Time series classification from scratch with deep neural networks: A strong baseline

Zhiguang WangWeizhong YanTim Oates

article2016IEEE International Joint Conference on Neural Network2,122 citations

Establishes Fully Convolutional Networks and Residual Networks as standard end-to-end baselines for raw time series classification, eliminating manual feature engineering while providing visual interpretability through Class Activation Maps.

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Time series data is ubiquitous across sectors such as healthcare, finance, and industrial operations, where accurate classification is essential for operational decisions and risk management. Existing state-of-the-art methods frequently depend on complex data preprocessing, heavy manual feature engineering, or massive classifier ensembles, which make them computationally expensive, difficult to maintain, and slow to deploy.

The article evaluates whether standard deep neural network architectures can serve as strong, end-to-end baselines for time series classification directly from raw data without manual feature extraction or extensive data preparation.

The authors conducted an empirical evaluation across 44 standardized benchmark datasets from the University of California, Riverside repository. They tested three neural network architectures—a Multilayer Perceptron, a Fully Convolutional Network, and a deep Residual Network—using only basic data scaling. The models were evaluated using the lowest training loss configuration without hyperparameter tuning or cross-validation, and performance was compared against seven leading benchmarks using a proposed metric, Mean Per-Class Error, alongside standard statistical significance tests.

The analysis yielded four major findings. First, the Fully Convolutional Network achieved the highest overall performance, winning the lowest error rate on 18 of the 44 datasets and recording the lowest average per-class error score (0.0219). Second, the Residual Network and Fully Convolutional Network delivered performance statistically indistinguishable from top ensemble and multi-scale methods while eliminating the need for multi-model ensembles or custom sampling. Third, the global average pooling design in the convolutional models enabled the use of class activation mapping, which accurately visualizes and localizes the exact temporal regions driving classification decisions. Fourth, standard Multilayer Perceptrons equipped with modern activation and regularization matched traditional distance-based baselines, though they lagged behind convolutional architectures.

These findings indicate that organizations can replace complex, labor-intensive classification pipelines with straightforward neural network architectures. This shift significantly reduces model development time, decreases maintenance complexity, and improves auditability through visual interpretability. Furthermore, the distinct feature representations learned by neural networks relative to traditional models indicate substantial opportunities to enhance existing systems without requiring costly bespoke feature engineering.

Decision-makers should consider adopting Fully Convolutional Networks as a default standard baseline for operational time series classification tasks. When adopting these models, teams can leverage class activation maps to provide explainability for safety-critical and high-compliance workflows. Where datasets are larger and feature more complex structural patterns, engineering teams should pilot Residual Networks, ensuring adequate regularization to prevent overfitting.

While confidence in the baseline findings across standard univariate benchmarks is high, readers should note that the evaluations were restricted to univariate datasets of relatively modest size without extensive hyperparameter optimization. Caution is advised when generalizing these specific network configurations directly to large-scale, multivariate, or highly noisy production environments without initial domain-specific validation.

Computer Science and Electric Engineering General Electric Company University of Maryland, Baltimore County cam classification convolutional neural networks Time Series Classi Cation Networks

arXiv: 1611.06455 cauchyturing/UCR_Time_Series_Classification_Deep_Learning_Baseline

Paper: Learning Deep Features for Discriminative Localization, Bolei Zhou et al. (2016). This paper introduces Class Activation Mapping (CAM) via global average pooling, the foundational interpretability mechanism adapted by the source paper to identify contributing temporal regions.
Paper: Fully convolutional networks for semantic segmentation, Jonathan Long et al. (2015). This work establishes the fully convolutional network architecture without dense layers, providing the architectural foundation the source paper transfers to 1D time series data.

Paper: Deep learning for time series classification: a review, Hassan Ismail Fawaz et al. (2018). This comprehensive benchmark extensively validates and analyzes the source paper's FCN and ResNet baselines across the full UCR/UEA time series archive.
Paper: 1D Convolutional Neural Networks and Applications: A Survey, Serkan Kiranyaz et al. (2019). This survey explores advanced applications and specialized design patterns for one-dimensional convolutional networks on sequential signal analysis.
Paper: TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis, Haixu Wu et al. (2023). This work advances beyond pure 1D convolutional baselines by transforming multi-periodic temporal signals into 2D variation spaces for generalized time series analysis.

Cover for Time series classification from scratch with deep neural networks: A strong baseline

Abstract

We propose a simple but strong baseline for time series classification from scratch with deep neural networks. Our proposed baseline models are pure end-to-end without any heavy preprocessing on the raw data or feature crafting. The proposed Fully Convolutional Network (FCN) achieves premium performance to other state-of-the-art approaches and our exploration of the very deep neural networks with the ResNet structure is also competitive. The global average pooling in our convolutional model enables the exploitation of the Class Activation Map (CAM) to find out the contributing region in the raw data for the specific labels. Our models provides a simple choice for the real world application and a good starting point for the future research. An overall analysis is provided to discuss the generalization capability of our models, learned features, network structures and the classification semantics.

Topics

cam classification convolutional neural networks semantics classification models network architecture recurrent neural networks

Keywords

Time Series Classi Cation Networks Deep Neural Networks Baseline Deep Neural Deep Neural Networks Data ResNet

I Introduction
II Network Architectures
II-A Multilayer Perceptrons
II-B Fully Convolutional Networks
II-C Residual Network
III Experiments and Results
III-A Experiment Settings
III-B Evaluation
III-C Results and Analysis
IV Localize the Contributing Regions with Class Activation Map
V Discussion
V-A Overfitting and Generalization
V-B Feature Visualization and Analysis
V-C Deep and Shallow
V-D Classification Semantics
VI Conclusions
References

Knowls

Knowl 1 — Fully Convolutional Network Architecture for Time Series Classification
model/method
The Fully Convolutional Network (FCN) for univariate time series classification is an end-to-end feature extractor without striding or pooling operations between convolutional blocks.

The network comprises three sequential 1-D convolutional blocks followed by a Global Average Pooling (GAP) layer and a final softmax classifier. Each basic convolutional block applies a 1-D convolution, batch normalization (BN), and a Rectified Linear Unit (ReLU) activation:

$y = W \otimes x + b$ $s = \text{BN}(y)$ $h = \text{ReLU}(s)$

where $\otimes$ denotes the 1-D convolution operator, $x$ is the input sequence or previous feature map, $W$ is the filter weight matrix, and $b$ is the bias vector.

Structural specifications across the three convolutional blocks are:
- First block: 128 filters of kernel size 8.
- Second block: 256 filters of kernel size 5.
- Third block: 128 filters of kernel size 3.
After the third block, the feature maps are processed by GAP across the temporal dimension to produce a fixed-dimensional vector representing the average response of each filter, replacing fully-connected layers to reduce parameter count and mitigate overfitting before the softmax layer.
Knowl 2 — Residual Network Architecture for Time Series Classification
model/method
The Residual Network (ResNet) baseline for time series classification is an 11-layer architecture composed of three residual blocks, followed by a Global Average Pooling (GAP) layer and a softmax output layer.

Each residual block consists of three sequential 1-D convolutional sub-blocks with a linear shortcut connection adding the residual block's input directly to the output of the third sub-block prior to a final ReLU activation:

$h_1 = \text{Block}_{k_1}(x)$ $h_2 = \text{Block}_{k_2}(h_1)$ $h_3 = \text{Block}_{k_3}(h_2)$ $\hat{h} = \text{ReLU}(h_3 + x)$

where each $\text{Block}_{k_i}$ performs a 1-D convolution with $k_i$ filters without striding, followed by batch normalization and a ReLU activation. The filter lengths (kernel sizes) in the three sub-blocks of each residual block are 8, 5, and 3, respectively.

The number of filters across the three residual blocks is configured as:
- Residual block 1: $k_1 = k_2 = k_3 = 64$
- Residual block 2: $k_1 = k_2 = k_3 = 128$
- Residual block 3: $k_1 = k_2 = k_3 = 128$
The output of the third residual block is fed into a GAP layer and classified with a softmax layer.
Knowl 3 — Mean Per-Class Error Metric for Multi-Dataset Evaluation
equation
Mean Per-Class Error (MPCE) evaluates and aggregates the performance of classification models across multiple datasets containing varying numbers of target classes:

$PCE_k = \frac{e_k}{c_k}$

$MPCE_i = \frac{1}{K} \sum_{k=1}^K PCE_k$

where:
- $k \in \{1, 2, \dots, K\}$ indexes the evaluation datasets in dataset pool $D = \{d_k\}$ .
- $i$ denotes the specific classification model under evaluation from model pool $M = \{m_i\}$ .
- $e_k \in [0, 1]$ is the test error rate achieved by model $i$ on dataset $k$ .
- $c_k \in \mathbb{N}_{\ge 2}$ is the number of distinct class labels in dataset $k$ .
- $PCE_k$ is the Per-Class Error for dataset $k$ , representing the expected error rate per individual class.
- $MPCE_i$ is the average per-class error across all $K$ datasets for model $i$ .
Unlike raw test error averaging, best-dataset win counting, or ranking-based metrics, MPCE normalizes by class cardinality to prevent datasets with large numbers of classes from dominating aggregate performance comparisons.
Knowl 4 — Class Activation Mapping for 1D Temporal Localization
model/method
In a 1-D Fully Convolutional Network equipped with a Global Average Pooling (GAP) layer, the Class Activation Map (CAM) identifies and localizes discriminative temporal regions responsible for predicting specific class labels.

Let $S_k(x)$ denote the activation of filter $k$ in the last convolutional layer at temporal location $x$ . Global average pooling computes the spatial summary $f_k = \sum_x S_k(x)$ . For class $c$ , let $w_k^c$ be the weight parameter connecting the pooled feature $f_k$ to the class $c$ logit in the softmax layer. The pre-softmax input $g_c$ is expressed as:

$g_c = \sum_k w_k^c f_k = \sum_k w_k^c \sum_x S_k(x) = \sum_x \sum_k w_k^c S_k(x)$

The 1-D Class Activation Map $M_c(x)$ for class $c$ is defined at each temporal index $x$ as:

$M_c(x) = \sum_k w_k^c S_k(x)$

$M_c(x)$ directly indicates the relative importance of temporal index $x$ in categorizing the input time series as class $c$ . If the temporal resolution of $S_k(x)$ differs from the input sequence length, $M_c(x)$ is upsampled to the original input time series length.
Knowl 5 — Multilayer Perceptron Baseline Architecture for Time Series Classification
model/method
The Multilayer Perceptron (MLP) baseline is a feedforward neural network comprising three fully connected hidden layers with 500 neurons each, terminating in a softmax layer.

Each layer block applies dropout to its input, performs an affine transformation, and applies a Rectified Linear Unit (ReLU) activation function:

$\tilde{x} = f_{\text{dropout}, p}(x)$ $y = W \cdot \tilde{x} + b$ $h = \text{ReLU}(y)$

where $x$ is the input vector, $p$ is the dropout retention probability parameter, $W$ is the weight matrix, and $b$ is the bias vector.

Dropout rates at the respective stages are:
- Input layer: $p = 0.1$
- First hidden layer: $p = 0.2$
- Second hidden layer: $p = 0.2$
- Softmax layer input: $p = 0.3$
Knowl 6 — End-to-End Deep Learning Training Protocol on 44 UCR Benchmarks
experimental setup
Deep neural network baselines (MLP, FCN, ResNet) are evaluated on 44 univariate time series datasets from the UCR repository using standard default training and testing splits.

Experimental conditions include:
- Data preprocessing: Only z-normalization is applied to both training and test splits using the mean and standard deviation computed solely from the training split of each dataset.
- Optimization algorithms:
  - MLP: Adadelta optimizer with initial learning rate $\eta = 0.1$ , decay factor $\rho = 0.95$ , and numerical stability constant $\epsilon = 10^{-8}$ .
  - FCN and ResNet: Adam optimizer with learning rate $\eta = 0.001$ , $\beta_1 = 0.9$ , $\beta_2 = 0.999$ , and $\epsilon = 10^{-8}$ .
- Loss function: Categorical cross-entropy for all networks.
- Model selection: For each architecture, the model checkpoint achieving the minimum training loss is chosen for test set evaluation without hyperparameter tuning or cross-validation.

Knowl 7 — Comparative Performance of Deep Neural Networks and State-of-the-Art TSC Baselines

data/table

Testing error rates, best-method win counts, average arithmetic/geometric ranks, and Mean Per-Class Error (MPCE) across 44 UCR time series datasets comparing 1-NN Dynamic Time Warping (DTW), Collective of Transformation-Based Ensembles (COTE), Multi-scale CNN (MCNN), Bag-of-SFA-Symbols in Vector Space (BOSSVS), Elastic Ensemble (PROP), Bag-of-SFA-Symbols (BOSS), Shapelet Ensemble (SE1), Time Series Bag-of-Features (TSBF), Multilayer Perceptron (MLP), Fully Convolutional Network (FCN), and Residual Network (ResNet):

Dataset	DTW	COTE	MCNN	BOSSVS	PROP	BOSS	SE1	TSBF	MLP	FCN	ResNet
Adiac	0.396	0.233	0.231	0.302	0.353	0.220	0.373	0.245	0.248	0.143	0.174
Beef	0.367	0.133	0.367	0.267	0.367	0.200	0.133	0.287	0.167	0.250	0.233
CBF	0.003	0.001	0.002	0.001	0.002	0.000	0.010	0.009	0.140	0.000	0.006
ChlorineCon	0.352	0.314	0.203	0.345	0.360	0.340	0.312	0.336	0.128	0.157	0.172
CinCECGTorso	0.349	0.064	0.058	0.130	0.062	0.125	0.021	0.262	0.158	0.187	0.229
Coffee	0.000	0.000	0.036	0.036	0.000	0.000	0.000	0.004	0.000	0.000	0.000
CricketX	0.246	0.154	0.182	0.346	0.203	0.259	0.297	0.278	0.431	0.185	0.179
CricketY	0.256	0.167	0.154	0.328	0.156	0.208	0.326	0.259	0.405	0.208	0.195
CricketZ	0.246	0.128	0.142	0.313	0.156	0.246	0.277	0.263	0.408	0.187	0.187
DiatomSizeR	0.033	0.082	0.023	0.036	0.059	0.046	0.069	0.126	0.036	0.070	0.069
ECGFiveDays	0.232	0.000	0.000	0.000	0.178	0.000	0.055	0.183	0.030	0.015	0.045
FaceAll	0.192	0.105	0.235	0.241	0.152	0.210	0.247	0.234	0.115	0.071	0.166
FaceFour	0.170	0.091	0.000	0.034	0.091	0.000	0.034	0.051	0.170	0.068	0.068
FacesUCR	0.095	0.057	0.063	0.103	0.063	0.042	0.079	0.090	0.185	0.052	0.042
50words	0.310	0.191	0.190	0.367	0.180	0.301	0.288	0.209	0.288	0.321	0.273
fish	0.177	0.029	0.051	0.017	0.034	0.011	0.057	0.080	0.126	0.029	0.011
GunPoint	0.093	0.007	0.000	0.000	0.007	0.000	0.060	0.011	0.067	0.000	0.007
Haptics	0.623	0.488	0.530	0.584	0.584	0.536	0.607	0.488	0.539	0.449	0.495
InlineSkate	0.616	0.551	0.618	0.573	0.567	0.511	0.653	0.603	0.649	0.589	0.635
ItalyPower	0.050	0.036	0.030	0.086	0.039	0.053	0.053	0.096	0.034	0.030	0.040
Lightning2	0.131	0.164	0.164	0.262	0.115	0.148	0.098	0.257	0.279	0.197	0.246
Lightning7	0.274	0.247	0.219	0.288	0.233	0.342	0.274	0.262	0.356	0.137	0.164
MALLAT	0.066	0.036	0.057	0.064	0.050	0.058	0.092	0.037	0.064	0.020	0.021
MedicalImages	0.263	0.258	0.260	0.474	0.245	0.288	0.305	0.269	0.271	0.208	0.228
MoteStrain	0.165	0.085	0.079	0.115	0.114	0.073	0.113	0.135	0.131	0.050	0.105
NonInvThorax1	0.210	0.093	0.064	0.169	0.178	0.161	0.174	0.138	0.058	0.039	0.052
NonInvThorax2	0.135	0.073	0.060	0.118	0.112	0.101	0.118	0.130	0.057	0.045	0.049
OliveOil	0.167	0.100	0.133	0.133	0.133	0.100	0.133	0.090	0.600	0.167	0.133
OSULeaf	0.409	0.145	0.271	0.074	0.194	0.012	0.273	0.329	0.430	0.012	0.021
SonyAIBORobot	0.275	0.146	0.230	0.265	0.293	0.321	0.238	0.175	0.273	0.032	0.015
SonyAIBORobotII	0.169	0.076	0.070	0.188	0.124	0.098	0.066	0.196	0.161	0.038	0.038
StarLightCurves	0.093	0.031	0.023	0.096	0.079	0.021	0.093	0.022	0.043	0.033	0.029
SwedishLeaf	0.208	0.046	0.066	0.141	0.085	0.072	0.120	0.075	0.107	0.034	0.042
Symbols	0.050	0.046	0.049	0.029	0.049	0.032	0.083	0.034	0.147	0.038	0.128
SyntheticControl	0.007	0.000	0.003	0.040	0.010	0.030	0.033	0.008	0.050	0.010	0.000
Trace	0.000	0.010	0.000	0.000	0.010	0.000	0.050	0.020	0.180	0.000	0.000
TwoLeadECG	0.000	0.015	0.001	0.015	0.000	0.004	0.029	0.001	0.147	0.000	0.000
TwoPatterns	0.096	0.000	0.002	0.001	0.067	0.016	0.048	0.046	0.114	0.103	0.000
UWaveX	0.272	0.196	0.180	0.270	0.199	0.241	0.248	0.164	0.232	0.246	0.213
UWaveY	0.366	0.267	0.268	0.364	0.283	0.313	0.322	0.249	0.297	0.275	0.332
UWaveZ	0.342	0.265	0.232	0.336	0.290	0.312	0.346	0.217	0.295	0.271	0.245
wafer	0.020	0.001	0.002	0.001	0.003	0.001	0.002	0.004	0.004	0.003	0.003
WordSynonyms	0.351	0.266	0.276	0.439	0.226	0.345	0.357	0.302	0.406	0.420	0.368
yoga	0.164	0.113	0.112	0.169	0.121	0.081	0.159	0.149	0.145	0.155	0.142
Win	3	8	7	5	4	13	4	4	2	18	8
AVG Arithmetic rank	8.205	3.682	3.932	7.318	5.545	4.614	7.455	6.614	7.909	3.977	4.386
AVG Geometric rank	7.160	3.054	3.249	5.997	4.744	3.388	6.431	5.598	6.941	2.780	3.481
MPCE	0.0397	0.0226	0.0241	0.0330	0.0304	0.0256	0.0302	0.0335	0.0407	0.0219	0.0231

FCN achieves the lowest overall MPCE (0.0219), the best geometric rank (2.780), and wins on 18 out of 44 datasets. ResNet achieves the third-lowest MPCE (0.0231), outperforming MCNN (0.0241) and trailing only COTE (0.0226).

Knowl 8 — Statistical Clustering of Time Series Classifiers via Paired T-Tests on PCE
empirical result
Statistical significance testing using paired $t$ -tests of the Mean Per-Class Error (MPCE) across the 44 UCR benchmark datasets clusters the 11 evaluated models into distinct performance groups:
- The top-performing cluster consists of FCN ( $MPCE = 0.0219$ ), COTE ( $MPCE = 0.0226$ ), ResNet ( $MPCE = 0.0231$ ), MCNN ( $MPCE = 0.0241$ ), and BOSS ( $MPCE = 0.0256$ ). The pairwise MPCE differences between any two models in this group are not statistically significant at the $p < 0.05$ level (e.g., FCN vs. ResNet $p = 0.2508$ , FCN vs. COTE $p = 0.3978$ , FCN vs. MCNN $p = 0.2495$ , COTE vs. ResNet $p = 0.4351$ , BOSS vs. FCN $p = 0.1879$ , BOSS vs. ResNet $p = 0.2751$ ).
- A second tier comprises SE1 ( $MPCE = 0.0302$ ), PROP ( $MPCE = 0.0304$ ), BOSSVS ( $MPCE = 0.0330$ ), and TSBF ( $MPCE = 0.0335$ ).
- 1-NN DTW ( $MPCE = 0.0397$ ) and 3-layer MLP ( $MPCE = 0.0407$ ) exhibit the highest error rates; the paired $t$ -test between DTW and MLP yields $p = 0.4234$ , indicating that MLP performance is not statistically distinguishable from standard 1-NN DTW.
- Pairwise Wilcoxon rank-sum tests with tie correction confirm that FCN and ResNet are not significantly different from COTE ( $p = 0.8445, 0.8347$ ), MCNN ( $p = 0.9834, 0.9468$ ), or BOSS ( $p = 0.8905, 0.8740$ ).
Knowl 9 — Classification Semantics and Representation Divergence via PCA
empirical result
Applying Principal Component Analysis (PCA) to the 44-dimensional Per-Class Error (PCE) vectors across all evaluated benchmark classifiers maps the decision behaviors of the models into a 2-D semantic space:
- FCN and ResNet project in close proximity to each other and near convolutional and ensemble approaches (MCNN, COTE, BOSS), indicating that 1-D convolutional features yield similar classification decisions and error distributions.
- MLP is isolated into a distant quadrant of the PCA space away from distance-based (DTW), ensemble, and convolutional architectures.
- The large semantic distance between MLP and convolutional baselines demonstrates that fully connected layers extract fundamentally different classification criteria on time series data, suggesting potential performance gains from combining MLP and CNN representations in a wide-and-deep framework.
Knowl 10 — Overfitting and Regularization Dynamics in Deep TSC Architectures
limitation
End-to-end deep neural network baselines (MLP, FCN, ResNet) trained on raw univariate time series achieve near 100% training accuracy across almost all UCR datasets, creating severe vulnerability to overfitting due to limited sample sizes and low pattern complexity:
- The 11-layer ResNet overfits more readily than the 3-block FCN, leading to a slightly higher test MPCE (0.0231 for ResNet vs. 0.0219 for FCN) despite ResNet's higher representational capacity.
- Architectural regularization is critical for generalization: replacing dense fully-connected layers with Global Average Pooling (GAP) eliminates the majority of network parameters, while 1-D batch normalization accelerates convergence and prevents covariate shift.
- In MLPs, dropout across all layers is necessary to prevent neuron co-adaptation and achieve parity with 1-NN DTW.

Coverage note — Deliberately omitted the Gramian Angular Summation Field (GASF) filter visualization equations and figures, as GASF is an existing visualization technique adopted from prior literature rather than a core novel contribution.

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Citation

MLA

Wang, Z., et al. “Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline”. arXiv, 2016, http://arxiv.org/abs/1611.06455v4.

APA

Wang, Z., Yan, W., & Oates, T. (2016). Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline. arXiv. http://arxiv.org/abs/1611.06455v4

Chicago

Wang, Z., W. Yan, and T. Oates. 2016. “Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline”. arXiv. http://arxiv.org/abs/1611.06455v4.

Harvard

Wang, Z., Yan, W. and Oates, T. (2016) “Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline”, arXiv [Preprint]. Available at: http://arxiv.org/abs/1611.06455v4.

Vancouver

1. Wang Z, Yan W, Oates T (2016) Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline. arXiv

BibTeX

@article{wang2016time,
  title = {Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline},
  author = {Wang, Zhiguang and Yan, Weizhong and Oates, Tim},
  year = {2016},
  journal = {arXiv},
  url = {http://arxiv.org/abs/1611.06455v4},
  eprint = {1611.06455}
}

Metadata:arXiv

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Time series classification from scratch with deep neural networks: A strong baseline

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Knowls

Knowl 1 — Fully Convolutional Network Architecture for Time Series Classification

Knowl 2 — Residual Network Architecture for Time Series Classification

Knowl 3 — Mean Per-Class Error Metric for Multi-Dataset Evaluation

Knowl 4 — Class Activation Mapping for 1D Temporal Localization

Knowl 5 — Multilayer Perceptron Baseline Architecture for Time Series Classification

Knowl 6 — End-to-End Deep Learning Training Protocol on 44 UCR Benchmarks

Knowl 7 — Comparative Performance of Deep Neural Networks and State-of-the-Art TSC Baselines

Knowl 8 — Statistical Clustering of Time Series Classifiers via Paired T-Tests on PCE

Knowl 9 — Classification Semantics and Representation Divergence via PCA

Knowl 10 — Overfitting and Regularization Dynamics in Deep TSC Architectures

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