Datasets:

xln3
/

bamboo-papers

+# Battling the Non-stationarity in Time Series Forecasting via Test-time Adaptation
+HyunGi ${ \bf K i m } ^ { 1 }$ , Siwon ${ \bf K i m } ^ { 1 }$ , Jisoo Mok1, Sungroh Yoon1, 2, 3 †
+1Department of Electrical and Computer Engineering, Seoul National University
+2Interdisciplinary Program in Artificial Intelligence, Seoul National University
+3AIIS, ASRI, and INMC, Seoul National University
+† Corresponding Author
+rlagusrl0128@snu.ac.kr, tuslkk17@gmail.com, magicshop1118@snu.ac.kr, sryoon@snu.ac.kr
+# Abstract
+Deep Neural Networks have spearheaded remarkable advancements in time series forecasting (TSF), one of the major tasks in time series modeling. Nonetheless, the nonstationarity of time series undermines the reliability of pretrained source time series forecasters in mission-critical deployment settings. In this study, we introduce a pioneering test-time adaptation framework tailored for TSF (TSF-TTA). TAFAS, the proposed approach to TSF-TTA, flexibly adapts source forecasters to continuously shifting test distributions while preserving the core semantic information learned during pre-training. The novel utilization of partially-observed ground truth and gated calibration module enables proactive, robust, and model-agnostic adaptation of source forecasters. Experiments on diverse benchmark datasets and cuttingedge architectures demonstrate the efficacy and generality of TAFAS, especially in long-term forecasting scenarios that suffer from significant distribution shifts. The code is available at https://github.com/kimanki/TAFAS.
+# Introduction
+Time series forecasting (TSF), which is one of the most core tasks in time series modeling, aims to predict future values based on historical data points. The widespread applications of TSF across various industries include but are not limited to: weather prediction (Verma, Heinonen, and Garg 2024), traffic forecasting (Liu et al. 2023a), stock market prediction (Li et al. 2023a), and supply chain management (Hosseinnia Shavaki and Ebrahimi Ghahnavieh 2023). Such a broad and over-arching impact of TSF results highlights the importance of developing a dependable time series forecaster, whose predictions maintain reliability despite changes in external factors.
+A critical bottleneck in the reliable deployment of pretrained time series forecasters is created by the nonstationary nature of real-world time series data that leads to continuous data distribution shifts (Petropoulos et al. 2022). Previous works on alleviating the effect of nonstationarity aim to improve the robustness of time series forecasters through advancements in the pre-training process (Kim et al. 2021; Fan et al. 2023; Liu et al. 2024). Unfortunately, as the non-stationarity worsens the distributional discrepancy between training and test data over time, the pre-trained forecaster becomes increasingly unreliable, even
+![](images/a319c3e271baf52a720298e3beba6184c649ddd0470c88631ced6ff4119d4372.jpg)
+Figure 1: (a) The performance of a pre-trained source forecaster degrades when it encounters distribution-shifted inputs at test-time. In the figure, the distribution shift occurs through the gradual increase of mean value. (b) The sequential nature of time series provides the opportunity to proactively adapt the forecaster with partially-observed ground truth (POGT) before acquiring full ground truth (GT).
+if it has learned meaningful temporal semantics from training data (Kuznetsov and Mohri 2014). In Figure 1(a), we visualize how constantly evolving, non-stationary test data negatively affect the forecasting results of a pre-trained time series forecaster.
+This shortcoming of existing approaches underscores the need to continuously adapt the pre-trained source forecaster on shifted test-time inputs while preserving its core semantics. Adapting the source forecaster to incorporate new time-variant semantics within test-time inputs allows it to reflect the ever-changing test distributions. In this regard, we pioneer a test-time adaptation (TTA) framework tailored for TSF (TSF-TTA). TTA, which has been primarily studied in the computer vision domain under classification settings (Wang et al. 2021; Niu et al. 2022, 2023; Lee et al. 2024), dynamically adjusts a pre-trained classifier on test inputs; this objective of TTA makes it well-aligned with the aforementioned motivation of adapting the source forecaster to newly arriving test data. Traditionally, TTA has operated under two main assumptions on the nature of test inputs. First, TTA assumes a complete absence of test labels because it is infeasible to hand annotate inputs at test-time. Second, because most of the image data are assumed to be Independent and Identically Distributed (IID), TTA generally operates under the same IID assumption. In TSF-TTA, however, these assumptions no longer hold due to the intrin-
+sic characteristics of time series data.
+Unlike the first assumption of TTA, in TSF-TTA, ground truth for predicted time steps eventually becomes accessible, albeit in a delayed manner. For instance, when predicting electricity consumption for the next 30 days, the actual amount of electricity consumption becomes known to us after 30 days. Interestingly, as depicted in Figure 1(b), the sequential nature of time series makes ground truth values partially observable before acquiring the full ground truth. In the aforementioned example, the partial ground truth for the first 7 days is obtainable only after a week. Utilizing this partially-observable ground truth offers an invaluable opportunity to preemptively perform TSF-TTA prior to the arrival of full ground truth. Moreover, the second assumption is violated in TSF-TTA because temporal dependency exists in time series. This necessitates a technique for addressing the non-IIDness of time series on local (within window) and global (throughout the entire test-time) levels.
+By considering these challenges and opportunities presented by properties of time series, we propose a Testtime Adaptive ForecAsting for non-stationary time Series (TAFAS) that is extensible to various TSF architectures. TAFAS consists of periodicity-aware adaptation scheduling (PAAS) and a gated calibration module (GCM). PAAS adaptively obtains partially-observed ground truth of sufficient length to represent semantically meaningful periodic patterns. After then, model-agnostic GCMs are adapted to calibrate test-time inputs such that they conform to the distribution the source forecaster effectively handles. The gating mechanism in GCMs controls how much the calibrated results should be utilized by considering global distribution shifts. Together, PAAS and GCM allow the source forecaster to be proactively adapted on non-stationary test-time inputs. Throughout the adaptation, the source forecaster remains frozen to preserve the core semantics it has learned from the extensive historical data. With the proactively adapted forecaster, TAFAS adjusts the latter part of the original predictions, where ground truths are yet to be observed, with the adapted predictions reflecting the distribution shift.
+Comprehensive experimental results demonstrate that the TAFAS consistently enhances forecasting capabilities across source forecasters of various architectures. TAFAS leads to particularly large performance gains in long-term forecasting scenarios where distribution shifts become more pronounced. Moreover, the seamless integration of TAFAS with methods addressing the non-stationarity in pre-training stage and time series foundation models further enhances their ability to navigate test-time distribution shifts. Notably, TAFAS improves the forecasting error of Chronos (Ansari et al. 2024) on unseen test data streams by up to $45 \%$ .
+Our contributions are summarized as follows:
+• We pioneer test-time adaptation in time series forecasting (TSF-TTA) to address the non-stationarity in time series. Our examination of the properties of time series reveals the challenges in extending existing TTA frameworks to TSF, necessitating a new avenue to enable TSF-TTA.
+• We introduce TAFAS, a model-agnostic TSF-TTA framework that consists of periodicity-aware adapta-
+tion scheduling (PAAS) and Gated Calibration Module (GCM). These two technical components collectively enable proactive adaptation of the source forecaster on testtime inputs while preserving its core semantics.
+• TAFAS consistently excels in test-time adaptation across various TSF benchmark datasets and architectures, significantly improving test errors on highly non-stationary data and in long-term forecasting scenarios.
+# Related Works
+As TSF has become a pivotal application in various industries, diverse TSF architectures have been developed. Due to the page limit, an exhaustive discussion on TSF architectures and TTA is included in Appendix. Here, we focus on studies that improve the time series forecaster by mitigating distribution shifts caused by the non-stationarity of time series. A line of studies introduces normalization and de-normalization modules before and after the forecaster to remove and restore the non-stationary statistics (Kim et al. 2021; Liu et al. 2022; Fan et al. 2023; Liu et al. 2024). RevIN (Kim et al. 2021) performs instance normalization with learnable scale and bias factors, whereas NST (Liu et al. 2022) uses a non-parametric approach without learnable transformations. Dish-TS (Fan et al. 2023) and SAN (Liu et al. 2024) perform statistical prediction both within the look-back window and between the look-back and prediction windows to appropriately execute normalization and denormalization. However, their generalization capability to the continuously evolving test data distribution is inherently limited as they address non-stationarity only within training distributions. Although TSF-TTA and online TSF share a common ground in learning from streaming inputs (Wen et al. 2024; Ao and Fayek 2023; Guo et al. 2016; Pham et al. 2023), their primary objectives are fundamentally different. Online TSF aims to train a time series forecaster from scratch with streaming data, but TSF-TTA aims to adapt a pre-trained source forecaster.
+# Challenges and Opportunities in TSF-TTA
+Generally, TTA leverages unlabeled test-time inputs to adapt classifiers on shifted distributions. In this study, we aim to extend TTA to TSF to improve the ability of the pre-trained source time series forecaster to handle newly arriving test data. While the task characteristics of TSF and the properties of time series make applying the existing TTA frameworks to TSF a non-trivial problem, they also open new doors to develop a tailored approach to TSF-TTA. In this section, we highlight the challenges (C) and opportunities (O) unique to TSF-TTA after introducing task definition and formulations.
+Task definition & formulations. TSF is the task of predicting the future horizon window of $H$ time steps $( \{ \pmb { x } _ { t + 1 } , . . . , \pmb { x } _ { t + H } \} )$ given the past look-back window of $L$ time steps $( \{ \pmb { x } _ { t - L + 1 } , . . . , \pmb { x } _ { t } \} )$ . $\mathbf { \boldsymbol { x } } _ { t } \in \mathbb { R } ^ { C }$ denotes $C$ number of variables observed at time $t .$ . To perform TSF, a time series forecaster $\mathcal { F } _ { \theta }$ : $\mathbb { R } ^ { L \times C }  \mathbb { R } ^ { H \times C }$ is trained to predict subsequent future $H$ time steps given $L$ past time steps.
+The train, validation, and test sets of TSF datasets are obtained by splitting a single continuous time se-
+ries $\{ \pmb { x } _ { 1 } , . . . , \pmb { x } _ { T } \}$ in chronological order. Then, the (past, future) pairs are obtained using a sliding window, i.e., $( \pmb { X } _ { t } , \pmb { Y } _ { t } ) = ( \{ \pmb { x } _ { t - L + 1 } , . . . , \pmb { x } _ { t } \} , \{ \pmb { x } _ { t + 1 } , . . . , \pmb { x } _ { t + H } \} )$ $\{ \pmb { x } _ { t + 1 } , . . . , \pmb { x } _ { t + H } \} )$ . In non-stationary time series, data distribution continuously changes over time, resulting in distribution shifts between data splits and also within each split.
+C1. Entropy-based TTA losses are infeasible for regression-based TSF. TTA fundamentally assumes that ground truth labels are not available. Therefore, existing TTA methods utilize the entropy of predicted class probability distributions to formulate objective functions for the adaptation (Wang et al. 2021; Niu et al. 2022; Lee et al. 2024). However, TSF is a regression task, where the entropy of class probabilities is ill-defined, rendering the straightforward extension of entropy-based losses impossible.
+O1. Ground truth is accessible in TSF. In TSF, ground truth values become accessible as the predicted future time steps eventually arrive. Therefore, instead of entropy-based losses, the Mean Squared Error (MSE) loss, the de facto objective function used for regression tasks, can be used as a learning signal to perform TSF-TTA.
+C2. Full ground truth is accessible in a delayed time, resulting in a delayed adaptation. However, computing the MSE loss after observing full ground truth results in a delay of $H$ time steps between the point of forecasting (t) and obtaining the full ground truth $( t ^ { \prime } = t + H )$ . Thus, na¨ıvely waiting for the arrival of full ground truth to perform TSF-TTA implies that none of the forecasted predictions in $H$ time steps can be adapted. As the length of the forecasting window increases, the point at which full ground truth becomes obtainable is further delayed. This further delay in the point of adaptation inhibits performing TSF-TTA in a timely manner to reflect the adjacent distribution shifts.
+O2. Utilizing partially-observed ground truth enables proactive TSF-TTA. The sequential nature of test-time inputs makes ground truth partially observable before acquiring the full ground truth. After $p$ time steps $( p < H )$ from the forecasting time step $t$ of $X _ { t }$ , the first $p$ time steps out of the full ground truth (i.e., $\{ \pmb { x } _ { t + 1 } , \ldots , \pmb { x } _ { t + p } \} \in \mathbb { R } ^ { \bar { p } \times C } )$ are observable. Replacing the full ground truth in the MSE loss with its partially-observed counterpart reduces the adaptation delay and thus enables proactive adaptation.
+# TAFAS: Test-time Adaptive Forecasting for Non-stationary Time Series
+In this section, we introduce TAFAS, a novel framework that considers the challenges and opportunities of TSF-TTA. The overall pipeline of TAFAS is provided in Figure 2.
+# Periodicity-Aware Adaptation Scheduling (PAAS)
+To enable a proactive adaptation of the pre-trained source forecaster by reducing the adaptation delay, in TAFAS, we utilize partially-observed ground truth (POGT). However, as stated in Section O2., POGT does not eliminate the adaptation delay because to obtain POGT of length $p$ , we must wait for $p$ time steps. Therefore, choosing the appropriate value of $p$ is important for balancing the trade-off between
+the amount of semantic information in POGT and the adaptation delay. When $p$ is large, the POGT contains copious semantic information, but the adaptation delay increases, offsetting the advantage of employing the POGT. Conversely, when $p$ is small, the forecaster can be adapted more proactively, but the POGT may contain meaningless patterns.
+To ensure that the POGT incorporates semantically meaningful temporal patterns while preventing an excessive time delay, we introduce a periodicity-aware adaptation scheduling (PAAS) scheme that reflects the inherent periodic patterns of the test-time inputs. Several studies have demonstrated that the look-back window contains meaningful periodic patterns (Wu et al. 2023, 2021). PAAS thus extracts these patterns from the look-back window to determine $p$ . From here on, $t _ { 0 }$ denotes the time step at which the first testtime look-back window is obtained. PAAS applies variablewise Fast Fourier Transform (FFT) on the first look-back window $X _ { t _ { 0 } }$ to identify the variable with the highest signal power (Eq. 1). Before FFT, the mean of $X _ { t _ { 0 } }$ is set to zero to remove the influence of bias. For the identified variable $c ^ { * }$ , PAAS calculates the amplitude of each frequency component to determine the dominant frequency (Eq. 2).
+$$
+c ^ {*} = \arg \max  _ {c} \sum_ {f} \left\| \operatorname {F F T} \left(\boldsymbol {X} _ {t _ {0}} ^ {c}\right) \right\| ^ {2} \tag {1}
+$$
+$$
+f ^ {*} = \underset {f} {\arg \max } \| \operatorname {F F T} \left(\boldsymbol {X} _ {t _ {0}} ^ {c ^ {*}}\right) \| ^ {2} \tag {2}
+$$
+Based on the relationship between the frequency and period, PAAS derives the period of the dominant periodic patterns of $X _ { t _ { 0 } }$ and set it to the length of POGT as $\begin{array} { r } { \dot { p } _ { t _ { 0 } } = \left\lceil \frac { \bar { L } } { f ^ { * } } \right\rceil } \end{array}$ The resulting periodicity-aware POGT Yt [: $p _ { t _ { 0 } } ]$ includes relevant semantics embodied in the dominant periodic patterns.
+Once $p _ { t _ { 0 } }$ is determined, $p _ { t _ { 0 } } + 1$ instances are aggregated into a test mini-batch: {X}t0+t0 $\{ X \} _ { t _ { 0 } } ^ { t _ { 0 } + p _ { t _ { 0 } } } = \{ X _ { t _ { 0 } , . . . , X _ { t _ { 0 } + p _ { t _ { 0 } } } } \}$ pt0 . 0When the subsequent look-back window arrives at time step $t _ { 0 } + p _ { t _ { 0 } } + 1$ , PAAS is repeated to calculate the subsequent length of POGT adaptively. Considering the inherent periodic patterns vary across datasets and instances, the adaptive characteristic of PAAS assures data-agnostic TSF-TTA.
+# Gated Calibration Module (GCM)
+Selecting the module to adapt is a critical design choice in TTA. Existing TTA methods generally adapt normalization layers, e.g., Batch Normalization (Ioffe and Szegedy 2015), to adjust the distributions of the intermediate features. However, state-of-the-art TSF methods adopt various forms of architectures, many of which are missing such normalization layers. Hence, we introduce a model-agnostic Gated Calibration Module (GCM) to guarantee that TAFAS can be applied generally to diverse pre-trained source forecasters.
+TAFAS adapts the GCM with the source forecaster frozen to preserve the core temporal semantics that the forecaster has learned from extensive historical data. GCM is attached to both the front and tail ends of the source forecaster, referred to as input and output GCMs. The input GCM maps the distribution-shifted test input $X _ { t }$ to a calibrated input $\pmb { X } _ { t } ^ { \mathrm { c a l i } }$ that belong in a distribution the source forecaster can
+![](images/ec88277bbf3586341b8699c955492b8299762bfa0e4b0a40b266f70805165f39.jpg)
+Figure 2: An overview of TAFAS. (1: Blue) By computing the periodicity of dominant patterns for $X _ { t ^ { * } }$ , PAAS determines the length of partially-observed ground truth (POGT) $p _ { t ^ { * } }$ . (2: Yellow) Then input and output GCMs are proactively adapted on $X _ { t ^ { * } }$ at $t ^ { * } + p _ { t ^ { * } }$ to mitigate local and global distribution shifts through Temporal Calibration (TC) and gating (tanh) mechanisms, by minimizing MSE between the POGT and corresponding prediction. The source forecaster is frozen to preserve its core semantic information learned. (3: Green) Following the proactive adaptation, predictions for test mini-batch $\{ \bar { X } \} _ { t ^ { * } } ^ { t ^ { * } + p _ { t ^ { * } } }$ are recalculated to reflect the distribution shift and the unobserved part of the original predictions is adjusted with the adapted predictions.
+handle. The output GCM remaps the source forecaster’s prediction $\hat { Y } _ { t }$ to $\hat { Y } _ { t } ^ { \mathrm { c a l i } }$ in order to calibrate $\hat { Y } _ { t }$ back to the continuously changing test distribution.
+GCM consists of variable-wise temporal calibration and gating mechanisms to handle both the local (within the lookback window) and global (throughout the entire test-time) non-stationarity. The temporal calibration handles local distribution shifts by transforming the given window to calculate calibrated results. The gating mechanism handles global distribution shifts by updating how much to reflect calibrated results over time. Both temporal calibration and gating mechanisms are applied variable-wise, since each variable can have a different degree of non-stationarity. The two operations in the input GCM are expressed as the following:
+$$
+\operatorname {G C M} \left(\boldsymbol {X} _ {t}\right) = \boldsymbol {X} _ {t} +
+$$
+$$
+\operatorname {T i l e} (\tanh  (\boldsymbol {\alpha})) \circ \left(\operatorname {C o n c a t} \left(\left\{\boldsymbol {W} ^ {c} \boldsymbol {X} _ {t} ^ {c} \right\} _ {c = 1} ^ {C}\right) + \boldsymbol {b}\right), \tag {3}
+$$
+where $W ^ { c } \in \mathbb { R } ^ { L \times L }$ , $\pmb { b } \in \mathbb { R } ^ { L \times C }$ , and ${ \pmb { \alpha } } \in \mathbb { R } ^ { C }$ . Tile(·) : $\mathbb { R } ^ { C }  \mathbb { R } ^ { L \times C }$ broadcasts the gating vector in a temporal dimension, Concat(·) concatenates the calibrated signals along variable dimension, and $\circ$ denotes a Hadamard product. $W ^ { c }$ and $^ { b }$ are initialized to be zero so that at the first test time step when the test data diverge little from the training distribution, the original input is passed without calibration. The mechanism of the output GCM follows Eq. 3 with $X _ { t }$ replaced with $\hat { Y } _ { t }$ , and the dimensions of $W ^ { c }$ and $^ { b }$ adjusted accordingly to $H \times H$ and $H \times C$ .
+Let $t ^ { * }$ denote a time step at which PAAS calculates the POGT length $( t _ { 0 } , t _ { 0 } + p _ { t _ { 0 } } + 1 , \dots )$ and $p _ { t ^ { * } }$ denote the POGT length computed at $t ^ { * }$ . After a test mini-batch $\{ X \} _ { t ^ { * } } ^ { t ^ { * } + p _ { t ^ { * } } }$ is obtained at $t ^ { * } + p _ { t ^ { * } }$ , GCMs are adapted by minimizing the TAFAS loss defined as the following:
+$$
+\mathcal {L} ^ {\text {p a r t i a l}} = \operatorname {M S E} \left(\hat {\mathbf {Y}} _ {t ^ {*}} ^ {\text {c a l i}} [: p _ {t ^ {*}} ], \mathbf {Y} _ {t ^ {*}} [: p _ {t ^ {*}} ]\right) \tag {4}
+$$
+$$
+\mathcal {L} ^ {\text {f u l l}} = \operatorname {M S E} \left(\left\{\hat {\boldsymbol {Y}} ^ {\text {c a l i}} \right\} _ {\tilde {t} ^ {*}} ^ {\tilde {t} ^ {*} + p _ {\tilde {t} ^ {*}}}, \left\{\boldsymbol {Y} \right\} _ {\tilde {t} ^ {*}} ^ {\tilde {t} ^ {*} + p _ {\tilde {t} ^ {*}}}\right) \tag {5}
+$$
+$$
+\mathcal {L} ^ {\text {T A F A S}} = \mathcal {L} ^ {\text {p a r t i a l}} + \mathcal {L} ^ {\text {f u l l}}, \tag {6}
+$$
+where $\tilde { t } ^ { * }$ represents the most recent time step among the past POGT-computing steps whose corresponding mini-batches have now observed their full ground truths. $\bar { \mathcal { L } } ^ { \mathrm { p a r t i a l } }$ is computed between the first $p _ { t ^ { * } }$ time steps of the calibrated prediction for $X _ { t ^ { * } }$ whose periodicity-aware POGT is available
+$( \hat { Y } _ { t _ { * } ^ { * } } ^ { \mathrm { c a l i } } \left[ : p _ { t ^ { * } } \right] )$ and the corresponding POGT $\left( Y _ { t ^ { * } } \left[ : p _ { t ^ { * } } \right] \right)$ . $\dot { \mathcal { L } } ^ { \mathrm { f u l l } }$ is calculated between the calibrated predictions of all look-back windows within the past mini-batch constructed at $\tilde { t } ^ { * } + p _ { \tilde { t } ^ { * } }$ and the associated full ground truths to use their longer semantic information for adaptation. This adaption process of TAFAS enables proactive adaptation right when the semantically meaningful POGT is obtained while utilizing the extended semantic details from the full ground truths of the past mini-batch. When no past mini-batch with full ground truths is available, e.g., at the beginning of the adaptation phase, TAFAS uses only $\mathcal { L } ^ { \mathrm { p a r t i a l } }$ for adaptation.
+# Prediction Adjustment (PA)
+Because the forecaster is proactively adapted, TAFAS can replace the latter part of original predictions, whose ground truths are yet to be observed, with adjusted predictions that reflect the distribution shift. After the forecaster is adapted at $t ^ { * } + p _ { t ^ { * } }$ , TAFAS recalculates the predictions for all lookback windows in $\{ X \} _ { t ^ { * } } ^ { t ^ { * } + p _ { t ^ { * } } }$ and then substitutes the original predictions for time steps after $t ^ { * } + p _ { t ^ { * } }$ with the adapted predictions. Specifically, for the look-back window $X _ { t ^ { * } + k }$ , where $k \in \{ 0 , \ldots , p _ { t ^ { * } } \}$ , the corresponding prediction $\hat { Y } _ { t ^ { * } + k } ^ { \mathrm { c a l i } }$ predicts time steps $\{ ( t ^ { * } + k + 1 ) , \ldots , ( t ^ { * } + k + H ) \}$ . For the time steps $\{ ( t ^ { * } + p _ { t ^ { * } } + 1 ) , \ldots , ( t ^ { * } + k + H ) \}$ which are yet to be observed, TAFAS substitutes the original prediction $\hat { Y } _ { t ^ { * } + k } ^ { \mathrm { c a l i } }$ with the adapted prediction $\hat { Y } _ { t ^ { * } + 1 } ^ { \mathrm { c a l i } , }$ adaptedk that reflects distribution shifts as the following:
+$$
+\hat {\mathbf {Y}} _ {t ^ {*} + k, i} ^ {\text {a d j u s t}} = \left\{ \begin{array}{l l} \hat {\mathbf {Y}} _ {t ^ {*} + k, i} ^ {\text {c a l i}} & \text {i f} i \leq \left(t ^ {*} + p _ {t ^ {*}}\right) \\ \hat {\mathbf {Y}} _ {t ^ {*} + k, i} ^ {\text {c a l i , a d p a t e d}} & \text {i f} i > \left(t ^ {*} + p _ {t ^ {*}}\right). \end{array} \right. \tag {7}
+$$
+Yˆ cali, adaptedt∗+k, i denotes the adapted prediction values for the time step $i$ of $\hat { Y } _ { t ^ { * } + k } ^ { \mathrm { c a l i } }$ . We summarize the overall pipeline of TAFAS in Appendix.
+# Experiments
+# Experimental Setup
+Datasets. We demonstrate the effectiveness of TAFAS using the seven widely used multivariate TSF benchmark datasets: ETTh1, ETTm1, ETTh2, ETTm2, Exchange, Illness, and
+Table 1: Test MSE on multivariate time series forecasting datasets with and without TAFAS across various TSF architectures: Transformer-based (iTransformer, PatchTST), Linear-based (DLinear, OLS), and MLP-based (FreTS, MICN). $+$ TAFAS denotes whether the TAFAS framework is applied to the corresponding source forecaster. The lower MSE is marked in bold.
+<table><tr><td rowspan="3" colspan="2">Models + TAFAS</td><td colspan="4">Transformer-based</td><td colspan="4">Linear-based</td><td colspan="4">MLP-based</td></tr><tr><td colspan="2">iTransformer</td><td colspan="2">PatchTST</td><td colspan="2">DLinear</td><td colspan="2">OLS</td><td colspan="2">FreTS</td><td colspan="2">MICN</td></tr><tr><td>x</td><td>✓</td><td>x</td><td>✓</td><td>x</td><td>✓</td><td>x</td><td>✓</td><td>x</td><td>✓</td><td>x</td><td>✓</td></tr><tr><td rowspan="4">ETh1</td><td>96</td><td>0.444</td><td>0.438</td><td>0.436</td><td>0.429</td><td>0.451</td><td>0.442</td><td>0.451</td><td>0.441</td><td>0.441</td><td>0.437</td><td>0.455</td><td>0.446</td></tr><tr><td>192</td><td>0.503</td><td>0.492</td><td>0.492</td><td>0.481</td><td>0.504</td><td>0.493</td><td>0.504</td><td>0.494</td><td>0.498</td><td>0.491</td><td>0.513</td><td>0.501</td></tr><tr><td>336</td><td>0.562</td><td>0.554</td><td>0.539</td><td>0.529</td><td>0.551</td><td>0.541</td><td>0.551</td><td>0.540</td><td>0.563</td><td>0.555</td><td>0.574</td><td>0.561</td></tr><tr><td>720</td><td>0.786</td><td>0.704</td><td>0.713</td><td>0.690</td><td>0.700</td><td>0.669</td><td>0.700</td><td>0.662</td><td>0.715</td><td>0.684</td><td>0.736</td><td>0.702</td></tr><tr><td rowspan="4">ETTm1</td><td>96</td><td>0.388</td><td>0.362</td><td>0.386</td><td>0.377</td><td>0.371</td><td>0.351</td><td>0.371</td><td>0.353</td><td>0.367</td><td>0.355</td><td>0.398</td><td>0.372</td></tr><tr><td>192</td><td>0.448</td><td>0.429</td><td>0.440</td><td>0.429</td><td>0.443</td><td>0.418</td><td>0.444</td><td>0.417</td><td>0.429</td><td>0.418</td><td>0.448</td><td>0.428</td></tr><tr><td>336</td><td>0.519</td><td>0.493</td><td>0.500</td><td>0.487</td><td>0.518</td><td>0.481</td><td>0.518</td><td>0.479</td><td>0.493</td><td>0.476</td><td>0.524</td><td>0.493</td></tr><tr><td>720</td><td>0.592</td><td>0.560</td><td>0.562</td><td>0.542</td><td>0.592</td><td>0.549</td><td>0.592</td><td>0.549</td><td>0.560</td><td>0.539</td><td>0.602</td><td>0.567</td></tr><tr><td rowspan="4">ETh2</td><td>96</td><td>0.241</td><td>0.239</td><td>0.233</td><td>0.232</td><td>0.229</td><td>0.227</td><td>0.231</td><td>0.229</td><td>0.234</td><td>0.232</td><td>0.234</td><td>0.231</td></tr><tr><td>192</td><td>0.291</td><td>0.287</td><td>0.282</td><td>0.277</td><td>0.283</td><td>0.281</td><td>0.284</td><td>0.281</td><td>0.286</td><td>0.282</td><td>0.285</td><td>0.282</td></tr><tr><td>336</td><td>0.333</td><td>0.326</td><td>0.328</td><td>0.318</td><td>0.325</td><td>0.317</td><td>0.326</td><td>0.317</td><td>0.328</td><td>0.318</td><td>0.330</td><td>0.320</td></tr><tr><td>720</td><td>0.415</td><td>0.393</td><td>0.416</td><td>0.396</td><td>0.415</td><td>0.391</td><td>0.416</td><td>0.386</td><td>0.420</td><td>0.390</td><td>0.414</td><td>0.398</td></tr><tr><td rowspan="4">ETTm2</td><td>96</td><td>0.159</td><td>0.157</td><td>0.157</td><td>0.156</td><td>0.159</td><td>0.158</td><td>0.160</td><td>0.159</td><td>0.158</td><td>0.156</td><td>0.161</td><td>0.160</td></tr><tr><td>192</td><td>0.197</td><td>0.192</td><td>0.194</td><td>0.194</td><td>0.193</td><td>0.191</td><td>0.194</td><td>0.192</td><td>0.193</td><td>0.192</td><td>0.195</td><td>0.193</td></tr><tr><td>336</td><td>0.244</td><td>0.235</td><td>0.234</td><td>0.232</td><td>0.232</td><td>0.229</td><td>0.233</td><td>0.230</td><td>0.233</td><td>0.230</td><td>0.235</td><td>0.232</td></tr><tr><td>720</td><td>0.312</td><td>0.301</td><td>0.307</td><td>0.299</td><td>0.306</td><td>0.297</td><td>0.307</td><td>0.298</td><td>0.302</td><td>0.293</td><td>0.308</td><td>0.299</td></tr><tr><td rowspan="4">Exchange</td><td>96</td><td>0.086</td><td>0.084</td><td>0.084</td><td>0.081</td><td>0.078</td><td>0.079</td><td>0.081</td><td>0.079</td><td>0.084</td><td>0.079</td><td>0.083</td><td>0.079</td></tr><tr><td>192</td><td>0.175</td><td>0.165</td><td>0.179</td><td>0.168</td><td>0.171</td><td>0.161</td><td>0.172</td><td>0.162</td><td>0.176</td><td>0.163</td><td>0.183</td><td>0.170</td></tr><tr><td>336</td><td>0.329</td><td>0.280</td><td>0.350</td><td>0.286</td><td>0.321</td><td>0.280</td><td>0.323</td><td>0.265</td><td>0.326</td><td>0.283</td><td>0.342</td><td>0.296</td></tr><tr><td>720</td><td>0.844</td><td>0.773</td><td>0.845</td><td>0.844</td><td>0.837</td><td>0.711</td><td>0.836</td><td>0.583</td><td>0.840</td><td>0.772</td><td>1.276</td><td>0.942</td></tr><tr><td rowspan="4">Illness</td><td>24</td><td>2.119</td><td>2.124</td><td>2.078</td><td>2.078</td><td>2.642</td><td>2.631</td><td>2.509</td><td>2.506</td><td>2.516</td><td>2.516</td><td>3.280</td><td>3.306</td></tr><tr><td>36</td><td>1.989</td><td>1.988</td><td>2.095</td><td>2.095</td><td>2.501</td><td>2.450</td><td>2.435</td><td>2.384</td><td>2.441</td><td>2.441</td><td>3.503</td><td>3.524</td></tr><tr><td>48</td><td>2.173</td><td>2.155</td><td>1.964</td><td>1.964</td><td>2.487</td><td>2.403</td><td>2.417</td><td>2.336</td><td>2.257</td><td>2.198</td><td>2.066</td><td>2.033</td></tr><tr><td>60</td><td>1.925</td><td>1.876</td><td>1.833</td><td>1.833</td><td>2.530</td><td>2.444</td><td>2.490</td><td>2.415</td><td>2.074</td><td>2.056</td><td>1.915</td><td>1.881</td></tr><tr><td rowspan="4">Weather</td><td>96</td><td>0.179</td><td>0.170</td><td>0.174</td><td>0.171</td><td>0.195</td><td>0.179</td><td>0.196</td><td>0.179</td><td>0.181</td><td>0.169</td><td>0.176</td><td>0.175</td></tr><tr><td>192</td><td>0.227</td><td>0.214</td><td>0.221</td><td>0.215</td><td>0.240</td><td>0.223</td><td>0.240</td><td>0.223</td><td>0.225</td><td>0.212</td><td>0.224</td><td>0.222</td></tr><tr><td>336</td><td>0.284</td><td>0.265</td><td>0.276</td><td>0.265</td><td>0.292</td><td>0.270</td><td>0.292</td><td>0.270</td><td>0.280</td><td>0.260</td><td>0.280</td><td>0.274</td></tr><tr><td>720</td><td>0.360</td><td>0.343</td><td>0.352</td><td>0.334</td><td>0.364</td><td>0.345</td><td>0.364</td><td>0.343</td><td>0.356</td><td>0.336</td><td>0.350</td><td>0.349</td></tr></table>
+Weather (Wu et al. 2021). In Appendix, we report the results of the ADF test (Elliott, Rothenberg, and Stock 1992) to demonstrate that a substantial degree of non-stationarity exists in all these datasets.
+Time series forecasters. For the source time series forecasters, we adopt six state-of-the-art forecasters across various architectures: Transformer-based (iTransformer (Liu et al. 2023b), PatchTST (Nie et al. 2022)), Linear-based (DLinear (Zeng et al. 2023), OLS (Toner and Darlow 2024)), and MLP-based (FreTS (Yi et al. 2024), MICN (Wang et al. 2023)). Moreover, we verify the effectiveness of TAFAS on TSF foundation model (Ansari et al. 2024) pre-trained on a large corpus of time series data. TAFAS can be applied in combination with all of these forecasters regardless of the architecture design due to its fully model-agnostic design.
+Implementation details. Unless stated otherwise, we follow the standard protocol in TSF evaluation (Wu et al. 2023). We use the look-back window length $L \ = \ 3 6$ for Illness and $L ~ = ~ 9 6$ for the other datasets. For forecasting window length $H$ , we evaluate on 4 different lengths, $H \in$ $\{ 2 4 , 3 6 , 4 8 , 6 0 \}$ for Illness and $H \in \{ 9 6 , 1 9 2 , 3 3 6 , 7 2 0 \}$ for the other datasets. We split datasets in chronological order
+with the ratio of (0.6, 0.2, 0.2) for ETTh1, ETTm1, ETTh2, and ETTm2 and (0.7, 0.1, 0.2) for Exchange, Illness, and Weather to construct train, validation, and test sets. We repeat each pre-training run over three different seeds and select the pre-trained source forecaster with the lowest average validation MSE. More details on training processes are provided in Appendix.
+# TAFAS on Various TSF Architectures
+Table 1 presents the MSE of forecasting results with and without TAFAS across various source TSF architectures and multiple forecasting windows. The full results, including Mean Absolute Error (MAE) and standard deviations, are reported in Appendix due to the space limit. TAFAS consistently reduces the forecasting error at test-time, effectively handling the test-time non-stationarity of time series. We highlight that the effectiveness of TAFAS at mitigating test-time distribution shifts remains strong across various architectures and datasets, consolidating its broad model- and data-agnostic applicability. Furthermore, when $H  { \mathrm { ~ = ~ } } 3 3 6$ , TAFAS improves the average MSE of iTransformer and DLinear by $4 . 9 5 \%$ and $5 . 2 0 \%$ , respectively, and on an even
+Table 2: Compatability of TAFAS with various normalization modules addressing non-stationarity in the pre-training stage. We report test MSE with and without TAFAS where each source forecaster (iTransformer, DLinear, and FreTS) is pre-trained with the normalization modules of RevIN, Dish-TS, or SAN.
+<table><tr><td colspan="2">Models</td><td colspan="5">iTransformer</td><td colspan="5">DLinear</td><td colspan="5">FreTS</td><td></td><td></td><td></td></tr><tr><td colspan="2">Norm. + TAFAS</td><td>RevIN ✘</td><td>Dish-TS ✘</td><td>SAN ✘</td><td>RevIN ✘</td><td>Dish-TS ✘</td><td>SAN ✘</td><td>RevIN ✘</td><td>Dish-TS ✘</td><td>SAN ✘</td><td>RevIN ✘</td><td>Dish-TS ✘</td><td>SAN ✘</td><td>RevIN ✘</td><td>Dish-TS ✘</td><td>SAN ✘</td><td></td><td></td><td></td></tr><tr><td rowspan="4">ETTh1</td><td>96</td><td>0.444</td><td>0.437</td><td>0.457</td><td>0.441</td><td>0.451</td><td>0.439</td><td>0.451</td><td>0.444</td><td>0.452</td><td>0.439</td><td>0.438</td><td>0.433</td><td>0.448</td><td>0.436</td><td>0.440</td><td>0.421</td><td>0.438</td><td>0.434</td></tr><tr><td>192</td><td>0.503</td><td>0.490</td><td>0.507</td><td>0.499</td><td>0.511</td><td>0.497</td><td>0.504</td><td>0.497</td><td>0.507</td><td>0.488</td><td>0.489</td><td>0.480</td><td>0.511</td><td>0.491</td><td>0.494</td><td>0.472</td><td>0.485</td><td>0.478</td></tr><tr><td>336</td><td>0.561</td><td>0.548</td><td>0.560</td><td>0.549</td><td>0.596</td><td>0.564</td><td>0.550</td><td>0.548</td><td>0.555</td><td>0.531</td><td>0.534</td><td>0.527</td><td>0.567</td><td>0.551</td><td>0.547</td><td>0.521</td><td>0.529</td><td>0.523</td></tr><tr><td>720</td><td>0.785</td><td>0.702</td><td>0.720</td><td>0.669</td><td>0.727</td><td>0.689</td><td>0.699</td><td>0.669</td><td>0.708</td><td>0.642</td><td>0.664</td><td>0.652</td><td>0.729</td><td>0.682</td><td>0.706</td><td>0.641</td><td>0.665</td><td>0.640</td></tr><tr><td rowspan="4">ETTh1</td><td>96</td><td>0.754</td><td>0.652</td><td>0.418</td><td>0.367</td><td>0.360</td><td>0.351</td><td>0.371</td><td>0.354</td><td>0.371</td><td>0.350</td><td>0.353</td><td>0.345</td><td>1.071</td><td>0.360</td><td>0.375</td><td>0.354</td><td>0.355</td><td>0.347</td></tr><tr><td>192</td><td>0.817</td><td>0.791</td><td>0.487</td><td>0.430</td><td>0.418</td><td>0.408</td><td>0.445</td><td>0.422</td><td>0.445</td><td>0.416</td><td>0.415</td><td>0.405</td><td>0.893</td><td>0.421</td><td>0.447</td><td>0.418</td><td>0.415</td><td>0.405</td></tr><tr><td>336</td><td>0.870</td><td>0.833</td><td>0.543</td><td>0.493</td><td>0.480</td><td>0.463</td><td>0.520</td><td>0.484</td><td>0.520</td><td>0.477</td><td>0.474</td><td>0.460</td><td>0.556</td><td>0.478</td><td>0.522</td><td>0.478</td><td>0.472</td><td>0.460</td></tr><tr><td>720</td><td>0.940</td><td>0.897</td><td>0.606</td><td>0.554</td><td>0.530</td><td>0.517</td><td>0.593</td><td>0.553</td><td>0.597</td><td>0.539</td><td>0.526</td><td>0.514</td><td>0.599</td><td>0.535</td><td>0.598</td><td>0.541</td><td>0.525</td><td>0.512</td></tr><tr><td rowspan="4">ETTh2</td><td>96</td><td>0.241</td><td>0.240</td><td>0.263</td><td>0.259</td><td>0.243</td><td>0.242</td><td>0.230</td><td>0.228</td><td>0.232</td><td>0.231</td><td>0.228</td><td>0.228</td><td>0.244</td><td>0.241</td><td>0.247</td><td>0.246</td><td>0.239</td><td>0.239</td></tr><tr><td>192</td><td>0.295</td><td>0.292</td><td>0.308</td><td>0.335</td><td>0.303</td><td>0.300</td><td>0.284</td><td>0.279</td><td>0.286</td><td>0.276</td><td>0.277</td><td>0.276</td><td>0.290</td><td>0.283</td><td>0.304</td><td>0.288</td><td>0.282</td><td>0.281</td></tr><tr><td>336</td><td>0.333</td><td>0.325</td><td>0.354</td><td>0.367</td><td>0.336</td><td>0.328</td><td>0.325</td><td>0.314</td><td>0.328</td><td>0.298</td><td>0.308</td><td>0.305</td><td>0.333</td><td>0.318</td><td>0.336</td><td>0.303</td><td>0.307</td><td>0.305</td></tr><tr><td>720</td><td>0.415</td><td>0.392</td><td>0.469</td><td>0.424</td><td>0.434</td><td>0.405</td><td>0.409</td><td>0.383</td><td>0.424</td><td>0.358</td><td>0.381</td><td>0.364</td><td>0.422</td><td>0.384</td><td>0.435</td><td>0.366</td><td>0.368</td><td>0.356</td></tr><tr><td rowspan="4">ETTm2</td><td>96</td><td>0.179</td><td>0.178</td><td>0.165</td><td>0.162</td><td>0.156</td><td>0.156</td><td>0.160</td><td>0.159</td><td>0.160</td><td>0.159</td><td>0.161</td><td>0.155</td><td>0.173</td><td>0.154</td><td>0.159</td><td>0.158</td><td>0.161</td><td>0.155</td></tr><tr><td>192</td><td>0.204</td><td>0.202</td><td>0.196</td><td>0.201</td><td>0.190</td><td>0.189</td><td>0.193</td><td>0.192</td><td>0.195</td><td>0.193</td><td>0.197</td><td>0.190</td><td>0.210</td><td>0.189</td><td>0.193</td><td>0.196</td><td>0.201</td><td>0.192</td></tr><tr><td>336</td><td>0.245</td><td>0.242</td><td>0.258</td><td>0.257</td><td>0.228</td><td>0.225</td><td>0.232</td><td>0.232</td><td>0.234</td><td>0.233</td><td>0.237</td><td>0.229</td><td>0.247</td><td>0.228</td><td>0.235</td><td>0.241</td><td>0.238</td><td>0.230</td></tr><tr><td>720</td><td>0.316</td><td>0.309</td><td>0.315</td><td>0.328</td><td>0.299</td><td>0.292</td><td>0.306</td><td>0.301</td><td>0.306</td><td>0.298</td><td>0.296</td><td>0.291</td><td>0.306</td><td>0.297</td><td>0.312</td><td>0.308</td><td>0.297</td><td>0.289</td></tr><tr><td rowspan="4">Exchange</td><td>96</td><td>0.086</td><td>0.084</td><td>0.091</td><td>0.119</td><td>0.079</td><td>0.078</td><td>0.081</td><td>0.078</td><td>0.081</td><td>0.076</td><td>0.079</td><td>0.078</td><td>0.084</td><td>0.079</td><td>0.084</td><td>0.080</td><td>0.079</td><td>0.078</td></tr><tr><td>192</td><td>0.175</td><td>0.164</td><td>0.199</td><td>0.310</td><td>0.161</td><td>0.155</td><td>0.169</td><td>0.164</td><td>0.167</td><td>0.149</td><td>0.163</td><td>0.158</td><td>0.177</td><td>0.164</td><td>0.187</td><td>0.162</td><td>0.161</td><td>0.158</td></tr><tr><td>336</td><td>0.329</td><td>0.282</td><td>0.366</td><td>0.546</td><td>0.307</td><td>0.275</td><td>0.317</td><td>0.293</td><td>0.307</td><td>0.254</td><td>0.300</td><td>0.275</td><td>0.328</td><td>0.302</td><td>0.336</td><td>0.295</td><td>0.298</td><td>0.276</td></tr><tr><td>720</td><td>0.844</td><td>0.557</td><td>0.919</td><td>1.529</td><td>1.110</td><td>0.645</td><td>0.834</td><td>0.815</td><td>0.929</td><td>0.546</td><td>0.845</td><td>0.802</td><td>0.837</td><td>0.738</td><td>0.812</td><td>0.675</td><td>0.846</td><td>0.704</td></tr><tr><td rowspan="4">Illness</td><td>24</td><td>2.118</td><td>2.121</td><td>2.765</td><td>2.571</td><td>2.587</td><td>2.589</td><td>2.654</td><td>2.613</td><td>2.778</td><td>2.865</td><td>2.460</td><td>2.423</td><td>2.480</td><td>2.438</td><td>2.577</td><td>2.542</td><td>2.536</td><td>2.500</td></tr><tr><td>36</td><td>1.989</td><td>1.984</td><td>2.701</td><td>2.494</td><td>2.492</td><td>2.465</td><td>2.503</td><td>2.441</td><td>2.606</td><td>2.702</td><td>2.513</td><td>2.472</td><td>2.420</td><td>2.386</td><td>2.530</td><td>2.661</td><td>2.477</td><td>2.431</td></tr><tr><td>48</td><td>2.183</td><td>2.132</td><td>2.527</td><td>2.409</td><td>2.386</td><td>2.292</td><td>2.487</td><td>2.406</td><td>2.525</td><td>2.702</td><td>2.443</td><td>2.392</td><td>2.247</td><td>2.153</td><td>2.246</td><td>2.434</td><td>2.416</td><td>2.340</td></tr><tr><td>60</td><td>2.030</td><td>2.029</td><td>3.372</td><td>2.738</td><td>2.363</td><td>2.298</td><td>2.529</td><td>2.452</td><td>2.549</td><td>2.785</td><td>2.423</td><td>2.383</td><td>2.081</td><td>1.997</td><td>2.068</td><td>2.453</td><td>2.408</td><td>2.354</td></tr><tr><td rowspan="4">Weather</td><td>96</td><td>0.205</td><td>0.199</td><td>0.183</td><td>0.164</td><td>0.168</td><td>0.163</td><td>0.198</td><td>0.184</td><td>0.195</td><td>0.178</td><td>0.171</td><td>0.165</td><td>0.195</td><td>0.165</td><td>0.193</td><td>0.166</td><td>0.169</td><td>0.164</td></tr><tr><td>192</td><td>0.256</td><td>0.246</td><td>0.231</td><td>0.209</td><td>0.213</td><td>0.203</td><td>0.243</td><td>0.225</td><td>0.240</td><td>0.219</td><td>0.214</td><td>0.207</td><td>0.251</td><td>0.204</td><td>0.240</td><td>0.206</td><td>0.212</td><td>0.204</td></tr><tr><td>336</td><td>0.306</td><td>0.286</td><td>0.286</td><td>0.257</td><td>0.266</td><td>0.253</td><td>0.295</td><td>0.269</td><td>0.292</td><td>0.267</td><td>0.269</td><td>0.258</td><td>0.304</td><td>0.253</td><td>0.293</td><td>0.253</td><td>0.266</td><td>0.256</td></tr><tr><td>720</td><td>0.376</td><td>0.356</td><td>0.364</td><td>0.326</td><td>0.340</td><td>0.325</td><td>0.367</td><td>0.342</td><td>0.366</td><td>0.337</td><td>0.342</td><td>0.335</td><td>0.379</td><td>0.331</td><td>0.367</td><td>0.321</td><td>0.338</td><td>0.328</td></tr></table>
+longer forecasting window $\mathit { \Delta } H \ = \ 7 2 0 ,$ ), the performance improvement brought upon by TAFAS reaches $5 . 7 6 \%$ and $6 . 3 0 \%$ . These results indicate that TAFAS is particularly advantageous in long-term forecasting scenarios with more severe distribution shifts.
+To further demonstrate the effectiveness of TAFAS at mitigating extreme test-time distribution shifts in long-term forecasting scenarios, we verify TAFAS under the forecasting lengths of $H ~ \in ~ \{ 7 8 0 , 8 4 0 , 9 0 0 \}$ on DLinear. In Appendix, we plot the percentage of improvement in MSE achieved by TAFAS. Applying TAFAS exhibits a noticeable jump in performance improvement when compared to $H = 3 3 6$ ; we note that on the ETTh2 dataset, the degree of improvement increases by more than $8 \%$ .
+# Compatibility with Methods Addressing Non-stationarity in Pre-training time
+One of the mainstream approaches to mitigating nonstationarity in TSF is to employ normalization and denormalization modules (Kim et al. 2021; Fan et al. 2023; Liu et al. 2024). However, they address non-stationarity only in the pre-training stage using training distributions, and thus, they may not generalize to consistently changing test distributions. As TAFAS is pluggable to any source fore-
+casters in test-time, this compatibility can further enhance the robustness of source forecasters pre-trained with these widely adopted normalization modules. Table 2 presents the results of applying TAFAS on source forecasters equipped with RevIN (Kim et al. 2021), Dish-TS (Fan et al. 2023), or SAN (Liu et al. 2024). Across all datasets and architectures, TAFAS further improves the forecasting capability of these advanced source forecasters. The strength of TAFAS in long-range time series forecasting is again demonstrated here. For iTransformer with $H = 7 2 0$ , TAFAS reduces the MSE of RevIN and SAN by $8 . 9 0 \%$ and $9 . 3 9 \%$ on average. Likewise, for DLinear with $H \ = \ 7 2 0$ , TAFAS improves RevIN and SAN by $4 . 4 5 \%$ and $2 . 7 2 \%$ on average.
+Interestingly, the normalization approaches significantly increase the test MSE of the source forecaster in some experimental settings, e.g., from 0.367 to 1.071 in FreTS + RevIN on ETTm1 with $H = 9 6$ . This observation highlights that addressing non-stationarity only in the pre-training phase can fail to generalize on the changing test distributions. In the above-mentioned setting, TAFAS improves the performance of $\mathrm { F r e T S } + \mathrm { R e v I N }$ by $6 6 . 3 9 \%$ , indicating that it can overcome this limitation of pre-training-based approaches.
+Table 3: Test MSE with and without TAFAS on Chronos, a foundation model pre-trained on a massive corpus of time series data. We report test MSE for $H = 9 6$ .
+<table><tr><td>Models</td><td>TAFAS</td><td>ETTh1</td><td>ETTm1</td><td>ETTh2</td><td>ETTm2</td></tr><tr><td rowspan="2">Chronos-small</td><td>✘</td><td>0.795</td><td>1.317</td><td>0.904</td><td>0.609</td></tr><tr><td>✓</td><td>0.624</td><td>0.858</td><td>0.611</td><td>0.492</td></tr><tr><td rowspan="2">Chronos-base</td><td>✘</td><td>0.770</td><td>1.385</td><td>1.357</td><td>0.934</td></tr><tr><td>✓</td><td>0.611</td><td>0.761</td><td>0.708</td><td>0.668</td></tr><tr><td rowspan="2">Chronos-large</td><td>✘</td><td>0.838</td><td>1.397</td><td>0.485</td><td>0.459</td></tr><tr><td>✓</td><td>0.635</td><td>0.772</td><td>0.477</td><td>0.431</td></tr></table>
+Table 4: Comparison of test MSE with the state-of-the-art online TSF methods: FSNet and OneNet for $H = 7 2 0$ .
+<table><tr><td></td><td>ETTh1</td><td>ETTm1</td><td>ETTh2</td><td>ETTm2</td><td>Exchange</td></tr><tr><td>FSNet</td><td>0.615</td><td>1.641</td><td>0.788</td><td>0.431</td><td>1.464</td></tr><tr><td>OneNet</td><td>0.620</td><td>1.593</td><td>0.543</td><td>0.410</td><td>0.977</td></tr><tr><td>TAFAS</td><td>0.640</td><td>0.512</td><td>0.356</td><td>0.289</td><td>0.704</td></tr></table>
+# Unleashing the Knowledge of Foundation Models
+Recently, TSF foundation models pre-trained on up to billions of time steps (Garza and Mergenthaler-Canseco 2023; Das et al. 2024; Ansari et al. 2024; Goswami et al. 2024) have shown promising forecasting performance. Here, we demonstrate that TAFAS can further improve the performance of such a powerful source forecaster. According to Table 3, TAFAS significantly improves the test MSE of Chronos (Ansari et al. 2024) on ETT datasets by up to $45 \%$ . The performance improvement is observed consistently on varying model sizes: small, base, and large. We highlight that ETT datasets were not included in pre-training data, demonstrating that TAFAS effectively adapts TSF foundation models to unseen time series data streams. The compatibility of TAFAS with foundation models alludes that it can adapt their predictions effectively without overwriting the rich semantic information encoded in these models.
+# Comparison with Online TSF Methods
+As mentioned in Related Works, online TSF is another line of research that leverages sequentially arriving data to update forecasters, but it differs from of TSF-TTA in that online TSF trains forecasters from scratch, whereas TSF-TTA adapts a pre-trained source forecaster. Here, we compare TAFAS with online TSF methods to corroborate that TAFAS has tangible advantages over online TSF. Table 4 presents test MSE of the state-of-the-art online TSF methods: FS-Net (Pham et al. 2023) and OneNet (Wen et al. 2024), in the long-term forecasting scenario of $H \ = \ 7 2 0$ . In most experimental settings, TAFAS significantly outperforms online TSF methods. The empirical superiority of TAFAS to online TSF can be attributed to the following factors: 1) proactive adaptation of forecaster using periodicity-aware POGT, 2) the timely adjustment of predictions to reflect adjacent distribution shifts, and 3) preservation of the knowledge in the source forecaster through the use of auxiliary non-stationarity-aware GCM modules.
+![](images/112d06d80d68dffb41068be2be9e56a850fe23e0f128ff77fcdf473a143a62fb.jpg)
+Figure 3: Comparison of PAAS against using a fixed POGT length on the ETTh1 dataset.
+Table 5: Forecasting errors as different modules are adapted in iTransformer. “Norm.” denotes the layer normalization.
+<table><tr><td rowspan="2">Modules to Adapt</td><td colspan="2">ETTh1</td><td colspan="2">ETTh2</td></tr><tr><td>MSE</td><td>MAE</td><td>MSE</td><td>MAE</td></tr><tr><td>None (baseline)</td><td>0.786</td><td>0.657</td><td>0.415</td><td>0.441</td></tr><tr><td>Norm.</td><td>0.776</td><td>0.657</td><td>0.409</td><td>0.436</td></tr><tr><td>Encoder</td><td>0.840</td><td>0.678</td><td>0.414</td><td>0.438</td></tr><tr><td>Decoder</td><td>0.808</td><td>0.664</td><td>0.410</td><td>0.436</td></tr><tr><td>All</td><td>0.832</td><td>0.673</td><td>0.414</td><td>0.438</td></tr><tr><td>GCM (TAFAS)</td><td>0.704</td><td>0.627</td><td>0.393</td><td>0.425</td></tr></table>
+# Analysis of Each Technical Component in TAFAS
+We explore alternative design choices for two main technical components in TAFAS. First, we study the effect of replacing PAAS with a fixed POGT length. Even though experiments are conducted with DLinear on all seven datasets, due to the page limit, Figure 3 only shows the results on the ETTh1 dataset. Extended results and the range of POGT lengths computed by PAAS are in Appendix. Figure 3 shows that too short or long POGT curtails the effect of TAFAS, supporting the motivation behind dynamically adjusting its length. Second, we demonstrate the effectiveness of introducing GCM. Table 5 presents forecasting errors for iTransformer with $H = 7 2 0$ when other modules inside iTransformer are adapted. Modifying internal modules results in reduced performance improvement. In some cases, the forecasting performance drops below the baseline, likely due to the overwriting of core semantics in the source forecaster. The effectiveness of each component in TAFAS is shown through ablation studies in Appendix. Lastly, to validate that TAFAS can be deployed at test-time without significant hyper-parameter tuning, we demonstrate its robustness to changes in hyper-parameters in Appendix.
+# Conclusion
+To address the ever-changing distributions in non-stationary time series, we propose TAFAS, a pioneering TSF-TTA framework that dynamically adapts the source forecaster at test-time while preserving the knowledge of the source forecaster. Using PAAS, the partially-observed ground truth with semantically meaningful patterns is acquired for proactive adaptation. Then GCM, which considers both local and global temporal distribution shifts is adapted to address changing distributions. TAFAS serves as a dataset- and model-agnostic framework, demonstrated by thorough experimental results and analyses. The TSF-TTA framework pioneered in our work paves a new avenue toward sustainable deployment of state-of-the-art time series forecasters.
+# Acknowledgments
+This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) [No.RS-2021-II211343, Artificial Intelligence Graduate School Program (Seoul National University)], the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A3B1077720, 2022R1A5A708390811), the BK21 FOUR program of the Education and the Research Program for Future ICT Pioneers, Seoul National University in 2024, Hyundai Motor Company, and Samsung Electronics Co., Ltd (IO240124- 08661-01).
+# References
+Ansari, A. F.; Stella, L.; Turkmen, C.; Zhang, X.; Mercado, P.; Shen, H.; Shchur, O.; Rangapuram, S. S.; Arango, S. P.; Kapoor, S.; et al. 2024. Chronos: Learning the language of time series. arXiv preprint arXiv:2403.07815.
+Ao, S.-I.; and Fayek, H. 2023. Continual Deep Learning for Time Series Modeling. Sensors, 23(16): 7167.
+Ba, J. L.; Kiros, J. R.; and Hinton, G. E. 2016. Layer Normalization. https://arxiv.org/pdf/1607.06450.pdf.
+Challu, C.; Olivares, K. G.; Oreshkin, B. N.; Garza, F.; Mergenthaler, M.; and Dubrawski, A. 2022. N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting. arXiv preprint arXiv:2201.12886.
+Das, A.; Kong, W.; Leach, A.; Mathur, S.; Sen, R.; and Yu, R. 2023. Long-term forecasting with tide: Time-series dense encoder. arXiv preprint arXiv:2304.08424.
+Das, A.; Kong, W.; Sen, R.; and Zhou, Y. 2024. A decoderonly foundation model for time-series forecasting. In Fortyfirst International Conference on Machine Learning.
+Ekambaram, V.; Jati, A.; Nguyen, N.; Sinthong, P.; and Kalagnanam, J. 2023. Tsmixer: Lightweight mlp-mixer model for multivariate time series forecasting. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 459–469.
+Elliott, G.; Rothenberg, T. J.; and Stock, J. H. 1992. Efficient tests for an autoregressive unit root.
+Fan, W.; Wang, P.; Wang, D.; Wang, D.; Zhou, Y.; and Fu, Y. 2023. Dish-ts: a general paradigm for alleviating distribution shift in time series forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37(6), 7522– 7529.
+Garza, A.; and Mergenthaler-Canseco, M. 2023. TimeGPT-1. arXiv preprint arXiv:2310.03589.
+Girard, A.; Rasmussen, C.; Candela, J. Q.; and Murray-Smith, R. 2002. Gaussian process priors with uncertain inputs application to multiple-step ahead time series forecasting. Advances in neural information processing systems, 15.
+Gong, T.; Jeong, J.; Kim, T.; Kim, Y.; Shin, J.; and Lee, S.-J. 2022. NOTE: Robust Continual Test-time Adaptation Against Temporal Correlation. In Advances in Neural Information Processing Systems (NeurIPS).
+Goswami, M.; Szafer, K.; Choudhry, A.; Cai, Y.; Li, S.; and Dubrawski, A. 2024. MOMENT: A Family of Open Timeseries Foundation Models. In International Conference on Machine Learning.
+Guo, T.; Xu, Z.; Yao, X.; Chen, H.; Aberer, K.; and Funaya, K. 2016. Robust online time series prediction with recurrent neural networks. In 2016 IEEE international conference on data science and advanced analytics (DSAA), 816–825. Ieee.
+Hosseinnia Shavaki, F.; and Ebrahimi Ghahnavieh, A. 2023. Applications of deep learning into supply chain management: a systematic literature review and a framework for future research. Artificial Intelligence Review, 56(5): 4447– 4489.
+Hyndman, R. J.; and Athanasopoulos, G. 2018. Forecasting: principles and practice. OTexts.
+Ioffe, S.; and Szegedy, C. 2015. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In International conference on machine learning, 448– 456. pmlr.
+Kim, T.; Kim, J.; Tae, Y.; Park, C.; Choi, J.-H.; and Choo, J. 2021. Reversible instance normalization for accurate timeseries forecasting against distribution shift. In International Conference on Learning Representations.
+Kingma, D. P.; and Ba, J. 2014. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980.
+Kitaev, N.; Kaiser, Ł.; and Levskaya, A. 2020. Reformer: The efficient transformer. arXiv preprint arXiv:2001.04451.
+Kuznetsov, V.; and Mohri, M. 2014. Generalization bounds for time series prediction with non-stationary processes. In Algorithmic Learning Theory: 25th International Conference, ALT 2014, Bled, Slovenia, October 8-10, 2014. Proceedings 25, 260–274. Springer.
+Lee, J.; Jung, D.; Lee, S.; Park, J.; Shin, J.; Hwang, U.; and Yoon, S. 2024. Entropy is not Enough for Test-Time Adaptation: From the Perspective of Disentangled Factors. In The Twelfth International Conference on Learning Representations.
+Li, M.; Zhu, Y.; Shen, Y.; and Angelova, M. 2023a. Clustering-enhanced stock price prediction using deep learning. World wide web, 26(1): 207–232.
+Li, S.; Jin, X.; Xuan, Y.; Zhou, X.; Chen, W.; Wang, Y.-X.; and Yan, X. 2019. Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting. Advances in neural information processing systems, 32. Li, Z.; Qi, S.; Li, Y.; and Xu, Z. 2023b. Revisiting long-term time series forecasting: An investigation on linear mapping. arXiv preprint arXiv:2305.10721.
+Liu, H.; Dong, Z.; Jiang, R.; Deng, J.; Deng, J.; Chen, Q.; and Song, X. 2023a. Spatio-temporal adaptive embedding makes vanilla transformer sota for traffic forecasting. In Proceedings of the 32nd ACM international conference on information and knowledge management, 4125–4129.
+Liu, S.; Yu, H.; Liao, C.; Li, J.; Lin, W.; Liu, A. X.; and Dustdar, S. 2021. Pyraformer: Low-complexity pyramidal attention for long-range time series modeling and forecasting. International conference on learning representations.
+Liu, Y.; Hu, T.; Zhang, H.; Wu, H.; Wang, S.; Ma, L.; and Long, M. 2023b. itransformer: Inverted transformers are effective for time series forecasting. arXiv preprint arXiv:2310.06625.
+Liu, Y.; Wu, H.; Wang, J.; and Long, M. 2022. Nonstationary Transformers: Rethinking the Stationarity in Time Series Forecasting. NeurIPS.
+Liu, Z.; Cheng, M.; Li, Z.; Huang, Z.; Liu, Q.; Xie, Y.; and Chen, E. 2024. Adaptive normalization for non-stationary time series forecasting: A temporal slice perspective. Advances in Neural Information Processing Systems, 36.
+Loshchilov, I.; and Hutter, F. 2016. Sgdr: Stochastic gradient descent with warm restarts. arXiv preprint arXiv:1608.03983.
+Masini, R. P.; Medeiros, M. C.; and Mendes, E. F. 2023. Machine learning advances for time series forecasting. Journal of economic surveys, 37(1): 76–111.
+Nelson, B. K. 1998. Time series analysis using autoregressive integrated moving average (ARIMA) models. Academic emergency medicine, 5(7): 739–744.
+Nie, Y.; Nguyen, N. H.; Sinthong, P.; and Kalagnanam, J. 2022. A time series is worth 64 words: Long-term forecasting with transformers. arXiv preprint arXiv:2211.14730.
+Niu, S.; Wu, J.; Zhang, Y.; Chen, Y.; Zheng, S.; Zhao, P.; and Tan, M. 2022. Efficient Test-Time Model Adaptation without Forgetting. In Chaudhuri, K.; Jegelka, S.; Song, L.; Szepesvari, C.; Niu, G.; and Sabato, S., eds., Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, 16888–16905. PMLR.
+Niu, S.; Wu, J.; Zhang, Y.; Wen, Z.; Chen, Y.; Zhao, P.; and Tan, M. 2023. Towards Stable Test-time Adaptation in Dynamic Wild World. In The Eleventh International Conference on Learning Representations.
+Petropoulos, F.; Apiletti, D.; Assimakopoulos, V.; Babai, M. Z.; Barrow, D. K.; Taieb, S. B.; Bergmeir, C.; Bessa, R. J.; Bijak, J.; Boylan, J. E.; et al. 2022. Forecasting: theory and practice. International Journal of Forecasting, 38(3): 705–871.
+Pham, Q.; Liu, C.; Sahoo, D.; and Hoi, S. 2023. Learning Fast and Slow for Online Time Series Forecasting. In The Eleventh International Conference on Learning Representations.
+Toner, W.; and Darlow, L. 2024. An Analysis of Linear Time Series Forecasting Models. arXiv preprint arXiv:2403.14587.
+Vaswani, A.; Shazeer, N.; Parmar, N.; Uszkoreit, J.; Jones, L.; Gomez, A. N.; Kaiser, Ł.; and Polosukhin, I. 2017. Attention is all you need. Advances in neural information processing systems, 30.
+Verma, Y.; Heinonen, M.; and Garg, V. 2024. ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs. In The Twelfth International Conference on Learning Representations.
+Wang, D.; Shelhamer, E.; Liu, S.; Olshausen, B.; and Darrell, T. 2021. Tent: Fully Test-Time Adaptation by Entropy
+Minimization. In International Conference on Learning Representations.
+Wang, H.; Peng, J.; Huang, F.; Wang, J.; Chen, J.; and Xiao, Y. 2023. Micn: Multi-scale local and global context modeling for long-term series forecasting. In The eleventh international conference on learning representations.
+Wang, S.; Wu, H.; Shi, X.; Hu, T.; Luo, H.; Ma, L.; Zhang, J. Y.; and ZHOU, J. 2024. TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting. In The Twelfth International Conference on Learning Representations.
+Wen, Q.; Chen, W.; Sun, L.; Zhang, Z.; Wang, L.; Jin, R.; Tan, T.; et al. 2024. Onenet: Enhancing time series forecasting models under concept drift by online ensembling. Advances in Neural Information Processing Systems, 36.
+Wen, Q.; Zhou, T.; Zhang, C.; Chen, W.; Ma, Z.; Yan, J.; and Sun, L. 2022. Transformers in time series: A survey. arXiv preprint arXiv:2202.07125.
+Wu, H.; Hu, T.; Liu, Y.; Zhou, H.; Wang, J.; and Long, M. 2023. TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis. ICLR.
+Wu, H.; Wu, J.; Xu, J.; Wang, J.; and Long, M. 2022. Flowformer: Linearizing transformers with conservation flows. ICML.
+Wu, H.; Xu, J.; Wang, J.; and Long, M. 2021. Autoformer: Decomposition transformers with auto-correlation for longterm series forecasting. Advances in neural information processing systems, 34: 22419–22430.
+Xu, Z.; Zeng, A.; and Xu, Q. 2024. FITS: Modeling Time Series with $\$ 101$ Parameters. In The Twelfth International Conference on Learning Representations.
+Yi, K.; Zhang, Q.; Fan, W.; Wang, S.; Wang, P.; He, H.; An, N.; Lian, D.; Cao, L.; and Niu, Z. 2024. Frequency-domain MLPs are more effective learners in time series forecasting. Advances in Neural Information Processing Systems, 36.
+Zeng, A.; Chen, M.; Zhang, L.; and Xu, Q. 2023. Are transformers effective for time series forecasting? In Proceedings of the AAAI conference on artificial intelligence, volume 37(9), 11121–11128.
+Zhang, Y.; and Yan, J. 2022. Crossformer: Transformer utilizing cross-dimension dependency for multivariate time series forecasting. In The eleventh international conference on learning representations.
+Zhou, H.; Zhang, S.; Peng, J.; Zhang, S.; Li, J.; Xiong, H.; and Zhang, W. 2021. Informer: Beyond efficient transformer for long sequence time-series forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 35(12), 11106–11115.
+Zhou, T.; Ma, Z.; Wen, Q.; Wang, X.; Sun, L.; and Jin, R. 2022. Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting. In International conference on machine learning, 27268–27286. PMLR.
+# Appendix Algorithm of TAFAS
+Algorithm 1 summarizes the overall pipeline of TAFAS.
+# Detailed Explanations on Datasets
+Table A1 shows the characteristics of the seven widely used public TSF benchmark datasets used throughout experiments. (Train, Validation, Test) shows the number of time steps in the train, validation, and test set, respectively. ADF shows the results of the Augmented Dickey-Fuller Test (Elliott, Rothenberg, and Stock 1992), which quantify the nonstationarity of each dataset. A higher ADF test statistic suggests greater non-stationarity, indicating prevalent distribution shifts.
+Table A1: Characteristics of the seven widely used public TSF benchmark datasets.
+<table><tr><td>Dataset</td><td>Var.</td><td>Time Steps</td><td>Sampling Rate</td><td>ADF</td></tr><tr><td>ETTh1</td><td>7</td><td>17420</td><td>1 hour</td><td>-5.91</td></tr><tr><td>ETTm1</td><td>7</td><td>69680</td><td>1 hour</td><td>-14.98</td></tr><tr><td>ETTh2</td><td>7</td><td>17420</td><td>15 minutes</td><td>-4.13</td></tr><tr><td>ETTm2</td><td>7</td><td>69680</td><td>15 minutes</td><td>-5.66</td></tr><tr><td>Exchange</td><td>8</td><td>7588</td><td>1 day</td><td>-1.90</td></tr><tr><td>Illness</td><td>7</td><td>966</td><td>1 week</td><td>-5.33</td></tr><tr><td>Weather</td><td>21</td><td>52696</td><td>10 minutes</td><td>-26.68</td></tr></table>
+# Training Details
+A hyper-parameter search was conducted for each source forecaster, exploring learning rates of 1e-3, 1e-4, and 1e-5, and weight decay values of 0.0, 1e-3, and 1e-4. For each combination, models were trained using three different seeds. The hyper-parameter combination that resulted in the lowest validation MSE loss was selected for use. Pretraining was performed for 30 epochs with a batch size of 64, ensuring that the validation MSE loss had sufficiently saturated. We employed the Adam optimizer (Kingma and Ba 2014) and adjusted the learning rate using cosine learning rate scheduling (Loshchilov and Hutter 2016). All experiments were conducted using a single NVIDIA A40 GPU. We referred the configuration (e.g., number of layers) of each source forecaster to the Time Series Library (Wu et al. 2023). When incorporating the normalization-based approaches (RevIN (Kim et al. 2021), Dish-TS (Fan et al. 2023), and SAN (Liu et al. 2024)) for pre-training the source forecaster, the hyper-parameter searches for RevIN and Dish-TS were conducted in the same manner as for training the baseline source forecaster. For SAN, a two-stage pre-training process is required, involving the training of the statistics prediction module. According to the settings in the original paper, the statistics prediction module was trained for 10 epochs, with a hyper-parameter search for learning rates of 1e-3 and 1e-4. When performing TSF-TTA with TAFAS, the learning rate was searched among 5e-3, 3e-3, 1e-3, 5e-4, and 1e-4. The initial value of the gating parameter $\alpha$ was searched among 0.01, 0.05, 0.1, and 0.3. For reproducibility, we will make our code publicly available in the final version.
+Algorithm 1: PyTorch-style Pseudocode for TAFAS
+```python
+1 # L: look-back window length
+2 # forecaster: source forecaster
+3 # in_GCM: input GCM
+4 # out_GCM: output GCM
+5
+6 forecasterrequires_grad_(False)
+7 do_PAAS = True
+8 test_batch = []
+9
+10 for test_input in testloader:
+11 # PAAS
+12 if do_PAAS:
+13 period = PAAS(test_input)
+14 bsz = 0
+15 do_PAAS = False
+16
+17 # get mini-batch based on PAAS
+18 if bsz < period + 1:
+19 test_batch.append(test_input)
+20 bsz += 1
+21 if bsz == period + 1:
+22 do_PAAS = True
+23 else:
+24 continue
+25
+26 # get POGT
+27 test_batch = torch.stack(test_batch)
+28 POGT = test_batch[-1][-:period]
+29
+30 # adapt GCM
+31 input_cali = in_GCM(test_input)
+32 pred = forecaster(input_cali)
+33 pred_cali = out_GCM(pred)
+34 l_p = MSE(pred_cali)[-:period], POGT)
+35 if fullgt-available:
+36 l_f = MSE(full_pred, full_GT)
+37 else:
+38 l_f = 0.0
+39 l_tafas = l_p + l_f
+40 l_tafas.backup()
+41 optimizer.zero_grad()
+42 optimizer.step()
+43
+44 # PA
+45 with torch.no_grad():
+46 pred_adapted = out_CGM( Forecaster(in_GCM(test_batch)))
+47 for i in range(bsz - 1):
+48 pred_cali[i, period-i] =
+49 pred_adapted[i, period-i]
+50 test_batch = []
+51
+52
+53 def PAAS(test_input):
+54 # test_input: (L, C)
+55 test_input -= test_input.mean(dim=0)
+56 amplitude = abs(fft(test_input))
+57 var_idx = (amplitude ** 2).sum(dim=0)
+58 avgmax()
+59 freq = amplitude[:, var_idx].argmax()
+60 p = test_input.shape[0] // freq
+61 return p
+```
+# Additional Related Works
+# Time Series Forecasting Models
+As time series forecasting has become a pivotal application in various industries, diverse time series forecasting architectures have been developed to accurately predict future time steps (Wen et al. 2022; Masini, Medeiros, and Mendes 2023). They range from traditional statistical methods (Nelson 1998; Girard et al. 2002; Hyndman and Athanasopoulos 2018) to deep neural network-based architectures, including Transformers (Vaswani et al. 2017; Zhou et al. 2021; Li et al. 2019; Liu et al. 2021, 2023b; Wu et al. 2021; Nie et al. 2022; Zhang and Yan 2022; Kitaev, Kaiser, and Levskaya 2020; Zhou et al. 2022; Wu et al. 2022), Linear layers (Zeng et al. 2023; Li et al. 2023b; Toner and Darlow 2024), and MLPs (Yi et al. 2024; Wang et al. 2023; Ekambaram et al. 2023; Das et al. 2023; Xu, Zeng, and Xu 2024; Wang et al. 2024; Challu et al. 2022). Transformer-based models aim to capture temporal dependencies as well as inter-variable dependencies utilizing the attention mechanism. To address the quadratic time and memory complexity of self-attention operation, a line of work has been proposed to modify the self-attention module to be more efficient, facilitating longterm forecasting (Zhou et al. 2021; Kitaev, Kaiser, and Levskaya 2020; Li et al. 2019). Some works have revised the Transformer architecture to better exploit the properties of time series, such as sub-series periodicity or frequency information (Wu et al. 2021; Zhou et al. 2022). Other works remain the architecture untouched, but consider how to input time series by patching or inverting (Nie et al. 2022; Liu et al. 2023b). On the other hand, in response to a recent work that raised questions to the modeling capability of Transformer-based TSF models (Zeng et al. 2023), a series of Linear (Zeng et al. 2023; Li et al. 2023b; Toner and Darlow 2024) and MLP-based architectures (Yi et al. 2024; Wang et al. 2023; Ekambaram et al. 2023; Das et al. 2023; Xu, Zeng, and Xu 2024; Wang et al. 2024; Challu et al. 2022) have been developed, achieving comparable or outperforming TSF capabilities compared to Transformerbased models. Still, there is no consensus on the most representative TSF architecture, making the model-agnosticism of the TSF-TTA framework more desirable. More recently, time series foundation models, pre-trained on up to billions of time steps, have shown promising forecasting capabilities (Ansari et al. 2024; Das et al. 2024; Goswami et al. 2024; Garza and Mergenthaler-Canseco 2023). The emergence of foundation models highlighted exploiting rich semantic information encoded in pre-trained models on unseen data streams.
+# Test-Time Adaptation (TTA)
+The goal of test-time adaptation is to adapt a pre-trained source model to distributionally shifted inputs encountered during testing, thereby improving generalization performance on unseen test distributions. Test-time adaptation has primarily evolved in classification tasks, leveraging the characteristic components of classification tasks (Wang et al. 2021; Niu et al. 2022, 2023; Lee et al. 2024; Gong et al. 2022). TTA methods commonly rely on the entropy of
+class probabilities, which is only applicable to classification tasks and infeasible to TSF, which is a regression task. TENT (Wang et al. 2021) minimizes the entropy of the target class probability by updating the channel-wise affine transformation of the normalization layer. EATA (Niu et al. 2022) builds on the entropy minimization framework by proposing a sample filtering method for sample-efficient entropy minimization. SAR (Niu et al. 2023) considers additional scenarios in classification tasks, such as label imbalance, and proposes sharpness-aware entropy minimization. DEYO (Lee et al. 2024) combines entropy minimization with imagespecific data augmentation, utilizing pseudo label probability for the transformed test input. Moreover, they do not consider the properties of time series data, such as instance-wise distribution shifts within a window input and the global temporal dependency across streaming window data. Although NOTE (Gong et al. 2022) considers the temporal correlation between streaming images, it still relies on an entropy-based approach and does not account for the distribution shifts that can occur within a single instance window in time series data. Additionally, they are not fully model-agnostic because they adapt specific types of normalization layers (e.g., Batch Norm (Ioffe and Szegedy 2015) or Layer Norm (Ba, Kiros, and Hinton 2016)) and are inapplicable to models without normalization layers. Given that TSF has been developed based on various architectural advances, model dependence significantly limits the generality of TSF-TTA framework.
+![](images/6c798fbf302c1c859ad8a4333ea7077b84e8ddaee2d23c13a09ef83d68dacfac.jpg)
+Figure A1: Improvements of MSE $( \% )$ as the forecasting window length increases.
+Table A2: Comparison of average test MSE between TAFAS and baseline models. Both TAFAS and the baselines are adapted using the same input with sequentially arriving test data. Baselines include DLinear and DLinear pre-trained with Dish-TS.
+<table><tr><td></td><td>ETTh1</td><td>ETTm1</td><td>ETTh2</td><td>ETTm2</td><td>Exchange</td></tr><tr><td>DLinear</td><td>0.553</td><td>0.476</td><td>0.313</td><td>0.222</td><td>0.350</td></tr><tr><td>+TAFAS</td><td>0.538</td><td>0.450</td><td>0.304</td><td>0.219</td><td>0.337</td></tr><tr><td>DLinear w/ Dish-TS</td><td>0.550</td><td>0.452</td><td>0.308</td><td>0.234</td><td>0.300</td></tr><tr><td>+TAFAS</td><td>0.525</td><td>0.446</td><td>0.291</td><td>0.221</td><td>0.256</td></tr></table>
+# Additional Experimental Results
+Figure A1 presents the effectiveness of TAFAS in long-term forecasting scenarios that we stated in the Experiments Section in the manuscript.
+# Comparison with Baselines using POGT
+To further verify the effectiveness of TAFAS, we have conducted experiments where the baselines are also adapted using the same input as TAFAS. The baselines includee DLinear and DLinear with Dish-TS. All results are reported in terms of MSE averaged over $H \in \{ 9 6 , 1 9 2 , 3 3 6 , \hat { 7 } 2 0 \}$ . According to Table A2, the baselines fall short of TAFAS even when they use POGT for further training. This demonstrates that TAFAS consistently outperforms the baselines by effectively leveraging sequentially arriving test data.
+# Hyperparameter Robustness Analysis
+To validate that TAFAS can be deployed at test-time without significant hyper-parameter tuning, we show its robustness to changes in hyper-parameters. Table A3 presents test MSE and MAE for different combinations of the two hyperparameters involved in TAFAS: the test-time learning rate $\mu$ and initialization value for gating parameter $\alpha$ . The experiments were conducted using DLinear on the ETTh1 dataset with $H = 7 2 0$ . TAFAS constantly achieves low MSE and MAE across different parameter settings with consistently low standard deviations, indicating that it is reasonably robust against changes in hyper-parameters.
+# Component-wise Ablation Studies
+Table A4 presents ablative experiments aimed at demonstrating the necessity of various components of TAFAS for successfully performing TSF-TTA. When GCM is excluded, the entire source forecaster is adapted to maintain model-agnosticity of TSF-TTA. In the absence of PAAS,
+Table A3: Forecasting errors for different $( \mu , \alpha )$ .
+<table><tr><td>(μ, α)</td><td>MSE</td><td>MAE</td></tr><tr><td>(1e-3, 0.01)</td><td>0.669 ± 0.002</td><td>0.600 ± 0.002</td></tr><tr><td>(1e-3, 0.05)</td><td>0.669 ± 0.001</td><td>0.598 ± 0.000</td></tr><tr><td>(1e-3, 0.1)</td><td>0.691 ± 0.001</td><td>0.609 ± 0.001</td></tr><tr><td>(5e-4, 0.01)</td><td>0.682 ± 0.000</td><td>0.602 ± 0.000</td></tr><tr><td>(5e-4, 0.05)</td><td>0.671 ± 0.001</td><td>0.599 ± 0.000</td></tr><tr><td>(5e-4, 0.1)</td><td>0.670 ± 0.001</td><td>0.599 ± 0.000</td></tr><tr><td>(1e-4, 0.05)</td><td>0.683 ± 0.001</td><td>0.601 ± 0.001</td></tr><tr><td>(1e-4, 0.1)</td><td>0.676 ± 0.001</td><td>0.599 ± 0.000</td></tr><tr><td>(1e-4, 0.3)</td><td>0.669 ± 0.001</td><td>0.599 ± 0.000</td></tr></table>
+Table A4: Ablation study on each component of TAFAS. The “-” denotes the excluded component from TAFAS.
+<table><tr><td></td><td></td><td colspan="2">Exchange</td><td colspan="2">ETTh1</td><td colspan="2">ETTh2</td></tr><tr><td></td><td></td><td>MSE</td><td>MAE</td><td>MSE</td><td>MAE</td><td>MSE</td><td>MAE</td></tr><tr><td colspan="2">Baseline</td><td>0.844</td><td>0.692</td><td>0.786</td><td>0.662</td><td>0.415</td><td>0.441</td></tr><tr><td rowspan="3">TAFAS</td><td>- PAAS</td><td>0.795</td><td>0.672</td><td>0.740</td><td>0.645</td><td>0.393</td><td>0.425</td></tr><tr><td>- GCM</td><td>0.979</td><td>0.756</td><td>1.320</td><td>0.839</td><td>0.491</td><td>0.480</td></tr><tr><td>- PA</td><td>0.809</td><td>0.679</td><td>0.706</td><td>0.628</td><td>0.392</td><td>0.425</td></tr><tr><td colspan="2">TAFAS</td><td>0.773</td><td>0.665</td><td>0.704</td><td>0.627</td><td>0.393</td><td>0.425</td></tr></table>
+a test batch size of 64 is arbitrarily selected. The experiments are conducted for iTransformer with $H = 7 2 0$ . Each row in Table A4 indicates which component was removed for ablation; besides the removed component, the rest of TAFAS remains unchanged. The results show that removing each component of TAFAS subsequently degrades the performance of TAFAS, validating its effectiveness. Figure A3 illustrates the MSE values for each dataset when test batches are adaptively composed using PAAS compared to using fixed batch sizes. In most instances, PAAS consistently achieves superior performance. The variation in effective batch sizes across different datasets underscores the importance of identifying an optimal batch size for each dataset. PAAS demonstrates its capability to configure these batch sizes at test time effectively. Table A5 shows the range of test batch sizes derived through PAAS for each dataset.
+The results show that introducing each component of TAFAS subsequently reduces the MSE, validating its effectiveness.
+# Qualitative Analysis
+Figure A2 shows the qualitative comparison of forecasting results with and without TAFAS for iTransformer. In the top row, the baseline produces repetitive patterns that resemble the latest periodic pattern within the look-back window. In contrast, TAFAS preemptively adapts the source forecaster to changing distributions and outputs significantly more accurate predictions. Furthermore, TAFAS effectively adapts to both low-frequency (top left) and high-frequency (top right) dominant patterns. The two panels on the bottom row highlight the particular advantages of TAFAS in more chal-
+Ground truth Prediction (baseline) Prediction (TAFAS)
+![](images/760f5fad8857256d522145b7f780f61b039b1df60bd678494b5573104e898851.jpg)
+![](images/4c8a07f7b2ae953c95d5c05c99256aa627cbcf7abdc787f6eaa74e872eedbace.jpg)
+![](images/dadf27a8e04db410e205355362ae6b7b2a4fb9e882c4793e49a2ec5640ca676e.jpg)
+![](images/b2892e273fbc2033d3b7eb5af06fd0a946c559fe7b2cb2eb7ec99628e9f210cc.jpg)
+Figure A2: Visualization of forecasting results with and without TAFAS. The top row illustrates that TAFAS effectively adapts to both low-frequency (top left) and high-frequency (top right) dominant patterns within the look-back window. The bottom row highlights the promising aspect of TAFAS in significantly more challenging scenarios characterized by pronounced global distribution shifts.
+Table A5: Range of POGT length $p$ constructed via PAAS.
+<table><tr><td>Dataset</td><td>Range of p</td></tr><tr><td>ETTh1</td><td>12-96</td></tr><tr><td>ETTm1</td><td>32-96</td></tr><tr><td>ETTh2</td><td>8-96</td></tr><tr><td>ETTm2</td><td>6-96</td></tr><tr><td>Exchange</td><td>48-96</td></tr><tr><td>Illness</td><td>36-36</td></tr><tr><td>Weather</td><td>2-96</td></tr></table>
+lenging long-term forecasting scenarios where test data digress noticeably from historical data, resulting in a more extreme distribution shift. In the examples in these two panels, the time series in the prediction window visible differs from that in the look-back window, which is indicative of a global shift in distribution. Here, the baseline merely repeats the pattern within the look-back window, while TAFAS effectively captures the global distribution shift.
+# MAE and Standard Deviations of TAFAS
+Table A6 presents the MAE and standard deviations for the three different runs. The standard deviations were rounded to the fourth decimal place. When TAFAS is applied, most standard deviations are 0.000, demonstrating the stability of TAFAS in test-time adaptation.
+ICN (Wang et al. 2023. +TAFAS denotes whether the TAFAS framework is applied to the corresp t al. 2023b, PatchTST (Nie et al. 2022, Linear-based (DLinear (Zeng et al. 2023, OLS (Toner and Darlo )) ndard deviations on multivariate time series forecasting datasets with and without TAFAS across various TSF ))))
+<table><tr><td rowspan="3" colspan="2">Models + TAFAS</td><td colspan="4">Transformer-based</td><td colspan="4">Linear-based</td><td colspan="4">MLP-based</td></tr><tr><td colspan="2">iTransformer</td><td colspan="2">PatchTST</td><td colspan="2">DLinear</td><td colspan="2">OLS</td><td colspan="2">FreTS</td><td colspan="2">MICN</td></tr><tr><td>x</td><td>✓</td><td>x</td><td>✓</td><td>x</td><td>✓</td><td>x</td><td>✓</td><td>x</td><td>✓</td><td>x</td><td>✓</td></tr><tr><td rowspan="4">ETTh1</td><td>96</td><td>0.448 (0.000)</td><td>0.443 (0.000)</td><td>0.450 (0.001)</td><td>0.444 (0.000)</td><td>0.446 (0.000)</td><td>0.442 (0.000)</td><td>0.446 (0.000)</td><td>0.444 (0.000)</td><td>0.447 (0.000)</td><td>0.444 (0.000)</td><td>0.459 (0.000)</td><td>0.453 (0.000)</td></tr><tr><td>192</td><td>0.494 (0.000)</td><td>0.489 (0.000)</td><td>0.489 (0.001)</td><td>0.483 (0.000)</td><td>0.483 (0.000)</td><td>0.480 (0.000)</td><td>0.483 (0.000)</td><td>0.482 (0.000)</td><td>0.486 (0.000)</td><td>0.483 (0.000)</td><td>0.503 (0.004)</td><td>0.497 (0.002)</td></tr><tr><td>336</td><td>0.532 (0.001)</td><td>0.532 (0.000)</td><td>0.520 (0.001)</td><td>0.519 (0.001)</td><td>0.515 (0.000)</td><td>0.516 (0.000)</td><td>0.514 (0.000)</td><td>0.512 (0.000)</td><td>0.527 (0.000)</td><td>0.525 (0.000)</td><td>0.546 (0.002)</td><td>0.544 (0.001)</td></tr><tr><td>720</td><td>0.662 (0.006)</td><td>0.627 (0.000)</td><td>0.621 (0.006)</td><td>0.621 (0.005)</td><td>0.605 (0.000)</td><td>0.598 (0.002)</td><td>0.605 (0.000)</td><td>0.599 (0.000)</td><td>0.619 (0.000)</td><td>0.610 (0.000)</td><td>0.642 (0.006)</td><td>0.633 (0.005)</td></tr><tr><td rowspan="4">ETTh1</td><td>96</td><td>0.405 (0.003)</td><td>0.387 (0.001)</td><td>0.403 (0.002)</td><td>0.397 (0.001)</td><td>0.393 (0.000)</td><td>0.381 (0.000)</td><td>0.393 (0.000)</td><td>0.382 (0.000)</td><td>0.391 (0.000)</td><td>0.386 (0.001)</td><td>0.412 (0.009)</td><td>0.397 (0.004)</td></tr><tr><td>192</td><td>0.438 (0.001)</td><td>0.430 (0.000)</td><td>0.435 (0.000)</td><td>0.428 (0.000)</td><td>0.428 (0.000)</td><td>0.416 (0.000)</td><td>0.429 (0.000)</td><td>0.416 (0.000)</td><td>0.426 (0.001)</td><td>0.423 (0.001)</td><td>0.431 (0.000)</td><td>0.423 (0.000)</td></tr><tr><td>336</td><td>0.475 (0.002)</td><td>0.466 (0.001)</td><td>0.468 (0.000)</td><td>0.461 (0.000)</td><td>0.467 (0.000)</td><td>0.452 (0.000)</td><td>0.467 (0.000)</td><td>0.452 (0.000)</td><td>0.463 (0.001)</td><td>0.458 (0.000)</td><td>0.471 (0.001)</td><td>0.461 (0.001)</td></tr><tr><td>720</td><td>0.523 (0.001)</td><td>0.511 (0.001)</td><td>0.517 (0.001)</td><td>0.509 (0.000)</td><td>0.515 (0.000)</td><td>0.497 (0.000)</td><td>0.515 (0.000)</td><td>0.499 (0.000)</td><td>0.510 (0.001)</td><td>0.504 (0.001)</td><td>0.532 (0.002)</td><td>0.516 (0.001)</td></tr><tr><td rowspan="4">ETTh2</td><td>96</td><td>0.330 (0.001)</td><td>0.329 (0.001)</td><td>0.321 (0.001)</td><td>0.320 (0.001)</td><td>0.315 (0.000)</td><td>0.314 (0.000)</td><td>0.317 (0.000)</td><td>0.316 (0.000)</td><td>0.322 (0.000)</td><td>0.321 (0.001)</td><td>0.321 (0.001)</td><td>0.320 (0.001)</td></tr><tr><td>192</td><td>0.365 (0.001)</td><td>0.362 (0.001)</td><td>0.357 (0.002)</td><td>0.353 (0.002)</td><td>0.352 (0.000)</td><td>0.350 (0.000)</td><td>0.352 (0.000)</td><td>0.349 (0.000)</td><td>0.359 (0.000)</td><td>0.355 (0.000)</td><td>0.357 (0.001)</td><td>0.354 (0.001)</td></tr><tr><td>336</td><td>0.392 (0.001)</td><td>0.386 (0.001)</td><td>0.386 (0.002)</td><td>0.382 (0.001)</td><td>0.379 (0.000)</td><td>0.374 (0.000)</td><td>0.379 (0.000)</td><td>0.372 (0.000)</td><td>0.386 (0.000)</td><td>0.378 (0.000)</td><td>0.386 (0.004)</td><td>0.378 (0.001)</td></tr><tr><td>720</td><td>0.441 (0.001)</td><td>0.425 (0.001)</td><td>0.438 (0.004)</td><td>0.427 (0.003)</td><td>0.433 (0.000)</td><td>0.417 (0.000)</td><td>0.434 (0.000)</td><td>0.412 (0.000)</td><td>0.441 (0.000)</td><td>0.419 (0.000)</td><td>0.434 (0.003)</td><td>0.421 (0.003)</td></tr><tr><td rowspan="4">ETTh2</td><td>96</td><td>0.265 (0.000)</td><td>0.263 (0.001)</td><td>0.262 (0.000)</td><td>0.262 (0.000)</td><td>0.264 (0.000)</td><td>0.262 (0.000)</td><td>0.264 (0.000)</td><td>0.263 (0.000)</td><td>0.260 (0.001)</td><td>0.259 (0.000)</td><td>0.265 (0.000)</td><td>0.264 (0.000)</td></tr><tr><td>192</td><td>0.296 (0.000)</td><td>0.292 (0.000)</td><td>0.295 (0.000)</td><td>0.294 (0.000)</td><td>0.290 (0.000)</td><td>0.289 (0.000)</td><td>0.291 (0.000)</td><td>0.290 (0.000)</td><td>0.291 (0.000)</td><td>0.290 (0.000)</td><td>0.293 (0.000)</td><td>0.291 (0.000)</td></tr><tr><td>336</td><td>0.331 (0.001)</td><td>0.324 (0.000)</td><td>0.325 (0.001)</td><td>0.323 (0.000)</td><td>0.319 (0.000)</td><td>0.317 (0.000)</td><td>0.320 (0.000)</td><td>0.317 (0.000)</td><td>0.321 (0.000)</td><td>0.319 (0.000)</td><td>0.322 (0.000)</td><td>0.320 (0.000)</td></tr><tr><td>720</td><td>0.373 (0.001)</td><td>0.366 (0.000)</td><td>0.371 (0.001)</td><td>0.367 (0.001)</td><td>0.365 (0.000)</td><td>0.359 (0.000)</td><td>0.365 (0.000)</td><td>0.359 (0.000)</td><td>0.366 (0.001)</td><td>0.359 (0.001)</td><td>0.366 (0.000)</td><td>0.361 (0.000)</td></tr><tr><td rowspan="4">Exchange</td><td>96</td><td>0.207 (0.000)</td><td>0.208 (0.000)</td><td>0.202 (0.001)</td><td>0.200 (0.001)</td><td>0.197 (0.000)</td><td>0.197 (0.000)</td><td>0.197 (0.000)</td><td>0.195 (0.000)</td><td>0.201 (0.000)</td><td>0.198 (0.000)</td><td>0.200 (0.000)</td><td>0.198 (0.000)</td></tr><tr><td>192</td><td>0.298 (0.000)</td><td>0.293 (0.000)</td><td>0.301 (0.001)</td><td>0.296 (0.001)</td><td>0.292 (0.000)</td><td>0.289 (0.000)</td><td>0.293 (0.000)</td><td>0.289 (0.000)</td><td>0.297 (0.001)</td><td>0.291 (0.001)</td><td>0.303 (0.001)</td><td>0.297 (0.000)</td></tr><tr><td>336</td><td>0.415 (0.001)</td><td>0.389 (0.003)</td><td>0.431 (0.010)</td><td>0.395 (0.005)</td><td>0.408 (0.000)</td><td>0.387 (0.001)</td><td>0.409 (0.000)</td><td>0.384 (0.000)</td><td>0.412 (0.000)</td><td>0.393 (0.002)</td><td>0.420 (0.004)</td><td>0.403 (0.005)</td></tr><tr><td>720</td><td>0.692 (0.001)</td><td>0.665 (0.000)</td><td>0.691 (0.004)</td><td>0.690 (0.004)</td><td>0.688 (0.001)</td><td>0.684 (0.000)</td><td>0.687 (0.000)</td><td>0.577 (0.000)</td><td>0.689 (0.004)</td><td>0.668 (0.018)</td><td>0.839 (0.015)</td><td>0.726 (0.031)</td></tr><tr><td rowspan="4">Illness</td><td>24</td><td>0.906 (0.008)</td><td>0.907 (0.008)</td><td>0.841 (0.003)</td><td>0.841 (0.003)</td><td>1.055 (0.002)</td><td>1.042 (0.002)</td><td>1.008 (0.001)</td><td>0.993 (0.000)</td><td>0.946 (0.002)</td><td>0.946 (0.002)</td><td>1.029 (0.002)</td><td>1.030 (0.002)</td></tr><tr><td>36</td><td>0.922 (0.006)</td><td>0.922 (0.006)</td><td>0.860 (0.007)</td><td>0.860 (0.007)</td><td>1.026 (0.001)</td><td>1.001 (0.005)</td><td>1.000 (0.001)</td><td>0.948 (0.000)</td><td>0.961 (0.007)</td><td>0.961 (0.007)</td><td>1.062 (0.002)</td><td>1.063 (0.001)</td></tr><tr><td>48</td><td>0.939 (0.001)</td><td>0.933 (0.002)</td><td>0.854 (0.018)</td><td>0.854 (0.018)</td><td>1.030 (0.000)</td><td>0.015 (0.000)</td><td>1.005 (0.002)</td><td>0.957 (0.000)</td><td>0.947 (0.004)</td><td>0.913 (0.004)</td><td>0.923 (0.004)</td><td>0.913 (0.005)</td></tr><tr><td>60</td><td>0.895 (0.007)</td><td>0.872 (0.008)</td><td>0.862 (0.005)</td><td>0.862 (0.005)</td><td>1.046 (0.001)</td><td>1.033 (0.001)</td><td>1.029 (0.000)</td><td>0.975 (0.000)</td><td>0.934 (0.004)</td><td>0.915 (0.004)</td><td>0.914 (0.005)</td><td>0.906 (0.003)</td></tr><tr><td rowspan="4">Weather</td><td>96</td><td>0.220 (0.002)</td><td>0.219 (0.002)</td><td>0.215 (0.001)</td><td>0.219 (0.001)</td><td>0.235 (0.000)</td><td>0.235 (0.000)</td><td>0.234 (0.000)</td><td>0.237 (0.000)</td><td>0.220 (0.000)</td><td>0.220 (0.000)</td><td>0.219 (0.001)</td><td>0.219 (0.000)</td></tr><tr><td>192</td><td>0.260 (0.000)</td><td>0.257 (0.001)</td><td>0.257 (0.000)</td><td>0.260 (0.000)</td><td>0.270 (0.000)</td><td>0.267 (0.000)</td><td>0.270 (0.000)</td><td>0.273 (0.000)</td><td>0.259 (0.000)</td><td>0.261 (0.001)</td><td>0.262 (0.001)</td><td>0.264 (0.001)</td></tr><tr><td>336</td><td>0.301 (0.000)</td><td>0.300 (0.000)</td><td>0.297 (0.000)</td><td>0.300 (0.000)</td><td>0.306 (0.000)</td><td>0.303 (0.000)</td><td>0.306 (0.000)</td><td>0.305 (0.000)</td><td>0.298 (0.000)</td><td>0.295 (0.000)</td><td>0.302 (0.001)</td><td>0.303 (0.001)</td></tr><tr><td>720</td><td>0.352 (0.001)</td><td>0.352 (0.001)</td><td>0.346 (0.000)</td><td>0.356 (0.000)</td><td>0.353 (0.000)</td><td>0.348 (0.000)</td><td>0.353 (0.000)</td><td>0.351 (0.000)</td><td>0.347 (0.000)</td><td>0.344 (0.000)</td><td>0.346 (0.001)</td><td>0.356 (0.003)</td></tr></table>
+![](images/9437df6484534a1786e9f0d2bfa3d1aec259ff3dd11a9082d816cbc39233f027.jpg)
+![](images/a84536f3e3738b47770a09e18d1ef2dfcddf65303f0966311e653be4cd3058fb.jpg)
+![](images/5124780d347980daabb75ed1b81b97bc5e79a401a22df63e2fc0c19235c99665.jpg)
+![](images/364b78d50a3e0b9f7240828bdf98c2b37ac7d3a2c7c8e513e6f0a685de5dd2ee.jpg)
+![](images/02d962314c7ed48fb440b6e80a8b64272b40ed3a33eda2dac45bca5d039681c5.jpg)
+![](images/3a4163ca3a54991ad514c59413af361b2f1984e5380eabec7018cc83a404a305.jpg)
+![](images/d0d0f3c1c9e3975f8dd8f69727154f72028998d1192d60e2c226780f62cde684.jpg)
+![](images/3d317eb038bb28cb168e2369ba0b1e4eab20c224e857fd8af6dcb5f6855a1673.jpg)
+![](images/543461884926f983320f14b8e04c1516095f23fc6a44d7baf87db2ed5c49ead1.jpg)
+![](images/e26d4f8891c3bba1ace01387a65d40ef9fcacf7339c383420b3d3837d4f60b6a.jpg)
+![](images/47ed8b552ca8a6340e01d56259dec9a33e2fb8abdb781461f0187d326c85a3f3.jpg)
+![](images/6f5de749566bcefd6f24e81a03b510b7123fd7d7cc8a7e3ff6e79c8993bf5d42.jpg)
+![](images/1a5008dea46b3ad71e3b6b281d386f7af55e59a869becd3555b5be89cb24afd7.jpg)
+![](images/f4ab5eed702cc27e9bfc3cca09b869767f83fdf86798476f7e0a65d90cc78121.jpg)
+![](images/969785be173b8f5af5e6c912ae664bcb28c52ee1bd4415ee7fc1cbb1620f0cbf.jpg)
+![](images/dcffa8d51146459b0f2e967f6d1e10ce961c2f1eba8cac220cc0d5e3bc8ea43a.jpg)
+![](images/ca9eaf8d88a6d4dc191a3105f70991f626cb7c3863742093817fdce8621e51be.jpg)
+![](images/6f8d6d38f028eebbb2e61d85c38be4710f41292357a53f1cb62721a2ea1549a0.jpg)
+![](images/9c2986d6c2d82a8cd8edff4c1ad990b2455986243f265b5b7521626d806b397c.jpg)
+![](images/1b5e692a67c03f3ac32c9310a8146b19fe87393bec3a1446878f12ade7aec0dc.jpg)
+![](images/7343c72d7ba470b53b514cb779d4b30b50fe4fcbc3816055e61f45b0292363d4.jpg)
+![](images/2b8dcc5bd03ee27ef3576f75ee551f1ddfe87b9ddc8fd2d98b35806f2f7db9f2.jpg)
+![](images/91c83eab2a1950c768a0bf4a3f152b54c1ae9f070ce7c2cb038ef8e279790adb.jpg)
+![](images/bccd4656751712f804d1ab3fdfab324f9357e97589d7357e4b4c0448a37b5346.jpg)
+![](images/7570177f5bd0ca45fcb85bdd9224bbcb14174028e68d5390533ffeac0aae9b7d.jpg)
+![](images/b96bee9e6f0a18b7d046696f061356b2291707210d6be2e1ef02b5b37a9b0549.jpg)
+![](images/a53d726016872d28bd460682b2cd45947885a109f6e041c4a45ac273e52beb8e.jpg)
+![](images/70bf6f31501e4b9df17e24ffeb35977125319b19beff6f377bdf1caecc71646f.jpg)
+Figure A3: Comparison of test MSE when using PAAS against fixed length POGT.

paper_markdowns/bamboo-00569.md ADDED Viewed

	@@ -0,0 +1,373 @@

+# Reasoning is All You Need for Video Generalization: A Counterfactual Benchmark with Sub-question Evaluation
+Qiji Zhou* 1, YiFan Gong* 2, Guangsheng $\mathbf { B a o ^ { 1 } }$ , Hongjie $\mathbf { Q i u } ^ { 2 }$ , Jinqiang $\mathbf { L i } ^ { 2 }$ Xiangrong $\mathbf { Z } \mathbf { h } \mathbf { u } ^ { 2 }$ , Huajian Zhang1, Yue Zhang† 1
+1School of Engineering, Westlake University
+2College of Computer Science and Technology, Hangzhou Dianzi University {zhouqiji, baoguangsheng, zhanghuajian, zhangyue}@westlake.edu.cn {gongyifan, qiuhongjie, lijinqiang, zhuxiangrong}@hdu.edu.cn
+# Abstract
+Counterfactual reasoning is crucial for robust video understanding but remains underexplored in existing multimodal benchmarks. In this paper, we introduce COVER (COunterfactual VidEo Reasoning), a multidimensional multimodal benchmark that systematically evaluates MLLMs across the abstract-concrete and perception-cognition dimensions. Beyond prior multimodal benchmarks, COVER decomposes complex queries into structured sub-questions, enabling fine-grained reasoning analysis. Experiments on commercial and open-source models reveal a strong correlation between subquestion accuracy and counterfactual reasoning performance, highlighting the role of structured inference in video understanding. Furthermore, our results suggest a key insight: enhancing the reasoning capability of models is essential for improving the robustness of video understanding. COVER establishes a new standard for assessing MLLMs’ logical reasoning abilities in dynamic environments. Our work is available at https://github.com/gongyifan-hash/COVER-Benchmark.
+# 1 Introduction
+In recent years, the rapid advancement of large language models (LLMs) has spurred growing interest in multimodal large language models (MLLMs) (Hurst et al., 2024; Anthropic, 2024; Chen et al., 2024; Zhang et al., 2024a, 2025; Wang et al., 2024; Wu et al., 2024b). Various early benchmarks have been proposed to assess multimodal understanding ability of MLLMs, particularly in static images (Fu et al., 2023; Hudson and Manning, 2019; Liu et al., 2024; Yu et al., 2024). More recently, benchmarks involving complex images and dynamic videos have emerged to evaluate MLLM’s capabilities in temporal reasoning, spatio-temporal recognition, and object detection (Fu et al., 2024;
+Li et al., 2024b, 2023). Despite these advances, these benchmarks often overlook counterfactual reasoning, which is a critical component for evaluating inference in complex and realistic environments. As a result, they fall short of providing a comprehensive assessment of MLLMs’ reasoning capabilities.
+Counterfactual reasoning, which posits hypothetical alternatives to observed realities, is pivotal for advanced video inference and is closely tied to outof-distribution generalization (Yang et al., 2023; Bao et al., 2025). Previous work has attempted to construct counterfactual queries for images and videos (Li et al., 2024d,e,c; Patel et al., 2022; Wu et al., 2023). Most existing multimodal counterfactual benchmarks tend to focus on assessing subtaskspecific robustness of reasoning ability (Li et al., 2024e; Wu et al., 2024c, 2023). However, they do not assess the underlying factors that contribute to the robustness of these reasoning capabilities. Such benchmarks often lack a systematic progression from abstract to concrete dimensions and from low-level perception to high-level cognition, limiting their ability to comprehensively capture multimodal reasoning processes in MLLMs. Furthermore, these benchmarks rarely investigate how robust video understanding interacts with stepwise reasoning in dynamic environments, leaving a gap in our assessment of advanced inference skills.
+To bridge this gap, we propose COVER, a counterfactual video reasoning benchmark driven by a multidimensional abstraction level evaluation mechanism. Unlike existing multimodal counterfactual benchmarks, which often focus on multitask-oriented questions, COVER systematically classifies tasks into four quadrants. We define specific tasks for each quadrant to evaluate MLLMs’ diverse reasoning capabilities in complex video scenarios. Beyond merely posing counterfactual questions, COVER introduces a sub-question reasoning mechanism derived from necessary con-
+![](images/fc8c8cca584b431cc14c4b84443ab2e7beab9a964afac5b9b1bbc6f285027073.jpg)
+![](images/58ab2d09740f15f05cf18d5c89a6846f485bb6e60984afad27afbd0e22e3147f.jpg)
+![](images/e1e88ecd14ac072fba16a9aff7a4aeb92db27ce8987de3132ac4c5d377585458.jpg)
+Figure 1: An example from the COVER benchmark. The ground-truth answers are highlighted in green. All data—including original questions, counterfactual questions, sub-questions, and videos—have been manually verified as part of COVER. The diagram in the upper right corner illustrates the division of each COVER task into four quadrants.
+ditions, enabling a deeper evaluation of performance across MLLMs. This approach allows us to establish a connection between the accuracy of intermediate steps and the overall robustness of counterfactual reasoning. As shown in Figure 1, when asked to determine whether a boy completes a series of actions in a specified order, COVER decomposes the problem into multiple steps, each representing a necessary condition. For instance, sub-question $Q I$ may inquire about which action occurs first in the reversed video, while subquestion $Q 2$ targets the final action. This structured approach not only helps evaluate how a model adapts to event-sequence changes but also reveals its strengths and weaknesses in extracting and synthesizing critical information under counterfactual assumptions. By encompassing a broad range of abstraction levels, COVER stands as the most comprehensive dataset of its kind, paving the way for more rigorous and holistic evaluations of MLLMs’ dynamic and counterfactual reasoning capabilities.
+Building on the COVER benchmark, we conducted a series of systematic experiments using both open-source and commercial closed-source models of varying scales. Our results indicate a strong positive correlation between the models’ sub-question accuracy and performance in counterfactual reasoning and robust video understanding. The findings underscore the tight linkage
+between sophisticated inference capabilities and high-level video comprehension. Furthermore, we examine how automatically generated versus human-guided sub-question decomposition (chainof-thought, CoT (Wei et al., 2022)) influences complex reasoning and identifies the key factors impacting inference accuracy in MLLMs. Through these experiments, COVER offers valuable insights into how structured reasoning can enhance the robustness of video understanding by constructing a subquestion–based counterfactual video QA benchmark across multiple levels of abstraction and thoroughly evaluating mainstream MLLMs’ logical reasoning abilities.
+# 2 Related Work
+Multimodal Large Language Models and Their Evaluation. Recent advances in MLLMs have greatly improved their capacity to understand and reason over diverse modalities, such as images, text, and videos. To evaluate these models, benchmarks targeting static image comprehension have emerged, including MM-Vet (Yu et al., 2024), MME (Fu et al., 2023), MMBench (Liu et al., 2024), and GQA (Hudson and Manning, 2019). These primarily assess visual recognition and spatial reasoning. Extending beyond static content, video-centric benchmarks like Video-MME (Fu et al., 2024), MvBench (Li et al., 2024b), and
+Table 1: Comparison with existing benchmarks. Video: whether the benchmark involves video data; Q&A: whether it follows a question-and-answer format; Qs source: H indicates human annotation, A indicates automatic annotation; CF: whether counterfactual questions are included; PCD: whether the benchmark is categorized by the model’s perceptual and cognitive demands; ACD: whether tasks are divided based on object abstraction (abstract vs. concrete).
+<table><tr><td>Benchmark</td><td>Video</td><td>Q&amp;A</td><td>Qs Source</td><td>CF</td><td>SQP</td><td>PCD</td><td>ACD</td></tr><tr><td>CoFCA (Wu et al., 2024a)</td><td>X</td><td>✓</td><td>H&amp;A</td><td>✓</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>CFMM (Li et al., 2024e)</td><td>X</td><td>✓</td><td>H</td><td>✓</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Video-MME (Fu et al., 2024)</td><td>✓</td><td>✓</td><td>H</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>CRIPP-VQA (Patel et al., 2022)</td><td>✓</td><td>✓</td><td>H</td><td>✓</td><td>X</td><td>X</td><td>X</td></tr><tr><td>VITATECS (Li et al., 2024c)</td><td>✓</td><td>X</td><td>H&amp;A</td><td>✓</td><td>X</td><td>X</td><td>X</td></tr><tr><td>COVER (ours)</td><td>✓</td><td>✓</td><td>H&amp;A</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr></table>
+SEED-Bench (Li et al., 2023) focus on temporal dynamics and contextual reasoning. Together, these benchmarks reflect the growing demand for evaluating multimodal understanding in both static and dynamic environments.
+Chain-of-Thought and Counterfactual Reasoning in MLLMs. Chain-of-Thought (CoT) reasoning (Wei et al., 2022) enhances logical inference by breaking down complex tasks into intermediate steps. Multimodal adaptations (Zhang et al., 2024b; Zheng et al., 2023) extend this strategy across modalities, showing gains in structured reasoning. Counterfactual reasoning, which examines hypothetical changes and their consequences, has also gained traction. Prior work explores this in text (Wu et al., 2024c,a), visual QA (Li et al., 2024e), and hybrid settings. ACQUIRED (Wu et al., 2023) proposes a taxonomy of counterfactual types, while AuroraCap (Chai et al., 2024) and CoFCA (Wu et al., 2024a) assess models’ sub-task decomposition and multi-step reasoning. These approaches collectively underscore the importance of structured, causal reasoning in complex multimodal tasks.
+Multimodal Generalization and Video Counterfactual Benchmarks. Although several benchmarks target video-based counterfactual understanding—such as CRIPP-VQA for physical properties, VITATECS for captioning, and ACQUIRED for scenario taxonomy (Li et al., 2024c; Patel et al., 2022)—they remain narrow in scope. Most fail to capture the breadth of reasoning demands in real-world counterfactual scenarios.
+To address this, COVER introduces a fine-grained framework for evaluating counterfactual video reasoning via sub-question decomposition. It explicitly distinguishes between abstract vs. concrete ob-
+ject attributes and perceptual vs. cognitive reasoning demands. As summarized in Table 1, COVER broadens the evaluation spectrum, enabling a more nuanced and comprehensive assessment of multimodal counterfactual reasoning than prior efforts.
+![](images/a5db89a1c4ed7d89765ab1b906c41c436c98c38eb0c1114871ed4dbac3363152.jpg)
+3 The COVER Benchmark
+Figure 2: Overview of the 13 tasks in COVER. Numbers on the outer edge of the rose chart indicate the total number of question pairs for each task, while inner labels denote the corresponding dimension: A&C (Abstract Cognition), C&C (Concrete Cognition), A&P (Abstract Perception), and C&P (Concrete Perception).
+This section provides a comprehensive overview of the construction of COVER. We introduce our data partitioning framework designed to evaluate MLLM reasoning ability across four complementary dimensions. Next, we describe the data curation process, which domain experts have rigorously validated to ensure the high quality and reliability of the benchmark.
+Our benchmark includes approximately 2,800
+videos, which are paired with around 12,000 to 13,000 individual QA instances. As stated in L-Figure 6, the enhanced version of our dataset consists of about $2 . 9 \mathrm { k }$ question pairs, with each pair comprising at least three individual QA items: one original question, one counterfactual question, and at least one sub-question (often multiple).
+# 3.1 Benchmark Definition
+As illustrated in Figure 2, we categorize the 13 benchmark tasks into four quadrants based on the abstract-concrete and perceptual-cognitive dimensions. Abstract-Perception: (1) Emotion: Understanding and recognizing emotional states. Concrete-Perception: (2) Counting: Quantity recognition and calculation. (3) Color: Perceiving object colors. (4) Direction: Sensing motion trends. (5) Size: Identifying object dimensions. (6) Shape: Perceiving object shapes. (7) Material: Recognizing object materials. (8) Location: Detecting object positions. Concrete-Cognition: (9) Action Recognition: Identifying specific actions. (10) Object Recognition: Recognizing specific objects. Abstract-Cognition: (11) Action Prediction: Forecasting future actions. (12) Procedure Understanding: Comprehending sequential processes and logic. (13) Social Relation: Understanding social relationships.
+Division of Abstract and Concrete Scenes. This distinction reflects a functional differentiation within cognitive representation systems. Neuroscientific studies (Katja Wiemer-Hastings and Xu, 2005) suggest that concrete concepts rely heavily on multi-modal perceptual simulations (e.g., object shape, material), while abstract concepts are primarily represented through language-mediated symbolic operations. Abstract tasks often require integrating non-perceptual information, such as contextual encoding for emotion recognition or constructing temporal causal models for action prediction.
+Division of Perception and Cognition. Perception involves the initial reception of external stimuli through sensory organs, converting them into neural signals that provide raw environmental data. Cognition, built upon perception, refers to the further processing of these signals, encompassing higher-level mental functions such as memory, attention, language comprehension, problem-solving, and reasoning. This distinction underscores different stages of information processing, with perception forming the foundation upon which cognitive
+functions are built.
+# 3.2 Data Construction
+![](images/d6c51ee28ac81acb8dec5f67cd2d0196ce4ad15a93b472667c902dd10b6c6263.jpg)
+![](images/5ed10a1dc89217b15a2407ea4cd858505552e180049cc5b11c03d8b90daa4cd1.jpg)
+Figure 3: (a) Distribution of question pairs across the four quadrants. (b) Distribution of question pairs across the 13 tasks.
+To construct COVER, we carefully selected a diverse range of open-source and research-available video sources, including Sigurdsson et al. (2016); Yi et al. (2020); Xie et al. (2024); Tan et al. (2020); Shahroudy et al. (2016); Patr˘ aucean et al.˘ (2023); Zhang et al. (2023); Gao et al. (2017); Jang et al. (2017); Wang et al. (2019); Krantz et al. (2020). These sources encompass various real-world scenarios, ranging from daily activity recognition to complex scene understanding. As shown in Appendix Figure 6, we collected 146 videos and designed 150 aspect-specific QA pairs, each of which underwent dual-team review for validation. To ensure balanced coverage across the four quadrants, we expanded the seed data using GPT-generated instances (720-760 per quadrant) to mitigate any potential biases. The detailed statistical findings are comprehensively presented in Figure 3. The frame count of videos in COVER ranges from 16 to 1739, with an average of 294.34 frames. We finally constructed 2,923 high-quality counterfactual question-answer pairs. Each question-answer pair consists of an original question, which presents no hypothetical context, and a counterfactual question, which introduces situational assumptions and sub-
+Table 2: General assessment results of COVER. $o r i _ { a c c }$ , $c f _ { a c c }$ , and $s u b _ { a c c }$ denote the accuracies of the original, counterfactual, and sub-questions, respectively.
+<table><tr><td></td><td>oriacc</td><td>cfacc</td><td>subacc</td></tr><tr><td>GPT-4o</td><td>70.26</td><td>45.93</td><td>56.94</td></tr><tr><td>GPT-4o-mini</td><td>67.32</td><td>51.47</td><td>55.94</td></tr><tr><td>Claude-3.5-Sonnet</td><td>63.60</td><td>38.04</td><td>49.40</td></tr><tr><td>Gemini-1.5-Pro</td><td>74.82</td><td>49.64</td><td>63.76</td></tr><tr><td>Gemini-1.5-Flash</td><td>73.90</td><td>48.75</td><td>62.52</td></tr><tr><td>Gemini-2.0-Flash</td><td>77.18</td><td>46.90</td><td>62.92</td></tr><tr><td>InternVL2.5-78B</td><td>76.74</td><td>59.46</td><td>67.23</td></tr><tr><td>LlaVA-Video-72B</td><td>64.35</td><td>56.04</td><td>61.54</td></tr><tr><td>InternVL2.5-26B</td><td>75.40</td><td>51.08</td><td>62.65</td></tr><tr><td>InternVL2.5-8B</td><td>74.31</td><td>57.75</td><td>61.65</td></tr><tr><td>VideoLlama3-8B</td><td>73.04</td><td>51.25</td><td>60.09</td></tr><tr><td>LlaVa-OV-7B</td><td>62.74</td><td>51.80</td><td>56.42</td></tr><tr><td>LLaVA-Video-7B</td><td>60.52</td><td>51.93</td><td>55.11</td></tr><tr><td>Qwen2-VL-7B</td><td>71.83</td><td>46.90</td><td>58.40</td></tr><tr><td>VILA-U-7B</td><td>60.01</td><td>38.42</td><td>47.32</td></tr><tr><td>VILA1.5-7B</td><td>60.25</td><td>57.34</td><td>53.18</td></tr></table>
+questions that enable granular reasoning analysis.
+Eight annotators further validated the dataset and checked logical consistency to ensure the reasoning relied solely on the video content. Additionally, three experts cross-validate the dataset (see Appendix Table 9) to confirm the structural balance.
+# 4 Experiments
+In this section, we systematically evaluate MLLMs of varying scales on the COVER benchmark to foster transparent and reproducible research. Our evaluation spans four key dimensions: cognition, perception, abstraction, and concreteness. It encompasses diverse reasoning sub-tasks, including counterfactual reasoning, direct inference, and subquestion-guided reasoning. We compare both opensource and proprietary models across different parameter scales to analyze their relative strengths and limitations. We begin by detailing the experimental setup.
+# 4.1 Settings
+To ensure a thorough evaluation, we selected a diverse set of representative MLLMs, including commercial closed-source models such as GPT-4o (Hurst et al., 2024), Claude (Anthropic, 2024), and Gemini (Reid et al., 2024), as well as leading open-source models such as InternVL2.5 (Chen et al., 2024), LLAVA-Video (Zhang et al., 2024a), LLaVA-OV (Li et al., 2024a), Qwen2-VL (Wang et al., 2024), VideoLLaMA3 (Zhang et al., 2025), vila-u (Wu et al., 2024b), and VILA (Lin et al., 2024). These models span a wide range of pa-
+rameter scales and design paradigms, offering a comprehensive view of the current landscape in multimodal learning.
+We evaluate model performance on video understanding using three metrics: $o r i _ { a c c }$ (original question accuracy), $c f _ { a c c }$ (counterfactual question accuracy), and $s u b _ { a c c }$ (sub-question accuracy), with scores averaged over at least three runs. All models are tested under identical conditions, using a consistent frame extraction strategy that samples 16 frames per video segment. The impact of alternative sampling strategies is discussed in Chapter 5.
+# 4.2 Main Results
+As shown in Table 2, Gemini-2.0-Flash $( o r i _ { a c c }$ $7 7 . 1 8 \% )$ ) and InternVL2.5-78B $( o r i _ { a c c } ~ 7 6 . 7 4 \% )$ rank as the top two models, demonstrating their strong foundational video understanding. The lower scores of VILA-U-7B $( o r i _ { a c c } 6 0 . 0 1 \% )$ and LLaVA-Video-7B $( o r i _ { a c c } ~ 6 0 . 5 2 \% )$ highlight the limitations of smaller models in processing long sequences. InternVL2.5-78B $( c f _ { a c c } 5 9 . 4 6 \% )$ shows significant dominance in handling conditional reasoning and complex contexts. Notably, counterfactual questions cause sharp accuracy drops compared to the original questions: GPT-4o (- $2 4 . 3 3 \%$ ) and Gemini-1.5-Pro $( - 2 5 . 1 8 \% )$ , indicating that most models struggle with counterfactual reasoning.
+Most models exhibit higher $s u b _ { a c c }$ than $c f _ { a c c }$ (e.g., Claude-3.5-Sonnet $4 9 . 4 0 \%$ vs. $3 8 . 0 4 \%$ LLaVA-Video-72B $6 1 . 5 4 \%$ vs. $5 6 . 0 4 \%$ ). This suggests better stability in localized reasoning tasks than in holistic tasks, where error accumulation impacts performance. In the Appendix, we provide detailed case demonstrations in Figure 8.
+Closed-source Model Performance. As shown in Table 3, Gemini 1.5 Pro demonstrates strong dominance in both concrete cognition $( o r i _ { a c c }$ $8 2 . 1 4 \%$ and abstract perception tasks $( o r i _ { a c c }$ $7 5 . 4 8 \%$ . Gemini 2.0 Flash excels in abstract perception $( o r i _ { a c c } 7 5 . 9 0 \% )$ and concrete perception tasks $( o r i _ { a c c } 7 4 . 2 2 \% )$ , showcasing strong capabilities in handling high-complexity perceptual tasks.
+Open-source Model Performance. As shown in Table 3, InternVL2.5-78B leads in abstract cognition $( o r i _ { a c c } 7 2 . 8 8 \% )$ and concrete perception tasks $( c f _ { a c c } 5 8 . 2 5 \% )$ , reflecting a deep understanding of abstract concepts and complex logic. Lightweight models like Qwen2-VL-7B perform well in concrete cognition $( o r i _ { a c c } 8 2 . 1 4 \% )$ but face limitations in abstract tasks $( o r i _ { a c c } 6 5 . 9 6 \%$ in A&C) due to
+Table 3: Performance of MLLMs on COVER, based on our quadrant formulation (A&C, C&C, C&P, A&P), measured by original, counterfactual, and sub-question accuracy.
+<table><tr><td rowspan="2">Models</td><td colspan="3">A&amp;C (%)</td><td colspan="3">C&amp;C (%)</td><td colspan="3">C&amp;P (%)</td><td colspan="3">A&amp;P (%)</td></tr><tr><td>oriacc</td><td>cfacc</td><td>subacc</td><td>oriacc</td><td>cfacc</td><td>subacc</td><td>oriacc</td><td>cfacc</td><td>subacc</td><td>oriacc</td><td>cfacc</td><td>subacc</td></tr><tr><td>GPT-4o</td><td>71.05</td><td>41.81</td><td>41.70</td><td>74.87</td><td>43.65</td><td>68.36</td><td>69.95</td><td>42.62</td><td>50.52</td><td>65.01</td><td>55.65</td><td>63.97</td></tr><tr><td>GPT-4o-mini</td><td>62.29</td><td>52.40</td><td>42.97</td><td>76.32</td><td>54.37</td><td>66.49</td><td>64.62</td><td>40.85</td><td>44.78</td><td>65.56</td><td>58.26</td><td>65.96</td></tr><tr><td>Claude-3.5-sonnet</td><td>56.92</td><td>37.01</td><td>35.55</td><td>70.11</td><td>42.33</td><td>61.77</td><td>60.03</td><td>32.88</td><td>40.08</td><td>66.94</td><td>39.81</td><td>56.81</td></tr><tr><td>Gemini 1.5 Pro</td><td>69.49</td><td>44.49</td><td>53.36</td><td>82.14</td><td>51.98</td><td>72.78</td><td>71.76</td><td>43.93</td><td>56.81</td><td>75.48</td><td>57.99</td><td>69.54</td></tr><tr><td>Gemini 1.5 Flash</td><td>70.48</td><td>45.34</td><td>52.23</td><td>82.01</td><td>49.34</td><td>71.51</td><td>70.67</td><td>42.02</td><td>51.90</td><td>72.04</td><td>58.26</td><td>71.36</td></tr><tr><td>Gemini 2.0 Flash</td><td>74.29</td><td>44.36</td><td>51.38</td><td>83.99</td><td>47.75</td><td>72.84</td><td>74.22</td><td>38.74</td><td>58.26</td><td>75.90</td><td>57.71</td><td>66.84</td></tr><tr><td>InternVL2.5-78B</td><td>72.88</td><td>59.60</td><td>57.67</td><td>80.95</td><td>63.62</td><td>75.62</td><td>75.99</td><td>58.25</td><td>63.65</td><td>76.86</td><td>56.20</td><td>70.07</td></tr><tr><td>LLaVA-Video-72B</td><td>53.11</td><td>54.94</td><td>53.14</td><td>65.34</td><td>60.45</td><td>67.03</td><td>67.94</td><td>52.39</td><td>53.49</td><td>70.66</td><td>56.20</td><td>70.01</td></tr><tr><td>InternVL2.5-26B</td><td>71.05</td><td>47.74</td><td>50.53</td><td>80.95</td><td>58.99</td><td>72.17</td><td>76.13</td><td>47.20</td><td>60.12</td><td>73.14</td><td>50.00</td><td>65.61</td></tr><tr><td>InternVL2.5-8B</td><td>69.77</td><td>58.62</td><td>49.96</td><td>80.95</td><td>64.55</td><td>71.02</td><td>73.94</td><td>55.80</td><td>54.66</td><td>72.18</td><td>51.79</td><td>68.19</td></tr><tr><td>VideoLLama3-8B</td><td>68.08</td><td>45.62</td><td>49.68</td><td>81.35</td><td>54.89</td><td>68.36</td><td>72.99</td><td>50.75</td><td>51.62</td><td>69.28</td><td>53.44</td><td>67.90</td></tr><tr><td>LLaVA-ov-7B</td><td>54.66</td><td>51.69</td><td>47.49</td><td>62.96</td><td>53.04</td><td>61.77</td><td>64.53</td><td>49.66</td><td>49.48</td><td>68.60</td><td>52.75</td><td>64.73</td></tr><tr><td>LLaVA-Video-7B</td><td>50.14</td><td>55.23</td><td>44.52</td><td>61.64</td><td>50.53</td><td>60.50</td><td>63.57</td><td>52.52</td><td>49.97</td><td>66.39</td><td>49.59</td><td>63.03</td></tr><tr><td>Qwen2-VL-7B</td><td>65.96</td><td>49.15</td><td>48.41</td><td>82.14</td><td>43.39</td><td>67.03</td><td>71.21</td><td>45.57</td><td>50.52</td><td>67.49</td><td>49.72</td><td>65.02</td></tr><tr><td>VILA-U-7B</td><td>58.19</td><td>39.83</td><td>38.87</td><td>63.10</td><td>41.93</td><td>54.51</td><td>59.07</td><td>37.93</td><td>37.94</td><td>59.50</td><td>33.88</td><td>55.34</td></tr><tr><td>VILA1.5-7B</td><td>54.80</td><td>55.93</td><td>39.29</td><td>66.93</td><td>62.30</td><td>63.52</td><td>55.25</td><td>58.53</td><td>44.64</td><td>63.64</td><td>52.34</td><td>61.91</td></tr></table>
+Table 4: Comparison between CoT and Guide-CoT performance across MLLMs on the COVER benchmark.
+<table><tr><td rowspan="2">Model</td><td>Without CoT</td><td>With CoT</td><td colspan="2">Guide-CoT</td></tr><tr><td>cfacc</td><td>cfacc</td><td>cfacc</td><td>cfwithans</td></tr><tr><td>GPT-4o-mini</td><td>51.47</td><td>58.62</td><td>57.93</td><td>68.07</td></tr><tr><td>InternVL2.5-78B</td><td>59.46</td><td>60.42</td><td>58.33</td><td>68.29</td></tr><tr><td>LlaVA-Video-72B</td><td>56.04</td><td>56.24</td><td>53.51</td><td>63.12</td></tr><tr><td>InternVL2.5-8B</td><td>57.75</td><td>57.06</td><td>52.41</td><td>57.75</td></tr><tr><td>VideoLlama3-8B</td><td>51.25</td><td>52.82</td><td>53.06</td><td>52.79</td></tr><tr><td>LLaVA-Video-7B</td><td>51.93</td><td>51.42</td><td>51.39</td><td>54.12</td></tr><tr><td>Qwen2-VL-7B</td><td>46.90</td><td>50.36</td><td>45.71</td><td>50.88</td></tr></table>
+their smaller parameter size, revealing distinct capabilities across model types. Commercial models, such as the Gemini series, maintain strong performance in concrete cognition and abstract perception tasks but generally fall behind open-source models in counterfactual reasoning. Most models struggle with counterfactual reasoning, with only InternVL2.5-7BB and VILA1.5-7B showing some task-specific advantages, highlighting the need for targeted optimization in conditional hypothesis modeling.
+# 4.3 Sub-question Guideline
+We propose Guide-CoT to study the influence of different reasoning paths on model performance through human-annotated sub-problems. We design comparative experiments between CoT and Guide-CoT to analyze how automatically generated sub-questions from CoT versus manually annotated sub-questions affect model reasoning capabilities.
+Comparing the Without CoT and CoT approaches based on Table 4, we find that the $c f _ { a c c }$
+of most models under CoT significantly exceeds the Without CoT baseline, such as Qwen2-VL-7B $( + 3 . 4 6 \% )$ and GPT-4o-mini $( + 7 . 1 5 \% )$ , which indicates that CoT enhances reasoning processes, particularly in more complex tasks.
+However, examining Guide-CoT results reveals that manually designed sub-questions may not always lead to substantial improvement over automatically generated ones, as seen with GPT-4omini’s $c f _ { a c c }$ of $5 7 . 9 3 \%$ under Guide-CoT, slightly lower than the $5 8 . 6 2 \%$ under CoT. This does not imply the ineffectiveness of manual sub-questions but suggests that model behaviors may not always align with human-designed reasoning paths, potentially due to task complexity or the nature of the sub-questions themselves. We hypothesize that manually provided sub-questions could introduce extraneous patterns or "pseudo-features" that are not directly relevant to the reasoning task, leading to a subtle reduction in performance.
+The cfwithans column in Guide-CoT indicates sub-questions that include standard answers. For
+Table 5: Performance of MLLMs on COVER using different frame sampling strategies. The frame selection follows standard practices in video QA benchmarks, where the number of input frames is set to min(video length, predefined sampling count).
+<table><tr><td rowspan="2">Frames</td><td colspan="3">InternVL2.5-1B</td><td colspan="3">InternVL2.5-2B</td><td colspan="3">InternVL2.5-4B</td><td colspan="3">InternVL2.5-8B</td></tr><tr><td>oriacc</td><td>cfacc</td><td>subacc</td><td>oriacc</td><td>cfacc</td><td>subacc</td><td>oriacc</td><td>cfacc</td><td>subacc</td><td>oriacc</td><td>cfacc</td><td>subacc</td></tr><tr><td>2</td><td>66.16</td><td>35.61</td><td>55.27</td><td>65.31</td><td>44.20</td><td>54.99</td><td>72.56</td><td>48.31</td><td>60.88</td><td>71.26</td><td>58.50</td><td>60.07</td></tr><tr><td>4</td><td>68.32</td><td>34.72</td><td>55.52</td><td>68.83</td><td>42.11</td><td>58.84</td><td>74.41</td><td>46.49</td><td>61.79</td><td>73.35</td><td>58.47</td><td>60.96</td></tr><tr><td>8</td><td>68.94</td><td>35.10</td><td>55.11</td><td>68.22</td><td>41.43</td><td>55.75</td><td>75.03</td><td>45.60</td><td>61.79</td><td>74.14</td><td>57.06</td><td>61.60</td></tr><tr><td>16</td><td>69.76</td><td>35.89</td><td>55.19</td><td>70.07</td><td>40.68</td><td>55.49</td><td>75.61</td><td>45.23</td><td>61.63</td><td>74.31</td><td>57.75</td><td>61.65</td></tr><tr><td>32</td><td>69.04</td><td>36.50</td><td>55.04</td><td>70.13</td><td>39.69</td><td>55.48</td><td>75.54</td><td>45.09</td><td>60.96</td><td>74.10</td><td>57.03</td><td>61.42</td></tr><tr><td>64</td><td>68.18</td><td>37.39</td><td>54.80</td><td>68.90</td><td>40.06</td><td>55.44</td><td>74.41</td><td>46.56</td><td>60.70</td><td>74.20</td><td>58.09</td><td>61.30</td></tr></table>
+InternVL2.5-78B, $c f _ { w i t h a n s }$ reaches $6 8 . 2 9 \%$ , reflecting an $8 . 6 3 \%$ improvement over the no-CoT baseline, in contrast to CoT’s modest gain of only $0 . 9 6 \%$ (from $5 9 . 4 6 \%$ to $6 0 . 4 2 \%$ ). This suggests that providing complete answers substantially enhances reasoning accuracy, particularly in complex or multi-step tasks. Standard-answer sub-questions enable the model to better integrate information and verify intermediate reasoning steps, resulting in improved consistency and overall performance. Detailed case studies are presented in Appendix Figure 9 to further illustrate these findings and analyze the interplay between reasoning paths and task complexity.
+The results from our experiments strongly support the notion that reasoning plays a pivotal role in model robustness and generalization. Our study extends these insights by demonstrating that multimodal models, especially in the context of video tasks, rely heavily on robust reasoning capabilities for effective generalization. The significant performance improvements observed with counterfactual reasoning and sub-question decomposition highlight that models’ ability to handle complex, conditional, and dynamic contexts is crucial for their robustness, a finding not fully explored in prior research.
+# 5 Analysis
+In this chapter, we begin by analyzing the impact of video frame sampling rates on MLLMs’ video understanding and reasoning abilities. We then proceed with an in-depth examination of MLLMs’ robustness and logical reasoning performance.
+# 5.1 Ablation Study of Video Frames
+As shown in Table 5, as the parameter size of LLMs increases, there is a rising trend in $o r i _ { a c c }$ , $c f _ { a c c }$ , and $s u b _ { a c c }$ . For instance, with 16 frames,
+the InternVL2.5-1B model achieves oriacc, $c f _ { a c c }$ , and $s u b _ { a c c }$ of $6 9 . 7 6 \%$ , $3 5 . 8 9 \%$ , and $5 5 . 1 9 \%$ respectively. The InternVL2.5-2B scores $7 0 . 0 7 \%$ , $4 0 . 6 2 \%$ , and $5 5 . 4 9 \%$ , while the InternVL2.5-4B reaches $7 5 . 6 1 \%$ , $4 5 . 2 3 \%$ , and $6 1 . 6 8 \%$ , indicating that larger LLMs have enhanced capabilities in handling complex problems. Under the same vision tower settings, $o r i _ { a c c }$ shows a clear upward trend as the number of frames increases. For example, the InternVL2.5-8B’s oriacc rises from $7 1 . 2 6 \%$ at 2 frames to $7 4 . 2 0 \%$ at 64 frames. However, $c f _ { a c c }$ tends to decrease with more frames. The InternVL2.5-2B’s $c f _ { a c c }$ drops from $4 4 . 2 0 \%$ at 2 frames to $4 0 . 0 6 \%$ at 64 frames. Models with more parameters generally perform better in $o r i _ { a c c }$ , $c f _ { a c c }$ , and $s u b _ { a c c }$ , highlighting the significant role of LLMs in multimodal reasoning. Additionally, increasing visual information (by raising the frame count) can enhance $o r i _ { a c c }$ , but excessive visual information, especially in complex or counterfactual reasoning scenarios, may impair the model’s reasoning ability, leading to a decline in $c f _ { a c c }$ .
+# 5.2 Robustness and Logical Reasoning in MLLMs
+The ability of MLLMs to answer original questions serves as a key indicator of their overall understanding capabilities, while performance on subquestions reveals single-step reasoning proficiency. A notable observation is the strong Pearson correlation between $o r i _ { a c c }$ and $s u b _ { a c c }$ reaches 0.836, indicating a strong connection between model understanding and reasoning capabilities. Furthermore, as shown in Figure 5, the correlation between $s u b _ { a c c }$ and $c f _ { a c c }$ is 0.608. These moderately strong correlations indicate that a model’s ability to comprehend original questions plays a fundamental role in enabling effective step-by-step reasoning. Similarly, the correlation between $o r i _ { a c c }$ and $s u b _ { a c c }$ suggests that models with a higher understanding
+![](images/53a99a488ba2bc1eaf418ffc81f01ec2f051683ca0be812c92b14cfe61687ec8.jpg)
+![](images/c63b50a9a4ed03b3e8d287da2a6e7e43025d33c697eeb0219ead8ff5f7395dac.jpg)
+![](images/085faf34ed38e3a87a4ad3dbab9a7f4c0a2cef8c2a0343e8a9564b5daff88119.jpg)
+![](images/9052f57657ee2310f2f888e3cf35f62922b18039ff1df033719e396a441bd6cd.jpg)
+![](images/c9a808d20b60011ddcc6bc83bf3ebd84c2a7efd8dd3efabf9d92a8ad2a9e1485.jpg)
+![](images/640db7918436429aee417638a25914e12ba2d1296a4b44cd6830dfdf641d53a9.jpg)
+Figure 4: Heatmaps of task performance for Gemini-1.5-pro and InternVL2.5-78B, using hollow circles to depict task distributions across the four quadrants. The top three panels show results for Gemini-1.5-pro, and the bottom three for InternVL2.5-78B. Left: Accuracy on original questions. Middle: Performance on counterfactual questions. Right: Accuracy on sub-questions. A gradient color bar—from azure (low accuracy) to crimson (high accuracy)—is placed along the right margin of each heatmap to indicate performance levels.
+Table 6: Conditional probabilities of counterfactual accuracy given sub-question outcomes. $\mathsf { P } ( c f _ { r i g h t } \mid s u b _ { r i g h t } )$ and $\mathsf { P } ( c f _ { w r o n g } \mid s u b _ { r i g h t } )$ denote the likelihood of answering the counterfactual question correctly or incorrectly when the sub-question is correct; similarly, $\mathsf { P } ( c f _ { r i g h t } \mid s u b _ { w r o n g } )$ and $\mathrm { P } ( c f _ { w r o n g } \mid s u b _ { w r o n g } )$ apply when the sub-question is incorrect.
+<table><tr><td>Model</td><td>P(cfright|subright)</td><td>P(cfwrong|subright)</td><td>P(cfright|subwrong)</td><td>P(cfwrong|subwrong)</td></tr><tr><td>gemini-1.5-pro</td><td>56.54</td><td>43.45</td><td>44.99</td><td>55.01</td></tr><tr><td>GPT-4o-mini</td><td>59.49</td><td>40.51</td><td>47.65</td><td>52.35</td></tr><tr><td>InternVL2.5-78B</td><td>62.90</td><td>37.10</td><td>56.67</td><td>43.34</td></tr><tr><td>LlaVA-Video-72B</td><td>63.28</td><td>36.72</td><td>51.60</td><td>48.40</td></tr></table>
+capability tend to perform better when solving decomposed sub-questions, reinforcing the notion that comprehension and reasoning are interdependent. However, the moderate correlation between $s u b _ { a c c }$ and $c f _ { a c c }$ suggests that counterfactual reasoning involves additional complexities, making it a more challenging task than single-step reasoning.
+As illustrated in Table 6, We observed that across multiple models, the probability $P$ (cf_right|sub_right) was significantly higher than $P ( \mathrm { c f \_ r i g h t } | \mathrm { s u b \_ w r o n g } )$ , clearly indicating that the correctness of sub-questions is a strong predictor of overall counterfactual performance.
+Analysis of the heat maps in Figure 4 reveals different performance patterns in the quadrants, high-
+lighting the interaction between comprehension, step-by-step reasoning, and counterfactual inference. In abstract reasoning tasks such as social inference and procedural understanding, the drop from $s u b _ { a c c }$ to $o r i _ { a c c }$ is minimal, and the transition to $c f _ { a c c }$ remains stable. This suggests that models can effectively leverage sub-question reasoning and maintain performance even under counterfactual assumptions. In contrast, the concrete perception quadrant—involving tasks like object recognition and motion understanding—shows a sharper decline from $s u b _ { a c c }$ to $o r i _ { a c c }$ , and further to $c f _ { a c c }$ . This indicates that perception-heavy tasks pose greater challenges, as models struggle to decompose complex sensory input into reasoning steps
+![](images/33f2bd7e3642f19bc43a503a801674b3f550d0026e108edb6875e9633b54e879.jpg)
+Original and Counterfactual Accuracy vs Sub Accuracy of Different Models
+Figure 5: Scatter plot showing correlations among oriacc, $s u b _ { a c c }$ , and $c f _ { a c c }$ across models. The red line represents the linear function fitted between $o r i _ { a c c }$ and $s u b _ { a c c }$ , while the purple line represents the linear function fitted between $c f _ { a c c }$ and $s u b _ { a c c }$ .
+required for counterfactual understanding.
+Overall, our findings indicate that counterfactual reasoning is inherently more challenging than single-step reasoning, especially in perceptionintensive tasks where models must infer causality beyond pattern recognition. In contrast, the relatively stable gap between $s u b _ { a c c }$ and $c f _ { a c c }$ in abstract-cognitive tasks suggests that models can better leverage conceptual knowledge. Enhancing counterfactual reasoning in perception-heavy scenarios remains a key challenge, likely requiring improved causal inference and reasoning mechanisms.
+# 5.3 The Effects of Model Scale
+We conduct systematic analyses to characterize performance gaps across original, counterfactual, and sub-question accuracies. Our goal is to mitigate these gaps by examining factors such as model scale, training alignment, and reasoning strategies. As shown in Table 7, with similar visual backbones, increasing language model size significantly reduces the performance gap—particularly between sub-question and counterfactual accuracy. Specifically, the absolute difference between $\mathrm { \ o r i _ { a c c } }$ $( 7 0 . 0 7 \% )$ and $\operatorname { c f } _ { \operatorname { a c c } }$ $( 4 0 . 6 8 \% )$ is $2 9 . 3 9 \%$ for the 2B model, increases slightly to $3 0 . 3 8 \%$ for the 4B
+model, and then drops substantially to $1 6 . 5 6 \%$ for the 8B model. Similarly, the gap between $\operatorname { c f } _ { \operatorname { a c c } }$ and $\operatorname { s u b } _ { \operatorname { a c c } }$ grows from $1 4 . 8 1 \%$ (2B) to $1 6 . 4 0 \%$ (4B), before narrowing sharply to $3 . 9 0 \%$ (8B).
+Table 7: Variations in three accuracy metrics across different model sizes.
+<table><tr><td>Model</td><td>oriacc</td><td>cfacc</td><td>subacc</td></tr><tr><td>InternVL2.5-2B</td><td>70.07</td><td>40.68</td><td>55.49</td></tr><tr><td>InternVL2.5-4B</td><td>75.61</td><td>45.23</td><td>61.63</td></tr><tr><td>InternVL2.5-8B</td><td>74.31</td><td>57.75</td><td>61.65</td></tr></table>
+# 6 Conclusion
+We introduce COVER, a comprehensive benchmark for counterfactual video reasoning that evaluates MLLMs across four dimensions: abstractconcrete and perception-cognition. By decomposing complex queries into structured sub-questions, COVER enables fine-grained analysis and reveals a strong correlation between sub-question accuracy and overall reasoning performance. Our results highlight the need for improved reasoning abilities in dynamic video tasks, and position COVER as a new standard for evaluating multimodal logical reasoning.
+# Acknowledgments
+We would like to thank the anonymous reviewers for their valuable feedback. We thank Junshu Pan, Panzhong Lu, Fang Guo, Zijie Yang, Pai Liu, and other global collaborators for their valuable discussions and help. This work is funded by the National Key R&D program of China (grant No. 2022YFE0204900), the National Natural Science Foundation of China Key Program (Grant No. 62336006), the Pioneer and “Leading Goose” R&D Program of Zhejiang (Grant No. 2022SDX-HDX0003), and the Research Program (Grant No. WU2023C020) of the Research Center for Industries of the Future, Westlake University.
+# Limitations
+COVER offers a novel benchmark for counterfactual video reasoning, but some limitations exist. First, while it focuses on video reasoning, its applicability to other multimodal tasks, such as image or text reasoning, remains unexplored. Second, COVER relies on sub-question decomposition, and automated methods may not always match humandesigned questions, especially in complex scenarios. Finally, while we demonstrate COVER’s effectiveness on various models, further validation across different model architectures and real-world tasks is needed to assess its generalizability.
+# Ethical Considerations
+COVER is designed with ethical considerations in mind, aiming to enhance counterfactual reasoning in video understanding while ensuring fairness, transparency, and responsible AI development. We acknowledge the ongoing challenges in bias mitigation, fairness, and environmental sustainability and encourage the broader research community to collaborate in addressing these concerns. By establishing COVER as an open and structured evaluation benchmark, we aim to promote robust and ethical AI advancements in multimodal reasoning.
+We ensured that the human annotators were compensated with fair remuneration, which exceeded the local minimum wage standards, reflecting the value of their work. Furthermore, we took steps to ensure that the annotation process did not pose any risks to their physical or mental well-being. The tasks were designed to be manageable, and we provided adequate support to ensure a safe and respectful working environment.
+In this study, AI was used solely for data augmentation and grammar/typo correction, with no involvement in generative or creative tasks. We carefully considered potential risks to ensure AI usage did not compromise the originality or transparency of the research.
+# References
+AI Anthropic. 2024. Claude 3.5 sonnet model card addendum. Claude-3.5 Model Card.
+Guangsheng Bao, Hongbo Zhang, Cunxiang Wang, Linyi Yang, and Yue Zhang. 2025. How likely do LLMs with CoT mimic human reasoning? In Proceedings of the 31st International Conference on Computational Linguistics, pages 7831–7850, Abu Dhabi, UAE. Association for Computational Linguistics.
+Wenhao Chai, Enxin Song, Yilun Du, Chenlin Meng, Vashisht Madhavan, Omer Bar-Tal, Jenq-Neng Hwang, Saining Xie, and Christopher D. Manning. 2024. Auroracap: Efficient, performant video detailed captioning and a new benchmark. CoRR, abs/2410.03051.
+Zhe Chen, Weiyun Wang, Yue Cao, Yangzhou Liu, Zhangwei Gao, Erfei Cui, Jinguo Zhu, Shenglong Ye, Hao Tian, Zhaoyang Liu, Lixin Gu, Xuehui Wang, Qingyun Li, Yimin Ren, Zixuan Chen, Jiapeng Luo, Jiahao Wang, Tan Jiang, Bo Wang, Conghui He, Botian Shi, Xingcheng Zhang, Han Lv, Yi Wang, Wenqi Shao, Pei Chu, Zhongying Tu, Tong He, Zhiyong Wu, Huipeng Deng, Jiaye Ge, Kai Chen, Min Dou, Lewei Lu, Xizhou Zhu, Tong Lu, Dahua Lin, Yu Qiao, Jifeng Dai, and Wenhai Wang. 2024. Expanding performance boundaries of open-source multimodal models with model, data, and test-time scaling. CoRR, abs/2412.05271.
+Chaoyou Fu, Peixian Chen, Yunhang Shen, Yulei Qin, Mengdan Zhang, Xu Lin, Zhenyu Qiu, Wei Lin, Jinrui Yang, Xiawu Zheng, Ke Li, Xing Sun, and Rongrong Ji. 2023. MME: A comprehensive evaluation benchmark for multimodal large language models. CoRR, abs/2306.13394.
+Chaoyou Fu, Yuhan Dai, Yondong Luo, Lei Li, Shuhuai Ren, Renrui Zhang, Zihan Wang, Chenyu Zhou, Yunhang Shen, Mengdan Zhang, Peixian Chen, Yanwei Li, Shaohui Lin, Sirui Zhao, Ke Li, Tong Xu, Xiawu Zheng, Enhong Chen, Rongrong Ji, and Xing Sun. 2024. Video-mme: The first-ever comprehensive evaluation benchmark of multi-modal llms in video analysis. CoRR, abs/2405.21075.
+Jiyang Gao, Chen Sun, Zhenheng Yang, and Ram Nevatia. 2017. TALL: temporal activity localization via language query. In IEEE International Conference on Computer Vision, ICCV 2017, Venice, Italy, October 22-29, 2017, pages 5277–5285. IEEE Computer Society.
+Drew A. Hudson and Christopher D. Manning. 2019. GQA: A new dataset for real-world visual reasoning and compositional question answering. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, pages 6700–6709. Computer Vision Foundation / IEEE.
+Aaron Hurst, Adam Lerer, Adam P. Goucher, Adam Perelman, Aditya Ramesh, Aidan Clark, AJ Ostrow, Akila Welihinda, Alan Hayes, Alec Radford, Aleksander Madry, Alex Baker-Whitcomb, Alex Beutel, Alex Borzunov, Alex Carney, Alex Chow, Alex Kirillov, Alex Nichol, Alex Paino, Alex Renzin, Alex Tachard Passos, Alexander Kirillov, Alexi Christakis, Alexis Conneau, Ali Kamali, Allan Jabri, Allison Moyer, Allison Tam, Amadou Crookes, Amin Tootoonchian, Ananya Kumar, Andrea Vallone, Andrej Karpathy, Andrew Braunstein, Andrew Cann, Andrew Codispoti, Andrew Galu, Andrew Kondrich, Andrew Tulloch, Andrey Mishchenko, Angela Baek, Angela Jiang, Antoine Pelisse, Antonia Woodford, Anuj Gosalia, Arka Dhar, Ashley Pantuliano, Avi Nayak, Avital Oliver, Barret Zoph, Behrooz Ghorbani, Ben Leimberger, Ben Rossen, Ben Sokolowsky, Ben Wang, Benjamin Zweig, Beth Hoover, Blake Samic, Bob McGrew, Bobby Spero, Bogo Giertler, Bowen Cheng, Brad Lightcap, Brandon Walkin, Brendan Quinn, Brian Guarraci, Brian Hsu, Bright Kellogg, Brydon Eastman, Camillo Lugaresi, Carroll L. Wainwright, Cary Bassin, Cary Hudson, Casey Chu, Chad Nelson, Chak Li, Chan Jun Shern, Channing Conger, Charlotte Barette, Chelsea Voss, Chen Ding, Cheng Lu, Chong Zhang, Chris Beaumont, Chris Hallacy, Chris Koch, Christian Gibson, Christina Kim, Christine Choi, Christine McLeavey, Christopher Hesse, Claudia Fischer, Clemens Winter, Coley Czarnecki, Colin Jarvis, Colin Wei, Constantin Koumouzelis, and Dane Sherburn. 2024. Gpt-4o system card. CoRR, abs/2410.21276.
+Yunseok Jang, Yale Song, Youngjae Yu, Youngjin Kim, and Gunhee Kim. 2017. TGIF-QA: toward spatiotemporal reasoning in visual question answering. In 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA, July 21-26, 2017, pages 1359–1367. IEEE Computer Society.
+Katja Katja Wiemer-Hastings and Xu Xu. 2005. Content differences for abstract and concrete concepts. Cognitive science, 29(5):719–736.
+Jacob Krantz, Erik Wijmans, Arjun Majumdar, Dhruv Batra, and Stefan Lee. 2020. Beyond the nav-graph: Vision-and-language navigation in continuous environments. In Computer Vision - ECCV 2020 - 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXVIII, volume 12373 of Lecture Notes in Computer Science, pages 104–120. Springer.
+Bo Li, Yuanhan Zhang, Dong Guo, Renrui Zhang, Feng Li, Hao Zhang, Kaichen Zhang, Yanwei Li, Ziwei
+Liu, and Chunyuan Li. 2024a. Llava-onevision: Easy visual task transfer. CoRR, abs/2408.03326.
+Bohao Li, Rui Wang, Guangzhi Wang, Yuying Ge, Yixiao Ge, and Ying Shan. 2023. Seed-bench: Benchmarking multimodal llms with generative comprehension. CoRR, abs/2307.16125.
+Kunchang Li, Yali Wang, Yinan He, Yizhuo Li, Yi Wang, Yi Liu, Zun Wang, Jilan Xu, Guo Chen, Ping Lou, Limin Wang, and Yu Qiao. 2024b. Mvbench: A comprehensive multi-modal video understanding benchmark. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2024, Seattle, WA, USA, June 16-22, 2024, pages 22195–22206. IEEE.
+Shicheng Li, Lei Li, Yi Liu, Shuhuai Ren, Yuanxin Liu, Rundong Gao, Xu Sun, and Lu Hou. 2024c. VITATECS: A diagnostic dataset for temporal concept understanding of video-language models. In Computer Vision - ECCV 2024 - 18th European Conference, Milan, Italy, September 29-October 4, 2024, Proceedings, Part LXX, volume 15128 of Lecture Notes in Computer Science, pages 331–348. Springer.
+Yian Li, Wentao Tian, Yang Jiao, Jingjing Chen, and Yu-Gang Jiang. 2024d. Eyes can deceive: Benchmarking counterfactual reasoning abilities of multi-modal large language models. CoRR, abs/2404.12966.
+Yian Li, Wentao Tian, Yang Jiao, Jingjing Chen, Na Zhao, and Yu-Gang Jiang. 2024e. Look before you decide: Prompting active deduction of mllms for assumptive reasoning. Preprint, arXiv:2404.12966.
+Ji Lin, Hongxu Yin, Wei Ping, Pavlo Molchanov, Mohammad Shoeybi, and Song Han. 2024. VILA: on pre-training for visual language models. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2024, Seattle, WA, USA, June 16-22, 2024, pages 26679–26689. IEEE.
+Yuan Liu, Haodong Duan, Yuanhan Zhang, Bo Li, Songyang Zhang, Wangbo Zhao, Yike Yuan, Jiaqi Wang, Conghui He, Ziwei Liu, Kai Chen, and Dahua Lin. 2024. Mmbench: Is your multi-modal model an all-around player? In Computer Vision - ECCV 2024 - 18th European Conference, Milan, Italy, September 29-October 4, 2024, Proceedings, Part VI, volume 15064 of Lecture Notes in Computer Science, pages 216–233. Springer.
+Maitreya Patel, Tejas Gokhale, Chitta Baral, and Yezhou Yang. 2022. CRIPP-VQA: counterfactual reasoning about implicit physical properties via video question answering. In Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, EMNLP 2022, Abu Dhabi, United Arab Emirates, December 7-11, 2022, pages 9856–9870. Association for Computational Linguistics.
+Viorica Patr˘ aucean, Lucas Smaira, Ankush Gupta,˘ Adrià Recasens Continente, Larisa Markeeva, Dylan Banarse, Skanda Koppula, Joseph Heyward, Mateusz Malinowski, Yi Yang, Carl Doersch, Tatiana
+Matejovicova, Yury Sulsky, Antoine Miech, Alex Frechette, Hanna Klimczak, Raphael Koster, Junlin Zhang, Stephanie Winkler, Yusuf Aytar, Simon Osindero, Dima Damen, Andrew Zisserman, and João Carreira. 2023. Perception test: A diagnostic benchmark for multimodal video models. Preprint, arXiv:2305.13786.
+Machel Reid, Nikolay Savinov, Denis Teplyashin, Dmitry Lepikhin, Timothy P. Lillicrap, Jean-Baptiste Alayrac, Radu Soricut, Angeliki Lazaridou, Orhan Firat, Julian Schrittwieser, Ioannis Antonoglou, Rohan Anil, Sebastian Borgeaud, Andrew M. Dai, Katie Millican, Ethan Dyer, Mia Glaese, Thibault Sottiaux, Benjamin Lee, Fabio Viola, Malcolm Reynolds, Yuanzhong Xu, James Molloy, Jilin Chen, Michael Isard, Paul Barham, Tom Hennigan, Ross McIlroy, Melvin Johnson, Johan Schalkwyk, Eli Collins, Eliza Rutherford, Erica Moreira, Kareem Ayoub, Megha Goel, Clemens Meyer, Gregory Thornton, Zhen Yang, Henryk Michalewski, Zaheer Abbas, Nathan Schucher, Ankesh Anand, Richard Ives, James Keeling, Karel Lenc, Salem Haykal, Siamak Shakeri, Pranav Shyam, Aakanksha Chowdhery, Roman Ring, Stephen Spencer, Eren Sezener, and et al. 2024. Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context. CoRR, abs/2403.05530.
+Amir Shahroudy, Jun Liu, Tian-Tsong Ng, and Gang Wang. 2016. NTU RGB+D: A large scale dataset for 3d human activity analysis. In 2016 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016, Las Vegas, NV, USA, June 27-30, 2016, pages 1010–1019. IEEE Computer Society.
+Gunnar A. Sigurdsson, Gül Varol, Xiaolong Wang, Ali Farhadi, Ivan Laptev, and Abhinav Gupta. 2016. Hollywood in homes: Crowdsourcing data collection for activity understanding. In Computer Vision - ECCV 2016 - 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part I, volume 9905 of Lecture Notes in Computer Science, pages 510–526. Springer.
+Ganchao Tan, Daqing Liu, Meng Wang, and Zheng-Jun Zha. 2020. Learning to discretely compose reasoning module networks for video captioning. In Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI 2020, pages 745–752. ijcai.org.
+Qwen Team. 2024. Qvq: To see the world with wisdom.
+Peng Wang, Shuai Bai, Sinan Tan, Shijie Wang, Zhihao Fan, Jinze Bai, Keqin Chen, Xuejing Liu, Jialin Wang, Wenbin Ge, Yang Fan, Kai Dang, Mengfei Du, Xuancheng Ren, Rui Men, Dayiheng Liu, Chang Zhou, Jingren Zhou, and Junyang Lin. 2024. Qwen2- vl: Enhancing vision-language model’s perception of the world at any resolution. CoRR, abs/2409.12191.
+Xin Wang, Jiawei Wu, Junkun Chen, Lei Li, Yuan-Fang Wang, and William Yang Wang. 2019. Vatex: A large-scale, high-quality multilingual dataset for
+video-and-language research. In 2019 IEEE/CVF International Conference on Computer Vision, ICCV 2019, Seoul, Korea (South), October 27 - November 2, 2019, pages 4580–4590. IEEE.
+Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Brian Ichter, Fei Xia, Ed H. Chi, Quoc V. Le, and Denny Zhou. 2022. Chain-of-thought prompting elicits reasoning in large language models. In Advances in Neural Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, NeurIPS 2022, New Orleans, LA, USA, November 28 - December 9, 2022.
+Jian Wu, Linyi Yang, Zhen Wang, Manabu Okumura, and Yue Zhang. 2024a. Cofca: A step-wise counterfactual multi-hop qa benchmark. Preprint, arXiv:2402.11924.
+Te-Lin Wu, Zi-Yi Dou, Qingyuan Hu, Yu Hou, Nischal Chandra, Marjorie Freedman, Ralph Weischedel, and Nanyun Peng. 2023. ACQUIRED: A dataset for answering counterfactual questions in real-life videos. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 11753–11770, Singapore. Association for Computational Linguistics.
+Yecheng Wu, Zhuoyang Zhang, Junyu Chen, Haotian Tang, Dacheng Li, Yunhao Fang, Ligeng Zhu, Enze Xie, Hongxu Yin, Li Yi, Song Han, and Yao Lu. 2024b. VILA-U: a unified foundation model integrating visual understanding and generation. CoRR, abs/2409.04429.
+Zhaofeng Wu, Linlu Qiu, Alexis Ross, Ekin Akyürek, Boyuan Chen, Bailin Wang, Najoung Kim, Jacob Andreas, and Yoon Kim. 2024c. Reasoning or reciting? exploring the capabilities and limitations of language models through counterfactual tasks. In Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers), pages 1819–1862, Mexico City, Mexico. Association for Computational Linguistics.
+Binzhu Xie, Sicheng Zhang, Zitang Zhou, Bo Li, Yuanhan Zhang, Jack Hessel, Jingkang Yang, and Ziwei Liu. 2024. [inline-graphic not available: see fulltext] funqa: Towards surprising video comprehension. In Computer Vision - ECCV 2024 - 18th European Conference, Milan, Italy, September 29-October 4, 2024, Proceedings, Part I, volume 15059 of Lecture Notes in Computer Science, pages 39–57. Springer.
+Linyi Yang, Shuibai Zhang, Libo Qin, Yafu Li, Yidong Wang, Hanmeng Liu, Jindong Wang, Xing Xie, and Yue Zhang. 2023. GLUE-X: Evaluating natural language understanding models from an out-ofdistribution generalization perspective. In Findings of the Association for Computational Linguistics: ACL 2023, pages 12731–12750, Toronto, Canada. Association for Computational Linguistics.
+Kexin Yi, Chuang Gan, Yunzhu Li, Pushmeet Kohli, Jiajun Wu, Antonio Torralba, and Joshua B. Tenenbaum.
+2020. Clevrer: Collision events for video representation and reasoning. Preprint, arXiv:1910.01442.
+Weihao Yu, Zhengyuan Yang, Linjie Li, Jianfeng Wang, Kevin Lin, Zicheng Liu, Xinchao Wang, and Lijuan Wang. 2024. Mm-vet: Evaluating large multimodal models for integrated capabilities. In Forty-first International Conference on Machine Learning, ICML 2024, Vienna, Austria, July 21-27, 2024. OpenReview.net.
+Boqiang Zhang, Kehan Li, Zesen Cheng, Zhiqiang Hu, Yuqian Yuan, Guanzheng Chen, Sicong Leng, Yuming Jiang, Hang Zhang, Xin Li, Peng Jin, Wenqi Zhang, Fan Wang, Lidong Bing, and Deli Zhao. 2025. Videollama 3: Frontier multimodal foundation models for image and video understanding. CoRR, abs/2501.13106.
+Hongjie Zhang, Yi Liu, Lu Dong, Yifei Huang, Zhen-Hua Ling, Yali Wang, Limin Wang, and Yu Qiao. 2023. Movqa: A benchmark of versatile question-answering for long-form movie understanding. Preprint, arXiv:2312.04817.
+Yuanhan Zhang, Jinming Wu, Wei Li, Bo Li, Zejun Ma, Ziwei Liu, and Chunyuan Li. 2024a. Video instruction tuning with synthetic data. CoRR, abs/2410.02713.
+Zhuosheng Zhang, Aston Zhang, Mu Li, Hai Zhao, George Karypis, and Alex Smola. 2024b. Multimodal chain-of-thought reasoning in language models. Preprint, arXiv:2302.00923.
+Ge Zheng, Bin Yang, Jiajin Tang, Hong-Yu Zhou, and Sibei Yang. 2023. Ddcot: Duty-distinct chain-ofthought prompting for multimodal reasoning in language models. In Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NeurIPS 2023, New Orleans, LA, USA, December $I O \mathrm { ~ - ~ } I 6 ,$ , 2023.
+# A Appendix
+# A.1 Data Construction Details
+In this section, we present additional details on COVER construction, including information about the task splitting scores, annotation agreements, data augmentation prompts and process flow.
+We invited three expert annotators to independently score each benchmark task based on our two-dimensional quadrant framework (abstract vs. concrete and perception vs. cognition). Their scoring results in Table 8 demonstrates the strictness, consistency, and logical coherence of our task categorization, effectively preventing overlaps and ambiguity.
+The annotators were recruited to evaluate COVER across multiple dimensions, with the resultant assessments systematically compiled in Table 9, ensuring comprehensive evaluation coverage. The methodological workflow for data augmentation is schematically outlined in Figure 6.
+The schematic framework outlined in Figure 7 delineates the methodology employed for contextual data augmentation, leveraging the generative capabilities of GPT-4o(Hurst et al., 2024) to construct domain-specific instructional prompts.
+# A.2 Additional Results
+In this section, we present additional experiments on COVER. The comprehensive evaluation framework delineated in Table 14 presents granular performance metrics across 13 meticulously defined tasks.
+GPT-4o exhibited notable vulnerability in the Procedure Understanding task. While it attained a respectable raw accuracy of $7 8 . 1 7 \%$ , its counterfactual accuracy plummeted to $2 8 . 9 7 \%$ , representing a precipitous decline of $4 9 . 2 \%$ . This substantial drop suggests that the performance of GPT-4o in understanding procedures may be overly reliant on surface-level features. Counterfactual perturbations, such as changes in conditions, can severely disrupt its reasoning capabilities, thereby highlighting a robustness limitation of the model when handling complex tasks.
+Figure 5 (a) depicts the relationship between $o r i _ { a c c }$ and $s u b _ { a c c }$ across different models, with a purple regression line characterizing the functional correlation between mean $o r i _ { a c c }$ and mean $s u b _ { a c c }$ . Figure 5 (b) demonstrates the association between $c f _ { a c c }$ and $s u b _ { a c c }$ across different models, with a red regression line characterizing the functional correlation between mean $c f _ { a c c }$ and mean $s u b _ { a c c }$ The bivariate correlation analysis delineated in Figure 5 demonstrates statistically significant covariation patterns $( \mathbf { r } = 0 . 8 3 6 )$ ) between semantic comprehension and multi-step reasoning capabilities in MLLMs.
+We conducted an additional ablation study to examine whether the observed trend where excessive visual information impairs reasoning accuracy holds consistently across both short and long videos. Our results are summarized in Table 10, 11. We observed a clear pattern across both short and long videos: model accuracy typically peaks within a moderate frame range (8–32 frames) and subsequently declines at the maximum
+Table 8: Annotator scoring table. Annotators A, B, and C provide ratings along two axes: the perceptual–cognitive dimension ( $\mathbf { \bar { x } }$ -axis, from $- 5$ to 5, where higher values indicate more cognitive tasks) and the concrete–abstract dimension (y-axis, from $- 5$ to 5, where higher values indicate more abstract tasks).
+<table><tr><td>Task</td><td>Ax</td><td>Ay</td><td>Bx</td><td>By</td><td>Cx</td><td>Cy</td><td>Avgx</td><td>Avgy</td></tr><tr><td>Counting</td><td>-3.2</td><td>-3.4</td><td>-3.1</td><td>-3.6</td><td>-3.3</td><td>-3.7</td><td>-3.2</td><td>-3.57</td></tr><tr><td>Color</td><td>-4.1</td><td>-4.4</td><td>-4.4</td><td>-4.2</td><td>-4.2</td><td>-4.3</td><td>-4.23</td><td>-4.3</td></tr><tr><td>Material</td><td>-3.8</td><td>-3.3</td><td>-3.9</td><td>-3.2</td><td>-4.0</td><td>-3.4</td><td>-3.9</td><td>-3.3</td></tr><tr><td>Size</td><td>-2.4</td><td>-2.5</td><td>-2.6</td><td>-2.3</td><td>-2.2</td><td>-2.4</td><td>-2.4</td><td>-2.4</td></tr><tr><td>Shape</td><td>-3.3</td><td>-3.2</td><td>-3.5</td><td>-3.2</td><td>-3.8</td><td>-4.0</td><td>-3.53</td><td>-3.47</td></tr><tr><td>Emotion</td><td>-2.4</td><td>4.0</td><td>-2.5</td><td>3.5</td><td>-2.4</td><td>3.1</td><td>-2.43</td><td>3.53</td></tr><tr><td>Location</td><td>-1.7</td><td>-1.4</td><td>-2.0</td><td>-1.6</td><td>-1.3</td><td>-1.7</td><td>-1.67</td><td>-1.57</td></tr><tr><td>Direction</td><td>-2.1</td><td>-1.7</td><td>-2.5</td><td>-1.5</td><td>-2.6</td><td>-1.8</td><td>-2.4</td><td>-1.67</td></tr><tr><td>Object Recognition</td><td>3.0</td><td>-3.0</td><td>2.4</td><td>-2.0</td><td>1.2</td><td>-2.3</td><td>2.2</td><td>-2.43</td></tr><tr><td>Action Recognition</td><td>2.5</td><td>-3.1</td><td>2.3</td><td>-3.0</td><td>2.1</td><td>-3.5</td><td>2.3</td><td>-3.2</td></tr><tr><td>Action Prediction</td><td>3.9</td><td>2.4</td><td>3.8</td><td>2.5</td><td>3.2</td><td>2.2</td><td>3.63</td><td>2.37</td></tr><tr><td>Procedure Understanding</td><td>3.0</td><td>3.5</td><td>3.6</td><td>3.2</td><td>2.2</td><td>3.3</td><td>2.93</td><td>3.33</td></tr><tr><td>Social Relation</td><td>3.4</td><td>4.3</td><td>3.0</td><td>4.4</td><td>3.1</td><td>4.1</td><td>3.17</td><td>4.27</td></tr></table>
+![](images/79dfb205c4e3113cef4d04000aa60906376fc2a35784d13f06e548fb1574b8d0.jpg)
+Figure 6: Flowchart depicting the data augmentation pipeline.
+setting (64 frames). This decline is particularly pronounced in tasks involving the original questions (ori) and sub questions (sub), suggesting that an excessive amount of visual input can indeed negatively impact model performance, regardless of video length.
+Additionally, we evaluated test-time reasoning
+strategies on manually curated seed data using longchain reasoning models in Table 12. Notably, models such as InternVL2.5-78B-CoT show significant improvement in bridging the cf–sub–ori gap, further supporting that reasoning-guided prompting (e.g., CoT) helps align sub-level and cf-level accuracy. These observations suggest a promising direc-
+![](images/44cc1bd67024004c35e24fdfb5efa9fbd8a8109f71cd478ca79e79ce1e967d12.jpg)
+Figure 7: Methodological framework for data augmentation using GPT-4o.
+Table 9: Cross-annotator validation on COVER. The table summarizes quality scores assigned by three annotators. A, B, and C denote randomly assigned codes for the assessment data, and Average indicates the mean score across all entries.
+<table><tr><td>Aspect</td><td>A</td><td>B</td><td>C</td><td>Average</td></tr><tr><td>Data Quality</td><td>4</td><td>4</td><td>5</td><td>4.3</td></tr><tr><td>Data Diversity</td><td>5</td><td>4</td><td>5</td><td>4.7</td></tr><tr><td>Relevance</td><td>4</td><td>5</td><td>4</td><td>4.3</td></tr><tr><td>Annotation Quality</td><td>4</td><td>5</td><td>5</td><td>4.7</td></tr><tr><td>Dataset Usability</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td>Innovation</td><td>5</td><td>5</td><td>4</td><td>4.7</td></tr></table>
+tion: larger and better-aligned models, when combined with explicit reasoning strategies, are more capable of maintaining coherence across perception, decomposition, and abstract reasoning tasks.
+# A.3 Sample Reaults on Test Time Long Reasoning Models
+As illustrated in Figure 10, the reasoning model QVQ-72B-Preview (Team, 2024), equipped with a built-in Chain-of-Thought (CoT) mechanism, exhibits human-aligned reasoning patterns. Its cog-
+Table 10: Performance of MLLMs with different numbers of sampled frames for short videos (1–64 frames).
+<table><tr><td>Frame</td><td colspan="3">InternVL2.5-4B</td><td colspan="3">InternVL2.5-8B</td></tr><tr><td></td><td>oriacc</td><td>cfacc</td><td>subacc</td><td>oriacc</td><td>cfacc</td><td>subacc</td></tr><tr><td>2</td><td>69.09</td><td>45.94</td><td>60.33</td><td>68.72</td><td>56.53</td><td>61.14</td></tr><tr><td>4</td><td>70.81</td><td>46.18</td><td>60.91</td><td>68.97</td><td>56.90</td><td>60.68</td></tr><tr><td>8</td><td>71.31</td><td>43.97</td><td>60.62</td><td>69.83</td><td>56.28</td><td>61.14</td></tr><tr><td>16</td><td>70.81</td><td>44.83</td><td>59.86</td><td>70.07</td><td>56.40</td><td>61.20</td></tr><tr><td>32</td><td>70.69</td><td>43.84</td><td>59.57</td><td>69.21</td><td>56.90</td><td>61.26</td></tr><tr><td>64</td><td>69.95</td><td>46.55</td><td>59.63</td><td>69.09</td><td>57.27</td><td>60.62</td></tr></table>
+Table 11: Effect of different frame sampling strategies on MLLM performance for long videos (64–2000 frames).
+<table><tr><td>Frame</td><td colspan="3">InternVL2.5-4B</td><td colspan="3">InternVL2.5-8B</td></tr><tr><td></td><td>oriacc</td><td>cfacc</td><td>subacc</td><td>oriacc</td><td>cfacc</td><td>subacc</td></tr><tr><td>2</td><td>73.90</td><td>49.22</td><td>61.09</td><td>72.24</td><td>59.26</td><td>59.67</td></tr><tr><td>4</td><td>75.79</td><td>46.61</td><td>62.13</td><td>75.04</td><td>59.07</td><td>61.07</td></tr><tr><td>8</td><td>76.46</td><td>46.23</td><td>62.24</td><td>75.79</td><td>57.37</td><td>61.78</td></tr><tr><td>16</td><td>77.45</td><td>45.38</td><td>62.31</td><td>75.94</td><td>58.27</td><td>61.82</td></tr><tr><td>32</td><td>77.40</td><td>45.57</td><td>61.49</td><td>75.98</td><td>57.08</td><td>61.49</td></tr><tr><td>64</td><td>76.13</td><td>46.57</td><td>61.11</td><td>76.17</td><td>58.41</td><td>61.55</td></tr></table>
+Table 12: Variation in accuracy across different testtime reasoning strategies.
+<table><tr><td>Model</td><td>ori_acc</td><td>cf_acc</td><td>sub_acc</td></tr><tr><td>QVQ-72B-Preview</td><td>69.33</td><td>59.33</td><td>58.76</td></tr><tr><td>InternVL2.5-78B-CoT</td><td>70.00</td><td>71.33</td><td>70.80</td></tr></table>
+nitive process integrates detailed scenario descriptions, systematic elimination of implausible options (e.g., excluding candidates A/B/C), and rigorous conclusion verification. In contrast, InternVL2.5- 78B employs a CoT mechanism that presents answers in a bullet-point format without explanatory justification, reflecting weaker anthropomorphic reasoning characteristics.
+However, the $c f _ { a c c }$ discrepancy in Table 13 (QVQ-72B-Preview: $5 9 . 3 3 \% <$ InternVL2.5-78B: $7 1 . 3 3 \%$ suggests that contemporary reasoning models may rely more on memorization than on structured reasoning. InternVL2.5-78B’s concise response paradigm appears to leverage rapid pattern recognition and information retrieval, leading to superior accuracy. While QVQ-72B-Preview’s elaborate reasoning workflow better approximates human cognition, potential redundancies or logical inconsistencies may reduce answer precision.
+Table 13 further indicates that InternVL2.5- 78B achieves a substantial lead in the $s u b _ { a c c }$ metric $( 7 0 . 8 0 \% )$ , significantly outperforming QVQ-72B-Preview $( 5 8 . 7 6 \% )$ and Claude-3.7-sonnect $( 4 6 . 7 2 \% )$ . This performance hierarchy remains consistent across models when evaluated on the oriacc metric: InternVL2.5-78B $( 7 0 . 0 0 \% ) > \mathrm { Q V Q - 7 2 B } .$ - Preview $( 6 9 . 3 3 \% )$ Claude-3.7-sonnect $( 4 6 . 0 0 \% )$ . Empirical evidence suggests a statistically significant positive correlation between reasoning capability $( s u b _ { a c c } )$ and comprehension ability $( o r i _ { a c c } )$ . In addition, under the CoT paradigm, reasoning capability demonstrates stronger generalization, exhibiting a positive correlation with performance on human-annotated essential logical sub-problems, thereby reinforcing the intrinsic relationship between logical reasoning and generalizability.
+Moreover, the reasoning processes of models such as QVQ frequently generate sub-problem content that aligns with human-annotated data, which to some extent suggests that the inferential patterns of test-time long-reasoning models demonstrate closer correspondence with human cognitive intuition. For instance, in the Figure 11 the analytical content regarding the opening and closing scenes
+Table 13: Performance of different chain-of-thought (CoT) reasoning architectures on a manually annotated dataset of 150 samples. QVQ and Claude-3.5-Sonnet represent dedicated reasoning models, while the others apply CoT-based augmentation.
+<table><tr><td></td><td>oriacc</td><td>cfacc</td><td>subacc</td></tr><tr><td>QVQ-72B-Preview</td><td>69.33</td><td>59.33</td><td>58.76</td></tr><tr><td>Claude-3.7-sonnect</td><td>46.00</td><td>59.33</td><td>46.72</td></tr><tr><td>InternVL2.5-78B</td><td>70.00</td><td>71.33</td><td>70.80</td></tr><tr><td>VILA1.5-13B</td><td>65.33</td><td>44.67</td><td>53.65</td></tr></table>
+of videos (highlighted in blue font) exhibits precise alignment with the manually curated sub-problems in the upper-right annotation (specifically addressing inquiries about video commencement and conclusion scenarios), thereby empirically validating this cognitive congruence.
+# A.4 Examples of Sub-question Guidelines
+Figure 8 illustrates how sub-question errors propagate to counterfactual question failures. In Figure 9, we observe that subtle errors in the reasoning process lead to reasoning failures, highlighting the model’s sensitivity to the integrity of its reasoning steps.
+Table 14: Overall performance of MLLMs on 13 tasks in COVER, including original accuracy, counterfactual accuracy, and sub-question accuracy.
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Type</td><td colspan="12">Task</td><td></td></tr><tr><td>Action Prediction</td><td>Procedure Understanding</td><td>Social Relation</td><td>Action Recognition</td><td>Object Recognition</td><td>Color</td><td>Counting</td><td>Direction</td><td>Location</td><td>Material</td><td>Shape</td><td>Size</td><td>Emotion</td></tr><tr><td rowspan="3">GPT-4o</td><td>oriacc</td><td>65.20</td><td>78.17</td><td>69.00</td><td>74.87</td><td>74.87</td><td>92.23</td><td>75.25</td><td>50.88</td><td>70.59</td><td>79.12</td><td>72.00</td><td>52.88</td><td>65.01</td></tr><tr><td>cfacc</td><td>41.41</td><td>28.97</td><td>56.33</td><td>44.65</td><td>42.67</td><td>37.86</td><td>40.59</td><td>33.33</td><td>42.86</td><td>59.34</td><td>58.00</td><td>29.81</td><td>55.65</td></tr><tr><td>subacc</td><td>51.85</td><td>22.82</td><td>52.43</td><td>69.54</td><td>67.09</td><td>51.94</td><td>47.52</td><td>56.90</td><td>48.96</td><td>58.08</td><td>55.56</td><td>36.08</td><td>63.97</td></tr><tr><td rowspan="3">GPT-4o-mini</td><td>oriacc</td><td>50.22</td><td>72.22</td><td>63.32</td><td>78.61</td><td>74.08</td><td>84.47</td><td>70.30</td><td>52.63</td><td>57.98</td><td>71.43</td><td>62.00</td><td>56.73</td><td>65.56</td></tr><tr><td>cfacc</td><td>44.05</td><td>51.19</td><td>62.01</td><td>56.42</td><td>52.36</td><td>26.21</td><td>39.60</td><td>36.84</td><td>59.66</td><td>52.75</td><td>53.00</td><td>17.31</td><td>58.26</td></tr><tr><td>subacc</td><td>53.16</td><td>19.44</td><td>58.85</td><td>68.03</td><td>64.82</td><td>38.35</td><td>38.12</td><td>53.88</td><td>47.72</td><td>53.89</td><td>53.44</td><td>28.85</td><td>65.96</td></tr><tr><td rowspan="3">Claude-3.5-Sonnet</td><td>oriacc</td><td>43.61</td><td>63.10</td><td>63.32</td><td>66.31</td><td>73.82</td><td>79.61</td><td>68.32</td><td>48.25</td><td>52.10</td><td>63.74</td><td>66.34</td><td>45.19</td><td>66.94</td></tr><tr><td>cfacc</td><td>39.21</td><td>33.33</td><td>38.86</td><td>43.85</td><td>40.84</td><td>36.89</td><td>19.80</td><td>35.96</td><td>40.34</td><td>37.36</td><td>40.59</td><td>18.27</td><td>39.81</td></tr><tr><td>subacc</td><td>46.19</td><td>15.87</td><td>46.68</td><td>62.54</td><td>60.93</td><td>39.81</td><td>24.26</td><td>48.28</td><td>48.55</td><td>46.11</td><td>37.70</td><td>34.13</td><td>56.81</td></tr><tr><td rowspan="3">Gemini-1.5-Pro</td><td>oriacc</td><td>54.63</td><td>80.95</td><td>71.62</td><td>83.42</td><td>80.89</td><td>84.47</td><td>73.27</td><td>61.40</td><td>76.47</td><td>81.32</td><td>67.33</td><td>59.62</td><td>75.48</td></tr><tr><td>cfacc</td><td>46.70</td><td>29.76</td><td>58.52</td><td>45.45</td><td>58.38</td><td>46.60</td><td>37.62</td><td>35.96</td><td>42.86</td><td>54.95</td><td>55.45</td><td>36.54</td><td>57.99</td></tr><tr><td>subacc</td><td>57.52</td><td>39.68</td><td>64.38</td><td>72.58</td><td>72.99</td><td>73.30</td><td>43.56</td><td>61.21</td><td>58.09</td><td>59.88</td><td>55.50</td><td>45.67</td><td>69.54</td></tr><tr><td rowspan="3">Gemini-1.5-Flash</td><td>oriacc</td><td>53.74</td><td>85.32</td><td>70.74</td><td>82.62</td><td>81.41</td><td>82.52</td><td>70.30</td><td>57.02</td><td>70.59</td><td>79.12</td><td>69.31</td><td>68.27</td><td>72.04</td></tr><tr><td>cfacc</td><td>45.81</td><td>34.92</td><td>56.33</td><td>49.20</td><td>49.48</td><td>41.75</td><td>37.62</td><td>33.33</td><td>41.18</td><td>64.84</td><td>53.47</td><td>25.96</td><td>58.26</td></tr><tr><td>subacc</td><td>61.87</td><td>32.94</td><td>63.94</td><td>73.28</td><td>69.60</td><td>46.60</td><td>43.07</td><td>62.93</td><td>54.77</td><td>62.87</td><td>55.50</td><td>37.98</td><td>71.36</td></tr><tr><td rowspan="3">Gemini-2.0-Flash</td><td>oriacc</td><td>60.35</td><td>86.90</td><td>74.24</td><td>87.97</td><td>80.10</td><td>90.29</td><td>69.31</td><td>64.04</td><td>78.99</td><td>81.32</td><td>70.30</td><td>66.35</td><td>75.90</td></tr><tr><td>cfacc</td><td>42.29</td><td>36.51</td><td>51.97</td><td>44.12</td><td>51.31</td><td>20.39</td><td>39.60</td><td>31.58</td><td>37.82</td><td>57.14</td><td>56.44</td><td>31.73</td><td>57.71</td></tr><tr><td>subacc</td><td>60.78</td><td>35.52</td><td>59.51</td><td>73.16</td><td>72.49</td><td>69.90</td><td>59.41</td><td>65.95</td><td>53.53</td><td>58.08</td><td>58.64</td><td>42.31</td><td>66.84</td></tr><tr><td rowspan="3">InternVL2.5-78B</td><td>oriacc</td><td>67.84</td><td>75.00</td><td>75.55</td><td>79.68</td><td>82.20</td><td>94.17</td><td>82.18</td><td>52.63</td><td>76.47</td><td>76.92</td><td>83.17</td><td>69.23</td><td>76.86</td></tr><tr><td>cfacc</td><td>43.61</td><td>76.19</td><td>57.21</td><td>65.51</td><td>61.78</td><td>87.38</td><td>37.62</td><td>47.37</td><td>75.63</td><td>61.54</td><td>57.43</td><td>39.43</td><td>56.20</td></tr><tr><td>subacc</td><td>62.09</td><td>44.64</td><td>67.70</td><td>76.90</td><td>62.28</td><td>79.13</td><td>69.80</td><td>66.38</td><td>58.09</td><td>62.28</td><td>59.69</td><td>50.48</td><td>70.07</td></tr><tr><td rowspan="3">LLaVA-Video-72B</td><td>oriacc</td><td>43.17</td><td>50.79</td><td>65.50</td><td>60.70</td><td>69.90</td><td>85.44</td><td>69.31</td><td>51.75</td><td>73.11</td><td>74.73</td><td>61.39</td><td>61.54</td><td>70.66</td></tr><tr><td>cfacc</td><td>44.93</td><td>59.92</td><td>59.39</td><td>63.10</td><td>57.85</td><td>62.14</td><td>42.57</td><td>47.37</td><td>66.39</td><td>53.85</td><td>51.49</td><td>41.35</td><td>56.20</td></tr><tr><td>subacc</td><td>59.26</td><td>32.94</td><td>69.47</td><td>67.56</td><td>66.46</td><td>63.59</td><td>52.97</td><td>61.21</td><td>45.23</td><td>55.69</td><td>53.40</td><td>43.27</td><td>70.01</td></tr><tr><td rowspan="3">InternVL2.5-26B</td><td>oriacc</td><td>57.27</td><td>78.58</td><td>76.42</td><td>82.35</td><td>79.58</td><td>91.26</td><td>74.26</td><td>62.28</td><td>85.71</td><td>74.73</td><td>78.22</td><td>66.35</td><td>73.14</td></tr><tr><td>cfacc</td><td>47.14</td><td>45.24</td><td>51.09</td><td>60.43</td><td>57.59</td><td>59.23</td><td>25.74</td><td>45.61</td><td>60.50</td><td>57.14</td><td>25.00</td><td>25.00</td><td>50.00</td></tr><tr><td>subacc</td><td>59.91</td><td>61.08</td><td>62.39</td><td>71.18</td><td>73.24</td><td>65.05</td><td>56.44</td><td>68.97</td><td>58.09</td><td>61/08</td><td>50.96</td><td>50.96</td><td>65.61</td></tr><tr><td rowspan="3">InternVL2.5-8B</td><td>oriacc</td><td>55.51</td><td>75.00</td><td>78.17</td><td>81.28</td><td>80.63</td><td>90.29</td><td>70.30</td><td>63.16</td><td>78.99</td><td>74.63</td><td>74.26</td><td>66.35</td><td>72.18</td></tr><tr><td>cfacc</td><td>48.02</td><td>76.19</td><td>49.78</td><td>71.39</td><td>57.85</td><td>84.47</td><td>36.63</td><td>53.51</td><td>70.59</td><td>59.34</td><td>55.45</td><td>28.85</td><td>51.79</td></tr><tr><td>subacc</td><td>55.99</td><td>29.37</td><td>66.81</td><td>69.89</td><td>72.24</td><td>52.43</td><td>52.97</td><td>60.34</td><td>53.53</td><td>56.89</td><td>54.97</td><td>51.44</td><td>68.19</td></tr><tr><td rowspan="3">VideoLLama3-8B</td><td>oriacc</td><td>52.42</td><td>81.75</td><td>68.56</td><td>80.48</td><td>82.20</td><td>94.17</td><td>70.30</td><td>63.16</td><td>81.51</td><td>70.33</td><td>68.32</td><td>62.50</td><td>69.28</td></tr><tr><td>cfacc</td><td>35.68</td><td>53.97</td><td>46.29</td><td>55.08</td><td>54.71</td><td>66.02</td><td>42.57</td><td>42.11</td><td>64.71</td><td>58.24</td><td>48.51</td><td>32.69</td><td>53.44</td></tr><tr><td>subacc</td><td>49.45</td><td>33.93</td><td>67.48</td><td>67.91</td><td>68.84</td><td>57.77</td><td>39.60</td><td>58.62</td><td>49.79</td><td>53.89</td><td>54.45</td><td>47.12</td><td>67.90</td></tr><tr><td rowspan="3">LLaVA-ov-7B</td><td>oriacc</td><td>48.90</td><td>48.81</td><td>66.81</td><td>60.43</td><td>65.45</td><td>86.41</td><td>63.37</td><td>44.74</td><td>63.03</td><td>72.53</td><td>61.39</td><td>63.46</td><td>68.60</td></tr><tr><td>cfacc</td><td>43.61</td><td>64.29</td><td>45.85</td><td>55.35</td><td>50.79</td><td>59.22</td><td>42.57</td><td>45.61</td><td>52.94</td><td>60.44</td><td>57.43</td><td>30.77</td><td>52.75</td></tr><tr><td>subacc</td><td>50.11</td><td>30.36</td><td>63.94</td><td>62.78</td><td>60.68</td><td>54.85</td><td>42.08</td><td>53.45</td><td>45.64</td><td>50.90</td><td>48.69</td><td>50.96</td><td>64.73</td></tr><tr><td rowspan="3">LLaVA-Video-7B</td><td>oriacc</td><td>50.66</td><td>35.71</td><td>65.50</td><td>56.15</td><td>67.02</td><td>83.50</td><td>67.33</td><td>41.23</td><td>58.82</td><td>74.72</td><td>64.36</td><td>59.62</td><td>66.39</td></tr><tr><td>cfacc</td><td>44.93</td><td>73.02</td><td>45.85</td><td>59.09</td><td>42.15</td><td>73.79</td><td>42.57</td><td>48.25</td><td>60.50</td><td>58.24</td><td>48.51</td><td>35.58</td><td>49.59</td></tr><tr><td>subacc</td><td>48.58</td><td>29.96</td><td>56.64</td><td>62.19</td><td>58.67</td><td>55.34</td><td>41.09</td><td>56.03</td><td>43.15</td><td>54.49</td><td>52.88</td><td>48.08</td><td>63.03</td></tr><tr><td rowspan="3">Qwen2-VL-7B</td><td>oriacc</td><td>44.49</td><td>84.12</td><td>67.25</td><td>84.22</td><td>80.10</td><td>88.35</td><td>70.29</td><td>57.89</td><td>73.94</td><td>74.73</td><td>65.34</td><td>69.23</td><td>67.49</td></tr><tr><td>cfacc</td><td>42.29</td><td>58.73</td><td>45.41</td><td>44.92</td><td>41.88</td><td>56.31</td><td>21.78</td><td>42.11</td><td>58.82</td><td>60.44</td><td>45.54</td><td>33.65</td><td>49.72</td></tr><tr><td>subacc</td><td>53.37</td><td>30.16</td><td>63.72</td><td>67.33</td><td>66.71</td><td>43.20</td><td>42.08</td><td>59.48</td><td>51.87</td><td>52.69</td><td>51.83</td><td>51.44</td><td>65.02</td></tr><tr><td rowspan="3">VILA-U-7B</td><td>oriacc</td><td>45.37</td><td>73.02</td><td>54.59</td><td>66.31</td><td>59.95</td><td>81.55</td><td>61.39</td><td>54.39</td><td>71.43</td><td>47.25</td><td>47.52</td><td>47.11</td><td>59.50</td></tr><tr><td>cfacc</td><td>22.47</td><td>53.17</td><td>42.36</td><td>44.39</td><td>39.53</td><td>45.63</td><td>45.54</td><td>23.68</td><td>43.70</td><td>35.16</td><td>35.64</td><td>36.54</td><td>33.88</td></tr><tr><td>subacc</td><td>38.78</td><td>34.33</td><td>44.03</td><td>52.16</td><td>57.04</td><td>41.26</td><td>22.28</td><td>39.22</td><td>40.66</td><td>35.93</td><td>42.93</td><td>42.31</td><td>55.34</td></tr><tr><td rowspan="3">VILA1.5-7B</td><td>oriacc</td><td>52.86</td><td>50.40</td><td>61.57</td><td>67.65</td><td>66.23</td><td>61.17</td><td>56.44</td><td>40.35</td><td>40.34</td><td>71.43</td><td>60.40</td><td>62.50</td><td>63.64</td></tr><tr><td>cfacc</td><td>28.64</td><td>85.71</td><td>50.22</td><td>68.45</td><td>56.29</td><td>86.41</td><td>57.43</td><td>49.12</td><td>76.47</td><td>51.65</td><td>41.58</td><td>44.23</td><td>52.34</td></tr><tr><td>subacc</td><td>34.86</td><td>24.80</td><td>59.96</td><td>61.73</td><td>65.45</td><td>48.06</td><td>31.19</td><td>50.86</td><td>42.74</td><td>47.31</td><td>45.55</td><td>46.63</td><td>61.91</td></tr></table>
+![](images/01aedfa65344062222208a8d0d0dd77752b516b9cdfa110f2e4b152ff5c4e859.jpg)
+Figure 8: Example from COVER, showing a video accompanied by three related questions. The video is divided into four key action frames (left), with dashed lines indicating reasoning steps. Single-step prediction errors are marked with red crosses on the right, while sub-questions that do not support counterfactual reasoning are marked with red crosses on the left.
+![](images/1d4ddf3b29d250e7ff8386a4bd605a7b064cc12710ea2057ceb4865b6dd03d27.jpg)
+Figure 9: An example from COVER. The top section shows the video input and corresponding counterfactual questions. The middle section presents three reasoning processes—CoT, Guide-CoT, and Standard—where correct steps are marked with green checkmarks. In the analysis, correct reasoning paths are shown in green text, while incorrect ones are highlighted in red. The bottom section displays the final model predictions, with green checkmarks indicating correct answers and red crosses denoting errors.
+![](images/d18e1f53ea2b1d566272fc51799dddbfa98f9f1cc115159f2a17955da0c97b43.jpg)
+Figure 10: An example from the 150 seed samples. The top section shows the video input and corresponding counterfactual questions. The middle section compares two reasoning frameworks: the test-time long reasoning model QVQ and InternVL2.5-78B with CoT, with green marks indicating validated response components. The bottom section displays final model predictions, where green checkmarks indicate correct answers.
+![](images/42bad4d7938bf6d51c9631a0f138481d6088a46f727806e17638a298a9103a52.jpg)
+Figure 11: An example from the 150 seed samples. The top section presents the video input and corresponding counterfactual questions. The middle section compares QVQ and InternVL2.5-78B with CoT, using a dual-color annotation scheme: blue indicates conceptual alignment with manual sub-problem annotations, and green highlights validated response components. The bottom section shows the final model predictions, with green checkmarks indicating correct answers.