Background

To date, various techniques have been proposed to interpret DNNs. For example, many model interpretability techniques provide task-specific and local explanations, such as saliency maps, attention maps, or Layer-wise Relevance Propagation (LRP), which interpret or visualize the localized influence of a region on the output. These ad-hoc approaches can be unstable, as even a minor change in a single pixel or hyperparameter can substantially affect the local relationships between input signals and output data [24]. Additionally, these local explanations fail to offer a global understanding of whether the selected architecture is well-suited to the task or how the DNN models experience learning. On the other hand, feature attribution methods like SHAP [66] and LIME [67], while conceptually easier to interpret and model-agnostic, tend to work more intuitively with interpretable dimensions typically found in structured tabular data. These methods are less effective for unstructured tasks, such as image and audio data, where feature dimensions are harder to define or interpret. While most techniques emphasize the qualitative interpretation of a model, such as what has been learned or captured by the DNN, the absence of quantifiable measurements makes cross-model comparisons in unstructured tasks particularly challenging [4, 5, 25]. We further provided a systematic description of different model explainability methods, along with their pros, cons, and use cases, as well as a comparison to our proposed approach in Table 1.

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Table 1. DNN Explainability Methods Comparison.

https://doi.org/10.1371/journal.pone.0313772.t001

In a foundational article on deep learning, LeCun and the colleagues [1] characterized DNNs as representation-learning methods utilizing multilayered large neural network-style models. Representations can be viewed as mental objects capturing semantic properties either observable or unobservable [26]. Different from traditional machine learning models, DNNs display remarkable flexibility and efficiency in encoding lower-level input signals, such as pixels, audio frequencies, or word tokens, into multidimensional vectors at a sophisticated level through multilayered nonlinear transformations [27]. These transformations generate multiple levels of representations that learn hierarchies of features at each layer [1]. The continuous numerical vectors (or hidden vectors) learned at each level are commonly referred to as “embeddings” and serve as dense representations of the original input data. Following this construction, numerous studies have demonstrated the correspondence between DNN-generated and real-world distributed representations among words and sentences [11, 28], speeches [29], images [9], objects [30] and scenes [31, 32]. Representational learning in DNNs offers fundamental contributions to cognitive science, as it can inform how cognitive systems process and organize knowledge, facilitating the comparison of learning processes between humans and machines [33–35].

Recently, several studies in cognitive science and neuroscience have highlighted the importance of integrative modeling between computation, human brains and behaviors [12]. Beyond comparisons of static end-point knowledge, scholars have begun exploring the potential correspondence in learning and information processing between DNNs and human cognitive systems, given that the current performance of DNNs can already approximate human performance across various domains [36–38] (see [18] for a review). For instance, the representations (i.e., embeddings) extracted from multilayered DNNs have shown significant accuracy in predicting neural and behavioral responses in humans throughout the hierarchy of learning and processing. This evidence spans multiple neural-behavioral measurements (e.g., fMRI, EEG, ECoG), modalities (e.g., visual, auditory, and language processing), and model architectures (ranging from simple embedding models like GloVe to more complex neural networks such as RNNs, convolutional neural networks (CNNs), and transformer models (for further details, see [9, 11, 12, 23, 39, 40]).

Given the extensive alignment observed between DNN embeddings and neural-behavioral activities, and their presumed meaningful representational mapping with human cognitive systems, an analysis of how they emerge in learning would seem important to understand these relationships. Goldstein and colleagues [11] identify the temporal correspondence between layer-by-layer embeddings in GPT-2 and evolving neural activities in language areas. However, this temporality is restricted to layerwise representations (from low-level to high-level representations) rather than how streams of signals have been received and processed by models or brains [38]. Our aim in this paper is to use temporal analysis in a systematic way by separating and tracking the time course of a network’s learning across classification tasks, thereby enhancing the understanding of the emergence of representations in DNNs.

The current study

The goal of this study is to unpack the “learning curve” of DNNs through a sequence of hidden representations when the model encounters any temporal processing tasks across its training. To do so, we sample the network’s performance by using its embedding vectors to classify groups of items in its training input. This allows us to map out the progression of the network’s discriminations across these groups – how the network’s internal knowledge, in the form of embedding vectors, evolves during training.

The model architecture we focus on is RNNs due to their capacity to model sequential data and time-dependent tasks [41], such as text generation, speech recognition and stock market prediction. Although other deep learning architectures, such as CNNs and Transformers, also have the capacity to process time-series data, RNNs are explicitly designed for processing sequential data, as they effectively capture temporal dependencies through their recurrent connections. CNNs excel in tasks such as image recognition by applying the kernel trick, where convolutional filters are used to extract spatial features from local regions of the input. While CNNs can be adapted to handle sequential data using techniques like 1D convolutional layers, they lack the inherent ability to capture temporal ordering in the data, as they process each segment of input independently. Transformers, on the other hand, rely on self-attention mechanisms to weigh the importance of different input tokens in parallel, allowing them to capture dependencies between distant elements (i.e., tokens). This feature makes Transformers better suited for tasks where relationships between tokens are not strictly ordered in time, and their parallel processing nature is less ideal for learning tasks that require explicit temporal progression. In sum, the strict sequential processing nature of RNNs makes them an intuitive architecture for studying cognitive processing that involves dynamic, changing contexts [42].

In this study, we propose a generalizable interpretability approach that maps the global learning curves of RNNs based on changes in classification performance between embeddings and output across timesteps of the input data. This performance reflects the predictive capacity or the amount of signal captured by the embeddings in predicting the final output. In RNN modeling, each timestep generates an embedding (e.g., in language processing, each timestep represents a word). These embeddings progressively incorporate information from the beginning up to timestep t. By examining changes in classification performance between these embeddings and the output, we can capture how the information evolves over time. To provide clarity, we use the term “learning curve” in this study to denote the holistic approach and intention behind mapping the underlying processing and developmental journey of DNNs. The method we propose separates two parts of the learning curve, one based on overall training, and another based on processing within input items during training. First, the “developmental trajectory” signifies the long-term learning process of DNNs, which is simulated by the increasing number of epochs (i.e., complete passes through an entire training dataset). Second, the “(information) processing trajectory” refers to the momentary accumulation of information across all timesteps (within an epoch), extractable from the performance of the RNN layer (see Fig 1 for a conceptual illustration). We detail each of these further below.

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Fig 1. A conceptual illustration of learning curves in DNNs.

The solid curve represents an individual information processing trajectory (across timesteps). For example, as an agent receives more signals over time in one session, its prediction of the gesture increases. The bundle of dotted lines represents a developmental trajectory (across epochs). For instance, this agent improves its ability to predict incoming gestures after repeatedly encountering similar patterns. In a typical binary classification task, the starting point at t=0 is expected to be near 0.50 (and gradually increase to 1.00 across timesteps and epochs) for all epochs because no signals have been provided at the first timestep for solving the underlying task. Hence, all information processing curves in this figure have the same starting point to reflect this pattern. In practice, certain classification tasks might contain structural information even at t=0 (e.g., gesture classification contains spatial information, such as the location of keypoints, at the initial timestep, which could help solve the gesture task from the very beginning).

https://doi.org/10.1371/journal.pcbi.1012286.g001

As Fig 1 illustrates, the resulting visualization consists of learning curves with timesteps on the x-axis and performance on the y-axis. Each epoch contains an information processing trajectory, and the set of curves together forms a developmental trajectory. Due to the multidimensional nature of this plot, while it provides rich qualitative information about the entire model learning experience, it can be challenging for researchers to comprehend all the constructed curves at once. Therefore, beyond the visual presentation and qualitative inspection of the multi-dimensional learning curves, this study further defines four measures: start performance (start, the initial capacity of each information processing), max performance (max, the maximum performance of each information processing), time at max (t_max, when the current information processing reaches the maximum performance), and end – start performance (end – start, the overall performance gain in this information processing) – to facilitate quantitative comparisons across tasks and datasets. Our study particularly focuses on these relatively easy-to-comprehend descriptive statistics (as opposed to more complex metrics like regression coefficients) to simplify the understanding of the already multidimensional and granular nature of the constructed learning curves.

To illustrate the generalizability of our approach, we chose two distinct classification tasks: (i) sentence classification and (ii) gesture detection. These tasks differ widely in terms of their modalities. We predicted this would lead to variation in the underlying data generation processes and associated cognitive processing for each modality. In particular, gesture and body movements primarily result from the coordinated contraction and relaxation of muscles, with signals produced at later timesteps derived from the previous timesteps with relatively high autocorrelation [43]. On the other hand, verbal language, being a predominantly semantic modality, exhibits degrees of surprisal and arbitrariness that enhance the cognitive capacity of language processing [44–46]. Therefore, the expected developmental and information processing trajectories will likely exhibit distinguishable patterns across the two different tasks when the DNN system processes them respectively.

As we discuss in detail in later sections, this method has a few benefits. Through tracking the learning trajectory of a neural network, researchers can explicitly identify the appropriateness of a model for a given task as well as examine the properties of underlying input signals. This approach could also serve as a standalone visualization to map the accumulation of the underlying signals processed, which can facilitate research on deep learning modeling and signal processing across various modalities. Finally, mapping the learning curve of DNNs has the potential to assist future computational cognitive and neuroscience research and address whether the learning experiences of models also correspond to (or fail to correspond to) the temporal processing in human cognition in addition to the emphasis on static representations in the current literature.

In the following sections, we will provide a step-by-step method for visualizing the learning curves of neural networks, illustrate how to holistically interpret signal processing in them and quantitatively compare these curves across two different datasets.

Datasets

This study utilized two datasets: the Identity-free Video Dataset for Micro-Gesture Understanding and Emotion Analysis (iMiGUE) by [48] and the Emotion dataset from Hugging Face by [49] to examine the possibility of mapping learning curves for tasks involving temporality. The two temporal tasks (i.e., gesture detection and sentence classification) are distinct in terms of their modalities, lengths, and the steps required to extract and preprocess the features, thereby enhancing the diversity of data to illustrate the learning curve analysis. We detail the preparation of each dataset separately below.

Gesture classification.

The iMiGUE is a high-quality dataset that contains 18,499 identity-free, ethnically-diverse, gender-balanced samples of 32 psychologically-meaningful micro-gestures (such as scratching an arm, adjusting the hair, or touching an ear [51]). These gestures were all curated from interview clips with athletes at post-match press conferences. Unlike other gesture and emotion datasets, which are typically drawn from staged performances or movie clips, the iMiGUE provides samples of actual gestures from real-life situations. This poses a more realistic, though more challenging, recognition task for deep learning networks [54, 55].

Due to copyright restrictions, the dataset includes only skeleton keypoints (rather than original interview clips) extracted from OpenPose, a multi-person computer-vision system that can simultaneously extract keypoints of the body, hands, face, and feet [56]¹. In total, 25 body, 70 facial, and 21 left hand and 21 right hand keypoints were extracted for each frame using OpenPose. Keypoint data were stored in the following format: [x0,y0,c0,x1,y1,c1… ], in which (x, y) represents the coordinate of each keypoint and c indicates the confidence score of each keypoint-coordinate prediction. The confidence score was excluded in the following processing steps.

Although the gesture clips have just 39 frames on average, they have a higher standard deviation at 84 frames with a 75th percentile of 72 frames. We therefore set the padded length of the input sequence to 150 frames to ensure that our input data contained sufficient information for training a classifier. Thus, the input size for each gesture clip was 274 units (137 keypoints × 2) × 150 timesteps (see Fig 3).

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Fig 3. Sequential data for Emotion Tweet (left) and Gesture Classifications (right).

NB: Gesture figures are adapted from Wikimedia Commons [47].

https://doi.org/10.1371/journal.pcbi.1012286.g003

It is important to note that our aim here is not to approach benchmark performance, but rather to examine successful learning. The learning curve analysis will show how that successful learning emerges, and which stimulus discriminations seem to underlie that emergence. Since even the state-of-the-art neural network can achieve only 55% accuracy on this multi-classification task [48], we further grouped the 32 micro-gestures into six categories (body, head, hand, body-head, head-hand movements and an absence of gestures) to ensure that our RNN-LSTM was indeed “learning” when we attempted to map its learning curve.

Model architecture

We selected a model architecture (see Fig 4) that is standardized for sequential stimulus processing in the following way. First, we had a batch normalization layer, a primary RNN-LSTM layer, and then a fully connected layer to connect the final dense embeddings with the output classes (for classification). We offer details below.

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Fig 4. Model architecture of RNN-LSTM.

NB: Gesture figures are adapted from Wikimedia Commons [47].

https://doi.org/10.1371/journal.pcbi.1012286.g004

Deep learning simulation

To ensure the generalizability of our learning curve mapping approach, we performed 15 rounds of simulation for both gesture and emotion detection tasks, each of which included 15 (6C2) pairwise binary classifications. We conducted 25 repetitions (reps) for each set of simulations (sims) to mitigate the idiosyncrasies of specific processing and developmental patterns we are extracting under each pairwise condition. In total, we collected 25 × 15 × 2 ( reps × sims × tasks) = 750 runs of simulation data. Having an adequate number of simulation runs also enables us to observe clustering tendencies in the convergence and divergence of trajectory patterns across various tasks and different classes.

In each simulation, 20% of the shuffled samples were used as the test data, while the remaining data were further split into 80% training data and 20% validation data. While validation data were used for reporting each epoch’s model performance, test data were used for reporting the final model performance on unseen data.

The number of epochs indicates the number of times an entire dataset has been passed forward and backward through the neural network. We set the number of epochs to 50 for both tasks, given that most of the variation in learning tends to unfold during the early stages of development. In S3 Text and S4 Text we also illustrate how using 20 and 100 epochs leads to similar observed patterns.

Because deep learning algorithms are very sensitive to unbalanced datasets, we applied data augmentation to the training and validation datasets. Specifically, the minority class was up-sampled to match the number of data points in the majority class, which ensured a balanced dataset [59].

Default initiation from PyTorch was used to standardize the model specification across simulations. All simulation runs were trained using the Adam optimizer with a learning rate of 0.001, and the loss function used was the cross-entropy loss for all pairwise classifications. All the other learning rate hyperparameters were kept at their default values.

Since deep learning is, computationally speaking, very expensive to train, the model was run on Nvidia RTX 4090 to expedite the processing. We set the batch size to 64 for gesture recognition and 256 for emotion classification to achieve an optimal balance between training speed and performance.²

To map a learning curve for each simulation, we first extracted embeddings of all LSTM timesteps from the hidden layer. We then applied multiple interpretable machine-learning models between these embeddings and the corresponding output labels to understand how the model’s confidence is updated during the LSTM timesteps.

Quantifying performance across epochs

These learning curves examine how the LSTM’s embeddings classify the stimulus as it is incrementally presented to the network. Visually, each curve is plotted as the proportion of correct classifications across the item. These constructed learning curves can be analyzed in various ways, either through qualitative interpretation of the visualizations or by applying statistical analysis for quantification and hypothesis testing. In this study, we utilized the four descriptives statistics introduced earlier to assess the multidimensional KKN classification performance of the RNN-LSTM (i.e, how the discriminability of the model is evolving) across its training on two datasets, reconstructing and analyzing the unfolding learning dynamics of these distinct learning tasks. Specifically, for each such curve, we extracted four simple descriptive metrics: start, end - start, max, t_max. In Fig 5, we illustrate these descriptive statistics from an example trajectory of a single classification run for each dataset.

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Fig 5. Examples at epoch 1 and 50 of binary classification across a test input for one run of the network.

From epoch 1 to epoch 50, the LSTM’s embeddings are able to classify successfully over the test item, and we can characterize this success as a change to its performance using four metrics described in the main body of the text (start, end - start, max, t_max). Top: Example item from the sentence task. Bottom: Example item from the gesture task.

https://doi.org/10.1371/journal.pcbi.1012286.g005

First, we defined the maximum performance (max) and the percentage of time at which that maximum was achieved in the presented item (t_max) over the whole timesteps. We included t_max alongside max because we discovered that max alone is not sufficient to determine performance, especially earlier in training. This is because the network may exhibit unstable performance, dropping across subsequent time slices, which may be indicative of a non-monotonic learning trend seen in related domains [62]. This also suggests the network has learned something about the initial segments of an item, but the later segments wash out its performance as it has not yet encoded these later features. To capture this trend, we use t_max to assess when that maximum was achieved within each information processing trajectory – specifically, the percentage of the time slice at which the observed maximum occurred. In Fig 5 above, we show an illustration of this in the top left. The network achieved a performance of 0.82 on this particular item, but failed to sustain this performance as it dropped to near 0.50 as the sequence unfolds (at epoch 1). In the top right, the performance improves approximately monotonically across time slices (by epoch 50), and t_max is achieved near the final bin of the training item.

Additionally, we assess the performance at the start and end of the presented stimulus (start, end). Performance at the start may indicate the relative gains that can be expected from a stimulus item. As shown in the bottom panels of Fig 5, the gesture input already has performance above chance ( ~  0.80) after the very first segment of the stimulus item. This suggests the model rapidly exploits spatial information in gesture (i.e., the location of keypoint coordinates can already vaguely differentiate gesture classes before sequential movement information is fed into the model). A model that achieves near-perfect performance at start and sustains it does not need to be exposed to the subsequent stimulus. The last measure we use is the subtraction of end - start performance. A high value on this measure suggests the network gets substantial information gains across a test item. For example, even at epoch 50 in the bottom right, the end - start of the gesture item is substantially lower than the simulation trained on the sentence task.

These measures can be plotted across epochs. Each learning curve now indicates how an item is being processed across an LSTM’s overall training. The measures are relevant to two timescales in the network’s behavior we conceptualized earlier: developmental (or learning) and information-processing timescales. For example, across epochs, movement along the start measure represents the initial performance at the item’s first time slice at the beginning of each information processing session. The end - start measure within an epoch can describe the relative information gains during each processing session from the item’s full presentation. The max represents the best performance achievable in a session, indicating the network’s current information processing capacity. Finally, if t_max is low, it suggests that the network’s maximum performance of the current session is hindered by subsequent timesteps, implying that additional training may be necessary.

Start performance

In Fig 6, we show the LSTM performance at the start of an item across epochs of training. In general, the sentence dataset shows low, near-chance performance, while gesture classifications are already well above chance performance. This chance-level performance for sentence items stays consistent across the entire training period, though the gestural dataset shows some improvement. For the gesture dataset, this suggests that the network has some information about a classification before much of a training item is even shown to the network. It would indicate that gestural data has spatial information in the point coordinates of the body and is exploited by the network at the very first time bin. With language, it takes time for word embedding vectors to be integrated in the network.

To confirm these trends, we tested a linear model that predicted start performance by training data, showing that dataset accounted for about 98.14% (p  <  .0001) of the variance seen in Fig 6. The classification of the gesture data accounts for 95.51% (p  <  .0001) of variance internally to that dataset, whereas for sentence classifications accounts only for 10.28% (lower but also significant, p  <  .0001). The learning curves reveal that the first word of a language task has low diagnostic accuracy for a classification, but the spatial variance over gestural classifications is much more informative.

The start performance for sentence null is the only metric that shows no significant difference between learning from ordered sentence classes and reshuffled data (among all significance tests; = 0.0001, p  <  .0879). This is expected, as all sentence binary classifications begin with a consistent initial performance of 0.50 (random guessing for binary classification), which remains unchanged even with randomly reshuffled sentence data. In contrast, the start performance significantly differs for ordered gesture classes versus reshuffled data because the various gesture pairs contain different levels of spatial information ( =0.0824, p  <  .0001), affecting their initial performance.

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Fig 6. Start performance for pairwise classifications.

Start metric over epochs, indicating that in the sentence task, the classification at the first time slice remains stable near change, whereas the LSTM’s embeddings for the gesture task are distinct across stimulus types, and also show slightly more improvement over training (while already being well above change relative to the sentence task).

https://doi.org/10.1371/journal.pcbi.1012286.g006

Max performance

Curiously, if one only investigated maximum performance across training, these classification tasks could be regarded as relatively similar in their behavior. As shown in Fig 7, both sentence and gesture datasets yield a classification performance that is high, between 0.75 and 1.0 depending on the classification. In the gesture dataset, there are more “difficult” classifications, shown by outliers in max performance across training. This can be helpful in diagnosing representational challenges in the network’s training, marking what pairs of training items may be more difficult to distinguish than others.

Again, as with the start measure, the max performance shows greater variance associated with classifications in the gesture case ( =0.8250, p  <  .0001) than the sentence case ( =0.2736, p  <  .0001). The difference between these two datasets is not as pronounced as in the start measure, as a linear model shows that only 2.11% (p  <  .0001) of the variance is associated with the dataset in a linear model predicting max performance observed within a trial. Despite the small value, it is nevertheless significant and driven by the relatively higher performance in the sentence task.

The max performance also differs for both sentence ( =0.0042, p  <  .0001) and gesture tasks ( =0.0722, p  <  .0001) when the network learns from ordered datasets compared to randomly shuffled ones. The sentence conditions appear to pick up more spurious signals, ultimately approaching 1.00 as the epochs increase, while the gesture condition remains consistently unlearned across epochs. The learning pattern for t_max across epochs (see next section) provides additional insights into these trends.

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Fig 7. Max performance for pairwise classifications.

Both sentence and gesture tasks show an increase in max performance over training epochs. On average this asymptotes near perfect performance but can vary depending on binary classification.

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Time at max

We would expect that completed training in the LSTM should show that maximum performance should appear near the end of an item, as this would suggest that the network has extracted useful information in the whole presentation. Indeed, this is indicated by lower time-at-max values earlier in the training. During the first few epochs, the maximum value occurs proportionally earlier in a training item, similar to the example shown above in Fig 5. However in both sentence and gesture datasets, networks slowly extract features across the stimulus items for classification, as shown in Fig 8. The time gradually rises for all classifications, though it can also vary widely and tends to be more irregular in gesture.

In a linear model predicting t_max from data source, sentence and gesture are only slightly different, with 0.34% (p  <  .0001) of the variance accounted for. Classifications in sentence and gesture both relate significantly in a linear model predicting time at max, with sentence classifications accounting for 9.51% (p  <  .0001) of the variance and gesture classifications 24.95% (p  <  .0001).

Interpreting t_max alongside max, we confirm that the learning experience of a language task is more reliant on spurious signals for reshuffled data compared to ordered data, as max continuously increases to reach 1.00 while t_max remains sporadic. The gesture condition remains consistently unlearned across epochs for reshuffled data, as the max performance can occur at any point along the processing trajectory (any timestep). Both t_max values indicate that no meaningful delayed signals were developed when the network was trained on superimposed reshuffled data. The time at max differs significantly for reshuffled versus ordered data in both sentence ( =0.0120, p  <  .0001) and gesture ( =0.0058, p  <  .0001) conditions.

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Fig 8. Time at max (t_max) for pairwise classifications.

Both sentence and gesture tasks show an increase in the proportion of time at which maximum performance is observed. Indicative of information gain, this rises in both – suggesting the LSTM comes to better integrate the full test items for its performance. However this is much more orderly in the sentence task than the gesture task.

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End - start performance

Finally, we wish to get a sense of how the LSTM models are extracting information within an information processing session. One way to do this is to discern how much higher its performance is at the end of a session compared to its performance initially. This is where we see the greatest difference between the datasets. As shown as Fig 9, sentence shows substantial information gain across stimulus items. By the end of training, the start and end of trials involves considerable difference, and the positive value of this difference shows that the network improves its performance significantly across presentations. With gesture, the situation is quite distinct. In most classifications, there is indeed a rise. But because gesture is informative even at the first time bin of an item, there isn’t much information gain remaining. Indeed even the highest instances of this value hover near 0.10. Therefore, while performance on gesture is higher at first, the network may find the task more difficult in integrating that spatial information over time to improve performance.

As in the start measure, the difference between datasets is quite large. When data source is used to predict the end - start measure, 39.23% (p  <  .0001) of the observed variance in this measure can be associated with data source, with sentence associated with much higher information gain than gesture results. When looking at each data source separately, only 13.01% (p  <  .0001) of the measure is associated with the classification pairs in sentence. In the gesture dataset, this association is 38.08% (p  <  .0001), showing much higher contribution of the class differences in gesture.

Both sentence’s (R² =0.0027, p  <  .0001) and gesture’s (R² =0.0340, p  <  .0001) end-start values differ significantly between ordered and reshuffled data. Consistent with max performance gradually reaching 1.00, the information gain of the sentence network increases incrementally from 0.00 to 0.50 when trained on reshuffled data. Combined with insights from t_max, we suggest that although learning may appear to occur even with reshuffled data, it is likely driven by spurious signals picked up during the processing session. Additionally, the end-start performance for gesture gradually improved from highly negative to slightly negative but was not able to reach 0.00 during the early epochs (e.g. epochs smaller than 50), which explains the flat max performance for the reshuffled gesture condition.

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Fig 9. End - start performance for pairwise classifications.

The information gain from start to end of stimulus item shows a stark difference between datasets. The sentence task shows that the LSTM’s performance rises as it integrates data from start to end. With gestures, the story is more complicated, showing less improvement overall, and in one classification task, it is almost entirely unlearned.

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Non-monotonicity

First, we observed a non-monotonic trend in the learning experiences of DNNs. In other words, learning does not always show an increasing monotonic improvement because networks sometimes reveal temporary decrements in their performance across training. This is a characteristic recognized in previous literature as a key advantage for their advancement in addressing the most challenging tasks. For example, in applying neural network models to language, the presence of non-monotonic learning was taken as evidence that networks “reorganize” their knowledge as they learn. This may mean networks are acquiring more efficient representations of a problem space and the drop in performance is indicative of a transition into that more efficient representation. Classically, in the case of models learning language, they show a decrement in performance when they “discover a rule” in grammars [68] Our results are a testament to the observation that both representational consolidation and “catastrophic forgetting” remain as important issues in DNN learning [69].

Specifically in our results, we found that RNNs exhibit different preferences for early versus late cues when addressing various sequential tasks. For instance, in the sentence task, we noted a more pronounced performance improvement occurring in the later stages of information processing (i.e., model development). In contrast, gesture learning tends to show quicker progress, with more variability across epochs and repetitions of simulations, suggesting that DNNs tend to rely on shortcuts, such as naive cues related to keypoint coordinates, for gesture classification, rather than focusing on high-level movement sequences. This shortcut-based “learning” also is evident in the higher initial performance (start) for gesture classification ( >  0.75). On the other hand, sentence classification begins at around 0.50 (the at-chance probability) and exhibits greater performance gains in later epochs, indicating that the models classify based on high-level semantic sequences.

Pairwise comparisons

Additionally, although multiclassification tends to exhibit collective model performance, our between-class pairwise comparisons reveal the presence of outliers within multiclassification. For example, “joy/fear”, “surprise/fear”, and “sadness/fear” demonstrate higher information gains across epochs compared to other emotion pairs, suggesting that these classes are further apart from each other. The “body/head” classification appears to experience learning challenges, possibly because these two movements have difficulty being completely separated, as the head’s movement in naturalistic data may inevitably coincide with that of the body due to joint coordination.

The combination of learning curve mapping and instance measures thus serves as an effective approach for “auditing” representations in multiclassification problems. The proposed pipeline improves model explainability beyond holistic evaluation of classification performance and ad-hoc attention visualization by unpacking pairwise class learning patterns to reveal any pairs that are unsuccessful in being discriminated or involve delayed knowledge gain. This granular examination allows modelers to better investigate a model’s appropriateness for the underlying task, as well as the properties of the processed input signals, reaffirming the value of our learning curve conceptualization.

Domain distinctions

With these findings, it is tempting to infer that there are domain distinctions among different modality classification tasks. Gesture learning, for instance, may rely on autocorrelated signals (as body movements result from the coordinated contraction and relaxation of muscles), potentially emphasizing spatial semantics as early cues ³, while language learning relies on higher degrees of surprisal, irregularities and arbitrariness, as suggested by previous literature (see [43–46]). These domain distinctions are valuable to cognitive science in understanding how humans process and distinguish between various modes of communication, shedding light on the neural mechanisms underlying the flexibility and adaptability of the human mind when processing different forms of information and communication modalities.

Though it is intuitive and tempting to explain these domain distinctions here, we cannot yet assert that these trends would hold for all sentence or gesture (keypoint) classification tasks, only the ones we investigate here. However the learning curve results would seem to align with an intuition of how linguistic symbols would be sequentially integrated into a neural network in contrast to the highly auto-correlated spatial information contained in gesture performance. Still, we cannot infer a broad generalization about “language vs. gesture” and only leave it as a potential path for future investigation. Indeed, this may be an additional benefit of a method like the one we present here. Learning curves could finely ascertain these domain distinctions, and expanding the set of data to test may permit generalization in future work. This may have theoretical implications itself. The learning curve analysis may provide information about the distinct sources of information from varied modalities. When neural models (or human brains, presumably) integrate distinctive sources of information, they may strengthen understanding of complex multimodal data by leveraging their unique information-processing and developmental benefits.

Limitations

This study provides conceptual and operational illustrations of applying learning curve methods to RNNs, though both the illustration and the proposed method come with certain considerations. First, we selected two distinct datasets to demonstrate how learning curves offer insights into different data and modality learning experiences. While illustrating significant domain distinctions, our study is limited in making broad generalizations between “language vs. behavioral.” Future cognitive and behavioral research interested in such conceptual generalization can apply our proposed method to various distinct language tasks (e.g., language translation) and behavioral datasets (e.g., facial expression detection) to achieve broader generalizations across different modalities. Additionally, as highlighted at the beginning, our method could have implications for multimodal DNN modeling, given that our simulations utilize datasets with distinct modalities. For the current scope, we focus on how our proposed method facilitates the understanding of distinguishable modalities as an initial step, while future work can explore adopting this method for multimodal DNNs and datasets (e.g., audiovisual emotion classification) to assess how multimodal learning differs from unimodal learning.

From a methodological standpoint, as detailed in the model explainability technique comparison (Table 1), our proposed method is currently limited to temporal tasks and DNN architectures, specifically RNNs. However, it has the potential to be relatively easily adapted to various tasks, modalities, multiclassification, and different performance measures, beyond the binary classification used in this study. We have provided illustrations of the multiclassification learning curve based on sentence classification in S2 Text. Additionally, because our method generates measures at every timestep and epoch, it may be more computationally expensive compared to other explainability methods. However, this arises from the tradeoff between obtaining a more granular measure across all training steps versus only obtaining snapshot visualizations of a single neural network layer or attribution scores for all input features. As documented in the DNN explainability comparison (Table 1), each technique has its strengths and considerations, and researchers can exercise discretion in choosing the appropriate method. The learning curve method excels in providing a more systematic understanding of the model’s learning process across models and modalities.