Angle-distance decomposition based on deep learning for active sonar detection

Jichao Zhang; Kunde Yang; Xiao-Lei Zhang

REVIEW 4 major objections 5 minor 12 references

Angle-distance decomposition based on deep learning for active sonar detection

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Deep learning sonar cuts angle error to 1.93 degrees at -10 dB.

desk verdict Plausible system-level combination of angle and distance nets for active sonar, but the headline low-SNR advantage over classical DOA methods is not yet established because Table III leaves matched filtering and snapshot handling unstated. read the letter →

arxiv 2507.20651 v1 pith:FGTY6OOJ submitted 2025-07-28 eess.SP

Jichao Zhang , Xiao-Lei Zhang , Kunde Yang This is my paper · ORCID

classification eess.SP

keywords activesonarunderwatertargetdetectiondirection-of-arrivalestimationaudiospectrogramtransformerphasefeaturestransferlearningdeepdistance

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that active sonar target detection is better solved by decomposing it into two independent deep-learning tasks than by classical single-step signal processing. Angle is estimated by a convolutional DNN that takes, as input, the phase of short-time Fourier transforms from each hydrophone element in a circular array; distance is estimated by an audio spectrogram transformer that classifies short received-signal segments, then converts the segment index into range. On simulated data, the method holds 1.93-degree mean absolute angle error and 94.06% distance AUC at -10 dB SNR, while CBF, MVDR, and MUSIC degrade to tens of degrees and TDNN/ResNet baselines lose more AUC. The paper's stated contribution is a flexible, decomposable architecture plus transfer learning from air acoustics to cope with underwater data scarcity.

What carries the argument

The angle-distance decomposition: the detection problem is split into angle estimation, where a DNN classifies a matrix of STFT phase values (array element by frequency bin) into a discretized direction-of-arrival grid using a multi-label softmax formulation, and distance estimation, where an Audio Spectrogram Transformer (AST) takes 16-by-16 patches of log-Mel filterbank features with trainable positional embeddings and a [CLS] token to classify each signal segment as target-containing or not. The segment-to-distance conversion uses the sound speed and segment timing, $S = V_s T_\nu / 2$, where $T_\nu = cL_\nu(1-h)$. This decomposition is what lets the authors replace the image-formation step used by prior deep-learning sonar work, which they argue loses signal information, and it is also what allows transfer learning, since the transformer is pre-trained on a large air-acoustic dataset and fine-tuned on underwater sonar segments.

What would settle it

Take the trained ASTD models and run them on a real active-sonar data set with known target angles and ranges at -10 dB SNR. If the angle MAE exceeds by a wide margin the reported 1.93 degrees, or the distance AUC falls well below 94%, then the claimed low-SNR robustness is an artifact of the simulation. A cheaper check is to regenerate the simulation with a different sound-speed profile and sediment model and compare the same metrics.

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Extended reading notes

Core claim

The central claim is that a phase-only DNN and a spectrogram transformer, trained separately and fused afterward, can localize active sonar targets at signal-to-noise ratios where classical beamforming (CBF), adaptive beamforming (MVDR), and subspace methods (MUSIC) break down. The authors report that at -10 dB the proposed ASTD method reaches an angle MAE of 1.93 degrees and RMSE of 4.18 degrees, compared with roughly 20-25 degrees for classical methods, and a distance-detection AUC of 94.06% with 83.70% recall, consistently ahead of the TDNN, ResNet18, and ResNet50 baselines at every tested SNR. They also show that the deep-learning angle estimator produces a single clean peak instead of the mirror peaks that symmetric array geometries induce in classical pseudo-spectra, and that performance degrades gracefully as the number of targets increases and across three simulated ocean environments.

Load-bearing premise

The load-bearing assumption is that the simulated underwater channel—eigenray multipath, sound-speed profile, sediment properties, and noise—behaves like the real ocean closely enough that models trained on it will perform as claimed on actual active sonar returns; the paper presents no real acoustic data.

Editorial extensions

If this is right

If the results hold, classical DOA estimators like CBF, MVDR, and MUSIC can be replaced at low SNR by a phase-input DNN, eliminating mirror peaks and reducing angle error by an order of magnitude.
The distance transformer's per-segment binary classification turns range estimation into a detection problem, meaning the same model can flag target presence and range simultaneously.
Transfer learning from air acoustics, if it generalizes, would give underwater acoustics a practical route around the scarcity of labeled active sonar data.
The decomposition into independent modules means the angle and distance networks can be upgraded separately, so new array geometries or new waveforms only require retraining one branch.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The phase-only DNN suggests that high-resolution DOA information lives in the inter-element phase structure, not the magnitude; a direct testable extension is to check whether the same architecture works on other array shapes, like linear or volumetric arrays, with no retraining of the distance branch.
Because all experiments are simulated, the strongest consequence the authors imply but do not demonstrate is that the model transfers to real ocean recordings; a field test with measured echoes would settle this.
The findings about HFM versus CW and LFM waveforms indicate that model performance tracks waveform time-frequency diversity, which could be used predictively to choose transmit signals in adaptive sonar systems.
The gradual degradation with two and three targets suggests the multi-label formulation saturates; combining the two branches into a joint end-to-end model might push the multi-target limit further than the paper tests.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper is a reasonable engineering contribution, not a theoretical one. It splits active sonar localization into a phase-input DNN for angle and an Audio Spectrogram Transformer for distance, linking the two through segment-to-distance conversion. That decomposition, as a complete system, is genuinely not in the cited literature. The internal experiments are coherent: SNR sweeps, three ocean environments, different waveforms, and a softmax-vs-one-hot encoding comparison. The softmax encoding ablation is a nice touch, and the distance results are internally consistent with what you'd expect from a transformer on spectrograms. For what it is, the work is clearly thought through and honestly framed as a simulation study.

The soft spots are real, and one is load-bearing. Table III compares ASTD against CBF, MVDR, and MUSIC without saying whether those baselines use matched filtering or how many snapshots form the covariance. The signal is HFM, so matched filtering is standard practice, and Fig. 6 uses "matched filtering-MVDR" elsewhere in the paper. If Table III's classical methods operate on raw STFT bins or single snapshots, the reported multi-fold RMSE margins at -10 dB (ASTD 4.18° vs MVDR 32.11°) are largely artifacts of handicapped baselines. That baseline specification is a must-fix, and it is the difference between "deep nets beat classical methods" and "deep nets beat strawmen." Minor but also important: no error bars anywhere, so the small AUC gaps between ASTD and ResNet50 at -10 dB are probably noise; no ablation of the transfer-learning step, which is advertised as a contribution; and everything is simulated with no real-data check, making every robustness claim conditional.

The paper is not circular, and the citation pattern is fine. The self-citation for softmax encoding is relevant and not self-serving. The central argument—that a decomposition into angle and distance classification works on simulated active sonar—holds up, but the margin over classical methods is not yet credible.

Who should read it: sonar engineers who want a concrete deep-learning pipeline for low-SNR localization and who can tolerate simulation-only evidence. It deserves a serious referee, but the referee should demand the baseline details, error bars, and ideally at least one real-data sanity check. I would send it to peer review with major revision, not desk reject it.

Recommendation: engage with it, but require the baseline specification before accepting any performance claims.

Referee Report

4 major / 5 minor

Summary. The paper proposes an active sonar target detection method (ASTD) that separates the detection task into angle estimation and distance estimation. Angle estimation is formulated as a multi-label classification problem using a DNN whose input is the STFT phase across array elements; distance estimation is a binary segmentation/classification problem solved with an Audio Spectrogram Transformer applied to Mel-spectrogram patches, with transfer learning from AudioSet. Experiments are conducted entirely on simulated circular-hydrophone-array data with an HFM waveform at SNRs of 10, 0, and -10 dB. The paper reports that ASTD outperforms CBF, MVDR, and MUSIC for angle estimation and TDNN, ResNet18, and ResNet50 for distance estimation, and that its performance degrades gracefully at low SNR.

Significance. If the claims hold, the decomposition into a phase-based DNN and a spectrogram transformer would be a useful contribution to low-SNR active sonar localization, and the transfer-learning strategy from air acoustics would be a practical response to underwater data scarcity. The paper also provides a reasonably broad set of simulation experiments, including different environments, multiple targets, and different transmit waveforms, which is a strength. However, the evidence is entirely simulated, the classical baselines are under-specified, and the transfer-learning contribution is not ablated; the headline robustness advantage over classical methods is therefore not yet established. The significance is conditional on resolving these load-bearing issues.

major comments (4)

[IV-B.1, Table III] The classical DOA baselines are not sufficiently specified to support the headline claim. The paper does not state whether CBF, MVDR, and MUSIC use matched filtering with the known HFM replica, how many snapshots or STFT frames are used to form the spatial covariance, or whether the same phase-only input is used. Because the transmitted waveform is wideband HFM (2-3 kHz) and the comparison is made at SNR = -10 dB, omitting matched filtering would substantially handicap the classical methods; the paper's own Fig. 6(a) uses 'matched filtering-MVDR,' indicating that the authors recognize this preprocessing is important. Without this information, the multi-fold RMSE advantage of ASTD (4.18 deg vs 30.26 deg for MUSIC and 32.11 deg for MVDR at -10 dB) cannot be taken as establishing superiority over classical methods.
[IV-A, Fig. 4; V] All experimental evidence comes from a single simulator, yet the abstract and conclusion claim 'effective and robust performance under challenging conditions' and 'strong robustness' without real data or a distribution-shift test. Table V changes three environmental parameters, but the paper does not state whether the model is retrained for each environment or evaluated with the Env 1 model; if the latter, it would be a useful generalization test, but the text is silent. The robustness claims should be scoped to the simulation, or supported by at-sea data, before being stated as general findings.
[III-B.3, Table II] The transfer-learning contribution is not demonstrated. Section III-B.3 motivates AudioSet pretraining, but no experiment compares the AST fine-tuned from AudioSet against one trained from scratch on the simulated active-sonar data. Without this ablation, the claimed benefit of transfer learning is unsupported, and the premise that air-acoustic features transfer to underwater sonar remains an unvalidated assumption.
[IV-B.3, Table VI] The multi-target comparison is confounded by the encoding choice. The single-source row uses softmax encoding while the two- and three-source rows use one-hot encoding, so the degradation in MAE/RMSE cannot be attributed solely to the number of sources. Moreover, the paper does not explain how a multi-label softmax output is decoded into a set of angles for the multi-target case, which is necessary to interpret MAE/RMSE for two or three sources.

minor comments (5)

[II, Eq. (5)] The notation in Eq. (5) is unclear: c is called the segment length while L_nu is called the position of the segment, and the units of T_nu are not made explicit; please define all symbols with units.
[III-A.2, Table I] The input and output dimensions in Table I are not tied to the array size N=4 or to the STFT parameters; please specify the STFT window length, hop, and frequency-bin count so the architecture is reproducible.
[IV-B.1, Fig. 5] The y-axis label 'Normalized Softmax' does not apply to CBF, MVDR, or MUSIC, which produce pseudo-spectra rather than softmax outputs; also the legend label 'ASSD' appears to be a typo for 'ASTD'.
[IV-B.1, Table III] The text says 'Under an SNR condition of -10' without the unit dB; please make the units consistent throughout the tables and prose.
[Algorithm 1] The pseudo-code lacks explicit control-flow delimiters (end if, end for) and does not define how the distance S and angle yhat are combined into the final distance-azimuth record; please add these details for clarity.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: the angle and distance outputs are supervised fits to simulated labels, and the sole self-citation (ref. [6] for softmax encoding) does not feed the central claim.

full rationale

The paper's derivation chain is supervised learning, not analytical reduction. Angle estimates come from a DNN trained on phase features with ground-truth DOA labels (Sec. III-A), and distance comes from a Transformer trained as a binary segment classifier (Sec. III-B); evaluation on the same simulation distribution is standard fitting and generalization behavior rather than circularity. The distance conversion S = Vs*Tnu/2 (Eq. 5) is a physical constant-time-to-range mapping, not a quantity fitted from the target outputs. The only self-citation is ref. [6] (Feng, Zhang, Li) for softmax encoding, used as an ablation in Table VI; it is a design choice and does not establish the central performance claims, so it does not make the argument circular. The underspecification of classical baselines (e.g., whether CBF/MVDR/MUSIC use matched filtering or sufficient snapshots in Table III) is a correctness risk about fair comparison, not a circularity. No equation in the paper defines a quantity in terms of the quantity it claims to predict, and no uniqueness theorem or prior-work citation is invoked to forbid alternatives. The paper is therefore self-contained for what it claims, subject to its simulation-only validation premise.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper is empirical, so most assumptions are domain modeling choices. The central claim depends on the simulator being a faithful proxy for the ocean, on phase-only features carrying sufficient angle information, on the segment-index-to-distance mapping being valid, and on air-acoustic pre-training transferring to underwater sonar.

free parameters (5)

DOA class count = 144
The 360-degree bearing is discretized into 144 classes (about 2.5-degree resolution); this hand-chosen grid limits achievable angle accuracy.
Segment length = 1 second
The signal is split into 1-second segments for distance classification; this sets the distance resolution to roughly 750 m at Vs = 1500 m/s using two-way travel.
AST patch size and overlap = 16x16 patches, overlap 6
These are design choices adopted from the Audio Spectrogram Transformer; they affect the feature granularity of the spectrogram.
Overlap rate h in Eq. (5) = not reported
The overlap rate shifts the segment index to absolute time; without its value the exact distance mapping is not reproducible.
Transfer learning source dataset = AudioSet
The transformer is initialized from AudioSet-pretrained weights; this choice is asserted to help but never ablated.

assumptions (5)

domain assumption Signal model in Eq. (1): received signal is a sum of scaled and delayed copies of the transmitted signal plus noise
Used throughout as the simulation and method foundation; real channels may include frequency-dependent absorption, Doppler, and non-stationary noise not captured here.
domain assumption Phase differences across the circular array are sufficient for DOA estimation
The angle DNN sees only phase, discarding magnitude; this presumes phase carries the angle information, which can be ambiguous at low SNR or for off-plane targets.
domain assumption Distance is recoverable from the detected segment index via S = Vs Tnu / 2
Requires that the first target echo is the one classified, that transmission and reception start at the same time, and that the overlap rate h is known.
ad hoc to paper Acoustic propagation in air and water are similar enough that AudioSet pre-training aids underwater sonar
Sec. III-B-3 states this without comparison; the time-frequency structure differs greatly due to sound speed, bandwidth, and source types.
ad hoc to paper Simulator (Fig. 4, Sec. IV-A) produces realistic multipath, reverberation, and noise
No real data validation, no comparison of simulated to measured channels, no sensitivity analysis of results to simulation parameters.

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Cite this review

Pith. "Pith review of Angle-distance decomposition based on deep learning for active sonar detection." pith.science (2026). https://pith.science/paper/FGTY6OOJ

@misc{pith2026250720651,
  author       = {Pith},
  title        = {Pith review of: Angle-distance decomposition based on deep learning for active sonar detection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FGTY6OOJ}},
  note         = {Machine review of arXiv:2507.20651}
}

read the original abstract

Underwater target detection using active sonar constitutes a critical research area in marine sciences and engineering. However, traditional signal processing methods face significant challenges in complex underwater environments due to noise, reverberation, and interference. To address these issues, this paper presents a deep learning-based active sonar target detection method that decomposes the detection process into separate angle and distance estimation tasks. Active sonar target detection employs deep learning models to predict target distance and angle, with the final target position determined by integrating these estimates. Limited underwater acoustic data hinders effective model training, but transfer learning and simulation offer practical solutions to this challenge. Experimental results verify that the method achieves effective and robust performance under challenging conditions.

Figures

Figures reproduced from arXiv: 2507.20651 by the authors.

**Figure 2.** FIG. 2. Proposed Architecture [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. DNN framework [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4. Simulated underwater acoustic environment [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5. Full bearing view normalized pseudo-spectrum [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6. Distance-azimuth graph. (a) Distance-azimuth graph [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

12 extracted references · 11 canonical work pages

[1]

First, the entire DOA range is discretized to form a set of possible DOA values, Θ = {θ1,

Problem transformation The multi-target DOA estimation problem is formu- lated as a y-class multi-label classification task. First, the entire DOA range is discretized to form a set of possible DOA values, Θ = {θ1, . . . , θy}. Then, a class vector y is constructed, where each target corresponds to a possible DOA value in the set Θ. In this task, we assum...

work page
[2]

Un- like other methods that directly use images as input fea- tures, we utilize phase information as the input feature representation in this research

DNN framework In this study, the objective is to learn features rele- vant to the DOA estimation task through training. Un- like other methods that directly use images as input fea- tures, we utilize phase information as the input feature representation in this research. The DNN framework takes the feature representa- tion corresponding to each STFT time ...

work page
[3]

Therefore, we transform the distance detection task into a binary classification problem p ∈ {p0, p1}

Problem transformation In this task, to obtain distance information, we split the signal into smaller segments and then identify the segments that contain information related to the target. Therefore, we transform the distance detection task into a binary classification problem p ∈ {p0, p1}. Segments containing the target signal are labeled as p1, while t...

work page 2025
[4]

Transformers dis- pense with recurrence and convolutions in favor of self– attention, which allows for global context aggregation at every layer

Transformer framework Over the past years, transformer models has shown excellent performance in various tasks. Transformers dis- pense with recurrence and convolutions in favor of self– attention, which allows for global context aggregation at every layer. To obtain the target location, we convert the sig- nal segment xk into a sequence of 128-dimensiona...

work page 2025
[5]

How- ever, in the field of underwater acoustics, there is a chal- lenge of data scarcity, mainly due to high costs, long acquisition times, and data security concerns

Transfer learning Compared to the CNN network, one disadvantage of the Transformer architecture is that it requires a large amount of data to achieve optimal performance. How- ever, in the field of underwater acoustics, there is a chal- lenge of data scarcity, mainly due to high costs, long acquisition times, and data security concerns. Addition- ally, th...

work page
[6]

Dataset Sonar Target Water Sediment FIG. 4. Simulated underwater acoustic environment The simulation environment is illustrated in Fig.4, where the circular hydrophone array (CHA) is positioned at a depth of 5 m underwater. The total water depth is 1000 m, underlain by a sediment layer. In the case of downward-refraction, the sound speed decreases from 15...

work page 2000
[7]

The model was trained for 20 epochs with an initial learning rate of 1 × 10−4 using the Adam optimizer

Parameter setting During the distance estimation training phase, the dataset was split into training, validation, and test sub- sets using an 8:1:1 ratio. The model was trained for 20 epochs with an initial learning rate of 1 × 10−4 using the Adam optimizer. A step-base learning rate scheduler with a step size of 1 epoch and a decay factor of 0.85 was emp...

work page
[8]

MAE represents the mean absolute difference between predictions and true values

Evaluation metrics In this paper, we employ mean absolute error (MAE), root mean square error (RMSE), Area Under Curve (AUC) and recall as metrics to evaluate model per- formance. MAE represents the mean absolute difference between predictions and true values. RMSE assesses pre- diction quality by computing the root of mean squared deviations, defined as:...

work page 2025

Show all 12 references

[9]

In Table II, we compare the performance of ASTD with other methods, such as TDNN 14, ResNet18, and ResNet5012, for the distance detection task under differ- ent SNR conditions

Main results In this section, the performance of active sonar tar- get detection (ASTD) is evaluated on both distance and angle estimation tasks, followed by the presentation of the final distance–azimuth map. In Table II, we compare the performance of ASTD with other methods,...

2025
[10]

Effect of marine environment TABLE IV. Environmental parameters for different environ- ments Parameter Env 1 Env 2 Env 3 Water depth(m) 1000 100 2000 Sound speed profiles(m/s) 1548–1501 1500–1510 1500–1550 Sediment density(g/cm3) 1.8 1.5 1.4 Sediment speed(m/s) 1800 2000 1450 ...

2000
[11]

Performance under different source numbers and encoding methods Source No

Multi-target detection TABLE VI. Performance under different source numbers and encoding methods Source No. Encoding MAE( ◦) RMSE( ◦) AUC(%) 1 softmax 1.52 3.61 97.24 1 one-hot 2.16 3.68 97.12 2 one-hot 5.25 8.36 95.53 3 one-hot 7.42 15.35 94.82 Table VI illustrates the impact...
[12]

Conventional beamforming techniques,

Transmit waveform Table VII presents the performance of the proposed method under different transmit waveforms, including Continuous Wave (CW), Linear Frequency Modulation (LFM), and Hyperbolic Frequency Modulation (HFM). The results indicate that the choice of transmit wavefo...

2006 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

First, the entire DOA range is discretized to form a set of possible DOA values, Θ = {θ1,

Problem transformation The multi-target DOA estimation problem is formu- lated as a y-class multi-label classification task. First, the entire DOA range is discretized to form a set of possible DOA values, Θ = {θ1, . . . , θy}. Then, a class vector y is constructed, where each target corresponds to a possible DOA value in the set Θ. In this task, we assum...

work page

[2] [2]

Un- like other methods that directly use images as input fea- tures, we utilize phase information as the input feature representation in this research

DNN framework In this study, the objective is to learn features rele- vant to the DOA estimation task through training. Un- like other methods that directly use images as input fea- tures, we utilize phase information as the input feature representation in this research. The DNN framework takes the feature representa- tion corresponding to each STFT time ...

work page

[3] [3]

Therefore, we transform the distance detection task into a binary classification problem p ∈ {p0, p1}

Problem transformation In this task, to obtain distance information, we split the signal into smaller segments and then identify the segments that contain information related to the target. Therefore, we transform the distance detection task into a binary classification problem p ∈ {p0, p1}. Segments containing the target signal are labeled as p1, while t...

work page 2025

[4] [4]

Transformers dis- pense with recurrence and convolutions in favor of self– attention, which allows for global context aggregation at every layer

Transformer framework Over the past years, transformer models has shown excellent performance in various tasks. Transformers dis- pense with recurrence and convolutions in favor of self– attention, which allows for global context aggregation at every layer. To obtain the target location, we convert the sig- nal segment xk into a sequence of 128-dimensiona...

work page 2025

[5] [5]

How- ever, in the field of underwater acoustics, there is a chal- lenge of data scarcity, mainly due to high costs, long acquisition times, and data security concerns

Transfer learning Compared to the CNN network, one disadvantage of the Transformer architecture is that it requires a large amount of data to achieve optimal performance. How- ever, in the field of underwater acoustics, there is a chal- lenge of data scarcity, mainly due to high costs, long acquisition times, and data security concerns. Addition- ally, th...

work page

[6] [6]

Dataset Sonar Target Water Sediment FIG. 4. Simulated underwater acoustic environment The simulation environment is illustrated in Fig.4, where the circular hydrophone array (CHA) is positioned at a depth of 5 m underwater. The total water depth is 1000 m, underlain by a sediment layer. In the case of downward-refraction, the sound speed decreases from 15...

work page 2000

[7] [7]

The model was trained for 20 epochs with an initial learning rate of 1 × 10−4 using the Adam optimizer

Parameter setting During the distance estimation training phase, the dataset was split into training, validation, and test sub- sets using an 8:1:1 ratio. The model was trained for 20 epochs with an initial learning rate of 1 × 10−4 using the Adam optimizer. A step-base learning rate scheduler with a step size of 1 epoch and a decay factor of 0.85 was emp...

work page

[8] [8]

MAE represents the mean absolute difference between predictions and true values

Evaluation metrics In this paper, we employ mean absolute error (MAE), root mean square error (RMSE), Area Under Curve (AUC) and recall as metrics to evaluate model per- formance. MAE represents the mean absolute difference between predictions and true values. RMSE assesses pre- diction quality by computing the root of mean squared deviations, defined as:...

work page 2025