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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>X (M. M. Kunik);</journal-title>
      </journal-title-group>
      <issn pub-type="ppub">1613-0073</issn>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Application of Spatio-Temporal Graph Convolutional Networks in Strength Sports: Predicting the One-Repetition Maximum (1-RM)</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Mateusz M. Kunik</string-name>
          <email>M.Kunik@issi.uz.zgora.pl</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Marek Kowal</string-name>
          <email>M.Kowal@issi.uz.zgora.pl</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Krzysztof Patan</string-name>
          <email>K.Patan@issi.uz.zgora.pl</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Workshop</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="editor">
          <string-name>One-Repetition Maximum, Relative Load Intensity, Spatio-Temporal Graph Convolutional Networks, Pose Esti-</string-name>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Institute of Control and Computation Engineering, University of Zielona Góra</institution>
          ,
          <addr-line>ul. Szafrana 2, 65-516 Zielona Góra</addr-line>
          ,
          <country country="PL">Poland</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>mation</institution>
          ,
          <addr-line>Strength Sports, Computer Vision, Deep Learning</addr-line>
        </aff>
      </contrib-group>
      <volume>000</volume>
      <fpage>0</fpage>
      <lpage>0002</lpage>
      <abstract>
        <p>Accurate One-Repetition Maximum (1-RM) assessment is crucial in strength sports for optimizing training loads, monitoring progress, and minimizing injury risk. Traditional assessment methods, whether through direct testing or mathematical estimation, are often time-consuming, invasive, or prone to significant inaccuracies. This study proposes a novel, non-invasive approach to 1-RM prediction using only video recordings of exercise execution. By leveraging BlazePose for pose estimation and Spatio-Temporal Graph Convolutional Networks (ST-GCNs) for modeling joint dynamics, we extract a movement representation termed Performance, a combination of component and latent features indicative of physical exertion. We accurately predict each squat attempt's relative load intensity (%1-RM) based on this representation. Our method introduces a new paradigm in strength evaluation, integrating biomechanics and deep learning to enable scalable, contactless feedback in real-world training settings. To support future research, we also provide a new dataset of weighted back squats annotated with biomechanical data and metadata. To our knowledge, this is the first application of ST-GCNs to predict 1-RM in strength sports, ofering a safer and more personalized alternative to conventional testing methods.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>In recent years, strength sports have increasingly embraced data-driven approaches to monitor, analyze,
and enhance athlete performance. One of the most critical metrics in this domain is the One-Repetition
Maximum, the maximal load an athlete can lift for a single repetition of a specific exercise. Accurate
determination of the 1-RM plays a pivotal role in prescribing training intensities, tracking progress,
and mitigating injury risk. Direct methods carry a heightened risk of injury and fatigue, while indirect
approaches usually lack accuracy due to their reliance on simplified, general-purpose models.</p>
      <p>Concurrently, the fields of computer vision and deep learning have made substantial advances in
modeling human movement. In particular, graph-based neural architectures such as Spatio-Temporal
Graph Convolutional Networks have demonstrated exceptional capability in capturing complex motion
patterns by treating the human body as a dynamic graph of interconnected joints. These models have
been successfully applied to tasks such as action recognition and rehabilitation assessment, but their
application in strength training remains largely unexplored.</p>
      <p>This study bridges that gap by introducing a novel, video-based method for predicting relative load
intensity during the back squat. Our approach defines Performance as a multifaceted representation of
exercise execution, combining kinematic data extracted via BlazePose and structured analysis through
ST-GCN. By modeling movement quality over time, we aim to infer how close a submaximal efort is to
an individual’s actual 1-RM, without the need for maximal lifting attempts.</p>
      <p>In this work, we propose the task of 1-RM prediction based purely on visual input, using
spatiotemporal graph-based modeling of human motion. To support this task, we introduce a new, annotated</p>
      <p>CEUR</p>
      <p>ceur-ws.org
dataset of weighted back squats that combines visual pose data with contextual training information,
which we will make publicly available to encourage future research. Finally, we demonstrate that
our approach not only ofers a safer alternative to direct testing, but also achieves superior accuracy
compared to traditional estimation methods.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Background</title>
      <sec id="sec-2-1">
        <title>2.1. One-Repetition Maximum Overview</title>
        <p>
          The One-Repetition Maximum is a parameter primarily used in strength sports that defines the maximum
load a person can lift in a single repetition of a given exercise [
          <xref ref-type="bibr" rid="ref1 ref2">1, 2</xref>
          ]. It serves as a key indicator for
assessing muscular strength and monitoring training progress. Furthermore, accurate measurement
allows for adjusting training intensity to individual capabilities and training goals. This approach
ensures optimal muscle stimulation while minimizing the risk of injury [
          <xref ref-type="bibr" rid="ref3 ref4 ref5">3, 4, 5</xref>
          ].
        </p>
        <p>
          The 1-RM is used primarily in sports such as powerlifting, Olympic weightlifting, and strongman
competitions. Additionally, it is also utilized in the physical preparation of athletes in disciplines such
as athletics, team sports, and combat sports. In these disciplines, high levels of muscular strength may
contribute to improved speed, explosiveness, and overall physical performance [
          <xref ref-type="bibr" rid="ref6 ref7">6, 7</xref>
          ].
        </p>
        <p>The 1-RM can be assessed in two ways: directly - by performing a maximum load test, or indirectly
by estimating it using submaximal loads, i.e., suficiently heavy but below the maximal capacity.</p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. Direct Method</title>
        <p>In the environment of strength athletes and enthusiasts, the 1-RM is most commonly determined directly
by performing a maximum load test. Due to the nature of this measurement, the method is also referred
to as a trial-and-error approach.</p>
        <p>The procedure for a 1-RM test follows a standardized protocol. Initially, the participant performs a
general warm-up tailored to their individual needs and musculoskeletal capabilities. This is followed
by a specific warm-up in the target strength exercise (e.g., the back squat). In subsequent attempts,
the participant gradually increases the load, performing increasingly heavier sets with a decreasing
number of repetitions. Initially, sets may consist of 3–5 repetitions with moderate weights, while in
the final sets only a single repetition is performed. Several minutes of rest are taken between attempts
to allow for full muscle recovery. The test is concluded when the participant is unable to complete a
single repetition correctly. The highest load lifted with proper technique is recorded as the 1-RM result.</p>
        <p>The traditional 1-RM test is considered the most accurate method for assessing an individual’s
maximal strength and is relatively easy to implement under controlled conditions. However, it also
comes with notable drawbacks: it increases the risk of injury places significant strain on the nervous
system, and can negatively impact health in underprepared individuals. Additionally, the procedure
is time-consuming, requires careful planning and warm-up, and may be psychologically demanding,
especially for less experienced athletes.</p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. Indirect Method</title>
        <p>An alternative to the 1-RM test is the use of indirect methods, which aim to assess an athlete’s muscular
strength using submaximal loads. Estimation of the 1-RM parameter is based on a low-complexity
mathematical model that describes the relationship between load, number of repetitions, and maximal
muscular strength.</p>
        <p>Initially, the testing procedure may resemble the direct 1-RM test — the athlete performs a warm-up
and gradually increases the load while simultaneously reducing the number of repetitions. This time,
however, the athlete stops at a submaximal load. With an appropriately selected weight, the athlete
performs the maximum number of repetitions possible while maintaining proper exercise technique.
Based on the results obtained, the 1-RM parameter is estimated using established mathematical models.</p>
        <p>The indirect method estimates 1-RM using submaximal loads, ofering a safer and more accessible
alternative to direct testing by reducing injury risk, minimizing strain on the nervous system, and
requiring less time and fewer resources. It can also ease psychological stress, as the loads used resemble
regular training intensities. However, this method is generally less accurate, relying on simplified
predictive models rather than actual maximal performance. Its efectiveness often depends on the
athlete’s training background and the specific formula used, which can limit its generalizability and
introduce variability in results.</p>
        <p>While 1-RM remains a fundamental measure of strength, both direct and indirect assessment methods
have notable trade-ofs in terms of accuracy, safety, and practicality. Therefore, the following section
focuses on data-driven approaches and deep learning methods, which motivated us to further investigate
this research problem and conduct our own analyses.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Related Works</title>
      <sec id="sec-3-1">
        <title>3.1. Pose Estimation for Strength Sports</title>
        <p>
          Markerless human pose estimation has played a key role in recent eforts to analyze athletic performance,
particularly in strength training. Deep learning models such as OpenPose and BlazePose have enabled
reliable extraction of skeletal keypoints from video, supporting automated analysis of exercises like the
squat [
          <xref ref-type="bibr" rid="ref14 ref15 ref16 ref17 ref18">14, 15, 16, 17, 18</xref>
          ].
        </p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Graph Convolutional Networks in Human Motion Analysis</title>
        <p>
          Building on this foundation, researchers have explored graph-based neural networks that move beyond
raw keypoints to model the human body as a structured graph. Yan et al. [
          <xref ref-type="bibr" rid="ref19">19</xref>
          ] pioneered the
SpatioTemporal Graph Convolutional Network for skeleton-based action recognition, where each joint
is treated as a graph node and spatial–temporal connections are modeled via graph convolutions.
This design captures inter-joint dependencies over time, making it particularly efective for complex,
coordinated motions. Compared to sequential models like LSTMs or CNNs, GCNs more efectively
encode biomechanical structure and have been widely adopted for movement classification, physical
therapy assessment, and rehabilitation tasks [
          <xref ref-type="bibr" rid="ref20 ref21 ref22 ref23">20, 21, 22, 23</xref>
          ]. For example, Deb et al. [
          <xref ref-type="bibr" rid="ref23">23</xref>
          ] used a variant
of ST-GCN with self-attention to evaluate physical therapy exercises, outperforming prior CNN- and
LSTM-based approaches on datasets like KIMORE and UI-PRMD [
          <xref ref-type="bibr" rid="ref24 ref25">24, 25</xref>
          ].
        </p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Squat Technique Analysis</title>
        <p>
          A representative use case of these methods is back squat assessment, where researchers have aimed
to classify technique and detect movement errors using pose data. Ogata et al. [
          <xref ref-type="bibr" rid="ref26">26</xref>
          ] proposed one
of the earliest vision-based squat evaluation methods, converting 3D joint coordinates into distance
matrices and analyzing them with a 1D CNN. Building on this, Youssef et al. [
          <xref ref-type="bibr" rid="ref17">17</xref>
          ] applied BlazePose and
deep learning to classify squat quality from video with high accuracy, efectively replicating coach-like
evaluations based on movement cues such as knee tracking or hip depth.
        </p>
      </sec>
      <sec id="sec-3-4">
        <title>3.4. Load-Velocity Relationship</title>
        <p>
          Pose estimation thus provides a strong kinematic foundation for evaluating lifting mechanics. Integrating
ST-GCN is a natural progression, as it enables modeling of joint coordination throughout the squat
motion. Recent studies have used such models to detect errors and provide feedback in home fitness
applications [
          <xref ref-type="bibr" rid="ref27 ref28">27, 28</xref>
          ]. Our work follows this trajectory, focusing specifically on back squats, and extends
it by predicting 1-RM. Directly testing 1-RM can be risky or impractical, so it is often estimated from
submaximal lifts. Velocity-based training relies on the established inverse relationship between lift
velocity and load: as the lifted weight increases, movement speed decreases in a predictable manner
[
          <xref ref-type="bibr" rid="ref29 ref30 ref31">29, 30, 31</xref>
          ]. This principle underlies many sensor and wearable-based methods that estimate 1-RM
through bar speed. For example, Balsalobre-Fernández et al. [
          <xref ref-type="bibr" rid="ref32">32</xref>
          ] demonstrated that both linear models
and neural networks can accurately predict bench press 1-RM from a few submaximal lifts. Recently,
smartphone-based video systems have achieved comparable accuracy to hardware-based sensors when
tracking barbell motion during squats [
          <xref ref-type="bibr" rid="ref29">29</xref>
          ]. Despite these advances, most indirect 1-RM prediction
approaches rely on isolated features such as bar velocity or repetition count, without leveraging full-body
movement data. Our method addresses this gap by using spatio-temporal pose sequences—extracted
with BlazePose and modeled via ST-GCN, to estimate the relative intensity of squat attempts based on
whole-body motion patterns.
        </p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Proposed Method</title>
      <sec id="sec-4-1">
        <title>4.1. Performance</title>
        <p>The starting point for improving the quality of 1-RM estimation lies in prediction based on Performance,
understood as the execution pattern of a full set or a single repetition of a selected exercise.</p>
        <p>We define Performance as a set of features that shape the overall quality of the attempt and provide
insight into an athlete’s maximal muscular strength. These features can be categorized into two
groups: component and latent. Component features refer to the externally visible aspects of exercise
execution, such as movement velocity, body trajectory, and the athlete’s stability during the lift. These
are typically extracted from video footage and represent the kinematic properties of the motion. In
contrast, latent features encompass internal or non-visible aspects that influence Performance, such as
training experience, athlete’s skill level, or the specifics of their training program. These are generally
obtained through a personal data acquisition form and are not directly inferable from visual observation.</p>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Methodology Workflow</title>
        <p>Performance analysis requires a well-structured and carefully designed workflow, divided into several
distinct stages: Below, we present our proposed sequence of steps, with the complete workflow illustrated
in Figure 1.</p>
        <p>
          1. Data Collection: Collection of video recordings of the athlete performing sets of repetitions
with submaximal loads - component features. Additional personal information is gathered via a
personal data acquisition form - latent features.
2. Raw Data Processing: The video recordings are processed using the BlazePose model [
          <xref ref-type="bibr" rid="ref16">16</xref>
          ] to
estimate body posture. The resulting data represent joint coordinates changing over time during
the exercise. In parallel, personal data are encrypted to ensure privacy and security.
3. Data Concatenation: All acquired data are concatenated into a unified structure to enable
further processing.
4. Data Preparation: All inputs are transformed into a consistent numerical format and imputed
where necessary. The data are then normalized and structured according to the input requirements
of the prediction model.
5. Model Inference: A model based on ST-GCNs analyzes the structured data and predicts the
relative load intensity, i.e., the percentage of One-Repetition Maximum lifted by the athlete in the
given recording.
6. 1-RM Estimation: Based on the predicted relative intensity and the actual weight used during
the recorded attempt, the athlete’s 1-RM value is estimated.
        </p>
      </sec>
      <sec id="sec-4-3">
        <title>4.3. Pose Estimation</title>
        <p>
          A key component of the proposed method is accurate human pose estimation from video, which serves
as the basis for analyzing movement patterns during strength exercises. We employ the BlazePose
model, following the findings from recent studies [
          <xref ref-type="bibr" rid="ref16 ref17 ref18">16, 18, 17</xref>
          ], which by default extracts 33 anatomical
landmarks per frame. This markerless solution is optimized for real-time applications and provides a
reliable skeletal representation of the athlete during the squat. The topology of the default 33 keypoints
is illustrated in Fig. 2 a.
        </p>
        <p>BlazePose employs a two-stage architecture consisting of a detector and a tracker, optimized for
high-throughput, low-latency inference. The detector locates the full-body region of interest, while the
tracker estimates landmark positions using a lightweight regression-based model. The system combines
heatmap-based localization for improved spatial accuracy with direct coordinate regression to maintain
speed. This hybrid approach enables robust performance even on mobile and edge devices, making
BlazePose particularly well suited for biomechanical applications in real-world training environments.</p>
        <p>In our pipeline, BlazePose processes each frame to generate a sequence of 3D coordinates, yielding a
spatio-temporal tensor of shape  ×  ×  , where  is the number of frames,  the number of keypoints,
and  the coordinate dimensions. These outputs serve as the structural foundation for graph-based
modeling, enabling the next stage: relational and temporal analysis of joint movements using ST-GCN.</p>
      </sec>
      <sec id="sec-4-4">
        <title>4.4. Spatio-Temporal Graph Convolutional Networks</title>
        <p>
          To analyze full-body movement during a lift, we adopt Spatio-Temporal Graph Convolutional Networks
as introduced by [
          <xref ref-type="bibr" rid="ref19">19</xref>
          ]. This model treats the human body as a dynamic graph, where joints are nodes
and anatomical connections are edges. Temporal edges capture motion across time, allowing for
simultaneous modeling of spatial relationships and movement dynamics.
        </p>
        <p>
          As demonstrated in [
          <xref ref-type="bibr" rid="ref17 ref23">23, 17</xref>
          ], ST-GCN models outperform sequential or CNN-based approaches in
motion quality assessment due to their ability to represent joint connectivity explicitly. Motivated
by these studies and supported by initial experiments with various architectures, we selected the
ST-GCN-based approach as the primary framework for our method. In our implementation, the model
is tailored for regression, predicting the relative intensity of each lift based on pose sequences.
        </p>
        <p>This graph-based approach ensures robust capture of movement patterns critical for estimating
exertion level, ofering a natural fit for analyzing complex multi-joint actions like the back squat.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Dataset</title>
      <p>To efectively analyze Performance and predict the 1-RM parameter, a deep neural network must be
trained on a suitably designed dataset. However, there are significant challenges in this regard. First, as
we have shown, there is a lack of existing research that explores 1-RM prediction using neural networks
based on video recordings. Second, the assumptions required to construct a reliable dataset for this
task are dificult to meet. Consequently, no publicly available datasets fully satisfies the needs of this
study. For these reasons, we were compelled to develop and annotate our own dataset of weighted back
squats. We intend to release this dataset publicly to facilitate future research on video-based strength
estimation.</p>
      <sec id="sec-5-1">
        <title>5.1. Data Collection</title>
        <p>Data were collected from two primary sources: video recordings and a personal data acquisition form.
Video data provided observable, kinematic features of movement execution, while the questionnaire
captured latent variables such as training experience and background information. The video recordings
were obtained during maximum efort back squat sessions, and the forms included demographic and
training-related details .</p>
        <p>A total of 15 volunteers participated in the study, including 11 males and 4 females. The collected data
span a diverse range of attributes such as age, sex, height, body weight, training experience, strength
level, equipment accessibility, training program type, weekly training frequency, and participation in
powerlifting competitions.</p>
        <p>The video recording protocol adhered to standard 1-RM testing procedures, as described in Section 2.
Each participant completed warm-up sets, progressively heavier squats, and single-rep attempts up
to failure, defined as an inability to complete a repetition with proper technique. This generated a
rich dataset of annotated squat recordings, including both submaximal and maximal eforts. After a
short rest, participants also performed an AMRAP (As Many Repetitions As Possible) set at 75% of their
current 1-RM, increasing sample diversity with higher-repetition submaximal examples. These sets
additionally served as a dedicated test subset for evaluating traditional indirect estimation methods,
with results summarized in Table2.</p>
        <p>From a technical standpoint, each squat session was recorded using three cameras placed at fixed
positions: front view, left 45 ∘ angle, and right 45∘ angle. All cameras were mounted on tripods at hip
height relative to the participant to ensure consistency and minimize distortion. Video footage was
captured at a frame rate of 30 frames per second (FPS), providing suficient temporal resolution for
detailed motion analysis.</p>
      </sec>
      <sec id="sec-5-2">
        <title>5.2. Raw Data Processing</title>
        <p>We began the raw data processing phase by segmenting the video recordings into short clips, each
containing a single repetition of the back squat. This step resulted in a total of 1322 unique samples.
Following expert review, 1255 of these repetitions were deemed technically valid and met the criteria
for successful execution. Only these verified attempts were included in the modeling phase for 1-RM
prediction.</p>
        <p>The next step involved applying pose estimation using the BlazePose model, as previously discussed.
Given the model’s default set of 33 keypoints and the specific focus of our study we simplified the
keypoint structure. Multiple landmarks representing each limb and the head were aggregated into a
single point per segment, as upper-limb and head movement have limited relevance to squat Performance.
However, we identified a key limitation of the BlazePose model: the lack of explicit estimation for the
center of the hips and the torso. To address this, we introduced two custom keypoints representing
the approximate center of the pelvis and the trunk, as these areas play a crucial role in assessing squat
mechanics. The topology of the resulting 19-keypoint configuration is illustrated in Fig. 2 b.</p>
        <p>As a result, we obtained a complete dataset ready for analysis and experimentation. The dataset is
publicly available at the following link. It is distributed in three formats: raw video recordings, cropped
and labeled video clips, and files containing pose estimations as described in Section 4. Each version
also includes encrypted participant metadata collected via the personal data acquisition form.</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>6. Experiment</title>
      <sec id="sec-6-1">
        <title>6.1. Model Architecture</title>
        <p>The predictive architecture developed in this study was specifically designed to estimate the relative
load intensity of a back squat attempt based on both submaximal and maximal loads. The model consists
of three main components: the Squat Encoder, the Context Encoder, and the Regression Head, which
collectively enable the analysis of squat Performance by incorporating observable kinematic features
and user-specific contextual data. The overall model architecture is illustrated in Figure 3.</p>
        <p>The Squat Encoder serves as the core module for processing the component features of Performance,
as described in Section 4. These features are extracted from pose sequences obtained using the BlazePose
model, which outputs 3D keypoint coordinates for each frame of the video. Each pose sequence is
represented as a spatio-temporal graph, where joints are modeled as nodes and anatomical or temporal
relationships are represented by edges. This graph is then passed through a ST-GCN, which captures
both spatial and temporal dependencies in the motion data.</p>
        <p>
          The implemented model includes ten consecutive ST-GCN blocks with progressively increasing
channel sizes of 64, 128, and 256 (Figure 3). Each block applies a spatial graph convolution followed by a
temporal convolution, allowing the network to analyze movement over an extended time window. This
facilitates the detection of temporal patterns such as rhythm and control throughout the squat. To define
neighborhood relations within the graph, we tested multiple partition strategies, including uniform,
distance-based, and spatial configurations, using either the thorax or pelvis as the skeleton center [
          <xref ref-type="bibr" rid="ref19">19</xref>
          ].
These strategies determine how node neighborhoods are grouped during convolution, enabling the
model to emphasize diferent anatomical or directional aspects of the movement depending on the
configuration. The final ST-GCN block is followed by global average pooling, which compresses the
entire sequence into a fixed-length vector of size 256. This vector serves as a compact and informative
representation of the component features extracted from the movement.
        </p>
        <p>In parallel, the Context Encoder processes the latent features of Performance, as defined in Section 4.
Such features provide valuable context that complements the visual motion data and support the Squat
Encoder. The Context Encoder is implemented as a fully connected neural network composed of three
linear layers with ReLU activation functions and dropout regularization. The layers have output sizes
of 64, 128, and 256, respectively (Figure 3). The final output is a vector that encodes the athlete’s profile
and aligns dimensionally with the output of the Squat Encoder.</p>
        <p>The output vectors from the encoders are concatenated and passed to the Regression Head, which
performs the final prediction of relative intensity. The Regression Head consists of three fully connected
layers with 1024, 512, and 64 neurons, respectively, each followed by ReLU activations and dropout. A
ifnal linear layer produces a single scalar value corresponding to the predicted %1-RM for the analyzed
squat attempt.</p>
      </sec>
      <sec id="sec-6-2">
        <title>6.2. Loss Function and Training Algorithm</title>
        <p>The model was trained in a supervised regression setting. To guide the learning process, we employed
the Root Mean Square Error (RMSE) as the loss function, due to its sensitivity to larger errors and its
alignment with the objective of minimizing prediction deviation. In addition to the training loss, two
evaluation metrics—Mean Absolute Error (MAE) and R-squared ( 2) were tracked to provide a more
comprehensive assessment of model performance across experiments.</p>
        <p>
          During the initial phase of model development, three optimization algorithms were evaluated:
Stochastic Gradient Descent (SGD), Adam, and AdamW [
          <xref ref-type="bibr" rid="ref33">33</xref>
          ]. Preliminary experiments indicated that
AdamW consistently achieved superior performance in terms of both convergence rate and validation
error. This outcome is consistent with recent empirical studies demonstrating the advantages of AdamW
over other optimizers, particularly due to its decoupled weight decay regularization and improved
generalization capabilities in deep neural networks. In light of these findings and the observed empirical
performance, AdamW was selected as the optimization algorithm for all experiments reported in this
study.
        </p>
      </sec>
      <sec id="sec-6-3">
        <title>6.3. Data Splitting and Cross-Validation Strategy</title>
        <p>To reliably assess the quality of the trained models, we adopted the assumption that any split of a given
dataset must take repetition structure into account. This means that samples originating from the same
repetition, recorded by diferent cameras, must be assigned to the same subset. This ensures that no
data leakage occurs between any two subsets. However, due to the limited number of participants, it
was not feasible to perform a split into train and test sets based on individual subjects.</p>
        <p>Due to the relatively small size of the dataset for training deep neural networks, we had to limit the
test set to a suficient minimum. Therefore, we adopted a 9:1 split ratio between the training and test
sets. This corresponded to 1129 samples in the training set and 126 samples in the test set. During
model training, we applied 4-fold cross-validation. The training set was divided into four subsets, three
of which served as a temporary training set, while the fourth was used as a temporary validation set for
model evaluation during training. The test set, which contained samples unseen by the model during
training, was used exclusively for evaluation with the final epoch weights as well as with the weights
that yielded the best model performance.</p>
      </sec>
      <sec id="sec-6-4">
        <title>6.4. Optimization of ST-GCN Hyperparameters</title>
        <p>To optimize the predictive accuracy of relative load intensity estimation, we conducted a series of
experiments focused on selecting the most efective structural parameters for the ST-GCN model. Given
the inherent architectural complexity of Spatio-Temporal Graph Convolutional Networks and the
multitude of possible configurations, we focused on two principal design variables: the temporal kernel
size and the maximum hop distance. Both hyperparameters were evaluated in conjunction with various
partition strategies, which govern how neighborhood information is propagated between graph nodes.
Each value of the temporal kernel size and max hop distance was assessed in combination with four
distinct partition strategies: uniform, distance-based, spatial with the skeleton center located at the
thorax, and spatial with the skeleton center located at the pelvis.</p>
        <p>The first stage of the experiments investigated the influence of the temporal kernel size, which
defines the size of the time window used in temporal convolutions. This hyperparameter controls
the model’s ability to capture long-range temporal dependencies within the input pose sequences.
Assuming a video frame rate of 30 FPS, we tested kernel sizes of 15, 31, 61, and 75, corresponding
to approximately 0.5, 1, 2, and 2.5 seconds of motion, respectively. Each kernel size was evaluated
in conjunction with the four aforementioned partition strategies. For the sake of comparability, the
maximum hop distance was fixed at 1 across all strategies in this stage, as the uniform strategy is
only defined for a hop distance of 1. Table 3 presents the results of these experiments. The lowest
RMSE overall (5.8157, SD = 0.3972) was achieved using the uniform partition strategy with a temporal
kernel size of 75. However, larger temporal kernels significantly increase inference time, which may
hinder real-time or resource-constrained deployment. Among the non-uniform strategies, the most
consistent and favorable performance was observed with a kernel size of 31. The best configuration
in this group (RMSE = 5.8596, SD = 0.2808) was obtained using the spatial strategy centered at the
pelvis. Considering the trade-of between accuracy and computational eficiency, a kernel size of 31
was selected for subsequent experiments.</p>
        <p>In the next phase of our study, we investigated the impact of the max hop distance hyperparameter,
which defines the maximum number of graph edges over which information can propagate during
spatial graph convolution. In practice, this hyperparameter controls how far each node can influence
others during message passing within the ST-GCN layers. Each partition strategy was evaluated with
max hop distances ranging from 1 to 4. Higher values were excluded from analysis, as the underlying
skeleton graph used in this work contains only 19 nodes. Beyond a certain threshold, increasing the hop
distance leads to a rapid saturation of graph connectivity—diminishing the benefits of localized spatial
structure and increasing computational cost without meaningful performance gain. Table 4 summarizes
the results. The lowest overall RMSE (4.8342, SD = 0.5930) was achieved using the distance-based
partition strategy with a max hop distance of 2. This configuration outperformed all other combinations
across the evaluated strategies. For the spatial partition strategy (both thorax- and pelvis-centered), the
best performance was observed at a hop distance of 1, although the corresponding RMSE values (5.3674
and 5.6552, respectively) remained higher than the optimal distance-based configuration.</p>
        <p>Based on the results of the architectural experiments, the optimal ST-GCN configuration was
determined to include a temporal kernel size of 31, the distance-based partition strategy, and a maximum
hop distance of 2. This setup provided the most favorable balance between prediction accuracy and
computational eficiency across tested variants. Accordingly, this configuration was adopted as the
default in all subsequent experiments. Furthermore, the model achieving the best performance (RMSE
= 4.8342, SD = 0.5930) with these optimal settings was designated as the baseline for the remainder of
the experimental study.</p>
        <p>All architecture-related experiments were conducted under fixed training conditions. To ensure
a fair comparison between configurations, all models were trained using identical hyperparameters,
which remained unchanged throughout this phase of the study. The only variables modified were the
structural parameters under investigation—namely, the temporal kernel size, the partition strategy,
and the maximum hop distance. Each model was trained for exactly 100 epochs, providing consistent
training duration across all configurations. This setup allowed us to isolate the efect of architectural
design choices on prediction performance, without introducing confounding factors from optimization
dynamics.</p>
      </sec>
      <sec id="sec-6-5">
        <title>6.5. Model Training</title>
        <p>The proposed was trained for a maximum of 200 epochs. Given the relatively small dataset, batch
sizes ranging from 16 to 64 were explored. A conventional early stopping strategy was employed
to ensure training stability and prevent overfitting by halting training when validation performance
ceased to improve over a specified window. Model checkpoints were monitored throughout training
and saved whenever the validation loss improved. However, only the best-performing checkpoint i.e.,
the one achieving the lowest RMSE on the validation set—was retained for final evaluation. Learning
rate scheduling was applied using strategies such as the StepLR scheduler to promote convergence.
Throughout training, model performance was continuously evaluated on the validation set using the
RMSE metric. After training completion, both the final epoch weights and the best checkpoint were
evaluated on the test set using RMSE, MAE, and  2.</p>
        <p>Data augmentation was applied exclusively to the training set and limited to the input of the Squat
Encoder, which processes pose data derived from BlazePose. Specifically, Gaussian noise was added to
the 3D keypoint coordinates. The noise was drawn from a normal distribution with a defined mean
and standard deviation. To introduce variability while preserving data diversity, this transformation
was applied probabilistically, ensuring that only a portion of the samples was augmented within each
training epoch.</p>
        <p>The final model was trained using a batch size of 64, with a learning rate of 0.0001 and a weight decay
of 1e-6. Dropout regularization was set to 0.1 across fully connected layers, and training was conducted
for 150 epochs. A StepLR learning rate scheduler with a step size of 50 and decay factor of 0.5 was used
to refine convergence. Noise-based data augmentation was applied to the pose input with a probability
of 0.9, using zero-mean Gaussian noise with a standard deviation of 0.01. The ST-GCN configuration
included a distance-based partition strategy, a maximum hop distance of 2, and a dilation factor of 1.</p>
        <p>The proposed model achieved the highest predictive accuracy across all evaluated metrics, as
illustrated in Table 5, outperforming both the baseline and the classical Mayhew model. It obtained the
lowest RMSE (4.5412) and MAE (3.3338), with notably low variance, indicating stable performance.
While the Mayhew model showed a slightly higher  2, this can be attributed to the limitations of
 2 in nonlinear settings—it favors models that explain overall variance, whereas our model captures
ifne-grained, nonlinear patterns that yield more precise predictions, better reflected by RMSE and MAE.</p>
        <p>The training curves, shown in Figure 4, confirm the model’s efective convergence and generalization.
Overall, the proposed model demonstrates superior performance and stability, ofering a more accurate
and nuanced alternative to traditional linear methods in estimating 1-RM.</p>
      </sec>
      <sec id="sec-6-6">
        <title>6.6. Hardware and Software Configuration</title>
        <p>The experiments were carried out on a system running Windows 11, equipped with an NVIDIA RTX 6000
Ada Generation (48 GB VRAM), an AMD Ryzen 9 7950X 16-Core Processor, and 64 GB of RAM, providing
a robust environment for deep learning tasks. Python 3.11 was used as the primary programming
language, with PyTorch 2.6.0+cu118 serving as the core deep learning framework.</p>
      </sec>
    </sec>
    <sec id="sec-7">
      <title>7. Conclusion</title>
      <p>This study presented a novel, vision-based approach for predicting One-Repetition Maximum in strength
sports, specifically targeting the estimation of relative load intensity in the back squat using
spatiotemporal pose data. By combining BlazePose-based pose estimation with Spatial-Temporal Graph
Convolutional Networks, the method successfully inferred %1-RM from full-body movement patterns,
ofering a more accurate, non-invasive alternative to traditional sensor-based or formulaic methods.</p>
      <p>The findings highlight the potential of data-driven, movement-based performance modeling,
particularly in settings where safety and scalability are essential. Future research will aim to improve model
generalizability through expanded datasets and enable real-time deployment in training environments
using lightweight architectures. These advancements could pave the way for intelligent coaching
systems that provide immediate, personalized feedback to athletes and coaches.</p>
    </sec>
    <sec id="sec-8">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the authors used o4-mini for Generate literature review and
Abstract drafting. Furthermore, GPT-4.1 was used for Text translation, Paraphrase and reword, Improve
writing style and Grammar and spelling check. After using these tool, the authors reviewed and edited
the content as needed and take full responsibility for the final version of the publication.
To support reproducibility and further research, the full source code and the dataset prepared for these
experiments are provided in the following repository
• GitHub</p>
    </sec>
  </body>
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