Network for Acoustic Non-Stationarity Assessment (NANSA)

• NANSA is a supervised neural architecture that converts multi-scale statistical descriptors into a binary non-stationarity classification with up to 99% accuracy.
• It employs a three-module design—ANS Encoder, Pattern Extractor, and Pattern Discriminator—to enable rapid assessment of acoustic signals, delivering inference speeds up to 500x faster than traditional INS.
• The framework leverages Hard Label Criteria to generate global labels, ensuring objective, scalable evaluations for diverse applications in acoustic processing.

Searching arXiv for the NANSA paper and closely related work on acoustic non-stationarity and neural assessment. First, I’ll locate the primary NANSA paper by title and then gather adjacent papers on non-stationary acoustic modeling for context. Using arXiv search now. Network for Acoustic Non-Stationarity Assessment (NANSA) is a supervised neural architecture for binary non-stationarity classification of acoustic signals, introduced together with the Hard Label Criteria (HLC) algorithm in "Acoustic Non-Stationarity Objective Assessment with Hard Label Criteria for Supervised Learning Models" (Zucatelli et al., 8 Aug 2025). NANSA was proposed in response to a specific methodological bottleneck: objective non-stationarity measures are resource intensive and impose critical limitations for real-time processing solutions, while the traditional Index of Non-Stationarity (INS) provides scale-dependent statistics that often require human interpretation for “global” stationarity labels. Within this framework, HLC supplies global labels for supervised learning, and NANSA serves as the first-of-its-kind HLC-based Network for Acoustic Non-Stationarity Assessment, with reported performance of up to 99\% classification accuracy and inference times that remove the computational infeasibility of traditional objective measures (Zucatelli et al., 8 Aug 2025).

1. Problem formulation and motivation

Acoustic signals, such as environmental sounds or speech, are often treated as non-stationary in many audio processing domains, including ASR, CASA, and SE (Zucatelli et al., 8 Aug 2025). The difficulty addressed by NANSA is not the general presence of temporal variability, but the absence of an objective, scalable, and consistent measure of acoustic non-stationarity that can be deployed at scale or under real-time constraints.

The traditional reference point is the Index of Non-Stationarity (INS). In the reported formulation, INS has two key drawbacks. First, it has high computational cost because it requires generating multiple stationary surrogates and computationally expensive multi-scale spectral comparisons. Second, it has a lack of global labeling, since INS provides scale-dependent statistics and often requires human interpretation for a signal-level decision (Zucatelli et al., 8 Aug 2025). These limitations make INS impractical in real-time or resource-constrained settings.

This problem setting is consistent with a broader literature in non-stationary acoustics. In speech activity detection, non-stationary acoustic environments are described as difficult because the time variance of the acoustic scene makes it hard to discriminate speech from noise, especially when noise is rapidly varying and utterances are short (Heitkaemper et al., 2020). In computational bioacoustics, non-stationarity is also associated with changing class dictionaries, where new species or sound classes may appear over time and must be handled without assuming a fixed set of classes (Acconcjaioco et al., 2021). NANSA differs from those lines of work by targeting global non-stationarity assessment itself rather than downstream detection or identification.

2. Hard Label Criteria as a labeling mechanism

The Hard Label Criteria (HLC) algorithm was introduced to generate a global non-stationarity label for acoustic signals and thereby enable supervised learning strategies to be trained as stationarity estimators (Zucatelli et al., 8 Aug 2025). Its role is foundational: NANSA does not replace labeling with an unsupervised criterion, but is trained on labels produced by HLC.

HLC begins by partitioning the range of observation scales $T_h/T$ into $K$ non-overlapping regions $\mathcal{T}_k$. The summary describes these regions as, for example, short-term, mid-term, and long-term. For each region, HLC counts the number of scales where INS exceeds an adaptive threshold $\gamma_{HLC} = \alpha_{HLC}\gamma$ with $\alpha_{HLC} > 1$, described as a stricter version of the usual INS threshold $\gamma \approx 1$:

$$\mathcal{T}^{NS}_k = \left\{ T_{kn} \in \mathcal{T}_k : \text{INS}(T_{kn}) > \gamma_{HLC} \right\}$$

Regional labeling is then defined by a majority condition within each region:

$$f_{region}(\mathcal{T}_k) = \begin{cases} 1 & \text{if } |\mathcal{T}^{NS}_k| > |\mathcal{T}_k|/2 \ 0 & \text{otherwise} \end{cases}$$

Finally, a majority voting rule over the $K$ regions produces the global label:

$$f_{HLC}(\mathcal{T}_1, \dots, \mathcal{T}_K) = \begin{cases} 1 & \text{if } \sum_{k=1}^{K} f_{region}(\mathcal{T}_k) > K/2 \ 0 & \text{otherwise} \end{cases}$$

Here, “1” means non-stationary, and “0” means stationary for the whole signal (Zucatelli et al., 8 Aug 2025).

On the RSG-10 acoustic database, the HLC algorithm achieved ~98% accuracy, and was reported to agree with human and physical interpretations across both stationary and non-stationary sounds (Zucatelli et al., 8 Aug 2025). This establishes HLC as the ground-truth generation mechanism for subsequent supervised learning. A plausible implication is that the paper treats the main challenge not only as inference efficiency, but also as the conversion of a multi-scale statistical descriptor into a scalable binary supervision target.

3. NANSA architecture and supervised training

NANSA is described as a neural network specifically designed and trained for binary non-stationarity classification using HLC-generated labels (Zucatelli et al., 8 Aug 2025). The network is built from three modules.

The first module, the ANS Encoder, processes spectrogram input using fully connected layers with frequency scaling and ReLU activations, producing a frequency embedding. The second module, the Pattern Extractor, utilizes self-attention layers. The full NANSA model uses 11 layers, 3 heads each, and 192-dimension input; the lightweight version uses 4 layers, 3 heads, and 64-dimension input. The third module, the Pattern Discriminator, computes the final probability $K$0 of non-stationarity from the extracted embeddings (Zucatelli et al., 8 Aug 2025).

The input configuration is explicitly specified. NANSA operates on 1.5-second audio segments, sampled at 16 kHz, processed by STFT, with frame size 20ms and 50% overlap. The embedding construction includes not only standard spectrogram features but also a classification embedding and positional encodings intended to reflect the time-localized computation of INS (Zucatelli et al., 8 Aug 2025).

Training is supervised. The labels are generated by the HLC algorithm, and the loss is binary cross-entropy:

$K$1

where $K$2 is the HLC label and $K$3 is the model output (Zucatelli et al., 8 Aug 2025). The datasets used for training and evaluation are AudioSet, DCASE, and FSD50K, described as large, diverse, standard acoustic datasets. The comparison set includes fine-tuned state-of-the-art pretrained acoustic models—PANNs, AST, and PaSST—as well as the proposed NANSA and NANSA\textsubscript{LW} (Zucatelli et al., 8 Aug 2025).

The reported design choice is significant because it places NANSA between classical objective assessment and generic audio tagging architectures. The paper explicitly reports that general-purpose acoustic models encode stationarity information, but that purpose-built NANSA models perform better (Zucatelli et al., 8 Aug 2025).

4. Empirical performance and computational profile

The evaluation uses Accuracy, Equal Error Rate (EER), F1 Score, and also ROC and AUC (Zucatelli et al., 8 Aug 2025). Reported accuracies across the three benchmark datasets are summarized below.

Model	#Params	Accuracy
PANNs	81M	90.8% / 98.3% / 92.5%
AST	94M	92.4% / 98.2% / 93.9%
PaSST	83M	92.0% / 98.3% / 94.2%
NANSA	5.5M	94.3% / 99.0% / 95.4%
NANSA\textsubscript{LW}	0.66M	93.3% / 98.9% / 94.9%

In this table, the accuracy entries correspond to AudioSet / DCASE / FSD50K (Zucatelli et al., 8 Aug 2025). The central empirical claim is that NANSA models outperform competing approaches, with the full model reaching 99.0\% accuracy on DCASE.

The computational comparison is equally central. Traditional INS requires ~12600 ms per audio segment. By contrast, NANSA requires ~27 ms, which is described as ≈ 500x faster than INS, and NANSA\textsubscript{LW} requires ~3 ms, described as ≈ 4000x faster. The baseline pretrained models require 32–133 ms per inference, which is also much faster than INS but slower than the lightweight NANSA variant (Zucatelli et al., 8 Aug 2025).

The ablation study reports that removing the ANS Encoder led to higher EER, indicating worse performance and supporting the importance of that module. The lightweight variant retains high accuracy and efficiency for on-device/real-time use. In addition, all models achieved high AUC, with AUC (≥0.99 for NANSA variants), indicating excellent discrimination between stationary and non-stationary signals (Zucatelli et al., 8 Aug 2025).

These results position NANSA as both a modeling contribution and a systems contribution: it improves classification performance while recasting non-stationarity assessment from a multi-second statistical procedure into a rapid feed-forward inference task.

5. Relation to prior acoustic modeling approaches

The paper’s comparison to PANNs, AST, and PaSST is informative because it shows that state-of-the-art pretrained acoustic models can be fine-tuned for non-stationarity classification, and that they already encode stationarity information to a substantial degree (Zucatelli et al., 8 Aug 2025). However, those models are not explicitly designed for non-stationarity assessment, whereas NANSA is.

This distinction aligns with related work in non-stationary acoustics. In "Statistical and Neural Network Based Speech Activity Detection in Non-Stationary Acoustic Environments" (Heitkaemper et al., 2020), a neural segment RNN is introduced to integrate temporal smoothing inside the network in the presence of non-stationary noise, while a strong statistical pipeline remains competitive for resource-constrained settings. In "One-shot learning for acoustic identification of bird species in non-stationary environments" (Acconcjaioco et al., 2021), a Siamese Neural Network operating on logMel spectrograms supports novelty detection and dynamic incorporation of new classes when the acoustic scene changes over time.

These adjacent approaches are not alternatives to NANSA in task definition. The speech activity detection system addresses frame-level speech/non-speech decisions in highly non-stationary noise, and the bioacoustics system addresses class-dictionary change and one-shot class expansion. NANSA instead addresses global non-stationarity assessment with HLC-generated binary labels. This suggests a useful conceptual distinction: non-stationarity may be treated either as an environmental condition to be handled by a task-specific model, or as the primary prediction target itself. NANSA belongs to the latter category.

6. Limitations, interpretation, and research significance

The limitations reported for NANSA and HLC are methodologically important (Zucatelli et al., 8 Aug 2025). The effectiveness of HLC and subsequent model performance is partly tied to the selection of thresholds and partitioning of scales, which were empirically chosen. The preliminary validation of HLC was conducted on selected sources, and generality across arbitrarily complex signals or edge cases may require further study. In addition, although inference is extremely fast, training requires a compute-intensive initial step to run INS + HLC on large datasets in order to generate the training labels.

These limitations clarify a common misunderstanding. NANSA does not eliminate the need for the traditional objective measure during dataset construction; rather, it shifts the expensive computation to an offline labeling stage and then amortizes that cost through supervised inference. Likewise, HLC does not remove modeling assumptions from global labeling; it formalizes them through partitioning and thresholding.

Within those constraints, the framework has clear significance. It automates the global labeling process, removes human subjectivity from large-scale dataset construction, and makes non-stationarity estimation tractable for real-time systems, on-device intelligence, and resource-constrained applications (Zucatelli et al., 8 Aug 2025). The lightweight variant is explicitly described as suitable for on-device or real-time use, and the overall framework broadens research possibilities in acoustic event analysis and further work on stationarity characterization and label design refinements. A plausible implication is that future work will focus less on whether supervised models can estimate non-stationarity, and more on how the ground-truth construction itself should be standardized across signal classes, scales, and application domains.