resnext-based architecture. Knowledge-Based Systems 323, p. 113726. Cited by: §1. [13] H. Tak, J. Patino, M. Todisco, A. Nautsch, N. Evans, and A. Larcher (2021) End-to-end anti-spoofing with rawnet2. In ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), p. 6369–6373. Cited by: §1. [14] H. Tak, M. Todisco, X. Wang, J. Jung, J. Yamagishi, and N. Evans (2022) Automatic Speaker Verification Spoofing and Deepfake Detection Using Wav2vec 2.0 and Data Augmentation. In The Speaker and Language Recognition Workshop (Odyssey 2022), p. 112–119. External Links: Document Cited by: §1. [15] X. Wang, H. Delgado, H. Tak, J. Jung, H. Shim, M. Todisco, I. Kukanov, X. Liu, M. Sahidullah, T. H. Kinnunen, N. Evans, K. A. Lee, and J. Yamagishi (2024) ASVspoof 5: crowdsourced speech data, deepfakes, and adversarial attacks at scale. In The Automatic Speaker Verification Spoofing Countermeasures Workshop (ASVspoof 2024), p. 1–8. External Links: Document Cited by: §1. [16] B. Xiang, C. Wen, H. Zhao, H. Wang, H. Wang, J. Jin, J. Cui, J. Chen, M. Nie, T. Zhao, et al. (2026) Qwen-audio-3.0-tts: freely controllable and highly robust speech synthesis with multi-stage training paradigm. arXiv preprint arXiv:2607.23938. Cited by: §1. [17] X. Xuan, D. Carbone, W. Zhang, R. Pandey, and T. H. Kinnunen (2026) Wst-x series: wavelet scattering transform for interpretable speech deepfake detection. arXiv preprint arXiv:2602.02980. Cited by: §1. [18] J. Yamagishi, X. Wang, M. Todisco, M. Sahidullah, J. Patino, A. Nautsch, X. Liu, K. A. Lee, T. Kinnunen, N. Evans, and H. Delgado (2021) ASVspoof 2021: accelerating progress in spoofed and deepfake speech detection. In 2021 Edition of the Automatic Speaker Verification and Spoofing Countermeasures Challenge, p. 47–54. External Links: Document Cited by: §1. [19] J. Yi, C. Wang, J. Tao, X. Zhang, C. Y. Zhang, and Y. Zhao (2023) Audio deepfake detection: a survey. arXiv preprint arXiv:2308.14970. Cited by: §1. [20] B. Zhang, C. Guo, G. Yang, H. Yu, H. Zhang, H. Lei, J. Mai, J. Yan, K. Yang, M. Yang, et al. (2025) Minimax-speech: intrinsic zero-shot text-to-speech with a learnable speaker encoder. arXiv preprint arXiv:2505.07916. Cited by: §1.