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egoppgheartrateestimationfromeyetrackingcamerasinegocentricsystemstobenefitdownstreamvisiontasks/full.md

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+# egoPPG: Heart Rate Estimation from Eye-Tracking Cameras in Egocentric Systems to Benefit Downstream Vision Tasks
+
+Björn Braun, Rayan Armani, Manuel Meier, Max Moebus, and Christian Holz  
+Department of Computer Science, ETH Zürich, Switzerland
+
+https://siplab.org/projects/egoPPG
+
+![](images/1724e17bb27953ade15bcb51b2ff24ea5f2693970c30834cc7acc3dd41321650.jpg)  
+Figure 1. We propose egoPPG as a novel computer vision task: tracking a person's heart rate (HR) on unmodified egocentric vision headsets. Taking eye tracking videos as input, our method PulseFormer estimates the photoplethysmogram (PPG) from areas around the eyes to derive HR values. For training and validation, we introduce egoPPG-DB, a dataset of eye tracking videos while participants performed everyday activities with synchronized ground-truth PPG (via nose-based contact sensor) and HR values (via ECG chest strap).
+
+![](images/c824c6fec23be4a1bff6b2fc2a8a5c585ead81e207f2b5445d4e78e02dbd6c81.jpg)
+
+# Abstract
+
+Egocentric vision systems aim to understand the spatial surroundings and the wearer's behavior inside it, including motions, activities, and interactions. We argue that egocentric systems must additionally detect physiological states to capture a person's attention and situational responses, which are critical for context-aware behavior modeling. In this paper, we propose egoPPG, a novel vision task for egocentric systems to recover a person's cardiac activity to aid downstream vision tasks. We introduce PulseFormer, a method to extract heart rate as a key indicator of physiological state from the eye tracking cameras on unmodified egocentric vision systems. PulseFormer continuously estimates the photoplethysmogram (PPG) from areas around the eyes and fuses motion cues from the headset's inertial measurement unit to track HR values. We demonstrate egoPPG's downstream benefit for a key task on EgoExo4D, an existing egocentric dataset for which we find PulseFormer's estimates of HR to improve proficiency estimation by  $14\%$ . To train and validate PulseFormer, we
+
+collected a dataset of  $13+$  hours of eye tracking videos from Project Aria and contact-based PPG signals as well as an electrocardiogram (ECG) for ground-truth HR values. Similar to EgoExo4D, 25 participants performed diverse everyday activities such as office work, cooking, dancing, and exercising, which induced significant natural motion and HR variation (44-164 bpm). Our model robustly estimates HR  $(\mathrm{MAE} = 7.67\mathrm{bpm})$  and captures patterns  $(r = 0.85)$ . Our results show how egocentric systems may unify environmental and physiological tracking to better understand users and that egoPPG as a complementary task provides meaningful augmentations for existing datasets and tasks. We release our code, dataset, and HR augmentations for EgoExo4D to inspire research on physiology-aware egocentric tasks.
+
+# 1. Introduction
+
+Egocentric vision systems, such as Mixed Reality (MR) glasses by Meta [56], Magic Leap [43], and others have emerged as powerful devices for capturing and analyzing a person's behavior and their environment from a first-person
+
+perspective. The wider availability of promising wearable capture platforms has sparked a large amount of research on egocentric vision tasks for environment understanding and navigation [18], including localization [39, 71, 74], and simultaneous localization and mapping [15, 33, 68]. Since egocentric systems simultaneously capture parts of the wearer's behavior in addition to their environment, prior work has investigated egocentric action recognition [51, 87, 89, 96] and hand-object interaction [26, 73, 97] to understand user behavior. Several large-scale datasets now accelerate data-driven research in this domain with multimodal data for training and evaluation (e.g., Ego4D [26], Nymeria [50], EgoExo4D [27]).
+
+Most recently, Meta's Project Aria 2 introduced a contact-based heart rate (HR) sensor, with which egocentric systems can gauge the wearer's cognitive performance, attention, and situational responses [13, 20, 52, 76, 83]. Numerous additional conditions manifest in a person's HR, such as emotions, stress and fatigue [1, 9, 59, 65, 80]—capturing these dynamics can thus benefit models of human behavior to enable a richer understanding of user behavior.
+
+In this paper, we introduce a method to make such HR estimates available to many existing egocentric systems and already recorded large datasets, such as EgoExo4D [27] or Nymeria [50]. Our method PulseFormer accurately recovers a person's HR from the eye tracking videos in egocentric headsets. PulseFormer first estimates the person's photoplethysmogram (PPG) from the subtle fluctuations in skin intensity due to pulsatile artery expansion beneath the surface following a blood volume pulse (BVP), in particular deriving it from regions around the wearer's eye for robust tracking. Our spatial attention module ensures that PPG is estimated from robust regions around the eye, while our cross-attention fusion with the system's inertial measurement unit (IMU) learns a motion-informed temporal attention to optimally weight the eye tracking images for more accurate PPG estimates in scenarios with heavy motion.
+
+We validate our method's efficacy on a novel dataset that we collected to capture some of the activities included in large-scale egocentric datasets alongside physiological reference recordings. Our dataset egoPPG-DB contains 13 hours of recordings from 25 participants, who wore Project Aria glasses and performed six real-world tasks with varying motion and intensity, causing their HR values to reach levels between 44–164 bpm.
+
+# Downstream benefits for egocentric vision tasks
+
+A key contribution of our paper is that we demonstrate that knowing a person's continuous HR values benefits egocentric vision tasks downstream. We augment an existing architecture with PulseFormer's HR estimates and show its impact on EgoExo4D's proficiency estimation benchmark, which improves accuracy on this task by  $14.1\%$ .
+
+# Contributions
+
+We summarize our key contributions as follows:
+
+1. egoPPG as a novel task and PulseFormer as an HR estimation method for egocentric systems that operates on eye tracking videos. Our method robustly predicts continuous HR across a series of activities and interactions (MAE=7.67 bpm), with a  $23.8\%$  lower error than current state-of-the-art rPPG models [10, 45, 90, 92, 93].
+
+2. egoPPG-DB, a dataset of eye tracking videos and synchronized BVP (contact-based) and ECG recordings (chest strap-based) to verify all physiological signals. We captured these across diverse everyday activities that were inspired by those included in existing large-scale egocentric datasets, such as EgoExo4D [26, 27, 50].
+
+3. a validation of egoPPG's downstream benefits for egocentric vision tasks. We demonstrate the implications of our method PulseFormer on the proficiency estimation benchmark of the EgoExo4D dataset, which increases the accuracy by  $14.1\%$  when augmenting EgoExo4D with our continuously predicted HR values.
+
+# 2. Related work
+
+Egocentric vision. In recent years, research in egocentric vision has surged, driven by advances in AR/VR glasses [4, 18, 31, 43, 56, 57], which provide new ways for understanding user interaction from a first-person perspective. Much of this work has focused on tasks such as action recognition [41, 51, 87, 89, 96] and anticipation [14, 25, 87], full-body pose estimation [36, 37, 75], responding to user needs [67, 69, 91], and social behavior analysis [21, 26, 35]. Additionally, tracking vital signs in AR/VR settings and for affective computing applications [1, 9, 59, 65, 80] has become an important tool for understanding users' physiological states [53], their behavior, attention, and intent [3, 58, 88].
+
+Physiological measurements. Wearable sensors have had a tremendous impact on health monitoring in recent years, enabling continuous measurement of key physiological metrics, such as heart rate (HR), oxygen saturation, and activity levels [11, 17, 55, 61, 62]. HR, in particular, is a key measure for assessing an individual's health and performance [19, 23, 40, 48, 72]. In parallel to wearable sensors such as smartwatches, recent research has extensively explored using cameras as an unobtrusive, non-contact alternative for measuring HR, generally called remote photoplethysmography (rPPG) [34, 66, 84]. rPPG measures HR based on the BVP via subtle color changes of the skin. Generally, rPPG methods can be broadly divided into traditional signal processing techniques [7, 16, 34, 66, 85] and deep learning-based approaches [8, 10, 45, 78, 90, 92]. So far, rPPG has been mostly applied to facial videos with the camera and user being stationary, such as while sitting in front of a laptop, as it requires a continuous video feed
+
+of the same skin region. This limitation is shown in current rPPG datasets, which primarily capture individuals in seated positions with either a stationary camera directed at their face [6, 29, 70, 79] or requiring users to hold a smartphone steadily in front of their face [82]. As a result, rPPG is not feasible to be deployed in more dynamic settings.
+
+Eye tracking cameras. Eye tracking in egocentric vision systems is mostly done using inward-facing cameras directed at the eyes [2]. Even during motion, eye tracking in VR devices demonstrated accurate performance showcasing that the cameras remain almost stationary relative to the user's eyes [12]. Furthermore, IR illumination makes them robust to lighting variations and low-light conditions [49]. To the best of our knowledge, videos from eye tracking cameras have not yet been explored for HR estimation.
+
+# 3. Overview
+
+Our aim is to enable egocentric vision systems i) to model a person's physiological state via continuously estimated HR and ii) to integrate these HR estimates into downstream tasks that benefit from knowledge of the user's state. Sec. 4 first describes our dataset of synchronized eye tracking videos and ground-truth HR measurements. Sec. 5 introduces our method PulseFormer for recovering continuous HR from eye tracking videos. Sec. 6 outlines the downstream benefits of our novel task, using HR as input for modeling user proficiency on the EgoExo4D dataset.
+
+# 4. egoPPG-DB
+
+The egoPPG-DB dataset was developed to support HR estimation from eye tracking videos under real-world conditions and contains significant motion and HR fluctuations. By including diverse everyday activities, we provide a challenging benchmark for egocentric HR estimation models.
+
+# 4.1. Recruiting and recording
+
+We recruited  $N = 25$  participants (12 female, 13 male, ages 19-32,  $\mu = 25.1$  and  $\sigma = 3.3$ ) on a voluntary basis, resulting in over 13 hours of video recordings. Based on the Fitzpatrick scale [22], 9 participants had skin type II, 8 had skin type III, 3 had skin type IV, and 5 had skin type V. All participants signed a consent form before the data collection, agreeing with using and sharing their data for academic and non-commercial purposes. The data collection was approved by the ETH Zurich Ethics Commission (no. 2023-N-08). In terms of duration, egoPPG-DB is among the longest rPPG datasets as listed in Tab. 10 (Supplementary). Participants of egoPPG-DB are not included in EgoExo4D.
+
+# 4.2. Apparatus
+
+Fig. 2 illustrates our experimental setup. We used Project Aria glasses [18] with Profile 21 to record eye tracking
+
+![](images/7ac2c332063a6493be3c1bd908f83cd100fe34196b696642ccc219b219b5d8c1.jpg)  
+Figure 2. Apparatus used to record the egoPPG-DB dataset.
+
+videos at 30 fps with a resolution of  $320 \times 240$  pixels per eye. To capture ground truth PPG measurements, with which we train our model, we developed a custom sensor that records PPG data offline at  $128\mathrm{Hz}$ . The sensor consists of a main board, mounted on the left side of the frame, featuring a DA14695 system-on-chip interfacing with a MAX86141ENP+ PPG sensor. The LEDs and photodiodes used by the PPG sensor are embedded in the left nose pad and connected to the main board using a flat flexible cable. For each participant, we individually adjusted the nose pad position to ensure the sensor aligned with their left angular artery [30]. To validate our custom PPG sensor, we also recorded gold-standard ECG data using a movisens ECGMove 4 chest belt sampling at  $1024\mathrm{Hz}$ . We synchronized all devices at the start and end of each recording with a synchronization pattern, using their built-in IMUs.
+
+# 4.3. Capture protocol
+
+The average recording lasted 32 minutes. The capture protocol comprised 5 activities (Tab. 1): watching a video, office work, kitchen work, dancing, and exercising on an indoor bike (Fig. 1). We included these activities for three purposes: (1) Incorporate everyday activities including the corresponding HR changes and motion artifacts; (2) cover a wide range of HR values (low HR when watching a video vs. high HR when exercising), and (3) resemble activities that were captured in large-scale egocentric vision datasets, such as EgoExo4D [27]. In Tab. 11 (Supplementary), we give a detailed description of all activities. Tab. 3 shows mean HR values for each activity. Exercising on the bike produced the highest mean HR values (113 bpm), whereas watching the video resulted in the lowest (71 bpm).
+
+# 4.4. Dataset and signal quality verification
+
+To ensure the contact PPG sensor, whose signal we later use as the target for model training, produces accurate HR
+
+<table><tr><td>Activity</td><td>Actions</td><td>Minutes</td></tr><tr><td rowspan="2">Watch video</td><td>Watch a documentary</td><td>5</td></tr><tr><td>Work on a computer</td><td>4</td></tr><tr><td rowspan="2">Office work</td><td>Write on a paper</td><td>2</td></tr><tr><td>Talk to the experimenter</td><td>2</td></tr><tr><td rowspan="2">Walking</td><td>Walk to the kitchen</td><td>1</td></tr><tr><td>Cut vegetables</td><td></td></tr><tr><td rowspan="2">Kitchen work</td><td>Prepare a sandwich</td><td>5</td></tr><tr><td>Wash the dishes</td><td></td></tr><tr><td>Walking</td><td>Walk to the dancing room</td><td>1.5</td></tr><tr><td>Dancing</td><td>Follow random dance video</td><td>5</td></tr><tr><td>Exercise bike</td><td>Ride an exercise bike</td><td>5</td></tr><tr><td>Walking</td><td>Walk back to the start</td><td>1.5</td></tr></table>
+
+Table 1. Capture protocol for recording the egoPPG-DB dataset.
+
+values, we evaluate it against the gold-standard ECG. We calculated the MAE and Pearson correlation between HR estimates from the ECG and PPG signals for each participant using a 30-second sliding window. For activity labeling, we manually annotated the start and end times of each task (see Tab. 1) for each participant using the Point of View (POV) RGB videos recorded by the Project Aria glasses. To ensure that the signal quality of the contact PPG is sufficient for model training, we excluded all tasks with an MAE over  $3.0\mathrm{~bpm}$  between the PPG and ECG (e.g. when the PPG sensor moved). This applied to 20 of 150 tasks ( $13\%$ , see Tab. 6 in Supplementary). During the remaining tasks, our custom-built PPG nose sensor achieved very high accuracy, with an MAE of  $1.3\mathrm{~bpm}$  and a correlation of 0.94 compared to the ECG signal, showing its suitability as ground truth.
+
+# 5. PulseFormer method
+
+# 5.1. Problem definition
+
+Our objective is to estimate BVP and HR from periodic changes in pixel intensity in eye tracking video frames  $\pmb{F} \in \mathbb{R}^{w \times h}$ . Physically, this means extracting physiological signals from the information in the light reflected by the arteries and arterioles that carry blood beneath the skin. This light reflection can be modeled as a combination of diffuse and specular reflections. Wang et al. [85] model the reflected light intensity  $C(t)$  as:
+
+$$
+\boldsymbol {C} (\boldsymbol {t}) = I (t) \left(\boldsymbol {v} _ {\boldsymbol {s}} (t) + \boldsymbol {v} _ {\boldsymbol {d}} (t)\right) + \boldsymbol {v} _ {\boldsymbol {n}} (t) \tag {1}
+$$
+
+where  $I(t)$  is the luminance intensity,  $\pmb{v}_{s}(t)$  the specular reflection,  $\pmb{v}_{d}(t)$  the diffuse reflection, and  $\pmb{v}_{n}(t)$  the sensor noise. While the specular reflection  $\pmb{v}_{s}(t)$  lacks pulsatile information, the diffuse reflection  $\pmb{v}_{d}(t)$  contains information about the absorption and scattering of the light in skin
+
+tissue [85]. Thus,  $\pmb{v}_d(t)$  can be further decomposed as:
+
+$$
+\boldsymbol {v} _ {\boldsymbol {d}} (t) = \boldsymbol {u} _ {\boldsymbol {d}} d _ {0} + \boldsymbol {u} _ {\boldsymbol {p}} p (t) \tag {2}
+$$
+
+where  $\pmb{u}_d$  is the unit color vector of the skin,  $d_0$  the stationary reflection strength,  $\pmb{u_p}$  the relative absorption, and  $p(t)$  the signals of interest.  $p(t)$  is in our case the BVP, which our model aims to learn from the camera recordings.
+
+# 5.2. Deep learning model
+
+Our architecture is built upon a 3D CNN backbone (PhysNet) [92] with a temporal input length of  $T = 128$  frames (corresponding to 4.3 seconds) downsampled to  $(h = 48) \times (w = 128)$  pixels, resulting in an input of dimensions  $(T, C, w, h)$ . The channel is  $C = 1$  in our case, as our input is from monochrome videos. The input in our network is the consecutive standardized frame differences (per participant frame-wise differences divided by the STD of the frames) of the eye tracking videos to help the network focus on the changes between frames [10]. As labels, we use the standardized consecutive differences of the PPG signals. Since eye tracking videos offer additional challenges compared to facial videos, usually used for rPPG tasks, we have designed our model to address these challenges (see Fig. 3).
+
+Motion-informed temporal attention (MITA). Egocentric glasses are body-worn and subject to considerable motion artifacts when the user moves. Therefore, we propose to leverage the IMU within the glasses to obtain a motion-informed temporal attention. We employ a cross-attention module to integrate the IMU data with the video input, allowing our model to weigh each frame differently along the temporal dimension based on the motion intensity encoded by the IMU. This allows the model, e.g., to give less emphasis to frames heavily affected by motion. Given the input feature map  $\mathbf{F}_{\mathrm{in}} \in \mathbb{R}^{T \times 1 \times w \times h}$ , we use ResNet18 [28] and a linear layer to obtain the image embeddings  $\mathbf{F}_e \in \mathbb{R}^{T \times D}$  where  $D = 128$  is the embedding dimension. Given IMU measurements  $\mathbf{I}_{\mathrm{in}} \in \mathbb{R}^{T \times 1}$ , we use two 1D convolutional layers to obtain the IMU embeddings  $\mathbf{I}_e \in \mathbb{R}^{T \times D}$ . We then calculate the cross-attention  $\mathbf{A} \in \mathbb{R}^{T \times D}$  as:
+
+$$
+\mathbf {A} = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q K} ^ {\top}}{\sqrt {D}}\right) \mathbf {V} \tag {3}
+$$
+
+where  $\mathbf{I}_{\mathrm{e}}$  serve as queries  $Q$  and  $\mathbf{F}_{\mathrm{e}}$  as keys  $K$  and values  $V$ . Using a linear layer, we obtain the motion-informed temporal attention  $\mathbf{T} \in \mathbb{R}^{T \times 1 \times 1 \times 1}$ , which we multiply with  $F_{in}$ . Spatial attention (SA). While the bulbar conjunctiva (white of the eyes) contains many blood vessels from which the BVP could theoretically be estimated, eyes typically move strongly during everyday situations and are closed while blinking (see participant 2 in Fig. 4). Consequently, extracting the BVP from the eye regions would introduce substantial motion artifacts and reduce the signal-to-noise
+
+![](images/214d747cf48fc2a92a922764a114d30dd88a84b7d31c0f750054f112ec60bcda.jpg)  
+Figure 3. Architecture of our model for continuous BVP estimation from eye tracking videos and consecutive HR computation.
+
+ratio (SNR). In contrast, when qualitatively analyzing eye tracking images, we see that the skin around the eyes exhibits considerably less motion than the eyes themselves and could thus provide a more stable source of BVP information. To address this, we introduce spatial attention modules [32, 64, 86] before each pooling (see Fig. 3) to allow our network to focus on high-SNR regions, such as the skin, and reduce the influence of low-SNR regions with frequent motion, like the eyes. Given some feature map  $\pmb{F} \in \mathbb{R}^{T \times C \times w \times h}$ , the spatial attention modules infer a spatial attention map  $M_{s} \in \mathbb{R}^{T \times 1 \times w \times h}$  as:
+
+$$
+M _ {s} (\boldsymbol {F}) = \sigma * (f ^ {7 \times 7} ([ \boldsymbol {F} _ {a v g}; \boldsymbol {F} _ {m a x} ])) \qquad (4)
+$$
+
+where  $\sigma$  is the sigmoid function,  $f^{7\times 7}$  a  $7\times 7$  convolution operation and  $F_{avg}\in \mathbb{R}^{T\times 1\times w\times h}$  and  $F_{max}\in \mathbb{R}^{T\times 1\times w\times h}$  are the average-pooled and max-pooled feature maps respectively. The final output  $F_{out}\in \mathbb{R}^{T\times C\times w\times h}$  of each attention process is then the product of  $M_{s}$  and  $F$ .
+
+Data augmentation. Furthermore, individual variations in the fit of the glasses result in different parts of the skin around the eyes being visible. For some individuals, the eye tracking cameras capture only the areas above the eyes, for others, only below, and in some cases, the glasses sit at an incline (see Fig. 4). To account for such variations, we apply three targeted data augmentations during training that reflect these specific differences in camera angles and coverage: (1) random rotation between -20 and +20 degrees to account for slight inclinations; (2) random horizontal cropping to help the network distinguish between high and low SNR regions across various skin areas and camera positions; and (3) horizontal and vertical flipping to further increase robustness to differences in skin region visibility. Our model requires approximately 399 GFLOPS per batch and has about 12M parameters. The frame rate is 2.9k fps on an RTX 4090 and 180 fps on an AMD EPYC CPU.
+
+# 5.3. Experiments setup
+
+Training. We trained all models using five-fold cross-validation split by participants to ensure a strict separation
+
+![](images/f6d0a910c278ba737a6985df2b7b4e1a99484842a4fbb3b64b5c57fbd2575ff1.jpg)
+
+![](images/bfc2ee38dde9f796edbb9b2b4694fdf8cef874b1432f78d7367b8187a063b113.jpg)
+
+![](images/5f67eeb752fc6c48a4757fdce41297ac772e221d5681760856c2cc0fde0a378a.jpg)  
+Figure 4. Left: Head geometry determines the regions that the eye tracker captures. Right: Learned spatial attention maps show that eye regions are excluded and PulseFormer instead extracts BVP from the surrounding skin regions, which moves less than the eyes.
+
+![](images/0f284d013faa6627b596f3cf454a5f32b804828e9413da1f886aa443973aee72.jpg)
+
+![](images/5def554dd65694728f438df85033d819b23949efb22d263584d4c3dc9062be10.jpg)
+
+![](images/48418df0a743d2836e0283a0c440a0921d88df1887088e537c2c36bafdc2819c.jpg)
+
+between training, validation, and test sets. We iteratively held out the data from five participants (20%) as the test set, two as validation, and trained on the remaining with a batch size of 4 for 100 epochs, a learning rate of 0.0009, and mean squared error (MSE) as loss. In addition to our model, we used ten state-of-the-art rPPG baseline networks to compare the performance of our proposed model to these established models. Our model was trained on a GeForce RTX 4090, with a total runtime of about 20 hours for all folds.
+
+Evaluation. To calculate the HR, we filter the predicted BVP with a Butterworth filter  $(0.5 - 2.8\mathrm{Hz})$  and then detect peaks. To assess model accuracy, we use the mean absolute error (MAE), root mean squared error (RMSE), mean absolute percentage error (MAPE), and Pearson correlation (r) using a non-overlapping 60-second window [16, 45, 46].
+
+Video sampling rate. While we recorded the eye tracking videos with 30 fps, large-scale datasets such as EgoExo4D [27] or Nymeria [50] used only 10 fps. To assess the impact of reduced fps, we evaluated model performance when (1) downsampling our videos to 10 fps by retaining only every third frame and (2) downsampling to 10 fps, then
+
+linearly interpolating between frames to upsample to 30 fps.
+
+# 6. Downstream use for proficiency estimation
+
+To demonstrate the utility of predicting a user's physiological state for egocentric vision applications, we use the user proficiency estimation benchmark from the EgoExo4D dataset, which contains over 5000 videos from 740 participants performing skilled human activities [27]. This benchmark aims to classify the proficiency of a user (novice, early expert, intermediate expert, late expert) using only egocentric videos  $(Ego)$ , only exocentric videos  $(Exo)$ , or all videos together  $(Ego + Exo)$ . Our goal was to assess if we can improve the performance of the current baseline model (TimeSFformer [5]) when integrating our predicted HR data into the network. This results in three additional configurations: using egocentric/exocentric videos and HR  $(Ego + HR/Exo + HR)$  and using all videos and HR  $(Ego + Exo + HR)$ . To predict the continuous HRs for all EgoExo4D videos, we use PulseFormer, pre-trained on egoPPG-DB.
+
+We implement the TimeSFormer model in exactly the same configuration as for the benchmark results [27] with a clip size of 16 frames and a sampling rate of 16, trained for 15 epochs. We use all videos of the EgoExo4D dataset, for which the proficiency estimation labels are available (using the official benchmark training/validation sets) and which have at least 16 frames at a sampling rate of 16, resulting in 2044 videos. From the official training set, we use  $10\%$  as validation, and the held-out official validation set for testing. We summarize our predicted HR data by calculating five features (mean, STD, minimum and maximum HR, and mean HR change) for the corresponding videos. We integrate these features via normalization and a 50-parameter linear layer whose output we concatenate with the output of TimeSformer's backbone before feeding it into the classification head. We train all models from random initialization and evaluate using top-1 accuracy per EgoExo4D protocol.
+
+# 7. Experiments
+
+# 7.1. Heart rate estimation
+
+# 7.1.1. Signal-processing baseline
+
+We employed signal processing to verify that the BVP signal is present in the eye tracking videos, to determine in which regions the SNR is highest, and to establish a baseline (see Tab. 2). Since the glasses remain mostly stable throughout the recording, we manually define two spatial cropping regions per participant. One region that includes mostly skin, and one region that includes mainly eyes (see Fig. 4). We calculate the mean pixel intensity for both regions, remove motion artifacts by discarding any changes outside the interquartile range and finally filter the signal with a  $4^{\text{th}}$  order Butterworth bandpass filter  $(0.5$  to  $2.8\mathrm{Hz})$  to obtain the BVP (see Fig. 5 in Supplementary).
+
+# 7.1.2. PulseFormer method
+
+Using our proposed network PulseFormer, we obtain an MAE of 7.67 bpm and a correlation of 0.85 between our predicted HR and the ground truth HR (see Tab. 2). This is an improvement of 2.40 bpm  $(23.8\%)$  of the MAE and 0.13 for the correlation compared to the current SOTA FactorizePhys [38]. Split by activity, we obtain the lowest MAE while the participants are watching a video (MAE=5.52 bpm) and the highest MAE during exercising on a bike (MAE=12.91 bpm), which is the task with the highest mean HR (113.1 bpm) and the second highest motion magnitude. In addition, the MAE decreases for all activities when adding MITA, with the greatest performance improvement for dancing. We define the motion magnitude as the root-mean-squared sum of the absolute differences across the 3-axis IMU recorded by the Aria glasses and normalize it between zero and one across all activities to get a measure of motion of each activity. See Fig. 6 (Supplementary) for a boxplot of the MAEs of PulseFormer's predictions. Using signal processing, we obtain an MAE of 12.40 bpm when using the skin region around the eyes and an MAE of 14.60 bpm using the eye regions as input. This is also reflected in the spatial attention maps that our model implicitly learns (see Fig. 4), which exclude the eyes to predict the HR. To qualitatively cross-check these results, Fig. 5 (Supplementary) shows an example plot of the raw mean intensity values (before filtering) of the skin region compared to the eye region, with the BVP clearly visible for the skin region. Tab. 4 shows the results when downsampling our videos to 10 fps. MAE increases to 11.13 bpm and the correlation decreases to 0.7 when training and testing using 10 fps. When upsampling the videos again to 30 fps, the MAE decreases to 10.20 bpm and the correlation increases to 0.77. In Sec. 16 (Supplementary), we show that PulseFormer also outperforms the baselines in a cross-dataset evaluation.
+
+# 7.2. Downstream task: proficiency estimation
+
+Tab. 5 summarizes the results of our experiments to evaluate the value of HR estimation for the proficiency estimation benchmark on EgoExo4D. We see that integrating our predicted HRs into the TimeSFformer model [5] improved accuracy for all scenarios but one (Soccer). We also achieved the highest accuracy for each of these individual scenarios with our HR integration. When combining the egocentric videos with our predicted HRs, we achieved an overall accuracy of  $45.29\%$ , a  $14.1\%$  increase compared to using egocentric videos alone. The largest gains appeared in the cooking and dancing tasks, where accuracy rose from  $20.00\%$  to  $40.00\%$  and from  $43.44\%$  to  $53.27\%$ . Also, when using the egocentric and exocentric videos, and our predicted HRs together, the accuracy increased by  $12.67\%$  (4.94 percentage points) from  $39.00\%$  to  $43.94\%$  compared
+
+<table><tr><td>Model</td><td>MAE</td><td>RMSE</td><td>MAPE</td><td>r</td></tr><tr><td>Yue et al. [94]</td><td>29.63</td><td>32.99</td><td>37.86</td><td>0.1</td></tr><tr><td>DeepPhys [10]</td><td>28.26</td><td>31.97</td><td>36.68</td><td>0.08</td></tr><tr><td>TS-CAN [45]</td><td>26.32</td><td>32.39</td><td>29.13</td><td>0.11</td></tr><tr><td>ContrastPhys+ [81]</td><td>19.12</td><td>24.13</td><td>22.57</td><td>0.21</td></tr><tr><td>RhythmMamba [99]</td><td>15.05</td><td>19.78</td><td>17.46</td><td>-0.16</td></tr><tr><td>Baseline eyes</td><td>14.60</td><td>18.18</td><td>18.37</td><td>0.20</td></tr><tr><td>PhysMamba [90]</td><td>13.94</td><td>16.86</td><td>17.76</td><td>0.61</td></tr><tr><td>RhythmFormer [98]</td><td>13.13</td><td>17.43</td><td>14.73</td><td>0.51</td></tr><tr><td>Baseline skin</td><td>12.40</td><td>15.54</td><td>15.29</td><td>0.50</td></tr><tr><td>PhysNet [92]</td><td>12.09</td><td>15.43</td><td>15.14</td><td>0.66</td></tr><tr><td>PhysFormer [93]</td><td>10.71</td><td>13.97</td><td>12.69</td><td>0.72</td></tr><tr><td>PulseFormer w/o SA</td><td>10.49</td><td>13.62</td><td>12.83</td><td>0.73</td></tr><tr><td>FactorizePhys [38]</td><td>10.07</td><td>13.43</td><td>12.36</td><td>0.67</td></tr><tr><td>PulseFormer w/o MITA</td><td>8.82</td><td>12.03</td><td>10.82</td><td>0.81</td></tr><tr><td>PulseFormer (ours)</td><td>7.67</td><td>10.69</td><td>9.45</td><td>0.85</td></tr><tr><td>Improvement over second-best method</td><td>-2.40</td><td>-2.74</td><td>-2.91</td><td>+0.13</td></tr></table>
+
+Table 2. Results for HR prediction from eye tracking videos using different models (PulseFormer, PulseFormer without SA, PulseFormer without MITA and established rPPG baselines).  
+
+<table><tr><td>Activity</td><td>μ HR</td><td>Motion magnitude</td><td>PulseFormer</td><td>PulseFormer w/o MITA</td></tr><tr><td>Video</td><td>71.5</td><td>0</td><td>5.52</td><td>5.97</td></tr><tr><td>Office</td><td>75.7</td><td>0.45</td><td>7.50</td><td>8.22</td></tr><tr><td>Kitchen</td><td>85.3</td><td>0.54</td><td>7.22</td><td>8.89</td></tr><tr><td>Dancing</td><td>89.1</td><td>1.00</td><td>7.85</td><td>10.54</td></tr><tr><td>Bike</td><td>113.1</td><td>0.77</td><td>12.91</td><td>14.62</td></tr><tr><td>Walking</td><td>93.7</td><td>0.30</td><td>8.23</td><td>8.29</td></tr></table>
+
+Table 3. Results for HR prediction (MAE) split by activity using PulseFormer and PulseFormer without MITA.  
+
+<table><tr><td>Input video</td><td>MAE</td><td>RMSE</td><td>MAPE</td><td>r</td></tr><tr><td>10 fps (other datasets)</td><td>11.13</td><td>15.18</td><td>12.28</td><td>0.70</td></tr><tr><td>Upsampled to 30 fps</td><td>10.18</td><td>13.07</td><td>12.48</td><td>0.77</td></tr></table>
+
+Table 4. Results for HR prediction with different frame rates. In the first row, we downsample our videos to a frame rate of 10 fps, commonly used by large-scale datasets such as EgoExo4D [27]. In the second row, we first downsample our videos to 10 fps and then upsample them to 30 fps by linearly interpolating between frames.
+
+to using only the egocentric and exocentric videos.
+
+# 8. Discussion
+
+# 8.1. Heart rate estimation
+
+Evaluating PulseFormer on egoPPG-DB, we showed that HR can be reliably predicted from eye tracking videos and IMU signals from unmodified egocentric vision headsets. While SOTA rPPG models (e.g., PhysFormer) achieve MAEs as low as 0.50 bpm [93, 98] on datasets such as UBFC-RPPG [6] or OBF [44], these datasets captured participants while calmly sitting at a table looking at the camera (with very little motion or HR changes). However, during even just light motion (e.g., on MMPD [82] or VIPLHR [63]), their MAE increases to 5.0–12.0 bpm [93, 98].
+
+On egoPPG-DB, which contains much stronger motion (dancing, exercise bike) and HR fluctuations (between 44-164 bpm), PulseFormer's MAE is 7.67 bpm and outperforms the rPPG SOTA FactorizePhys (MAE=10.07 bpm). Given the strong motion and diverse everyday activities in egoPPG-DB, we believe that our results demonstrate the robustness of PulseFormer in dynamic, everyday conditions. For context, even HR estimates from contact sensors tightened to the body (e.g., Apple Watch) yield an MAE of 3.0 bpm during rest and an MAE of 4.6 bpm on a bike [24].
+
+# 8.1.1. Performance depending on method
+
+We introduced MITA and leverage SA modules to improve the performance of our model. The performance of PulseFormer decreases from 7.67 bpm to 8.82 bpm when removing the MITA and to 10.49 bpm when removing the SA modules (see Tab. 2). When qualitatively analyzing the learned SA maps, we see that our model implicitly learned to exclude the eyes for estimating BVP from the eye tracking videos (see Fig. 4). This aligns with our results using signal processing, obtaining better performance for the skin region compared to the eyes (see Tab. 2).
+
+# 8.1.2. Performance depending on activity
+
+Analyzing our results split by activity (see Tab. 3), we obtain the highest MAE when exercising on a bike (MAE=12.91 bpm) and the lowest MAE when watching a video (MAE=5.52 bpm). While watching a video yields the lowest MAE, it is higher than MAEs typically reported for rPPG datasets, such as UBFC-RPPG [6], despite similar levels of motion. We attribute this to two factors: first, the higher variability in HR across egoPPG-DB, requiring improved generalization, and second, the inherent motion artifacts in eye tracking videos from blinking and natural eye movements, even during static tasks like watching videos. Such inherent motion artifacts and, e.g., slipping glasses can make capturing rPPG more difficult in this manner. Furthermore, although dancing has the highest motion magnitude, its MAE (7.85 bpm) is comparable to that of lower-motion tasks such as office and kitchen activities. When comparing performance with and without our MITA module, we
+
+<table><tr><td>Scenario</td><td>Majority</td><td>Ego</td><td>Ego + HR (ours)</td><td>Exo</td><td>Exo + HR (ours)</td><td>Ego + Exo</td><td>Ego + Exo + HR (ours)</td></tr><tr><td>Basketball</td><td>38.00</td><td>45.45</td><td>47.47</td><td>48.48</td><td>48.48</td><td>49.49</td><td>50.50</td></tr><tr><td>Cooking</td><td>0.00</td><td>20.00</td><td>40.00</td><td>35.00</td><td>40.00</td><td>25.00</td><td>40.00</td></tr><tr><td>Dancing</td><td>24.59</td><td>43.44</td><td>53.27</td><td>42.62</td><td>48.36</td><td>50.82</td><td>59.84</td></tr><tr><td>Music</td><td>57.89</td><td>78.94</td><td>81.58</td><td>57.89</td><td>57.89</td><td>57.89</td><td>60.53</td></tr><tr><td>Bouldering</td><td>15.29</td><td>24.50</td><td>27.81</td><td>8.61</td><td>12.58</td><td>15.89</td><td>21.19</td></tr><tr><td>Soccer</td><td>62.50</td><td>50.00</td><td>56.25</td><td>81.25</td><td>75.00</td><td>75.00</td><td>62.50</td></tr><tr><td>Overall</td><td>27.80</td><td>39.69</td><td>45.29</td><td>34.75</td><td>37.67</td><td>39.00</td><td>43.94</td></tr></table>
+
+Table 5. Results for proficiency estimation benchmark on EgoExo4D dataset. Note that for all scenarios except Soccer, the accuracy increases when integrating PulseFormer's heart rate estimate into the existing and otherwise unmodified baseline model.
+
+observe an improvement of  $2.6\mathrm{~bpm}$  for dancing, indicating that MITA effectively addresses motion-induced artifacts.
+
+# 8.1.3. Performance depending on camera fps
+
+Using eye tracking videos recorded at only 10 fps considerably decreases performance (see Tab. 4). However, up sampling the frame rate to 30 fps through linear interpolation between frames substantially improves the performance again. This is especially important as many large-scale datasets, such as EgoExo4D [27] or Nymeria [50], for which predicting a user's physiological state could help for further downstream tasks, are recorded at only 10 fps.
+
+# 8.2. Benefits for proficiency estimation downstream
+
+We found that incorporating HR data into the baseline model of the proficiency estimation task substantially improved accuracy across all three configurations. The egocentric videos combined with the HR achieved the highest overall accuracy at  $45.29\%$ , marking a  $14.1\%$  increase over using only egocentric videos  $(39.69\%)$ . Adding HR especially improved accuracy for cooking (from  $20\%$  to  $40\%$ ) and dancing (from  $43.44\%$  to  $53.27\%$ ), which had the lowest accuracies besides bouldering when using only egocentric videos, demonstrating the value of HR in enhancing model performance. Combining egocentric videos, exocentric videos, and HR provided further accuracy gains for some scenarios, achieving the best results for basketball, cooking, and dancing. Results using exocentric views alone were lower overall, which is consistent with benchmark results [27]. Soccer was the only scenario, for which the performance decreased for  $Exo+HR$  and  $Ego+Exo+HR$ . We see two reasons for that. 1) Of EgoExo4D's 2044 official train/test videos, only 77 are soccer, making it the scenario with the least training/test data by far. 2) Our HR estimates may be less accurate for "Stop-and-Go" sports, which are not captured in egoPPG-DB right now. In Tab. 9 (Supplementary), we show that we obtain the best downstream performance when using the HR features calculated with PulseFormer compared to the baselines. For training and testing, we used the available subset of EgoExo4D videos
+
+for which proficiency labels are available, following the official training and test splits. While our used data shows slight variations from the official release in majority class distributions and accuracy scores, the observed trends align well with the established benchmark results.
+
+# 8.3. Broader impacts
+
+Beyond health applications, such as predicting stress and fatigue [9, 60, 65], cardiac measurements could also help models better understand user behavior to, e.g., improve personalized assistance [42]. Furthermore, we believe that our approach requires the user's explicit consent, regardless of application. Mechanisms must make users aware of measurements and require consent, e.g., on the Aria platform.
+
+# 9. Conclusion
+
+egoPPG is a novel task for egocentric vision systems to extract the wearer's heart rate for integrating their physiological state into egocentric vision tasks downstream. We have introduced PulseFormer, a method that processes input from the eye tracking cameras on unmodified egocentric vision systems and fuses them with motion cues from the headset's IMU to robustly estimate the person's HR in various everyday scenarios. We validate PulseFormer's robustness on our dataset egoPPG-DB and demonstrate significant improvements over existing rPPG models. With HR estimations from PulseFormer, we also significantly improve the proficiency estimation benchmark on the largescale EgoExo4D dataset. Our results emphasize the potential of physiological insights obtained via egoPPG methods for further egocentric vision applications. By making our dataset available to the community, we aim to support physiological state estimation via HR in future research and new downstream tasks for egocentric vision systems. Given our promising results, we believe that future work could now focus on collecting more participants with a broader demographic background across different age groups, skin types, and ethnicities, and also extend data collection to outdoor settings to assess the impact of varying lighting conditions.
+
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+# iManip: Skill-Incremental Learning for Robotic Manipulation
+
+Zexin Zheng $^{1*}$ , Jia-Feng Cai $^{1*}$ , Xiao-Ming Wu $^{1}$ , Yi-Lin Wei $^{1}$
+
+Yu-Ming Tang $^{1}$ , Ancong Wu $^{1,2\dagger}$ , Wei-Shi Zheng $^{1,2\dagger}$
+
+$^{1}$ School of Computer Science and Engineering, Sun Yat-sen University, China  $^{2}$ Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education, China
+
+{zhengzx25, caijf23}@mail2.sysu.edu.cn wuanc@mail.sysu.edu.cn wszheng@ieee.org
+
+# Abstract
+
+The development of a generalist agent with adaptive multiple manipulation skills has been a long-standing goal in the robotics community. In this paper, we explore a crucial task, skill-incremental learning, in robotic manipulation, which is to endow the robots with the ability to learn new manipulation skills based on the previous learned knowledge without re-training. First, we build a skill-incremental environment based on the RLBench benchmark, and explore how traditional incremental methods perform in this setting. We find that they suffer from severe catastrophic forgetting due to the previous methods on classification overlooking the characteristics of temporality and action complexity in robotic manipulation tasks. Towards this end, we propose an incremental Manipulation framework, termed iManip, to mitigate the above issues. We firstly design a temporal replay strategy to maintain the integrity of old skills when learning new skill. Moreover, we propose the Extendable PerceiverIO, consisting of an action prompt with extendable weight to adapt to new action primitives in new skill. Extensive experiments show that our framework performs well in Skill-Incremental Learning.
+
+# 1. Introduction
+
+Imagine that we are in a household setting with a robot assistant that already has basic functions like folding clothes and fetching items. Now, as the owners, we want it to learn new skills. For instance, today we've purchased a dishwasher, and we'd like the robot to learn how to load dishes into it. It could quickly acquire these new skills by observing and mimicking our demonstrations. This is an interesting and challenging requirement for robotics manipulation, which needs the robot to learn new skills based on previously learned knowledge without retraining. However, in the area of robotic manipulation, previous research mainly
+
+![](images/6b85a78518db05dc9b1a8f9d5b967e11ffa78553939d675199133c1cb795ff56.jpg)  
+Figure 1. (a) An overview of our skill-incremental learning for robotic manipulation that requires the agent to learn skill sequences over time. (b) A comparison of model performance between the traditional incremental baseline (TIB) and our iManip.
+
+focuses on how to acquire better manipulation performance [6, 38, 47, 57, 69] or how to transfer the knowledge from the pretrained large language or vision models [4, 10, 21, 30] to learn robotics manipulations, rarely works explore how to incrementally learn new skills. LIBERO [35] is a preliminary benchmark to learn lifelong robotics control, but it explores the incremental abilities in new objects or new spatial positions, still limited in the characteristics of the same skills, where different tasks share the same skill.
+
+In this paper, we thoroughly explore this crucial task, skill-incremental learning, in robotic manipulation, which is to leverage the previous learned knowledge to enable the robots to learn new manipulation skills without training from scratch. To begin with, we construct a skill-
+
+incremental environment based on the RLBench benchmark. It requires the agent to continuously acquire a sequence of 10 challenging language-conditioned manipulation skills. Each skill consists of at least two variations encompassing several types, such as variations in shape and color, totaling 166 variations. Then, we explore how the traditional incremental learning methods work on this skill-incremental environment. As seen in Figure 1, we discover that after learning new manipulation skills, the agent's performance on prior skills significantly deteriorates. Thus, we can conclude that traditional incremental learning methods still suffer from catastrophic forgetting in this new setting, which, we regard, is due to their neglect of the temporality and action complexity in robotic manipulation tasks. The temporal complexity arises from the dynamic changes in the environment and in the robot states over time, resulting in each action having an impact on subsequent actions. And the complexity of actions requires the agent to learn new action primitives for action planning in novel environments and interactions, which is representative in 3D dimensions with rotation and shift, and highly complex.
+
+To mitigate the above problems, we propose a new skill incremental Manipulation framework, termed iManip, for this new setting. The key idea of our framework is to modify the traditional incremental learning methods to fully consider the characteristics of temporality and action complexity in robotic manipulation tasks. Two designs make our framework nontrivial. First, to address temporal complexity, we design the temporal replay strategy to maintain the integrity of the temporal data and propose to replay a fixed number of keyframe samples at different time points for each manipulation skill, using the farthest-distance entropy sampling strategy. Second, to address the complexity of actions, we propose the Extendable PerceiverIO, consisting of an action prompt with extendable weight to adapt to new action primitives. When learning new skills, we freeze the learned parameters of PerceiverIO while learning a new small set of skill-specific action prompts and weight matrices for new action primitives learning.
+
+Extensive experiments show that our iManip framework maintains several excellent capabilities: (1) Effectiveness: it performs well in the skill-incremental learning setting, outperforming the traditional incremental baseline with an increase of 9.4 points. (2) Robustness: it demonstrates robust performance in several different incremental settings. (3) Lightweight: it only needs lightweight finetuning of the policy decoder with fewer training steps, comparable with full weights finetuning. (4) Extendability: it also has extraordinary performance in real-world experiments.
+
+# 2. Related Work
+
+Robotic Manipulation. Learning robot manipulation conditioned on both vision and language has gained increas
+
+ing attention [11, 16-18, 49, 50, 53, 58-60, 63, 65], with robot imitation learning using scripted trajectories [23, 39] or tele-operation data [12, 42, 62] gradually becoming a mainstream approach. Previous work [5, 13, 24] has focused on using 2D images to predict actions, while more recent studies have leveraged the rich spatial information of 3D point clouds for motion planning. For instance, PerAct [51] feeds voxel tokens into a PerceiverIO [22]-based transformer policy, achieving impressive results across various tasks. GNFactor [67] optimizes a generalizable neural field for semantic extraction, while ManiGaussian [37] introduces a dynamic Gaussian Splatting [27] framework for semantic propagation. 3DDA [26] proposes a 3D denoising transformer to predict noise in noised 3D robot pose trajectories. However, these methods suffer from catastrophic forgetting in skill-incremental learning and we propose our iManip framework to continuously learn new skills and mitigate forgetting of learned knowledge.
+
+Conventional Lifelong Learning Approaches. One of the most commonly used methods is the rehearsal-based method [2, 8, 9, 19, 20, 25, 33, 46, 54, 56]. iCaRL [46] proposes a herding-based step for prioritized exemplar selection to store old exemplars. RWalk [8] proposes a hard-exemplar sampling strategy for replay. Distillation-based methods [7, 14, 19, 31, 34, 52, 55, 68] propose distilling old knowledge from the old network to the current network or maintaining the old feature space during new tasks. ABD [52] proposes distilling synthetic data for incremental learning and EEIL [7] proposes to distill the knowledge from the classification layers of the old classes. Moreover, there are dynamic-architecture-based methods [1, 32, 36, 43, 44, 66] that dynamically adjust the model's representation ability to fit the evolving data stream. In this work, we use the traditional rehearsal-based method [46] and the distillation-based methods [7] for robotic skill-incremental learning. We find that they also suffer from catastrophic forgetting due to overlooking the temporal and action complexities of robotic manipulation.
+
+A Preliminary Lifelong Robot Learning Benchmark LIBERO. Previous works [15, 28, 29, 40, 41, 61] explore different strategies for incremental robotic learning based on different testing environments. Recently, to promote community development, LIBERO [35] proposed a benchmark, which explores incremental abilities with new objects, goals, or spatial positions, as shown in Figure 2. The limitation of LIBERO lies in the fact that most tasks are constrained by similar skill characteristics. For example, it regards "Put the bowl on the plate" and "Put the bowl on stove" as different tasks. In this paper, we explore a more realistic and challenging task, skill-incremental learning, where the agent learns a sequence of skills over time, each involving multiple poses and object variations in placement, color, shape, size, and category.
+
+![](images/9e9a8f717d27a1ead0e89bee60f2db6f54dfa0c183e497bed7b66e01ea6cedcc.jpg)  
+Figure 2. Overview of robotic incremental learning. Previous works focus on incremental abilities in new objects, goals, or spatial positions, where different tasks may share the same skill. The iManip focuses on skill-incremental learning which better captures the true adaptability and flexibility required for real-world robotic learning.
+
+# 3. Skill-incremental Learning for Robotic Manipulation
+
+# 3.1. Challenges
+
+While robotic manipulation has received increasing attention, few previous studies explore how to incrementally learn new skills. In this paper, we focus on skill-incremental learning for robotic manipulation, a challenging setting that requires agents to continuously acquire new skills without training from scratch.
+
+In this new setting, we find that applying traditional incremental learning methods [7, 8, 37, 46, 51] still suffers from catastrophic forgetting of previously learned skills, as seen in Figure 1 (b). There are two key challenges when applying previous methods of visual classification to robotic skill-incremental learning: 1) Previous methods overlook the temporal complexity inherent in robotic manipulation tasks, where dynamic changes in the environment and the robot states over time cause actions to impact subsequent ones. For example, classical replay algorithms focus on sampling the most representative samples per class, directly storing representative samples from demonstrations may result in temporal imbalance of the trajectory, leading to instability during task execution. 2) Previous methods focus primarily on general visual features while neglecting the actions complexity in robotic manipulation. Robotic manipulation involves action planning through interactions with the physical environment, such as visual and language input. When a new manipulation skill arises, the agent learns new visual-language interactions and quickly acquires new action primitives based on prior knowledge.
+
+# 3.2. Overall Pipeline
+
+To tackle the two challenges, we propose the temporal replay strategy and the extendable PerceiverIO architecture in our iManip framework. Specifically, as shown in Figure 3, we present the overall framework for robotic skill-incremental learning, which can sequentially learn robotic manipulation skills while mitigating catastrophic forgetting of learned skills. Specifically, the agent learns a sequence of manipulation skills with a stream of training data denoted as  $\mathcal{D} = \{\mathcal{D}_i\}_{i=1}^T$ , where  $\mathcal{D}_i = \{(o_i^{(1)},a_i^{(1)}),(o_i^{(2)},a_i^{(2)}),\ldots\}$  represents the demonstration trajectories of skill  $i$ . The visual input  $o_i^{(t)} = (I_i^{(t)},D_i^{(t)},P_i^{(t)})$  consists of the  $t$ -th single-view images  $I_i^{(t)}$ , depth images  $D_i^{(t)}$ , and proprioception matrix  $P_i^{(t)} \in \mathbb{R}^4$  that includes the openness, end-effector position, and the current timestep. After learning skill  $i$ , a compact memory  $\mathcal{M}$  stores a fixed number of demonstration replays for skills up to  $i-1$ . Following [37, 51, 67], the agent combines the visual input  $o_i^{(t)}$  and language instructions  $l_i$  to generate the optimal action  $a_i^{(t)} = (a_{i,\mathrm{trans}}^{(t)},a_{i,\mathrm{rot}}^{(t)},a_{i,\mathrm{open}}^{(t)},a_{i,\mathrm{col}}^{(t)})$ , which respectively demonstrates the target translation in voxel  $a_{i,\mathrm{trans}}^{(t)} \in \mathbb{R}^{100^3}$ , rotation  $a_{i,\mathrm{rot}}^{(t)} \in \mathbb{R}^{(360/5)\times 3}$ , openness  $a_{i,\mathrm{open}}^{(t)} \in [0,1]$  and collision avoidance  $a_{i,\mathrm{col}}^{(t)} \in [0,1]$ .
+
+Our framework consists of a voxel encoder for learning 3D scene features, a latent transformer (the extendable PerceiverIO), and a policy decoder to predict optimal robot actions. Specifically, our approach employs a temporal replay strategy, maximizing the information entropy of replay demos to effectively address the first challenges caused by
+
+![](images/2cd7c2f50fc3c6e20ad9a895a5c0541d1b8ca0100ab12bb44e9bd9826b5b073b.jpg)  
+Figure 3. The overall framework of iManip, which primarily consists of a temporal replay strategy to store the samples with the farthest distance entropy for each keyframe of old demonstrations and an extendable PerceiverIO consisting of action prompts with extendable weights to adapt to new action primitives.
+
+classic replay methods. Additionally, we introduce the extendable PerceiverIO, consisting of action prompts with extendable weights to adapt to new action primitives, while preserving knowledge of previous skills to prevent catastrophic forgetting.
+
+# 3.3. The iManip Framework
+
+Temporal Replay Strategy. Rehearsal-based methods [8, 19, 46] are classic algorithms in incremental vision classification tasks while overlooking the temporal complexity inherent in robotic manipulation. Apart from random sampling, popular methods such as herding sampling [46] and hard-exemplar sampling [3, 8] effectively select the most representative samples from each class. However, robotic manipulation data consists of temporal samples from entire expert episodes. Directly storing representative samples can lead to temporal imbalance of episodes, resulting in instability during task execution.
+
+Therefore, we propose a temporal replay strategy to balance the sampling of different keyframes of episodes for each skill. Keyframes [51] are the samples from episodes when the end-effector changes state (e.g., gripper closing) or when its velocity approaches zero, representing critical temporal landmarks within the trajectory.
+
+Furthermore, to sample a greater variety of variants, we
+
+propose the farthest-distance entropy sampling to store an equal number of each keyframe. It requires the buffer to contain the replays that exhibit the largest entropy divergence as
+
+$$
+S = \underset {S \in E, | S | = K} {\arg \max } \sum_ {i \in S} \sum_ {j \in S} A [ i ] [ j ], \tag {1}
+$$
+
+where  $S$  is the sampled set with size  $K$ ,  $E$  is the demo set of a specific keyframe with size  $N$ , and  $A$  is the distance array of the demos' action prediction entropy  $\mathcal{L}_{\mathrm{act}}$ . Specifically, we propose to store the demo  $j$  to the replay buffer that has the farthest distance of sampled demos in  $S$  as
+
+$$
+j = \underset {j \in E} {\arg \max } \sum_ {k \in S} A [ j ] [ k ]. \tag {2}
+$$
+
+This ensures the storage of temporally balanced, information-rich samples from previous episodes, helping to mitigate catastrophic forgetting of learned skills.
+
+Based on the above analysis, the pseudocode for the temporal replay strategy is shown in Algorithm 1. The algorithm can get the optimal solution for the objective 1, with time complexity of  $O(N^2)$ , which is the size of a specific keyframe and not relevant to the size of the previous data, suitable for incremental skill learning.
+
+# Algorithm 1 Farthest-distance Entropy Sampling
+
+Require: Entropy set corresponding to the keyframe samples  $E = \{e_1, e_2, \ldots, e_N\}$ , sampling size  $K$
+
+Ensure: Sampled set  $S = \{s_1, s_2, \ldots, s_K\}$
+
+1: Calculate the distance array  $A$ , where  $A[i][j] = \text{distance}(e_i, e_j)$  
+2: Select the sample  $i$  and add to  $S$ , where  $i = \arg \max_{1 \leq i \leq N} \sum_{j=1}^{N} A[i][j]$  
+3: for  $k = 2$  to  $K$  do  
+4: Find the value in  $E$  that has the largest difference with the values in  $S$ ,
+
+$$
+j = \operatorname *{arg  max}_{j\in E}\sum_{k\in S}A[j][k]
+$$
+
+5: Add sample  $j$  to  $S$  as the  $k$ -th sample
+
+6: end for  
+7: return Sampled set  $S$
+
+Extendable PerceiverIO. Unlike traditional vision classification tasks, robotic manipulation requires the integration of multiple modalities to enable complex decision-making and long-term action planning through interactions with the physical environment. Classic methods [7, 8, 19, 46] for lifelong classification overlook the complexities of action in robotic manipulation tasks that require the agent to learn various action primitives for different skills. In our iManip framework, we propose an extendable PerceiverIO, which learns skill-specific action prompts with extendable weights to adapt to new action primitives.
+
+Specifically, as illustrated in Figure 3, the input to the extendable PerceiverIO consists of multimodal patches,  $X = [X_{\mathrm{voxel}}, X_{\mathrm{language}}, X_{\mathrm{action}}]$ , where  $X_{\mathrm{voxel}}$  and  $X_{\mathrm{language}}$  represent the input sequences of voxel and language encodings, respectively, and  $X_{\mathrm{action}} = [X_{\mathrm{action}}^{\mathrm{old}}, X_{\mathrm{action}}^{\mathrm{new}}]$  is the skill-specific action prompt that concatenates both the old and new action prompts. The notation  $[\cdot, \cdot]$  denotes the concatenation operation along the token dimension. Subsequently,  $X$  undergoes a cross-attention computation between the input and a much smaller set of latent vectors through the latent encoder, producing  $X_{\mathrm{latent}}$ . Then  $X_{\mathrm{latent}}$  is encoded with weight-extendable self-attention layers as
+
+$$
+\begin{array}{l} Q = X _ {\text {l a t e n t}} \cdot W _ {Q} ^ {\text {s c a l e}}, \quad K = X _ {\text {l a t e n t}} \cdot W _ {K} ^ {\text {s c a l e}}, \tag {3} \\ V = X _ {\text {l a t e n t}} \cdot W _ {V}, \\ \end{array}
+$$
+
+$$
+X _ {\text {a t t}} = \operatorname {s o f t m a x} \left[ \frac {Q \cdot K ^ {\top}}{\sqrt {d}} \right] \cdot V, \tag {4}
+$$
+
+where  $X_{\mathrm{latent}}, X_{\mathrm{att}} \in \mathbb{R}^{T \times d}$  are respectively a set of  $T$  input and output tokens with channel dimension  $d$ ,  $W_{Q}^{\mathrm{scale}}, W_{K}^{\mathrm{scale}} \in \mathbb{R}^{d \times d'}$ ,  $W_{V} \in \mathbb{R}^{d \times d}$  are learnable weight matrices. Notably,  $W_{Q}^{\mathrm{scale}}, W_{K}^{\mathrm{scale}}$  are extendable by appending newly weight matrices  $W_{Q}^{\mathrm{new}}$ ,  $W_{K}^{\mathrm{new}} \in \mathbb{R}^{d \times d_{\mathrm{new}}}$  as
+
+$$
+W _ {Q} ^ {\text {s c a l e}} = \left[ W _ {Q} ^ {\text {o l d}}, W _ {Q} ^ {\text {n e w}} \right], \quad W _ {K} ^ {\text {s c a l e}} = \left[ W _ {K} ^ {\text {o l d}}, W _ {K} ^ {\text {n e w}} \right], \tag {5}
+$$
+
+where  $W_{Q}^{\mathrm{old}}, W_{K}^{\mathrm{old}} \in \mathbb{R}^{d \times d_{\mathrm{old}}}$  are the old weight matrices and the expanded dimension  $d' = d_{\mathrm{old}} + d_{\mathrm{new}}$ . Finally, these encoded latents are cross-attended with the input once again through the latent decoder to ensure alignment with the input size. In our iManip framework, we freeze the old PerceiverIO while learning the action prompts  $X_{\mathrm{action}}^{\mathrm{new}}$  and a small set of newly weight matrices  $W_{Q}^{\mathrm{new}}, W_{K}^{\mathrm{new}}$  of new skills. This enables the agent to quickly adapt to new action primitives while preventing the forgetting of previous skills.
+
+Knowledge distillation between the old and new agents. To better preserve the knowledge of previous skills while learning new ones, we employ knowledge distillation [7, 64], where the output probability distribution of the old model is used to train the new model. This enables the transfer of knowledge from the old to the new agent, as defined by the following objective:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {d i s}} = \mathcal {L} _ {2} \left(\mathcal {Q} _ {\text {t r a n s}} ^ {\text {o l d}}, \mathcal {Q} _ {\text {t r a n s}} ^ {\text {n e w}}\right) + \mathcal {L} _ {2} \left(\mathcal {Q} _ {\text {r o t}} ^ {\text {o l d}}, \mathcal {Q} _ {\text {r o t}} ^ {\text {n e w}}\right) + \\ \left| \mathcal {Q} _ {\text {o p e n}} ^ {\text {o l d}} - \mathcal {Q} _ {\text {o p e n}} ^ {\text {n e w}} \right| + \left| \mathcal {Q} _ {\text {c o l l i d e}} ^ {\text {o l d}} - \mathcal {Q} _ {\text {c o l l i d e}} ^ {\text {n e w}} \right|, \\ \end{array}
+$$
+
+where  $\mathcal{L}_2$  is the MSE loss,  $[\mathcal{Q}_{\mathrm{trans}}^{\mathrm{old}},\mathcal{Q}_{\mathrm{rot}}^{\mathrm{old}},\mathcal{Q}_{\mathrm{open}}^{\mathrm{old}},\mathcal{Q}_{\mathrm{collide}}^{\mathrm{old}}]$  and  $[\mathcal{Q}_{\mathrm{trans}}^{\mathrm{new}},\mathcal{Q}_{\mathrm{rot}}^{\mathrm{new}},\mathcal{Q}_{\mathrm{open}}^{\mathrm{new}},\mathcal{Q}_{\mathrm{collide}}^{\mathrm{new}}]$  denote the probabilities of the ground truth actions in expert demonstrations for translation, rotation, gripper openness, and collision avoidance for the old and new robots, respectively.
+
+# 3.4. Learning Objectives
+
+Our approach is to address the problem of skill-incremental learning for robotic manipulation from multiple aspects. First, for each manipulation skill, there is an action loss to facilitate robot imitation learning. Following [37, 51, 67], we employ cross-entropy loss (CE) to ensure accurate action prediction:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {a c t}} = - \mathbb {E} _ {Y _ {\text {t r a n s}}} [ \log \mathcal {V} _ {\text {t r a n s}} ] - \mathbb {E} _ {Y _ {\text {r o t}}} [ \log \mathcal {V} _ {\text {r o t}} ] \tag {7} \\ - \mathbb {E} _ {\mathcal {Y} _ {\text {o p e n}}} \left[ \log \mathcal {V} _ {\text {o p e n}} \right] - \mathbb {E} _ {\mathcal {Y} _ {\text {c o l l i d e}}} \left[ \log \mathcal {V} _ {\text {c o l l i d e}} \right], \\ \end{array}
+$$
+
+where  $\mathcal{V}_i = \mathrm{softmax}(\mathcal{Q}_i)$  for  $\mathcal{Q}_i\in [\mathcal{Q}_{\mathrm{trans}},\mathcal{Q}_{\mathrm{open}},\mathcal{Q}_{\mathrm{rot}},$ $\mathcal{Q}_{\mathrm{collide}}]$  and  $Y_{i}\in [Y_{\mathrm{trans}},Y_{\mathrm{rot}},Y_{\mathrm{open}},Y_{\mathrm{collide}}]$  is the ground truth one-hot encoding.
+
+Furthermore, when learning new skills, we propose the temporal replay strategy to preserve a fixed number of representative samples from old demonstrations. The cached memory  $\mathcal{M}$  will be used in conjunction with the new skill demos  $\mathcal{D}_{\mathrm{new}}$  for learning new skills. Additionally, our extendable PerceiverIO will dynamically expand new learnable weights for the new skill. We find that training only the skill-specific action prompts  $X_{\mathrm{action}}^{\mathrm{new}}$  with newly appended weights  $W_{Q}^{\mathrm{new}}$ ,  $W_{K}^{\mathrm{new}}$  and the policy decoder effectively prevents catastrophic forgetting, more analysis can be seen in the 3rd experiments in Section 4.2. Finally, we employ knowledge distillation loss  $\mathcal{L}_{\mathrm{dis}}$  to help the agent retain the knowledge of previous skills. Overall, in skill-incremental
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">Base</td><td colspan="2">Step 1</td><td colspan="2">Step 2</td><td colspan="2">Step 3</td><td colspan="2">Step 4</td><td colspan="2">Step 5</td><td colspan="2">Average</td></tr><tr><td>Old</td><td>All</td><td>Old</td><td>All</td><td>Old</td><td>All</td><td>Old</td><td>All</td><td>Old</td><td>All</td><td>Old</td><td>All</td></tr><tr><td colspan="14">multi-task methods</td></tr><tr><td>PerAct [51]</td><td>44.0</td><td>4.0</td><td>7.3</td><td>2.7</td><td>5.1</td><td>1.1</td><td>9.0</td><td>2.5</td><td>6.7</td><td>1.3</td><td>1.6</td><td>2.3</td><td>5.9</td></tr><tr><td>ManiGaussian [37]</td><td>55.2</td><td>12.0</td><td>20.7</td><td>6.7</td><td>12.0</td><td>5.7</td><td>15.5</td><td>3.0</td><td>9.3</td><td>5.3</td><td>5.2</td><td>6.5</td><td>12.5</td></tr><tr><td colspan="14">skill-incremental methods</td></tr><tr><td>P-TIB [7, 46, 51]</td><td>44.0</td><td>33.6</td><td>34.7</td><td>26.0</td><td>25.1</td><td>22.3</td><td>26.0</td><td>17.0</td><td>16.4</td><td>11.6</td><td>10.4</td><td>22.1</td><td>22.5</td></tr><tr><td>M-TIB [7, 37, 46]</td><td>55.2</td><td>42.4</td><td>45.3</td><td>36.7</td><td>37.1</td><td>34.3</td><td>39.5</td><td>31.0</td><td>31.6</td><td>29.8</td><td>26.8</td><td>34.8</td><td>36.1</td></tr><tr><td>Ours (iManip)</td><td>56.0</td><td>57.6</td><td>56.7</td><td>50.7</td><td>48.0</td><td>45.1</td><td>47.5</td><td>42.0</td><td>39.1</td><td>38.7</td><td>36.0</td><td>46.8</td><td>45.5</td></tr></table>
+
+learning, our training loss is formulated as follows:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {a c t}} + \lambda_ {\text {d i s}} \mathcal {L} _ {\text {d i s}}, \tag {8}
+$$
+
+where  $\lambda_{\mathrm{dis}}$  is a hyperparameter that controls the importance of the knowledge distillation loss  $\mathcal{L}_{\mathrm{dis}}$  during training.
+
+# 4. Experiments
+
+# 4.1. Experimental setup and details
+
+Experimental setup. Following [37, 67], we select 10 representative manipulation skills in RLBench[23] and 5 daily manipulation skills in the real world for our experiments. Each skill has at least two variations and 20 demonstrations during training that cover multiple types, such as position, shape, and color. To achieve a high success rate for these skills, the manipulation policy needs to learn generalizable knowledge rather than overfitting the limited given demonstrations. For visual observation, we only use the front RGB-D image with  $128 \times 128$  resolutions. To demonstrate the performance of our method under different incremental settings, we define several configurations, represented as Bn-kNm. This notation indicates that the policy is initially trained on n base skills, followed by the addition of m new skills in each step, with a total of k steps.
+
+Evaluation Metric. We report the performance of the agent on each learned skill by the average success rate. At each incremental step, we present the average success rate for old, new, and all (combined old and new) skills. In the simulation, we evaluate the agent with 25 episodes per skill, whereas in the real world, we use 10 episodes per skill. During evaluation, the agent continues to take actions until an oracle signals task completion or the agent reaches a maximum of 25 steps.
+
+Implementation Details. For model design, we use different encoders to transform corresponding modality data into tokens, which serve as the input for the Extendable PerceiverIO. The RGB-D images are projected and transformed into voxels, which are then encoded by a 3D convolutional encoder with a UNet architecture, while text instructions are encoded using CLIP RN50 [45], and the proprioception data is encoded by a single-layer MLP. After
+
+Table 1. Performance comparison of different methods of B5-5N1 in Rlbench. We show the average success rate of old and all learned skills, and the average performance of all new steps. The traditional incremental methods [7, 46] on baseline [37, 51] is termed TIB.  
+
+<table><tr><td></td><td>TRS</td><td>EPIO</td><td>DIS</td><td>B5-1N1</td><td>B5-5N1</td></tr><tr><td>R1</td><td></td><td></td><td></td><td>20.7</td><td>5.2</td></tr><tr><td>R2</td><td>✓</td><td></td><td></td><td>49.3</td><td>27.6</td></tr><tr><td>R3</td><td>✓</td><td>✓</td><td></td><td>54.0</td><td>32.4</td></tr><tr><td>Ours</td><td>✓</td><td>✓</td><td>✓</td><td>56.7</td><td>36.0</td></tr></table>
+
+Table 2. Ablation Study on two experiment setup. We report the average success rate of all learned skills.
+
+encoding, the tokens from all modalities have the same dimension of 512. The hyperparameter  $\lambda_{\mathrm{dis}}$  is set as 0.01 and the action prompt length is 16. We store 2 keyframe replays of the total 20 demonstrations of learned skills and train the agent on two NVIDIA RTX 4090 GPUs with a batch size of 1, a learning rate of 0.002, and 100k iterations. More studies about the hyperparameters are shown in the Appendix.
+
+# 4.2. Simulation results
+
+Performance comparison with different methods. We conduct the skill-incremental learning experiment in the B5-5N1 setting, where we first train the policy on five base skills and then gradually learn a new skill at each subsequent step with a total of five steps.
+
+To demonstrate the performance of our method in robotic skill-incremental learning, we compare with two standard multi-task manipulation policies, PerAct [51] and Mani-Gaussian [37], by retraining the agent to learn new manipulation skills. Furthermore, we apply two Traditional Incremental Baselines (TIB) for visual classification to the above policies for comparison, termed P-TIB and M-TIB respectively. As shown in Table 1, the results demonstrate that the performance of our method significantly outperforms the others at each subsequent step. This demonstrates that our method better facilitates the learning of new skills while mitigating the forgetting of previous skills. More detailed results of each learning skill at every step are shown in the Appendix.
+
+Ablation Study. We conduct the ablation study to validate the effectiveness of each policy, as shown in Table 2. R1 is the control group where the agent does not have any incremental policy. When we add the Temporal Replay Strategy
+
+<table><tr><td rowspan="2">Frozen layer</td><td rowspan="2">Convergence steps</td><td rowspan="2">Trained param</td><td colspan="2">Slide block</td><td colspan="2">Put in drawer</td><td colspan="2">Drag stick</td><td colspan="2">Push buttons</td><td colspan="2">Stack blocks</td></tr><tr><td>Old</td><td>New</td><td>Old</td><td>New</td><td>Old</td><td>New</td><td>Old</td><td>New</td><td>Old</td><td>New</td></tr><tr><td>Non-frozen</td><td>100000</td><td>47M</td><td>43.2</td><td>60.0</td><td>44.8</td><td>16.0</td><td>40.8</td><td>92.0</td><td>44.0</td><td>28.0</td><td>45.6</td><td>12.0</td></tr><tr><td>Encoder</td><td>75000</td><td>37M</td><td>50.4</td><td>54.0</td><td>51.2</td><td>12.0</td><td>45.6</td><td>88.0</td><td>48.4</td><td>24.0</td><td>52..0</td><td>8.0</td></tr><tr><td>EPIO</td><td>70000</td><td>18M</td><td>52.0</td><td>52.0</td><td>52.8</td><td>16.0</td><td>46.4</td><td>84.0</td><td>50.4</td><td>24.0</td><td>49.6</td><td>8.0</td></tr><tr><td>Decoder</td><td>75000</td><td>39M</td><td>45.6</td><td>24.0</td><td>47.2</td><td>0.0</td><td>42.4</td><td>40.0</td><td>44.8</td><td>4.0</td><td>46.4</td><td>0.0</td></tr><tr><td>Encoder+EPIO</td><td>60000</td><td>8M</td><td>57.6</td><td>52.0</td><td>56.8</td><td>12.0</td><td>50.4</td><td>84.0</td><td>55.2</td><td>20.0</td><td>56.0</td><td>8.0</td></tr></table>
+
+Table 3. Performance of five sets B5-1N1 experiments with the same base skills and different new skills, while freezing different network layers. For each new skill, we train a total of 100k iterations and report the average success rate and the average model convergence steps.  
+
+<table><tr><td>Methods</td><td>B5-1N5</td><td>B2-4N2</td><td>B3-2N3</td></tr><tr><td>ManiGaussian [37]</td><td>25.6</td><td>10.4</td><td>17.3</td></tr><tr><td>M-TIB [7, 37, 46]</td><td>30.8</td><td>28.4</td><td>33.3</td></tr><tr><td>Ours (iManip)</td><td>37.2</td><td>36.8</td><td>41.3</td></tr></table>
+
+Table 4. Average success rate of all learned skills on different skill-incremental setup.
+
+(TRS) to the agent, the setup of B5-1N1 and B5-5N1 improve by  $28.6\%$  and  $22.4\%$  in the success rate, respectively (see R2). The significant performance improvement stems from the success of our temporal replay strategy that maintains the integrity of the temporal data.
+
+When we add Extendable PerceiverIO (EPIO) to the agent, the success rates of B5-1N1 and B5-5N1 further improve by  $4.7\%$  and  $4.8\%$ , respectively (see R3). The EPIO design works because the skill-specific action prompts help the agents incrementally learn action primitives for new skills, and the extendable weights designed in transformer blocks allow the model to preserve the old knowledge while adapting to new skills. Our complete policy achieves the best success rate, where the Distillation mechanism (DIS) improves the performance by  $2.7\%$  and  $3.6\%$ , respectively.
+
+Through the ablation study, we find that the replay policy has the greatest impact on overall performance. Without old data for retraining, the agent is more likely to forget previously learned knowledge. This occurs because data plays a crucial role in robotic manipulation, and without the support of previous data, the agent is prone to overfitting the data of new skills.
+
+Effect of parameter freezing on skill-incremental learning. The agent consists of three main components: the encoders, the extendable PerceiverIO, and the policy decoder. we freeze each component individually to evaluate its effect. As shown in Table 3, five sets B5-1N1 experiments on different new skills demonstrate the following: (1) Freezing the encoders or the extendable PerceiverIO helps retain knowledge from the old skills without significantly hindering the learning of the new skill (Lines 1,2,3). (2) The policy decoder is crucial for learning new skills (Lines 1,4). (3) Freezing the above components helps decrease the number of parameters and accelerate convergence.
+
+![](images/8be5d9e6aa45629464b497996141ab6ef5c57c585f78c107da5806e844e8548a.jpg)  
+Figure 4. Average success rate on different replay methods.
+
+Based on these findings, we freeze both the encoder and the extendable PerceiverIO, leaving only the decoder with newly appended action prompts and weights for new skill training, achieving faster convergence, fewer parameters, and better performance (Line 5)!
+
+Experiments on different skill-incremental setup. We implement different skill-incremental settings to validate the generalizability of our method and report the average success rate across all previously learned skills after the last incremental step. As shown in Table 4, compared to Mani-Gaussian and M-TIB, our method achieves higher success rates in all incremental experimental settings. This shows that our approach has stronger performance and better generalization capabilities.
+
+Exploring data replay methods. We compare our temporal replay strategy with the classical rehearsal-based method on the setup of B5-1N1, as shown in Figure 4. Herding [46] and Hardsample [8] are two methods for selecting the most representative samples from the data. Episode refers to replaying a complete trajectory. Random refers to random sampling. The results show that classic herding sampling and hard-exemplar sampling perform poorly on old skills due to neglecting temporal integrity in robotic demonstrations. In contrast, replaying complete trajectories or random sampling better preserves the temporal integrity of the samples, leading to better performance. Our temporal replay strategy, leveraging the farthest-distance entropy sampling for each keyframe can sample more different variants and achieves the best success rate.
+
+<table><tr><td rowspan="2">Manipulation skills</td><td colspan="2">Base</td><td colspan="2">Step 1</td><td colspan="2">Step 2</td><td colspan="2">Step 3</td><td colspan="2">Step 4</td></tr><tr><td>BL</td><td>Ours</td><td>BL</td><td>Ours</td><td>BL</td><td>Ours</td><td>BL</td><td>Ours</td><td>BL</td><td>Ours</td></tr><tr><td>Slide toy</td><td>90.0</td><td>90.0</td><td>10.0</td><td>80.0</td><td>0</td><td>80.0</td><td>0</td><td>60.0</td><td>0</td><td>60.0</td></tr><tr><td>Open drawer</td><td>-</td><td>-</td><td>70.0</td><td>60.0</td><td>0</td><td>60.0</td><td>0</td><td>50.0</td><td>0</td><td>40.0</td></tr><tr><td>Pick and place</td><td>-</td><td>-</td><td>-</td><td>-</td><td>60.0</td><td>60.0</td><td>0</td><td>60.0</td><td>0</td><td>50.0</td></tr><tr><td>Pour water</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>40.0</td><td>40.0</td><td>0</td><td>10.0</td></tr><tr><td>Close jar</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>50.0</td><td>40.0</td></tr><tr><td>Old manipulation skills</td><td>90.0</td><td>90.0</td><td>10.0</td><td>80.0 +70.0</td><td>0</td><td>70.0 +70.0</td><td>0</td><td>56.7 +56.7</td><td>0</td><td>40.0 +40.0</td></tr><tr><td>All manipulation skills</td><td>90.0</td><td>90.0</td><td>40.0</td><td>70.0 +30.0</td><td>20.0</td><td>66.7 +46.7</td><td>10.0</td><td>52.5 +42.5</td><td>10.0</td><td>40.0 +30.0</td></tr></table>
+
+Table 5. Real world experiments. The table reports the success rate of BaseLine (BL) and Ours.  $^{+}\mathrm{num}$  is the improvement of our method compared to the baseline.
+
+![](images/72510ab72b7257097afdda261ff23b985de09f8e1e96f409afc630d98e291b26.jpg)  
+Figure 5. Visualization of skill-specific action prompts by Grad-CAM as the agent executes two manipulation skills: close jar (the first row) and slide block (the second row).
+
+![](images/3addfa99c55557951d287571c934840b0c234fcab7499cac625b3345223c2967.jpg)
+
+Visualization of the skill-specific action prompts. We visualize our skill-specific action prompts by Grad-CAM [48], as shown in Figure 5. Our experiments train the agent in the B5-5N1 setting with totaling 10 action prompts. We first compute the sum of the parameter gradients for each action prompt and then normalize these values to calculate Grad-CAM weights, displayed in different colors. We show the results across two different skills. When the agent executes the same action, e.g., "move down to the target", the third action prompt weight is maximized (see the first column). Furthermore, when performing different actions, different weights of skill-specific action prompts are maximized (see the second column). It demonstrates that action prompts can learn skill-specific action primitives. Freezing old action prompts while learning new ones helps prevent forgetting and adapt to new action primitives.
+
+# 4.3. Real world experiments
+
+We conduct five manipulation skills in the real-world environment to further validate the effectiveness of our method. We use a Franka Panda robotic arm to execute the action and a Realsense D455 camera to capture RGB-D images as
+
+observations. For each training step, we collect 20 demonstrations. The training setup is B1-4N1 where we first train on a base skill, then incrementally add one new skill at a time for training, with a total of four new skills added. During testing, we perform 10 test runs for each learned skill and report the success rate of task execution. More details about the real world experiments and videos are shown in the supplementary material.
+
+We compare our method with the baseline [37] without any incremental policy. As shown in Table 5, it is evident that without the incremental strategy, the knowledge of previous skills is rapidly forgotten when training on new skills. After incorporating our incremental strategy, the success rate on new skills is lower than the baseline. This occurs because the baseline has overfitted to the new skill, while our model, which is designed to retain knowledge from previous skills, experiences a slight decrease in its ability to learn new skills. This trade-off is an inherent challenge in incremental learning.
+
+# 5. Conclusion
+
+In this work, we focus on a new and challenging setting, skill-incremental learning in robotic manipulation, which is to continually learn new skills while maintaining the previously learned skills. We conduct experiments on the RL-Bench benchmark and find that traditional methods suffer from catastrophic forgetting because they overlook the temporal and action complexities of robotic manipulation. Our approach proposes a temporal replay strategy to address the temporal complexities and an extendable PerceiverIO model with adaptive action prompts to address the action complexities. Extensive experiments demonstrate that our iManip framework excels in effectiveness, robustness, lightweight design, and extendability.
+
+# Acknowledgements
+
+This work was supported partially by NSFC (92470202, U21A20471), Guangdong NSF Project (No.2023B1515040025), Guangdong Key Research and Development Program (No.2024B0101040004).
+
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+# $\chi$ : Symmetry Understanding of 3D Shapes via Chirality Disentanglement
+
+Weikang Wang*
+
+Tobias Wei $\text{堡}$ rg\* University of Bonn
+
+Nafie El Amrani  
+Lamarr Institute
+
+Florian Bernard
+
+![](images/85d6d33df26ff04c521ef04252a1613c1b5ee1c9ec2465b67bd912871c32dd8f.jpg)  
+Figure 1. Left: Our chirality features can disentangle the left and right parts of 3D shapes. By leveraging the generalisation abilities of foundation image models, our method remains effective even on partial shapes. Right: Our chirality features resolve left-right ambiguities in 3D shape matching by augmenting state-of-the-art vertex features like Diff3F [16] with structural information.
+
+# Abstract
+
+Chirality information (i.e. information that allows distinguishing left from right) is ubiquitous for various data modes in computer vision, including images, videos, point clouds, and meshes. While chirality has been extensively studied in the image domain, its exploration in shape analysis (such as point clouds and meshes) remains underdeveloped. Although many shape vertex descriptors have shown appealing properties (e.g. robustness to rigid-body transformations), they are often not able to disambiguate between left and right symmetric parts. Considering the ubiquity of chirality information in different shape analysis problems and the lack of chirality-aware features within current shape descriptors, developing a chirality feature extractor becomes necessary and urgent. Based on the recent Diff3F framework [16], we propose an unsupervised chirality feature extraction pipeline to decorate shape vertices with chirality-aware information, extracted from 2D foundation models. We evaluated the extracted chirality features through quantitative and qualitative exper
+
+iments across diverse datasets. Results from downstream tasks including left-right disentanglement, shape matching, and part segmentation demonstrate their effectiveness and practical utility. Project page: https://wei-kang-wang.github.io/chirality/
+
+# 1. Introduction
+
+Symmetry and chirality are two sides of the same coin: Symmetry highlights the similarities between two parts, whereas chirality focuses on the differences between them. As a broadly applicable and intuitive assumption for many objects in the physical world, symmetry has been extensively studied in various computer vision domains for a long time, including 3D reconstruction [57, 58], pose estimation [10, 37, 43, 68], and generative models [1, 60]. However, chirality, despite its close relationship to symmetry, remains less explored and has just re-attracted researchers' attention in recent years [32, 34, 52, 62, 70].
+
+In the field of shape analysis, symmetry and chirality also play an important role in many problems, including matching [11, 33, 64, 67], deformation [69], symmetry plane detection [44], etc. For many shape analysis prob
+
+![](images/5e2be48211a2e38ae5125f0f2bc063358f8bf7b46a45f7b7eba861624b258632.jpg)  
+SD+DINO  
+(a) Left/Right
+
+![](images/f7e598aba66d8633ca3cec163a63edca590de082381e2337d373632a57ea701c.jpg)  
+Source  
+(b) Shape matching  
+Figure 2. Left: The 2-center clustering of vertex features aggregated from StableDiffusion and DINO [40, 49] features does not lead to the desired chirality indicator. Right: Shapes matched using Diff3F [16] display a lack of chirality awareness.
+
+![](images/59e5a5bd70a29b96e6174f10022a6fab566dd28328e52e9e819d5635abc6ff0b.jpg)  
+Target
+
+![](images/36c7b9b0c9fbe1db01aa51cfdc704c5b462204411c4b7eb71215d1c11eb6de2f.jpg)  
+Diff3F
+
+lems, vertex feature descriptors play a central role, and various methods to generate feature descriptors have been proposed [4, 8, 50]. Recently, Diff3F [16] was introduced as a novel framework for generating vertex feature descriptors. It aggregates 2D foundation model features from rendered multi-view images of a shape to create vertex feature descriptors. While recent features have shown semantic and geometric robustness, none of them are able to disambiguate between left-and-right symmetric shape parts, which could cause severe problems, as shown in Fig. 2.
+
+In order to fill this gap, we propose an unsupervised method based on Diff3F [16] that disentangles left-and-right (chirality) information to decorate shapes with chirality-aware vertex descriptors using features aggregated from 2D foundation models (such as DINO-V2 [40] and StableDiffusion [49]). We conduct experiments on various datasets and show that our extracted chirality feature provides left-and-right information of a shape. We show that left-and-right ambiguities, which are a common issue of state-of-the-art shape matching methods [8, 16], can be effectively mitigated by combining our chirality feature with other vertex feature descriptors. The generalization experiments of our pre-trained model on partial shapes and anisotropic shapes additionally prove the robustness of our chirality feature extractor.
+
+To summarize, our contributions are as follows:
+
+- We propose an unsupervised method to extract left-and-right (chirality) information for decorating shape vertex descriptors. Left-and-right disentanglement experiments on various datasets show the validity of our extracted chirality features quantitatively and qualitatively.  
+- For shape matching and part segmentation, we demonstrate that augmenting standard vertex descriptors with our chirality features effectively resolves left-right ambiguities across multiple datasets.  
+- Finally, cross-dataset and cross-category generalisation experiments, particularly those conducted on partial and anisotropic shapes, demonstrate the robustness of our trained chirality feature extractor.
+
+# 2. Related work
+
+We briefly review related work on chirality (Sec. 2.1), feature extraction (Sec. 2.2), and shape matching (Sec. 2.3).
+
+# 2.1. Chirality in visual computing
+
+In the context of studies on images, Lin et al. [32] explored how the statistics of visual data change under reflection and coined the term visual chirality. Yeh et al. [62] proposed a network whose layers can be mirror-flipped, using it for human pose estimation by resolving left/right ambiguities in the human body. Zheng et al. [70] investigated the vertical flipping associated with visual chirality in freehand sketches. Moreover, Tan et al. [52] leveraged the property of image-level visual chirality and reformulated it as a learnable pixel-level cue for mirror detection. In facial analysis, Lo et al. [34] employed chirality information from the left and right halves of faces to learn robust facial embeddings for expression recognition. Recently, to obtain geometry-aware features, Zhang et al. [65] fine-tuned a model on aggregated DINO-V2  $[40] + \mathrm{SD}$  [49] features with labelled keypoint correspondences between image pairs, inherently capturing chirality information.
+
+In the field of shape analysis, chirality extraction is closely related to the detection of intrinsic or extrinsic shape symmetries. Tevs et al. [53] showed that finding correspondences between shapes of widely varying geometry could benefit from extrinsic symmetry. Je et al. [26] applied Langevin dynamics within a redefined symmetry space to enhance robustness of extrinsic symmetry detection against noise. E3Sym [31] established robust point correspondences using E(3)-invariant features extracted from a lightweight neural network, enabling dense symmetry predictions. Ovsjanikov et al. [41] utilized Euclidean symmetries in the signature space defined by the eigenfunctions of the Laplace-Beltrami operator to identify intrinsic symmetries. Kim et al. [28] modelled intrinsic symmetry as Möbius transformations derived from critical points of the Average Geodesic Distance (AGD) function. Liu et al. [33] detected intrinsic symmetry on genus-zero mesh surfaces by extracting closed curves through conformal maps based on triplets of extrema points identified via the AGD function. Additionally, Nagar and Raman [38] hypothesized that if a shape was intrinsically symmetric, the shortest geodesic between two symmetric points was also intrinsically symmetric, facilitating the extraction of intrinsic correspondences.
+
+However, to our best knowledge, there exist no methods in the shape analysis field to extract chirality-aware vertex feature descriptors. Based on the recent paper Diff3F [16], which aggregated features from 2D foundation models (DINO-V2 [40] and StableDiffusion [49]) to obtain vertex descriptors, we propose an unsupervised pipeline to distil chirality information from features extracted by 2D foundation models to decorate vertex feature descriptors.
+
+# 2.2. Feature descriptors from 2D foundation models
+
+In recent years, various 2D foundation models have been proposed, including DINO [9], DINO-V2 [40], CLIP [45], StableDiffusion (SD) [49], etc. They have been used in various 2D/3D areas as feature descriptors and have surpassed both handcrafted features and other deep features, due to their rich semantic and geometric information obtained from large-scale and/or multi-modal datasets. Hedlin et al. [22] treated SD features as pixel-level feature descriptors to do semantic correspondence, while Hedlin et al. [23] leveraged SD features as an unsupervised 2D keypoint detector. FeatureNeRF [61] learned generalizable NeRFs by distilling pre-trained vision foundation models to perform on other downstream tasks beyond synthesis, such as semantic understanding and parsing. In this paper, similar to the setting in Diff3F [16] (see Sec. 3.1 for more details), we also aggregate per vertex features from 2D foundation model features of multiple views. However, we additionally derive chirality information embedded in the 2D foundation model features to augment vertex descriptors, enabling them to be left-right aware and consistent across shapes.
+
+# 2.3. Shape matching
+
+Shape matching is a well-studied problem in computer vision and graphics [51, 54], aimed at finding correspondences between pairs of shapes. Classical approaches solve this problem by establishing correspondences based on geometric relations [24, 48], while other methods rely on non-rigid shape registration [5, 19, 25]. One prominent mesh-based approach, the functional map framework [42], encodes shape correspondences into a compact matrix using truncated basis functions, usually the first  $k$  Laplacian eigenfunctions [30]. Although it has been extended to handle non-isometries [39, 46], partial shapes [3, 59] or multishape matching [8, 20], its reliance on spectral basis calculation involves high computational costs, pre-processing, mesh connectivity, and lacks semantic consideration.
+
+An alternative line of works focuses on spatial approaches and operates on point clouds directly, such as 3D-Coded [21] and Deprelle et al. [13], which deform a template shape to find correspondences. Other methods use supervised learning for point-to-point correspondences [14, 55, 63], while recent unsupervised approaches for point clouds, such as SE-ORNet [27], first align point clouds and then use a teacher-student network with DGCNN backbone [56] to learn point-wise embeddings. DPC [29] leverages self- and cross-attention to learn discriminative per-point features for smooth mappings. While both mesh- and point cloud-based methods achieve good matching performance, they primarily focus on geometric features and overlook semantic information. To address this, Diff3F [16] leverages foundation models to extract semantic vertex features. Our method builds on Diff3F [16] by incorporating chirality in
+
+formation, which makes features left/right aware and improves the quality of shape matching.
+
+# 3. Chirality feature optimization
+
+In this section, we introduce our unsupervised pipeline to decorate an textured shape with chirality-aware features. Our method is based on Diff3F [16], a recently proposed method that utilizes in-painting diffusion [49] along with DINO-V2 [40] features to decorate textured shapes with semantical aware features. We briefly introduce Diff3F [16] in Sec. 3.1. In Sec. 3.2, we introduce the generation of chiral image pairs and their features, and also the aggregation from image features to per-vertex chiral feature pairs, which are the core idea of our method. Finally, in Sec. 3.3, we introduce our model architecture and our unsupervised losses.
+
+# 3.1. Background: Diff3F
+
+In this subsection, we provide a summary of the Diff3F [16] method. We consider a 3D shape  $\mathcal{X}$  represented by a vertex set  $V\in \mathbb{R}^{|V|\times 3}$  and an edge set  $E\in \mathbb{N}^{|E|\times 2}$ . Diff3F [16] generates vertex-wise features as follows:
+
+1. Rendering from  $N$  different camera poses of shape  $\mathcal{X}$  results in  $N$  images  $I_{j}^{S} \in \mathbb{R}^{H \times W \times 3}$ , corresponding depth map  $D_{j} \in \mathbb{R}^{H \times W \times 1}$  and normal map  $N_{j} \in \mathbb{R}^{H \times W \times 3}$ , where  $j \in \{0, \dots, N-1\}$  and  $H$  and  $W$  denote the height and width, respectively.  
+2. Using a pre-trained StableDiffusion model [49] with ControlNet [66], the images  $I_{j}^{S}$  are textured with the guidance of depth and normal maps and a category prompt of the shape to produce  $I_{j}^{\mathrm{tex}} \in \mathbb{R}^{H \times W \times 3}$ .  
+3. During the texturing process, diffusion features from multiple layers are extracted and aggregated over multiple time steps of the diffusion process to form a set of features for each image,  $F_{j}^{\mathrm{SD}} \in \mathbb{R}^{H \times W \times 1280}$ .  
+4. The textured images  $I_{j}^{\mathrm{tex}}$  are fed through DINO-V2 [40] to extract features  $F_{j}^{\mathrm{DINO}} \in \mathbb{R}^{H \times W \times 768}$ .  
+5. Diffusion  $(F_{j}^{\mathrm{SD}})$  and DINO-V2  $(F_{j}^{\mathrm{DINO}})$  features are then normalised and concatenated to form the final image features  $F_{j}^{\mathrm{img}}\in \mathbb{R}^{H\times W\times 2048}$ .  
+6. Using the camera poses, each  $F_{j}^{\mathrm{img}}$  is projected back onto the vertices of  $\mathcal{X}$  and the final feature  $\mathcal{F}_v$  for vertex  $v\in V$  is the average of aggregated features from all  $N$  camera poses.
+
+For convenience, we refer to StableDiffusion as SD throughout the remainder of this paper. Similarly, we abbreviate DINO-V2 as DINO, as it is the only version used in this work.
+
+# 3.2. Generating chiral pairs
+
+In our method, the input is an untextured mesh  $\mathcal{X}$ , defined by a vertex set  $V\in \mathbb{R}^{|V|\times 3}$  and an edge set  $E\in \mathbb{N}^{|E|\times 2}$
+
+![](images/e9f900fce05e5dbd7c88074508fabf57c265534bfc2be869a94db957207118a2.jpg)  
+Figure 3. Overview of the pipeline of our method. We consider a single 3D mesh for which we generate  $N$  textured images following Diff3F [16]. We flip the images horizontally to receive  $N$  pairs of textured images. The images are then independently processed by a frozen feature extractor, supplying us with features  $F_{img}$  and  $\bar{F}_{img}$ . After reprojecting onto the shape, we aggregate the features to receive  $\mathcal{F}_v$  and  $\bar{\mathcal{F}}_v$ . Finally, we train a chirality network  $\tilde{g}_{\Phi}$  on  $\mathcal{F}_v$  and  $\bar{\mathcal{F}}_v$  to learn chirality features  $\chi$  and  $\bar{\chi}$  that tells left from right.
+
+without any feature descriptors but accompanied by a category label used for diffusion guidance.
+
+Following Diff3F [16], we get the textured images  $\{I_j\}_{j=1}^N$ . Then, we flip these textured images  $\{I_j\}_{j=1}^N$  horizontally to get a set of flipped textured images  $\{\bar{I}_j\}_{j=1}^N$ . Note that flipping the image vertically is equivalent to flipping the image horizontally together with a 180 degree in-plane rotation, and that in-plane rotations will not change the chirality of objects within an image.
+
+After that, we feed both the textured image set  $\{I_j\}_{j=1}^N$  and the flipped textured image set  $\{\bar{I}_j\}_{j=1}^N$  into DINO [40] and StableDiffusion [49] to get the feature sets  $\{(F_j^{\mathrm{SD}}, F_j^{\mathrm{DINO}})\}_{j=1}^N, \{(\bar{F}_j^{\mathrm{SD}}, \bar{F}_j^{\mathrm{DINO}})\}_{j=1}^N$ . We adopt a similar approach to [16, 65] for concatenating features from each DINO and SD feature pair: each feature is first normalized individually, then concatenated along the feature dimension, followed by normalization of the combined feature vector. This process yields  $\{F_j^{\mathrm{img}}\}_{j=1}^N$  and  $\{\bar{F}_j^{\mathrm{img}}\}_{j=1}^N$  corresponding to the textured images and their flipped versions, respectively. Next, we flip  $\{\bar{F}_j^{\mathrm{img}}\}_{j=1}^N$  horizontally to get  $\{\hat{F}_j^{\mathrm{img}}\}_{j=1}^N$ , which is spatially aligned with the original features  $\{F_j^{\mathrm{img}}\}_{j=1}^N$ .
+
+Finally, for each vertex  $v \in V$  of shape  $\mathcal{X}$ , we utilize the camera information to locate its corresponding pixels
+
+in each rendered view. The vertex feature  $\mathcal{F}_v$  is given by averaging the features of these pixels. Similarly, per vertex feature  $\bar{\mathcal{F}}_v$  are obtained from  $\hat{F}^{\mathrm{img}}$ . This process results in the chirality vertex feature pair  $(\mathcal{F}_v,\bar{\mathcal{F}}_v)$
+
+Using this construction,  $\mathcal{F}_v$  aggregates semantic and geometric information from the image foundation model features, while its counterpart  $\bar{\mathcal{F}}_v$  aggregates information differing only in left-and-right (chirality) information. For example, if  $v$  denotes the keypoint at the left eye in shape  $\mathcal{X}$ , then  $\mathcal{F}_v$  will average left eye image foundation model features from different views, while  $\bar{\mathcal{F}}_v$  gathers right eye features from different views (note that  $v$  still denotes the left eye keypoint of  $\mathcal{X}$ , and these right eye features are virtually constructed and gathered by our flipping process).
+
+# 3.3. Chirality feature extraction
+
+In this section, we describe the extraction of our chirality features  $\chi, \bar{\chi}$  from the generated pairs of vertex features  $\{(\mathcal{F}_v, \bar{\mathcal{F}}_v)\}_{v \in V}$ , where  $\mathcal{F}_v, \bar{\mathcal{F}}_v \in \mathbb{R}^D$ . We denote the stacked vertex features of  $\{\mathcal{F}_v\}_{v \in V}$  and  $\{\bar{\mathcal{F}}_v\}_{v \in V}$  as  $\mathcal{F} \in \mathbb{R}^{|V| \times D}$  and  $\bar{\mathcal{F}} \in \mathbb{R}^{|V| \times D}$ , respectively.
+
+To this end, we use an encoder  $g_{\Phi}:\mathbb{R}^{D}\to \mathbb{R}^{D}$  together with a linear projection layer  $A\in \mathbb{R}^{D\times D}$  as our chirality feature extractor denoted as  $\tilde{g} (\cdot) = Ag_{\Phi}(\cdot)$ , with  $\Phi$  and  $A$  being the optimised parameters. A decoder  $h_{\Psi}:\mathbb{R}^{D}\to \mathbb{R}^{D}$  is included to avoid trivial solutions.
+
+The chirality feature vector  $\chi := (\chi_{v_1},\dots ,\chi_{v_{|V|}})^\top \in \mathbb{R}^{|V|\times 1}$  of all vertices of shape  $\mathcal{X}$  is given by
+
+$$
+\chi_ {v} := \frac {[ \tilde {g} (\mathcal {F} _ {v}) ] _ {1}}{\| \tilde {g} (\mathcal {F} _ {v}) \| _ {2}} = \frac {[ A g (\mathcal {F} _ {v}) ] _ {1}}{\| A g (\mathcal {F} _ {v}) \| _ {2}}, \tag {1}
+$$
+
+where  $[\cdot ]_1$  denotes taking the first entry of the feature vector.
+
+This indexing and normalisation will ensure that chirality features  $\chi_v$  are in the range  $[-1, 1]$ . Similarly, we obtain  $\bar{\chi}$  from  $\bar{\mathcal{F}}$  using the model  $\tilde{g}$ . More details about the architecture of our feature extractor are included in Sec. B in the supplementary material. To train our model, we employ the following losses:
+
+Dissimilarity loss  $\mathcal{L}_{\mathrm{dis}}$ . The dissimilarity loss is defined as
+
+$$
+\mathcal {L} _ {\mathrm {d i s}} = - \frac {1}{\sqrt {| V |}} \| \chi - \bar {\chi} \| _ {2}. \tag {2}
+$$
+
+It serves as the main loss, since it maximises the difference between the chirality feature obtained from  $\mathcal{F}_v$  and  $\bar{\mathcal{F}}_v$ , which should only differ in left-and-right information.
+
+Invertibility loss  $\mathcal{L}_{\mathrm{inv}}$ . To keep our encoder  $g$  from learning trivial solutions, we introduce a decoder  $h_{\Psi}$ , where  $\Psi$  is the learnable parameter. The invertibility loss
+
+$$
+\mathcal {L} _ {\mathrm {i n v}} = \frac {1}{\sqrt {| V |}} \| \left[ \begin{array}{l l} \mathcal {F} ^ {\top} & \bar {\mathcal {F}} ^ {\top} \end{array} \right] ^ {\top} - h \left(g \left(\left[ \begin{array}{l l} \mathcal {F} ^ {\top} & \bar {\mathcal {F}} ^ {\top} \end{array} \right] ^ {\top}\right)\right) \| _ {F}, \tag {3}
+$$
+
+ensures that  $h$  is able to reconstruct the inputs  $\mathcal{F}$  and  $\bar{\mathcal{F}}$  from the outputs  $g(\mathcal{F})$  and  $g(\bar{\mathcal{F}})$ , respectively. Here,  $[\mathcal{F}^\top \bar{\mathcal{F}}^\top ]^\top$  corresponds to stacking the rows of  $\mathcal{F}$  and  $\bar{\mathcal{F}}$ , and  $g$  and  $h$  are applied row-wise.
+
+Total variation loss  $\mathcal{L}_{\mathrm{var}}$ . To achieve spatial smoothness, we add a total variation loss
+
+$$
+\mathcal {L} _ {\text {v a r}} = \frac {1}{| E |} \sum_ {(u, v) \in E} \| \chi_ {u} - \chi_ {v} \| _ {1} + \| \bar {\chi} _ {u} - \bar {\chi} _ {v} \| _ {1}, \tag {4}
+$$
+
+where  $|E|$  is the number of edges inside the mesh.
+
+Fifty-fifty loss  $\mathcal{L}_{\mathrm{ff}}$ . The total variation loss  $\mathcal{L}_{\mathrm{var}}$  introduces a bias towards solutions with small boundary length. We counteract this by introducing
+
+$$
+\mathcal {L} _ {\mathrm {f i f}} = \frac {1}{| V |} \left(\frac {| \chi^ {\top} \mathbf {1} _ {| V |} |}{\| \chi \| _ {\infty}} + \frac {| \bar {\chi} ^ {\top} \mathbf {1} _ {| V |} |}{\| \bar {\chi} \| _ {\infty}}\right), \tag {5}
+$$
+
+which penalises solutions which assign more vertices to one of the two halves of each shape.
+
+The overall training loss is the linear combination of the above losses, i.e.
+
+$$
+\mathcal {L} = \mathcal {L} _ {\text {d i s}} + \lambda_ {1} \mathcal {L} _ {\text {i n v}} + \lambda_ {2} \mathcal {L} _ {\text {v a r}} + \lambda_ {3} \mathcal {L} _ {\text {f i f}}. \tag {6}
+$$
+
+# 4. Experiments
+
+We conduct various experiments to show the effectiveness of our chirality feature. In Sec. 4.1, we compare the left- and right disentanglement performance using our chirality feature compared with other shape feature descriptors and methods. Then, in Sec. 4.2 and Sec. 4.3, we show the effectiveness of our chirality feature in various shape analysis tasks, including shape matching and shape segmentation. To evaluate the generalisation ability of our method, we test on partial and anisotropic shapes in Sec. 4.4 and Sec. 4.5, respectively. Finally, the ablation study of losses and 2D foundation features are conducted in Sec. 4.6. In each experiment section, we present the datasets, baselines and evaluation metrics used. For more details about the implementation, see Sec. E in the supplementary material.
+
+# 4.1. Left-right disentanglement
+
+Datasets. To evaluate our approach's ability to distinguish between left and right of 3D shapes, we use datasets where left/right annotations are available. To this end, we use Be-CoS [18], a recently proposed framework to generate shape matching datasets with dense correspondences and left/right annotations. This framework combines shapes from multiple shape matching datasets and connects them with cross-category and cross-class dense correspondences. Using this framework, we generate multiple versions to evaluate the performance and generalisation of our approach.
+
+- BeCoS consists of humanoid and four-legged animals with 1980/284/274 train/test/validation split, generated from 7 different shape datasets, namely TOSCA [7], FAUST [6], SCAPE [2], KIDS [47], DT4D [35], SMAL [72] and SHREC'20 [17]. See [18] for more details.  
+- BeCoS $_{h}$  consists of only humanoid shapes from TOSCA [7], FAUST [6], SCAPE [2], KIDS [47], DT4D [35] with 366/64/58 train/test/validation split.  
+- BeCoS-a consists of only four-legged animals from TOSCA [7], DT4D [35], SMAL [72] and SHREC'20 [17] with 1614/220/216 train/test/validation split.
+
+For more details about the data generation please refer to Sec. A in the supplementary material. Additionally, we use well-established shape matching datasets to evaluate our method, namely FAUST [6], SCAPE [2], SMAL [69], and TOSCA [7]. We use the same train/test/Validation splits given by BeCoS [18]. Since these datasets do not provide left/right annotations, we use the BeCoS [18] framework to get these annotations.
+
+Baselines. We compare the performance of our chirality features against other feature descriptors, including Diff3F [16], DINO+SD [40, 49], and DINO+SD fine-tuned with Zhang et al. [65]. We also include an axiomatic method Liu et al. [33] that extracts closed intrinsic/extrinsic symmetric
+
+<table><tr><td>Train</td><td>BeCoS</td><td colspan="2">BeCoS-h</td><td colspan="2">BeCoS-a</td><td colspan="2">FAUST</td><td colspan="2">SMAL</td></tr><tr><td>Test</td><td>BeCoS</td><td>BeCoS-h</td><td>BeCoS-a</td><td>BeCoS-h</td><td>BeCoS-a</td><td>FAUST</td><td>SCAPE</td><td>SMAL</td><td>TOSCA</td></tr><tr><td>Diff3F [16]</td><td>50.87</td><td>54.43</td><td>50.23</td><td>53.28</td><td>50.77</td><td>51.21</td><td>52.53</td><td>50.91</td><td>51.48</td></tr><tr><td>DINO+SD [40, 49]</td><td>51.16</td><td>54.31</td><td>50.30</td><td>52.68</td><td>50.96</td><td>51.05</td><td>52.55</td><td>50.80</td><td>51.42</td></tr><tr><td>Zhang et al. [65]</td><td>51.18</td><td>54.16</td><td>50.78</td><td>52.83</td><td>51.02</td><td>50.90</td><td>51.47</td><td>50.41</td><td>50.97</td></tr><tr><td>Liu et al. [33]</td><td>79.98</td><td>79.83</td><td>80.46</td><td>79.83</td><td>80.46</td><td>90.45</td><td>80.84</td><td>75.71</td><td>72.88</td></tr><tr><td>\( \chi_{\text{DINO+SD}} \)</td><td>91.84</td><td>94.09</td><td>84.19</td><td>90.36</td><td>91.10</td><td>94.76</td><td>95.51</td><td>96.59</td><td>94.09</td></tr></table>
+
+Table 1. Left and right distinguishment accuracy  $(acc_{\chi}\uparrow)$  on BeCoS [18] datasets for various methods. Our method outperforms all others across all datasets.
+
+![](images/e08e4ec9c463123fa8a5fc8fa9f5ffaee50d806fa4e269d02ba55e376ba0872f.jpg)  
+Figure 4. Qualitative results on left-right disentanglement of Zhang et al. [67], Liu et al. [33], DINO + SD [40, 49], Diff3F [16] and our features. Our method provides the only features that consistently and accurately distinguish between left and right of the object.
+
+curves on surfaces of a genus-0 mesh that splits the mesh into left and right parts.
+
+Evaluation metrics. Given a set of shapes  $X = \{\mathcal{X}_1, \dots, \mathcal{X}_N\}$ , where each shape  $\mathcal{X}_n$  has a vertex set  $V_{\mathcal{X}_n}$ , the chirality accuracy  $\mathrm{acc}_{\chi}$  is defined as
+
+$$
+\operatorname {a c c} _ {\chi} = \max  \left\{\operatorname {a c c}, 1 - \operatorname {a c c} \right\}, \tag {7}
+$$
+
+where
+
+$$
+\operatorname {a c c} = \frac {1}{N} \sum_ {n = 1} ^ {N} \frac {1}{| V _ {\chi_ {n}} |} \sum_ {v \in V _ {\chi_ {n}}} \mathbb {1} (\operatorname {s i g n} \left(\chi_ {v}\right) = \chi_ {v} ^ {g t}). \tag {8}
+$$
+
+$\chi_v$  is our chirality features for vertex  $v \in V_{\mathcal{X}_n}$  of each shape  $\mathcal{X}_n$ ,  $\mathbb{1}$  is the indicator function, and  $\chi_v^{gt}$  is the ground truth of left/right annotation of vertex  $v \in V_{\mathcal{X}_n}$ .
+
+Note that in Eq. 7, we use the maximum of acc and  $1 - \mathrm{acc}$  from Eq. 8, because there is no inherent assignment of whether  $\chi_v > 0$  or  $\chi_v < 0$  corresponds to left or right.
+
+Experiment results. The results are summarised in Tab. 1. Our method substantially outperforms all baselines in the context of distinguishing left/right of 3D shapes. Additionally, our method achieves good cross-dataset and cross-category generalisation ability. Fig. 4, provides qualitative results of our method compared to baselines.
+
+# 4.2. Shape matching
+
+In this section, we evaluate the performance of our chirality features on shape matching. To ensure a fair comparison with prior work, we adopt a similar experimental setup as in DPC [29], SE-ORNet [12] and Diff3F [16].
+
+<table><tr><td></td><td colspan="2">TOSCA-a</td><td colspan="2">SHREC&#x27;19</td></tr><tr><td></td><td>acc (↑)</td><td>err (↓)</td><td>acc (↑)</td><td>err (↓)</td></tr><tr><td>DPC [29]</td><td>30.79</td><td>3.74</td><td>17.40</td><td>6.26</td></tr><tr><td>SE-ORNet [12]</td><td>33.25</td><td>4.32</td><td>21.41</td><td>4.56</td></tr><tr><td>3D-CODED [21]</td><td>-</td><td>-</td><td>2.10</td><td>8.10</td></tr><tr><td>Diff3F [16]</td><td>20.25</td><td>5.44</td><td>26.40</td><td>1.69</td></tr><tr><td>Diff3F [16] + χDINO+SD</td><td>22.73</td><td>4.72</td><td>27.32</td><td>1.02</td></tr></table>
+
+Table 2. Shape matching results of TOSCA-a, SHREC'19. (The results of [12, 21, 29] are reported from [16]).
+
+![](images/87b73485d46b295b3abc280821ef1e5d696d7c254d52b2450c61e73f4d708b68.jpg)  
+Figure 5. Quantitative comparison (with (AUC x 100) shown in brackets) on TOSCA-A and SHREC'19 datasets. With our chirality features, the vertex feature descriptor archives better matching performance on both datasets.
+
+![](images/b1c8024e4874b3f3d7a7a10344d688fc5eb3354dca8ca1b36cafdde71dbf62f3.jpg)
+
+![](images/5c070798d5374502925945f597d5c95dcf9c443af30187dde7dbbede0d4ae27a.jpg)  
+Figure 6. Qualitative results of shape correspondence using Diff3F and our chirality features. Our approach is able to correct for the left/right ambiguity as shown by the blue ovals.
+
+Datasets. We test our features on both human and animal shapes. For human shapes, we evaluate our method on SHREC'19 [36]. This dataset comprises of 44 human scans with a test set of 430 shape pairs. We use the more challenging re-meshed version from [15]. For the non-human shapes, we use only animal the 41 shapes from TOSCA [7] (noted as TOSCA-a) and pair shapes from the same category to create a testing set of 286 pairs.
+
+Baselines. We compare our approach to recent state-of-the-art shape matching methods. One supervised method (3D-CODED [21]) that we only have access to its model trained on humans. And two unsupervised methods, namely DPC [29] and SR-ORNET [12], that were trained on hu
+
+man and animal datasets separately. We also compare our method to Diff3F [16] that extracts vertex features of each shape and requires no training.
+
+Evaluation metrics. Following Diff3F [16], we use the average matching error and the matching accuracy as our evaluation metrics. For a source shape  $\mathcal{X}$  and a target shape  $\mathcal{Y}$ , represented with a vertex sets  $V_{\mathcal{X}} \in \mathbb{R}^{|V_{\mathcal{X}}| \times 3}$  and  $V_{\mathcal{Y}} \in \mathbb{R}^{|V_{\mathcal{Y}}| \times 3}$ , respectively, the matching error is
+
+$$
+\operatorname {e r r} = \frac {1}{| V _ {\mathcal {X}} |} \sum_ {v \in V _ {\mathcal {X}}} \| f (v) - y _ {g t} \| _ {2}, \tag {9}
+$$
+
+where  $f(v)$  is the predicted matching point of  $v \in V_{\mathcal{X}}$  in  $\mathcal{Y}$  and  $y_{gt} \in V_{\mathcal{Y}}$  is the ground truth corresponding point of  $v$ . Furthermore, the matching accuracy is defined as
+
+$$
+a c c (\epsilon) = \frac {1}{| V _ {\mathcal {X}} |} \sum_ {v \in V _ {\mathcal {X}}} \mathbb {1} \left(\left\| f (v) - y _ {g t} \right\| _ {2} <   \epsilon d\right), \tag {10}
+$$
+
+where  $\mathbb{1}(\cdot)$  is the indicator function,  $d$  is the maximal Euclidean distance between points in  $V_{\mathcal{Y}}$ , and  $\epsilon \in [0,1]$  is the error tolerance.
+
+Experiment results. The results are summarised in Tab. 2. Our chirality features enhance Diff3F [16] performance in shape matching task since it resolves the left/right ambiguity. In Fig. 5, we summarise the PCK curves of our method compared to the state-of-the-art method on both human and animal dataset. Fig. 6 provides qualitative results of our method compared to baselines.
+
+# 4.3. Part segmentation
+
+We apply  $k$ -means clustering to our chirality features combined with Diff3F [16] features to segment shapes into  $k$  parts. Our features enhance Diff3F [16] features to be able to differentiate between left and right parts of shapes as seen in Fig. 7 (left and right legs are not clustered together; the part segmentation is still consistent across shapes).
+
+![](images/cb07e6d4b71919b4635ca2c66d1d5d0d16e2f63c31b9a3257542d4319446cc6a.jpg)  
+Figure 7. Visualisations of part segmentation using Diff3F [16] and our features. Our chirality features can differentiate between the left and right parts of the body (e.g. hands and legs), whereas Diff3F clusters the left and right hands and legs together.
+
+# 4.4. Partial shapes
+
+To showcase the potential of our method, we conduct a proof-of-concept experiment on partially observed meshes, which is a common real-world scenario for 3D shapes collected by scanning devices. To this end, we extract our chirality features from both human and animal shapes from CP2P dataset [3] and use a model trained on complete shapes from BeCoS [18]. In Fig. 8, we observe that our chirality features can distinguish between left and right parts of partial shapes even when most of the mesh is missing.
+
+![](images/98ba9f89af5c711555613b69cba2292b074991359089729f930e2e50c540fb97.jpg)  
+Figure 8. Our chirality features can distinguish left and right parts of partial shapes on both human and animal shapes.
+
+![](images/95e1694d665dd7b4b5ad8c2af01da47d5b65a59f1263d7c49519b5f212223a06.jpg)
+
+![](images/f01a9ad844ce40d5f9a591932b1631e83ee66ef0b8ac4dc0f331b7b7df941a16.jpg)
+
+# 4.5. Anisotropic shapes
+
+To further demonstrate the robustness of our method to different discretisation of shapes, we show its performance on anisotropic meshes. We use the anisotropic version of FAUST and SCAPE from [14]. These non-uniform meshes are often encountered in adaptive refinement and characterised by having a non-consistent discretisation granularity. Qualitative results of the model trained on isotropic BeCoS [18] on anisotropic shapes are shown in Fig. 9.
+
+![](images/b9128b5413fd5e986df62848d2b8d51e8e820bc13d51df76466185824d67d4b9.jpg)  
+Figure 9. Our approach is robust to anisotropic meshes and can handle meshes with different discretisation.
+
+![](images/5e4b52431ff3c35ccc3531e0beb229325f8cd22b052bf86af71c16c6644636b2.jpg)
+
+![](images/8be674e1b20f37d4ff4471ac1caaf86422b1d2356aa7546b11f9c63e747127fd.jpg)
+
+![](images/b4f1727dfd3c1098c39197d380bd5548ad7ec6ef070e52dafb48c7d5c25c0268.jpg)
+
+# 4.6. Ablation study
+
+We conduct ablative experiments to verify our design choices, using use the FAUST [6] and SMAL [69] datasets. Tab. 3 summarises our findings. By comparing the first four columns, we conclude all losses are crucial for obtaining accurate chirality features. By comparing the last three columns, we observe combining SD and DINO yields the best results across both human and animal datasets.
+
+# 5. Limitations & Future works
+
+Although our proposed method shows superiority compared to other methods for left-and-right disentanglement, and
+
+<table><tr><td>w/o</td><td>\( {\mathcal{L}}_{\text{dis }} \)</td><td>\( {\mathcal{L}}_{\text{var }} \)</td><td>\( {\mathcal{L}}_{\text{fif }} \)</td><td>\( {\mathcal{L}}_{\text{inv }} \)</td><td>SD</td><td>DINO</td><td>full</td></tr><tr><td>FAUST</td><td>51.34 ± 0.96</td><td>77.02 ± 8.87</td><td>90.95 ± 7.86</td><td>96.26 ± 0.49</td><td>89.21 ± 2.48</td><td>81.47 ± 24.96</td><td>95.79 ± 0.50</td></tr><tr><td>SMAL</td><td>51.33 ± 0.91</td><td>74.37 ± 0.97</td><td>96.41 ± 0.27</td><td>76.72 ± 3.80</td><td>71.65 ± 1.17</td><td>94.21 ± 3.89</td><td>94.71 ± 2.59</td></tr></table>
+
+Table 3. Ablation study on the FAUST and SMAL datasets. We use the chirality accuracy  $acc_{\chi}$  ( $\uparrow$ ) as evaluation metric. The best/second best results in each column are highlighted/underlined, respectively.
+
+the extracted chirality feature performs well on various downstream tasks, further improvements are still possible. Firstly, methods using 3D descriptors aggregated from 2D images (e.g. Diff3F [16], DenseMatcher [71]) struggle with occluded vertices and fail to learn reliable features. Our method simply inherits this shortcoming from Diff3F [16]. Deforming shapes, to reduce occlusions, is an interesting direction for future work. Secondly, our model takes meshes as input, since  $\mathcal{L}_{\mathrm{var}}$  relies on the edges of the mesh, which limits the direct applicability of our method to point clouds. However, we show in Sec. C of the supplementary material that our method (with a simple  $k$ -nearest neighbour approximation of the connectivity of the input point cloud) can give reasonable results. Additionally, despite incorporating the total variation loss, we occasionally observe patches with incorrect features, as seen in Fig. 1 (left side, top right). Another type of inaccuracy might arise when two body parts with different chirality are in close proximity or touching each other (Fig. 9, middle left). Future works combining geometric constraints might alleviate these problems.
+
+# 6. Conclusion
+
+Chirality information plays an important role in visual computing and has been severely under-explored in the shape analysis field. In this paper, we propose an unsupervised method to disentangle per vertex chirality features from semantic and geometric features aggregated from 2D foundation models (DINO-V2 [40] and StableDiffusion [49]). The chirality features disentangled by our proposed pipeline show superiority compared to various other features/methods on left-right distinguishing tasks both quantitatively and qualitatively. Furthermore, combined with our chirality features, other vertex feature descriptors show better performance on both shape matching and part segmentation tasks on various datasets. Additionally, the generalisation tests on partial and anisotropic shapes confirm the robustness of our method and also enlarge the application scenarios of our model due to more realistic properties. To conclude, we believe that our proposed pipeline and extracted chirality features will benefit future research in shape analysis and other visual computing areas.
+
+# Acknowledgments
+
+We thank Paul Roetzer for the valuable feedback on earlier drafts of this manuscript. This work is supported by the ERC starting grant no. 101160648 (Harmony).
+
+# References
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+# mmCooper: A Multi-agent Multi-stage Communication-efficient and Collaboration-robust Cooperative Perception Framework
+
+Bingyi Liu $^{1}$ , Jian Teng $^{1}$ , Hongfei Xue $^{2*}$ , Enshu Wang $^{3*}$ , Chuanhui Zhu $^{1}$ , Pu Wang $^{2}$ , Libing Wu $^{3}$ $^{1}$ Wuhan University Of Technology,  $^{2}$ University of North Carolina at Charlotte,  $^{3}$ Wuhan University  
+{byliu, tengjian, zhuchuanhui}@whut.edu.cn,  
+{hongfei.xue, Pu.Wang}@charlotte.edu, {wanges17, wu}@whu.edu.cn
+
+# Abstract
+
+Collaborative perception significantly enhances individual vehicle perception performance through the exchange of sensory information among agents. However, real-world deployment faces challenges due to bandwidth constraints and inevitable calibration errors during information exchange. To address these issues, we propose mm-Cooper, a novel multi-agent, multi-stage, communication-efficient, and collaboration-robust cooperative perception framework. Our framework leverages a multi-stage collaboration strategy that dynamically and adaptively balances intermediate- and late-stage information to share among agents, enhancing perceptual performance while maintaining communication efficiency. To support robust collaboration despite potential misalignments and calibration errors, our framework prevents misleading low-confidence sensing information from transmission and refines the received detection results from collaborators to improve accuracy. The extensive evaluation results on both real-world and simulated datasets demonstrate the effectiveness of the mm-Cooper framework and its components.
+
+# 1. Introduction
+
+With the advancement of autonomous driving systems [19, 57], perception devices such as cameras and LiDARs have been widely deployed. Although perception technologies have witnessed rapid advancements driven by deep learning-based algorithms, the traditional single-vehicle perception paradigms [23, 30, 52] cannot meet the safety and reliability requirements of autonomous vehicles due to unavoidable factors such as object occlusion and limitations in detection range [1, 6, 14, 27, 61].
+
+Benefiting from infrastructure improvements and the advancement of Internet of Vehicles (IoVs) technologies like V2X [25, 26], autonomous vehicles can achieve multi
+
+vehicle collaborative perception by sharing perception information [5, 47], which significantly enhances the performance of perception systems. Although cooperative perception has made progress recently, its practical deployment still faces challenges such as communication resource constraints [8, 13], localization errors [31, 34], and low information fusion efficiency [46, 55].
+
+In cooperative perception systems, the effectiveness of fusion strategies significantly affects both perception performance and communication efficiency. The fusion strategies can be divided into three categories: early, intermediate, and late fusion methods. Specifically, early fusion methods [7, 61] aggregate raw sensor observations from all agents, providing abundant information but requiring immense bandwidth, making this approach costly for communication. Intermediate fusion methods [8, 13, 53-55] partially mitigate this issue by sharing encoded features rather than raw data to reduce communication overhead. However, transmitting the feature map of the entire sensing scenario still results in substantial bandwidth consumption [13]. Late fusion methods [38, 40] on the other hand, minimize communication demands by sharing lightweight perception results among agents. However, this approach is highly sensitive to environmental noise, as even minor disturbances can degrade collaborative quality [31]. Overall, these above single-stage cooperative perception approaches face challenges in managing the trade-off between perception accuracy and communication efficiency, raising a compelling question: Can we improve the perception performance while preserving communication efficiency by strategically sharing information across multiple stages to harness the strengths of each fusion stage?
+
+In addition, the data exchanged by agents inevitably experiences misalignment and contains calibration errors during the synchronization process due to communication delays and pose noise [15, 41]. These calibration errors can produce misleading features and proposals in subsequent steps, thereby affecting the performance of the perception system. While existing intermediate fusion methods at
+
+tempt to address the calibration errors through position-wise feature fusion [20, 22, 29], they often overlook the critical role of neighboring region information for enhancing collaborative robustness. Meanwhile, late fusion methods [3, 36, 42] simply merge bounding boxes from collaborative agents, failing to leverage information-rich intermediate features from the ego agent, which could help refine and calibrate these bounding boxes for higher accuracy.
+
+To this end, we propose mmCooper, a novel multi-agent, multi-stage, communication-efficient, and collaboration-robust cooperative perception framework. The proposed mmCooper framework facilitates effective information aggregation across fusion stages and enhances communication efficiency through carefully designed core components. Specifically, we design an adaptive multistage data fusion mechanism that facilitates multi-agent cooperation by dynamically fusing information at both intermediate and late stages. Guided by a confidence-based filtering strategy, this mechanism automatically assesses and determines the data volume to be processed at intermediate and late stages. High-confidence bounding boxes are shared directly, while intermediate features are selectively shared instead of bounding boxes for regions requiring further contextual reference, and low-confidence areas are excluded to prevent propagating misleading information. This dual-stage fusion approach enhances perception performance while maintaining communication efficiency.
+
+Besides, to further address potential misalignment and calibration noise among agents, we incorporate specific designs in the proposed mmCooper framework for both intermediate and late stages. In the intermediate stage, we introduce a Multi-scale Offset-aware Fusion Module that not only fuses data from target locations related to cooperative agents' views but also from nearby regions, adding redundancy to mitigate calibration noise. For the late stage, we design a Bounding Box Filtering & Calibration Module that uses the information-rich intermediate-stage features from the ego agent to filter inaccurate bounding boxes received from other agents and refine the remaining noisy ones. By integrating these corrected and ego-generated bounding boxes, our mmCooper framework can achieve high perception accuracy and robustness. To summarize, our main contributions are summarized as follows:
+
+- We propose mmCooper, a multi-agent multi-stage communication-efficient collaboration-robust cooperative perception framework. To our knowledge, this is the first framework to address the tradeoff between limited communication bandwidth and desired perception performance by sharing both intermediate and late-stage information for multi-agent collaborative perception.  
+- To address the potential misalignment and calibration error among agents, we design a Multi-scale Offset-aware Fusion Module to integrate spatially adjacent contextual
+
+information at different feature scales in the intermediate stage and a Bounding Box Filtering & Calibration Module to filter and improve the bounding boxes from other agents in the late stage, guided by the information-rich intermediate features.
+
+- Extensive experiments show excellent performance on both real-world and simulated datasets, with a  $7.29\% / 1.31\% / 2.09\%$  improvement in AP@0.7 on OPV2V [50], DAIR-V2X [56] and V2XSet [49] datasets over the second-best SOTA methods. Meanwhile, our approach requires only 1/9153, 1/156, and 1/18305 of the communication volume used by comparable methods. Furthermore, our method consistently outperforms previous approaches under various configurations.
+
+# 2. Related Work
+
+# 2.1. Multi-Agent Communication
+
+Communication strategies in multi-agent systems have been widely studied [39]. Early works [21, 37, 44] often used predefined protocols or heuristic methods to determine how agents communicate with each other. However, these methods are difficult to generalize to complex tasks. Recently, several learning-based communication strategies have been proposed to adapt to diverse scenario applications. For instance, Vain [12] utilizes attention neural structures to specify the information that needs to be shared in agent interactions. ATOC [17] introduces recurrent units to decide who agents communicate with by receiving local observations and action intentions from other agents. TarMAC [9] designs an architecture oriented towards reinforcement learning, learning to communicate from task-specific rewards. CommNet [43] learns continuous communication in multi-agent systems. Most of these previous works have considered decision-making tasks and have employed reinforcement learning due to the lack of explicit supervision. Different from these works, our paper focuses on LiDAR-based 3D perception tasks in complex autonomous driving scenarios and achieves efficient communication between agents using a multi-stage communication strategy.
+
+# 2.2. Collaborative Perception
+
+Collaborative perception addresses the limitations of single-agent perception by aggregating perception information from surrounding agents to adapt to complex and dynamic autonomous driving environments. Current work is categorized into early, intermediate, and late fusion based on collaboration stages. Early fusion [7, 59, 61] shares raw point cloud data among agents, achieving high perception performance but consuming significant bandwidth resources. EMP [61] achieved scalability and adaptability on highly fluctuating open roads by dynamically partitioning the point cloud range shared by agents. Late fusion [38, 40, 51] shares lightweight proposals between agents but performs poorly and is sensitive to noise. VIPS [38] implemented
+
+![](images/059fbaa0bf57d05c170a6d9b333bf75773184ad7642b025d23f8a39f9ab09be3.jpg)  
+Figure 1. Comparison between our proposed multi-stage mmCooper framework and existing methods. The BEV (Bird's Eye View) communication map illustrates the information shared by agents at each scene location. (a)(b)(c) depict existing methods, which transmit the entire scene's data in a single stage without considering sensing confidence, leading to excessive communication overhead and degraded performance. (d) demonstrates how mmCooper selectively transmits non-overlapping information across multiple stages, reducing communication costs and enhancing model performance.
+
+efficient graph-structured matching to enable object-level fusion. Intermediate fusion [13, 22, 29, 49, 58] shared features among agents, yet complete Intermediate features still incur high bandwidth consumption. Recent work focused on novel communication mechanisms to filter Intermediate features and reduce communication volume. for instance, Where2comm [13] employed a confidence-based scheme to guide agents in focusing on sharing spatially critical information. ERMVP [58] adopted a hierarchical feature sampling strategy to reduce communication overhead while leveraging sparse consensus features to mitigate localization errors. Different from these works, our framework conducts multi-stage fusion instead of single-stage which balances the perception performance and communication overhead. As far as we know, only a few works have considered multi-stage settings. Zhang et al. [60] proposes a defense method that combines raw data and intermediate features to fuse redundant information, thereby reducing the impact of spurious data. However, this work focuses on security issues related to collaborative perception instead of improving sensing performance. Xie et al. [48] applies reinforcement learning for dynamic partitioning of early, intermediate, and late-stage information. However, this work merely divides the data without integrating information across stages. In contrast to these works, this paper introduces a collaborative perception framework that aims to improve sensing performance by conducting multi-stage data fusion.
+
+# 3. Methodology
+
+# 3.1. Overview
+
+As illustrated in Fig. 1, our key idea is to conduct selective multi-stage agent collaboration, rather than the single
+
+stage fusion used in existing methods. Conventional approaches indiscriminately transmit data encompassing the entire scene through a single stage, introducing undesired low-quality sensing information during communication. This not only increases communication overhead but also complicates fusion, as the system must first evaluate the quality of received data to ensure reliable results. In contrast, our approach adopts a selective multi-stage collaboration strategy, where the transmission decision, whether to send data and at which stage, is determined based on the sensing confidence level of each location. For high-confidence regions, we transmit late-stage bounding boxes, minimizing communication costs. For moderate-confidence regions, we transmit intermediate-stage features for richer information. For low-confidence regions, transmission is suppressed to prevent misleading other agents. Additionally, our framework incorporates alignment and calibration corrections during both intermediate and late-stage fusion, further enhancing the reliability of the fused results.
+
+The details of our proposed mmCooper framework are illustrated in Fig. 2, which comprises three main components: (1) the Information Broadcasting, (2) the Intermediate-stage Fusion, and (3) the Late-stage Fusion. The encoded point cloud features will be sent to two branches. In one branch, the Information Broadcasting (Sec. 3.3) employs a Confidence-based Filter Generation Module to dynamically determine whether data should be suppressed, transmitted at the intermediate stage, or transmitted at the late stage. In the other branch, the Intermediate-stage Fusion (Sec. 3.4) contains the Multi-scale Offset-aware Fusion Module, which uses cross-attention to integrate features from both target and neighboring regions. This module mitigates potential misalignment between features from the ego and other agents, ensuring robust feature fusion. In Late-stage Fusion (Sec. 3.5), a BBox Filtering & Calibration Module removes inaccurate bounding boxes from other agents and refines the remaining ones using the ego agent's information-rich intermediate features. The calibrated bounding boxes from all agents will be merged with those generated by the ego agent to produce the final outputs.
+
+# 3.2. Observation Encoding
+
+In a multi-agent cooperative perception scenario, consider the collaboration of  $n$  agents, represented by the agent set  $N = \{1,\dots,n\}$ . The  $i$ -th agent serves as the ego vehicle and the remaining  $n - 1$  agents act as collaborators. All the agents first broadcast basic positional information to their collaborators, including coordinates and heading angle. In this way, the agents obtain the necessary information to project the information from the collaborators' systems to the ego vehicle's coordinate system. The ego agent processes its point cloud through a shared encoder to extract Bird's Eye View (BEV) features, represented as
+
+![](images/d6269f5e5b6546661ddf04054790d05e3e55c69b6cc399b8d5e537fcee6076a5.jpg)  
+Figure 2. Overview of mmCooper framework: a cooperative perception system with adaptive multi-stage fusion. It consists of three main components: (1) Information Broadcasting (Sec. 3.3) filters features and bounding boxes to achieve bandwidth efficiency; (2) Intermediate-stage Fusion (Sec. 3.4) captures surrounding information from the received feature maps for robust feature fusion; (3) Late-stage Fusion (Sec. 3.5) utilizes the information-rich fused features for Filtering & Calibration of the received bounding boxes.
+
+![](images/a5e8ec273546d64c7a27a2c839a6b787abab5324c70ef45d2e421c46fc4d3a15.jpg)  
+Figure 3. The design of Filter Generator in CFG Module, generating confidence scores to guide information transmission at each location.
+
+$F^i = \psi_E(x^i) \in \mathbb{R}^{C \times H \times W}$ , where  $\psi_E$  denotes the shared PointPillar [18] encoder,  $x^i$  represents the projected local observation, and  $C$ ,  $H$ , and  $W$  correspond to the channel, height, and width of the feature map, respectively.
+
+# 3.3. Information Broadcasting
+
+As shown in the top-left corner of Fig. 2, when conducting information broadcasting, the Confidence-based Filter Generation (CFG) Module dynamically decides whether data at each location should be suppressed, transmitted as intermediate-stage features, or transmitted as late-stage bounding boxes. Notably, no additional model or data compression techniques [32] are applied in this framework, only raw features or bounding boxes are transmitted. The bounding boxes are generated by the Detection Decoder from the features and the transmitting decision is guided by the confidence filter generated by the Filter Generator (Fig. 3) based on the sensing confidence, as detailed below.
+
+Filter Generator. The encoded BEV features (i.e.,  $F^i$ ) are fed into this Confidence Generator to produce intermediate-stage confidence map  $C_f^i$  and late-stage confidence map  $C_b^i$  for all the locations of the scene using CNN. A Gaussian Filter is then applied to the generated confidence maps to smooth out noise and reduce anomalies, improving the selection of critical regions. To suppress the information of the locations with low confidence, only the top  $p\%$  highest-
+
+confidence positions are selected from each confidence map to generate the spatial filters  $M_{f / b,t}^{i}$  (i.e.,  $M_{f,t}^{i}$  or  $M_{b,t}^{i}$ ). Then, for each location, a classification is required to decide which stage to transmit the data. However, using the traditional Softmax will prevent the back-propagation of the gradient due to its non-differentiability as a discrete operation. Instead, we utilize the Gumbel Softmax [16] to obtain approximate samples from a discrete distribution ensuring the propagation of gradient through the straight-through estimator [2] while preserving standard forward propagation. The Gumbel filter  $M_{f / b,g}^{i}$  obtained in this process is given by the following equation:
+
+$$
+M _ {f / b, g} ^ {i} = f _ {m a x} \left(\frac {\exp \left((\log C _ {f / b} ^ {i} + g _ {f / b}) / \tau\right)}{\sum_ {s} \exp \left((\log C _ {s} ^ {i} + g _ {s}) / \tau\right)}\right),
+$$
+
+where  $g_{f / b}$  is Gumbel noise [33],  $\tau$  denotes the temperature parameter of the distribution  $(\tau >0)$ , and  $s\in \{f,b\}$ . Based on the above process, our final filter  $\mathcal{M}_{f / b}^{i}$  is represented as:
+
+$$
+\mathcal {M} _ {f / b} ^ {i} = M _ {f / b, g} ^ {i} \odot M _ {f / b, t} ^ {i}.
+$$
+
+Based on the aforementioned filter, the intermediate-stage feature  $F^i$  and the coarse bounding box  $\mathcal{B}^i$  are filtered to obtain the filtered feature  $\hat{F}^i$  and coarse bounding box  $\hat{\mathcal{B}}^i$ .
+
+# 3.4. Intermediate-stage Fusion
+
+The data shared between agents inevitably contains calibration errors, causing potential misalignment in feature maps. To address this, we propose a Multi-scale Offset-aware Fusion (MOF) Module in the intermediate-stage fusion, which aggregates information from neighboring regions, allowing the fusion process at each location to account for potential misalignment. By incorporating the surrounding context, it effectively mitigates the impact of calibration errors, ensuring more accurate and robust agent collaboration.
+
+Multi-scale Offset-aware Fusion (MOF). The overall pipeline of this module is shown in Fig. 4(a). First, the ego features and received collaborator features are encoded at
+
+![](images/05a67b23b20765ce2fb208830b51cad3fd57eef5b486d3232e9c55e3e9d2b295.jpg)  
+Figure 4. (a) The Multi-scale Offset-aware Fusion Module. (b) The Multi-scale Offset-aware Attention Module.
+
+![](images/256b77720cf1f6ad3e4516fae48de1908056bee20ee335cccbbe30d1cb134912.jpg)  
+Figure 5. (a) The BBox Filtering & Calibration (BFC) Module. (b) The Deformable BBox Attention (DBA) Module.
+
+three different scales to capture target information of varying sizes. Next, Multi-scale Offset-aware Attention (MOA) is applied for feature fusion. The features are then upsampled to a uniform size and concatenated across scales to generate the final fused feature  $F^i$ .
+
+Multi-scale Offset-aware Attention (MOA). As shown in Fig. 4(b), we encode the ego feature at each location into queries using MLP. Meanwhile, features from a small neighborhood around the corresponding positions in each collaborator's feature map are extracted as keys and values for cross-attention. Note that low-confidence features are suppressed by collaborators and not transmitted, making them irrelevant during cross-attention. Specifically, we denote the focused location as  $(r,c)$  on the feature map, with a neighborhood size of  $s\times s$ . The output representation of feature fusion at location  $(r,c)$  is expressed as:
+
+$$
+\mathcal {F} _ {r, c} ^ {i} = \operatorname {C r o s s A t t n} (M L P (F _ {r, c} ^ {i}), \hat {F} _ {r, c, s \times s} ^ {j}, \hat {F} _ {r, c, s \times s} ^ {j}),
+$$
+
+Where  $\hat{F}_{r,c,s\times s}^{j}$  represents the transmitted collaborator features within an  $s\times s$  neighborhood centered at position  $(r,c)$ . By selectively aggregating the features at this posi
+
+tion and its neighborhood, we achieve collaboratively robust feature fusion.
+
+# 3.5. Late-stage Fusion
+
+The bounding boxes received from collaborators are often redundant, imprecise, misaligned, or even incorrect. To address this, the BBox Filtering & Calibration (BFC) Module in the Late-stage Fusion leverages the information-abundant fused intermediate features to refine the received bounding boxes, either filtering out erroneous ones or correcting their positions for improved accuracy.
+
+BBox Filtering & Calibration (BFC). As depicted in Fig. 5(a), first, the received bounding boxes and the fused intermediate features will be put into the Deformable BBox Attention (DBA) Module as inputs. It then extracts relevant information for each received bounding box from collaborators, which is processed by a vanilla transformer [45] to generate quality scores and positional offsets. Note that, to prevent unreasonable offsets and scores, we bound the output range using the Tanh activation function. Finally, bounding boxes with low quality scores are discarded, while the remaining ones are refined by applying the predicted positional offsets. The refined bounding boxes are then merged with those detected by the ego agent, followed by Non-Maximum Suppression (NMS) to generate the final results. To train the BFC module, we compute the offset loss  $\mathcal{L}_{off}$  using the smooth absolute error loss [11] and the score loss  $\mathcal{L}_{score}$  using focal loss [24].
+
+Deformable BBox Attention (DBA). As shown in Fig. 5(b), we first encode the received bounding boxes  $\hat{\mathcal{B}}^j$  by applying am MLP to their coordinates, size, and orientation information to generate feature representations. These features are then mapped onto the BEV space based on the bounding box locations, forming the bounding box feature map  $F_{b}(q)$ . To enhance these representations, we employ the deformable cross-attention mechanism to selectively attend to and integrate relevant information from the fused intermediate features. Specifically, the initial bounding box features  $F_{b}(q)$  serve as the query embedding to calculate the offsets of reference points using MLP. Using these offsets, we retrieve the corresponding reference features from the fused intermediate feature map as  $F_{r}^{i} = \mathcal{F}^{i}(q + \triangle q_{m})$ . In the meanwhile, an MLP and Softmax are applied on  $F_{b}(q)$  to generate the aggregation weights for  $F_{r}^{i}$ , which are then used to weight and integrate the reference features. Finally, after another MLP layer, we obtain the enhanced bounding box feature map:
+
+$$
+D B A (q) = \sum_ {\alpha = 1} ^ {A} W _ {\alpha} \left[ \sum_ {n = 1} ^ {N} \sum_ {m = 1} ^ {M} \omega \left(W _ {\beta} F _ {b} (q)\right) F _ {r} ^ {i} \right] + F _ {b} (q),
+$$
+
+where  $A$  is the number of attention heads,  $W_{\alpha}$  and  $W_{\beta}$  are learnable parameters,  $m$  represents the number of reference locations, and  $\omega$  denotes the softmax operation.
+
+# 3.6. Loss Functions
+
+We use the regression head and classification head of the Detection Decoder [4] to generate the bounding box detection results. The regression results represent the position, size, and yaw angle of each predefined box, expressed as  $O_{reg} = f_{dec}^{r}(\mathcal{F}^{i}) \in \mathbb{R}^{7 \times H \times W}$ . The classification results indicate the confidence score for each predefined box, represented as  $O_{cls} = f_{dec}^{c}(\mathcal{F}^{i}) \in \mathbb{R}^{2 \times H \times W}$ . To optimize the proposed system, we use smooth absolute error loss to supervise regression and focal loss for classification, denoted as  $\mathcal{L}_{reg}$  and  $\mathcal{L}_{cls}$ , respectively. Combining the previous losses, our total loss is represented as:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {r e g}} + \mathcal {L} _ {\text {c l s}} + \mathcal {L} _ {\text {o f f}} + \mathcal {L} _ {\text {s c o r e}}.
+$$
+
+# 4. Experiments
+
+# 4.1. Datasets and experimental settings
+
+Datasets. We conduct an extensive evaluation on three benchmark datasets, namely OPV2V [50], DAIR-V2X [56], and V2XSet [49]. OPV2V is a large-scale public V2V cooperative perception simulation dataset, which comprises 73 different scenes, 11,464 frames of point clouds and RGB images, and over 230,000 annotated 3D detection boxes. The training, validation, and test sets are divided into 6,374, 1,980, and 2,170 frames, respectively. DAIR-V2X is a large-scale real-world 3D object detection dataset, including 71,254 frames of point cloud and image data, with the training, validation, and test sets split in a 5:2:3 ratio. The V2XSet dataset is a large-scale synthetic dataset designed for V2X perception. It contains a total of 11,447 frames, which is divided into training, validation, and test sets, consisting of 6,694, 1,920, and 2,833 frames, respectively.
+
+Evaluation metrics. To evaluate the 3D object detection performance of the baseline and the proposed framework, we use the average precision (AP) [10] at Intersection-over-Union (IoU) thresholds of 0.5 and 0.7 as the evaluation metric. The communication volume between agents is expressed by the following equation [13]:
+
+$$
+\mathbf {V} = \log_ {2} \left(\left(| M | \times H \times W \times C + N _ {b} \times 7\right) \times 3 2 / 8\right),
+$$
+
+where  $|M|$  represents the feature retention ratio,  $N_{b}$  denotes the number of bounding boxes per agent, and 7 is used to describe the coordinates, dimensions, and angle information of each bounding box. Each value is represented using float32, with a division by 8 for bytes.
+
+Implementation details. We implement our model on the PyTorch toolbox [35] and train it on NVIDIA GeForce RTX 4090 GPUs. We use the Adam optimizer and adopt batch sizes of 3, 5, and 3 for the OPV2V, DAIR-V2X, and V2XSet datasets, respectively, with 60 epochs for each. All models use the PointPillars [18] backbone to extract features from raw point clouds. The confidence ratio  $p$  selected for the CFG module is  $70\%$  for OPV2V,  $60\%$  for DAIR-V2X, and
+
+Table 1. Collaborative perception performance on the OPV2V, DAIR-V2X and V2XSet dataset with a time delay of  $100~ms$ , localization errors of  $0.2m$ , and heading errors of  $0.2^{\circ}$  using Average Percision(AP) $@0.7/0.5$  as metrics. Bold numbers indicate the best results, while underlined numbers represent the second-best results. * represents a variation of PointPillar [18].  
+
+<table><tr><td rowspan="2">Models</td><td>OPV2V</td><td>DAIR-V2X</td><td>V2XSet</td></tr><tr><td>AP@0.7/0.5</td><td>AP@0.7/0.5</td><td>AP@0.7/0.5</td></tr><tr><td>No Fusion* [18]</td><td>48.66/68.71</td><td>43.57/50.03</td><td>40.20/60.60</td></tr><tr><td>Late Fusion* [18]</td><td>59.48/79.62</td><td>34.47/51.14</td><td>30.75/54.92</td></tr><tr><td>Intermediate Fusion* [18]</td><td>70.82/ 88.41</td><td>39.38/56.22</td><td>59.38/83.18</td></tr><tr><td>When2com [29]</td><td>57.55/74.11</td><td>33.68/48.20</td><td>41.85/67.41</td></tr><tr><td>DiscoNet [22]</td><td>68.64/84.72</td><td>40.69/52.67</td><td>54.11/79.82</td></tr><tr><td>Where2comm [13]</td><td>69.73/85.16</td><td>43.71/59.52</td><td>63.77/83.17</td></tr><tr><td>V2X-ViT [49]</td><td>70.06/84.65</td><td>40.43/53.08</td><td>61.49/83.63</td></tr><tr><td>Select2col [28]</td><td>62.46/82.30</td><td>34.82/51.96</td><td>51.22/76.88</td></tr><tr><td>ERMVP [58]</td><td>69.71/86.63</td><td>46.96/64.21</td><td>58.44/81.54</td></tr><tr><td>Ours</td><td>78.11/ 88.93</td><td>48.27/ 65.12</td><td>65.86/84.40</td></tr></table>
+
+$70\%$  for V2XSet, and the surrounding grid size chosen for the MOF is  $3 \times 3$ . To closely simulate real traffic conditions, we introduce localization and heading errors with standard deviations of  $0.2 \, \text{m}$  and  $0.2^{\circ}$ , respectively, sampled from a Gaussian distribution. The communication range is limited to  $70 \, \text{m}$ , excluding agents beyond this range from collaborative communication.
+
+# 4.2.Quantitative Evaluation
+
+Detection Performance. Tab. 1 presents the comparison of the perception performance of our proposed mmCooper model and various baseline models on OPV2V, DAIR-V2X, and V2XSet datasets with a time delay of  $100~ms$ , localization errors of  $0.2m$ , and heading errors of  $0.2^{\circ}$ . The No Fusion relies solely on ego agent observations. Late Fusion shares only the bounding box results among agents. Intermediate Fusion allows agents to share complete features extracted from raw point clouds. The above three models are all variants based on the PointPillar [18] point cloud detector. Additionally, we consider SOTA models, including When2com [29], DisoNet [22], Where2comm [13], V2X-ViT [49], Select2col [28] and ERMVP [58]. As shown in the table, our proposed mmCooper outperforms all the baselines on both simulated and real-world datasets. Compared to existing SOTA models, mmCooper outperforms the second-best baseline on the OPV2V, DAIR-V2X, and V2XSet datasets by  $7.29\% / 0.59\%$ ,  $1.31\% / 0.91\%$  and  $2.09\% / 0.77\%$  in AP@0.7/0.5, respectively. This demonstrates the effectiveness and superiority of our multi-stage fusion framework.
+
+Communication Volume. Fig. 6 illustrates the model performance under different bandwidth conditions on the OPV2V, DAIR-V2X, and V2XSet datasets. Experimental results show that mmCooper significantly reduces communication costs, achieving performance levels comparable to late fusion. In comparison to other SOTA models, the communication volume required to achieve optimal performance is 9153/156/18305 times more than our method. Notably, on the OPV2V and V2XSet datasets, our
+
+Figure 6. Collaborative perception performance and communication volumes of all the models on the OPV2V, DAIR-V2X, and V2XSet datasets.  
+![](images/29ca86b54613944ac6a0ae3caceebc3d9701256e8fb86d85acc02638b9d979e8.jpg)  
+$\star$  mmCooper(Ours)---ERMVP Where2comm V2X-ViT When2com Select2Col Intermediate Fusion Late Fusion
+
+![](images/a32c12834aeb4d187f5947c8d06a36b4817758fac8d826c323302e2b345a9a26.jpg)
+
+![](images/427d19ddd9190e1051b8f28da4d9fb7d715a44fdcb0c0cd1c84df7b6f074901d.jpg)
+
+method even achieves lower communication volume than late fusion. This is because our CFG module suppresses low-confidence information from the transmission and selectively transmits complementary and exclusive information at intermediate and late stages rather than transmitting through only one stage encompassing all information of the entire scenario. In addition, since some Late Fusion methods (e.g., OpenCOOD [50]) transmit non-processed (e.g., NMS) BBoxes, our mmCooper even achieves a lower communication volume compared to the late fusion model on certain datasets.
+
+Robustness to Localization Errors and Transmission Delay. We verified the robustness of the agents during collaborative processes in the presence of localization errors and transmission delay on the OPV2V and DAIR-V2X datasets. Following the noise settings in [49], localization noise was sampled from a Gaussian distribution with a mean of  $0\,m$  and a standard deviation  $\sigma \in \{0, 0.2, 0.4\}m$ . As shown in Tab. 2, as the standard deviation of the localization noise gradually increases, the detection performance of the models decreases. On the DAIR-V2X dataset, when2com even performs worse than the No Fusion method when the localization error exceeds  $0.2\,m$ . Our method outperforms all the baselines under all localization noise settings, demonstrating its robustness to varying levels of localization error. Transmission delay can lead to misalignment of features and proposals, thereby impacting detection performance. We evaluated the models on the OPV2V and DAIR-V2X datasets with time delays  $\tau \in \{0, 200, 400\}ms$  set to  $0\,ms$ ,  $200\,ms$ , and  $400\,ms$ . With increasing time delay, the detection performance of all methods gradually degrades. However, mmCooper achieves the highest Average Precision (AP) over all the models on both datasets. This robustness to localization errors and transmission delay demonstrates the effectiveness of the MOF and BFC modules in addressing the potential misalignment and errors during communication among agents. For more results regarding errors during transmission, please refer to the supplementary.
+
+![](images/1ed8a4e237d15a7ad46ee7c8230d487ec8ff961ebb94ae4854006a71b7d40fc1.jpg)  
+Figure 7. Visualization of two-stage fusion on DAIR-V2X. We show the results from the Confidence-based Filtering Generation Module, including discarded information (white background), BBoxes for transmission (red dots), and features for transmission (yellow background). We also show the BFC module results, including uncalibrated BBoxes (blue boxes), calibrated BBoxes (red boxes), and ground truth BBoxes (green boxes).
+
+# 4.3. Ablation Study
+
+We conducted comprehensive ablation studies on the OPV2V and DAIR-V2X datasets to demonstrate the importance of different components, as shown in Tab. 3.
+
+Importance of Core Components. All the core components contribute to performance improvement. Removing the CFG module results in the transmission of information for both the intermediate and late stages across all locations without suppression or selection. While this variant increases the amount of transmitted information compared to mmCooper, it leads to a performance drop. This highlights the importance of filtering out low-confidence information and selectively transmitting data at different stages to optimize performance. The absence of the MOF module replaces the MOA module with a self-attention mechanism, while removing the BFC module eliminates the filtering and refinement of received bounding boxes. Both modifications result in a performance drop, highlighting the importance of incorporating spatial neighborhood information to mitigate misalignment and applying bounding box filtering and refinement to address redundancy, imprecision, or potential errors in received detections.
+
+Superiority of Multi-stage Fusion. We entirely removed the Late Fusion (LF) or the Intermediate Fusion (IF) to degrade our model to single-stage fusion. The experimental results indicate that removing either module leads to a performance decline, underscoring the effectiveness of the proposed multi-stage cooperation framework.
+
+Table 2. Results for different localization errors (m) and transmission delay (ms) on the OPV2V and DAIR-V2X dataset evaluated using AP@0.7. Bold numbers indicate the best results, while underlined numbers represent the second-best results.  
+
+<table><tr><td>Noise Type</td><td colspan="6">Localization Errors(m)</td><td colspan="6">Transmission Delay(ms)</td></tr><tr><td>Datasets</td><td colspan="3">OPV2V</td><td colspan="3">DAIR-V2X</td><td colspan="3">OPV2V</td><td colspan="3">DAIR-V2X</td></tr><tr><td>Noise Level</td><td>0.0</td><td>0.2</td><td>0.4</td><td>0.0</td><td>0.2</td><td>0.4</td><td>0</td><td>200</td><td>400</td><td>0</td><td>200</td><td>400</td></tr><tr><td>No Fusion</td><td>48.66</td><td>48.66</td><td>48.66</td><td>43.57</td><td>43.57</td><td>43.57</td><td>48.66</td><td>48.66</td><td>48.66</td><td>43.57</td><td>43.57</td><td>43.57</td></tr><tr><td>When2com [29]</td><td>70.82</td><td>64.35</td><td>59.98</td><td>39.50</td><td>36.62</td><td>35.03</td><td>70.82</td><td>43.96</td><td>36.55</td><td>39.50</td><td>36.83</td><td>33.72</td></tr><tr><td>DiscoNet [22]</td><td>76.05</td><td>73.59</td><td>65.85</td><td>46.94</td><td>46.03</td><td>44.96</td><td>76.05</td><td>60.08</td><td>50.33</td><td>46.94</td><td>44.03</td><td>41.57</td></tr><tr><td>Where2comm [13]</td><td>78.47</td><td>75.45</td><td>69.77</td><td>52.34</td><td>49.34</td><td>46.96</td><td>78.47</td><td>65.23</td><td>53.33</td><td>52.34</td><td>47.76</td><td>45.25</td></tr><tr><td>V2X-ViT [49]</td><td>77.83</td><td>75.21</td><td>66.72</td><td>46.12</td><td>43.81</td><td>42.53</td><td>77.83</td><td>66.08</td><td>50.33</td><td>46.12</td><td>45.49</td><td>43.99</td></tr><tr><td>ERMVP [58]</td><td>80.55</td><td>76.19</td><td>72.78</td><td>53.27</td><td>48.66</td><td>45.97</td><td>80.55</td><td>68.89</td><td>68.31</td><td>53.27</td><td>49.68</td><td>48.60</td></tr><tr><td>Ours</td><td>86.41</td><td>82.53</td><td>76.80</td><td>56.06</td><td>51.52</td><td>47.66</td><td>86.41</td><td>77.44</td><td>75.26</td><td>56.06</td><td>50.96</td><td>50.81</td></tr></table>
+
+Table 3. Ablation study results of different designs in mmCooper on the OPV2V and DAIR-V2X datasets. CFG: Confidence-based Filter Generation Module; MOF: Multi-scale Offset-aware Fusion; BFC: BBox Filtering & Calibration Module; LF: Late-stage Fusion; IF: Intermediate-stage Fusion.  
+
+<table><tr><td rowspan="2">CFG</td><td rowspan="2">MOF</td><td rowspan="2">BFC</td><td rowspan="2">LF</td><td rowspan="2">IF</td><td colspan="2">AP@0.7/0.5(↑)</td></tr><tr><td>OPV2V</td><td>DAIR-V2X</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>78.11/88.93</td><td>48.27/65.12</td></tr><tr><td colspan="7">Importance of Core Components</td></tr><tr><td>×</td><td>✓</td><td>✓</td><td>-</td><td>-</td><td>73.46/88.84</td><td>47.66/63.63</td></tr><tr><td>✓</td><td>×</td><td>✓</td><td>-</td><td>-</td><td>72.60/88.51</td><td>47.27/63.49</td></tr><tr><td>✓</td><td>✓</td><td>×</td><td>-</td><td>-</td><td>76.77/88.56</td><td>44.31/59.68</td></tr><tr><td colspan="7">Results of Single-stage Fusion</td></tr><tr><td>-</td><td>-</td><td>-</td><td>×</td><td>✓</td><td>76.83/88.65</td><td>46.65/62.84</td></tr><tr><td>-</td><td>-</td><td>-</td><td>✓</td><td>×</td><td>66.80/78.62</td><td>45.78/56.88</td></tr></table>
+
+# 4.4. Qualitative Evaluation
+
+Visualization of Two-stage Fusion. As shown in the Fig. 7, we visualize the transmission decisions and bounding boxes refinement in the two-stage fusion on the DAIR-V2X dataset. The yellow background and red dots show the selective transmission of data through two stages. The white background shows the locations discarded by the CFG module, showing a substantial amount of low-confidence or irrelevant information in the scenario. The removal and correction of the uncalibrated blue boxes demonstrates the BFC module's effectiveness in filtering and refining received bounding boxes by eliminating redundancies and improving alignment with the ground truth.
+
+Visualization of Detection Results. Fig. 8 shows visualization results for a scenario in the DAIR-V2X dataset. Compared to baseline methods, mmCooper demonstrates high-precision 3D object detection, accurately predicting nearly all ground truth objects. In contrast, baseline methods either fail to detect certain vehicles or produce inaccurate bounding boxes. †Refer to the supplementary materials for additional visualized detection results.
+
+# 5. Conclusion
+
+In this paper, we have proposed mmCooper, a novel multi-agent, multi-stage, communication-efficient, and
+
+![](images/2cce017427ea8143b0e824f643696330eb4a7ed0bd22ee14de751e05029b7d46.jpg)
+
+![](images/9f78615aa87cdb346ef96226927ff946f71c91cfb5838c867aa6950d9e86cb8f.jpg)
+
+![](images/faafa67d9cccb3cc0d64642f79990f0029143a867411e0ce43e0e47a888f5444.jpg)  
+(a) Where2comm  
+(c) ERMVP
+
+![](images/42380c077f7a2fee54647d54e03ae4c3cce81b2e73a802a4b5529598d8a8e969.jpg)  
+(b) V2X-ViT  
+(d) Ours  
+Figure 8. Visualization comparison of detection results on the DAIR-V2X dataset. Green and red boxes represent the ground truth and the model-predicted bounding boxes, respectively.
+
+collaboration-robust cooperative perception framework. mmCooper is the first framework to achieve adaptive fusion of complementary data across stages for cooperative perception. We introduce the Confidence-based Filter Generation Module to enable dynamic partitioning of intermediate features and late-stage bounding boxes, balancing communication load and perception performance. Additionally, the Multi-scale Offset-aware Fusion module and BBox Filtering & Calibration module are incorporated to address potential misalignment and calibration noise among agents. mmCooper outperforms the second-best state-of-the-art models on the OPV2V, DAIR-V2X, and V2Xset datasets, achieving improvements of  $7.29\%$ ,  $1.31\%$ , and  $2.09\%$  in AP@0.7, respectively, while reducing communication volume by factors of 9153, 156 and 18305.
+
+Acknowledgements. This work is supported by the National Natural Science Foundation of China under Grant 62272357 and 62302326, Wuhan Science and Technology Project for Key Research and Development under Grant 2024050702030090 and Wuhan Science and Technology Joint Project for Building a Strong Transportation Country under Grant 2024-2-7.
+
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+# monoVLN: Bridging the Observation Gap between Monocular and Panoramic Vision and Language Navigation
+
+Renjie Lu $^{1*}$ , Yu Zhou $^{1*}$ , Hao Cheng $^{2}$ , Jingke Meng $^{1\dagger}$ , Wei-Shi Zheng $^{1,3,4}$
+
+$^{1}$ School of Computer Science and Engineering, Sun Yat-sen University,  $^{2}$ Hunan University,
+
+<sup>3</sup>Pengcheng Lab, <sup>4</sup>Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education, China {lurj3, zhouy635}@mail2.sysu.edu.cn, haocheng@hnu.edu.cn, mengjke@gmail.com, wszheng@ieee.org
+
+# Abstract
+
+Vision and Language Navigation(VLN) requires agents to navigate 3D environments by following natural language instructions. While existing methods predominantly assume access to panoramic observations, many practical robotics are equipped with monocular RGBD cameras, creating a significant configuration disparity. In this work, we address this critical gap by developing a novel 3DGS-based framework for monocular VLN agents, focusing on the intrinsic information incompleteness challenge. Our approach incorporates two key innovations: (1) implicit partial completion module for inferring representations of missing regions in incompletely rendered panoramic feature maps, and (2) an uncertainty-aware active perception strategy that enables the agent to actively acquire visual observation when uncertain about its decision. Extensive experiments on R2R-CE and RxR-CE datasets demonstrate that our monoVLN outperforms all existing monocular methods, significantly improve  $8\%$  success rate on R2R-CE compared to previous monocular methods. We also validate our monoVLN in real-world environments, providing a practical solution for real-world VLN.
+
+# 1. Introduction
+
+Vision and Language Navigation (VLN) [5, 27] involves guiding an agent to navigate to a specified destination by interpreting natural language instructions. This process typically requires the agent to execute fine-grained actions (e.g., rotating 15 degrees left/right or advancing 0.25 meters) within navigable areas. VLN has attracted significant research interests[3, 10, 11, 13, 17, 20, 21, 34, 43, 46, 50, 52].
+
+Current researches in VLN predominantly focus on navigation utilizing panoramic observations, which assumes that the 360-degree area surrounding the agent is fully ac
+
+![](images/9ee83174b772e30e0a0899655dae9ce76245b7bd2333e29552a883157204d214.jpg)  
+observed rendered  
+Panoramic
+
+![](images/4863e12ee5d2248084a07e9ca8126d13a04a65de710b29e82f4bdc98738b8ec9.jpg)  
+Panoramic views captured by cameras
+
+![](images/ebd56567ea52678938cf0f6ac4244e96cfdbe1559e07850dc70df623eb4cca3f.jpg)
+
+![](images/9786de176a1af84ddcea475abb4a3ead5faece71d9cd9bd764f4a26a367df920.jpg)  
+Monocular
+
+![](images/6663b0c854e2d97251129b1bf4aefaa8685456bb81c486efc54c594a6b36777d.jpg)  
+Rendered incomplete panoramic views  
+□front   
+Figure 1. An example of panoramic views captured by cameras and rendered panoramic views. The rendered views are incomplete due to unobserved areas during navigation, resulting in certain regions being rendered with black.
+
+![](images/0e0e40532f91ac1da27080538faa8efd869804bc3faf2e55ddabee81a2eab9ec.jpg)
+
+cessible. These methods achieve notable performance but facing significant limitations in real-world robotic deployment. The primary constraint stems from the prevalent use of monocular RGBD cameras in practical robotic applications, which restrict the observable area to a limited field of view around the agent at a step. Consequently, the development of models compatible with monocular camera is imperative for enhancing practicality and compatibility in real-world scenarios. Recent methods [46, 50] address this challenge by reconstructing 3D feature fields that integrate previously observed information and rendering panoramic views, enabling the direct transfer of panoramic VLN models to monocular settings and achieving impressive results. However, they ignore a fundamental challenge inherent to monocular VLN: the intrinsic information incompleteness resulting from the limited field of view. As illustrated in Figure 1, the rendered views by works[46, 50] are often incomplete, which prevents visual encoders from extracting comprehensive features and leads to suboptimal performance. In this work, we present the first attempt to solve this problem.
+
+An intuitive solution is to perform a 360-degree rotation at each step to mimic panoramic observations. While this method is conceptually simple, it introduces significant inefficiencies, leading to an increase of over  $200\%$  in the num
+
+ber of navigation steps required. To alleviate this, drawing inspiration from human navigation, we first attempt to leverage the agent's subjective perspective, presenting a simple yet effective active perception strategy, enabling it to actively acquire visual observations when uncertain about its decision. Specifically, we focus on two key challenges: determining when to look, which involves identifying the moments for the agent to gather observations, and where to look, which involves selecting a informative direction for visual data collection. This strategy can potentially reduce severe incompleteness shown in Figure 1, where nearly all regions appear black in a given view while avoiding many extra steps.
+
+For the partial absence of the observation within a view, we further propose an implicit partial completion module. This module leverages contextual feature relationships to infer representations of missing regions rendered from feature field, enabling the extraction of comprehensive features for partially incomplete views. Specifically, to infer features for missing regions, we leverage the MAE framework, which operates on partial features. The view encoder takes rendered partial feature maps as input and generates corresponding latent representations. These latent features are then decoded to reconstruct complete feature maps, guided by the auxiliary loss inspired by MAE[18]. Through this reconstruction-based training paradigm, the decoder learns to predict full feature maps from partial inputs, enabling the view encoder to implicitly infer missing visual information.
+
+Based on the above, we propose monoVLN, a new 3DGS-based VLN framework designed for practical robotic applications using monocular RGB-D cameras. Unlike previous works [46, 50], which rely on NeRF for constructing 3D feature fields, we employ 3D Gaussian Splating(3DGS). This technique enables fast rendering and a training-free feature field, significantly improving efficiency. We conduct extensive experiments on the widely used R2R-CE[27] and RxR-CE[29] datasets. Our proposed model significantly improves  $8\%$  success rate compared to previous monocular methods on R2R-CE, while only including  $9\%$  extra steps. To validate practical applicability, we deploy monoVLN on real-world robotic platforms, where it achieves fast inference on RTX 4060 GPU, highlighting its potential for real-world application.
+
+In summary, our contributions are as follows:
+
+- We propose monoVLN, a 3DGS-based framework for monocular vision and language navigation, enabling efficiency and effectiveness.  
+- We present the first attempt to tackle the information incompleteness problem in monocular VLN by introducing implicit completion and active perception.  
+- Our model achieves a new state-of-the-art on R2R-CE and RxR-CE datasets, with an  $8\%$  higher success rate on R2R-CE compared to previous monocular VLN methods.
+
+# 2. Related Works
+
+Vision and Language Navigation. The field of natural language-guided navigation in unseen environments[5, 27, 29] has seen substantial progress in recent years. A primary focus has been on architectural innovations, particularly in developing advanced decision-making backbones[10, 20] and enhancing vision modeling techniques[1, 2, 19, 32]. Building upon these foundations, various planning strategies have been proposed, including self-correction mechanisms[25, 35], graph-level planning[11, 34, 44] and hierarchical frameworks[14]. Complementing these advances, visual data augmentation methods[30, 31, 43] have emerged for improving visual generalization ability. Other line of work focuses on enhancing visual-language representation, which leverage back-translation-based data generation[13, 24, 45] and domain-specific pretraining techniques[16, 17, 36, 38, 39]. More recently, [47, 48] focus on scaling data generation, approaching near human performance on the well-recognized R2R benchmark.
+
+VLN in Continuous Environments. Despite the remarkable progress in VLN, these agents are developed on discrete predefined topological graphs, making it impractical to real-world robot applications. To bridge the gap, VLN-CE[27] pioneers continuous environment navigation by constructing the R2R-CE dataset. Early methods[8, 15, 27, 28, 41] on R2R-CE demonstrated significantly inferior performance compared to their discrete VLN counterparts. Subsequent studies[21, 26] analyze the difference between discrete and continuous VLN and developed frameworks that transfers discrete VLN agents to continuous domains, substantially reducing the gap between these two paradigms. Recently, ETPNav[3] enhances the framework through improved waypoint predictor and topological mapping. HNR[49] introduces a feature field representation combined with an expanded frontier-based action space.
+
+Real World VLN Models. Both discrete and continuous models are trained and evaluated in simulators. [6] first deploy VLN models in real world. VLMap [22] introduces a framework that constructs BEV maps and use LLMs to generate high-level navigation code. To enable agents to comprehend free-form instructions and avoid noisy depth in real-world scenarios, NaVid [52] utilizes a video-based LLM to process RGB frames and predict actions in text form. While VLN agents are predominantly developed with panoramic observations, recent work 3DFF[50] transfers panoramic VLN models to monocular observations via feature field, g3D-LF[46] further enhances their quality. However, these approaches overlook the inherent information incompleteness of monocular observations. Our work presents the first attempt to tackle this challenge through active perception and implicit inference of complete views, effectively mitigating the issue.
+
+![](images/bb6f49486227fb6bb321724121baa20ab862147b0ccd37b65f46b3f2dee967f4.jpg)  
+Figure 2. Typical panoramic VLN model pipeline. The blue node represents the current location, while the gray nodes represent other positions in the environment. The planner predicts a sub-goal on the graph through node classification, guiding the agent to move toward the predicted node. If the target node is a direct neighbor of the current node, the agent simply rotates and moves to it. Otherwise, the agent navigates to the target node by following the shortest path on the graph.
+
+# 3. Method
+
+# 3.1. VLN Background
+
+Problem Formulation. In VLN, an agent is provided with a natural language instruction  $\mathcal{I}$  describing the navigation task. At time step  $t$ , the agent observes an RGB image  $r_t$  and a depth image  $d_t$  captured by a monocular RGB-D camera, and its current 4D pose  $p_t = (x_t, y_t, z_t, \theta_t)$ , where  $(x_t, y_t, z_t)$  represents the agent's coordinates and  $\theta_t$  denotes its heading direction. The agent selects an action  $a_t$  from a discrete action space  $\mathcal{A} = \{\text{turn left } 15^\circ, \text{turn right } 15^\circ, \text{move forward } 0.25\text{m}, \text{stop}\}$ . The navigation task is considered successful when the agent stops at the target location within 3 meters.
+
+VLN Models with Panoramic Views. In this part, we outline the general pipeline of panoramic VLN models. As illustrated in Figure 2, typical panoramic VLN framework facilitates navigation by constructing a topological map derived from panoramic views and planning paths on this map using visual observations and natural language instructions. Specifically, at step  $t$ , the agent observes panoramic RGB images  $\mathcal{R}_t = \{r_{t,i}\}_{i=1}^{12}$  and panoramic depths  $\mathcal{D}_t = \{d_{t,i}\}_{i=1}^{12}$  towards 12 different orientations with 30 degrees between each. The RGB images  $\mathcal{R}_t$  are encoded into features  $\{f_{t,i}^v\}_{i=1}^{12}$ , which are stored in nodes[3] or edges[34] of the topological map  $\mathcal{M}_t$ . The depth images  $\mathcal{D}_t$  are used to predict the coordinates of nearby navigable waypoints[3, 21, 34], enabling the update of the topological map from  $\mathcal{M}_{t-1}$  to  $\mathcal{M}_t$ . A planner then encodes the topological map  $\mathcal{M}_t$  along with the instruction  $\mathcal{I}$  and selects the optimal waypoint as the sub-goal to move. With the predicted sub-goal, the agent navigates to it along the shortest path on  $\mathcal{M}_t$ . If it fails to reach the sub-goal due to obstacles, we stop it immediately.
+
+# 3.2. Framework Overview
+
+We present the overall framework of our monoVLN in Figure 3, designed for practical VLN using monocular RGB-D cameras. Our framework primarily addresses the challenge of intrinsic information incompleteness caused by the limited field of view in monocular observations. Specif
+
+ically, with the monocular RGB-D observation, we incrementally construct a 3D feature field by leveraging the feature 3DGS [53]. This feature field is used for two functionalities: first, rendering an agent-centric top-down view feature map(BEV feature) input to a waypoint predictor to predict the coordinates of nearby navigable waypoints. Second, rendering panoramic feature maps processed by a implicit partial completion module to enable comprehensive panoramic understanding by inferring missing regions in rendered views. With the rendered panoramic features and predicted waypoints, we construct a topological map and perform decision planning, following the general pipeline of VLN models[3, 11, 21, 34]. When the agent encounters uncertainty in its decision-making process, it selects a informative directions and actively acquires visual observations to refine its decisions. Details are presented below.
+
+# 3.3. 3DGS-based Feature Field Construction
+
+In this section, we describe how we construct 3DGS feature field to effectively convert monocular observation to panoramic observation and enable transferring powerful panoramic VLN model to the monocular setting. By reconstructing the feature field during navigation and rendering panoramic views using it, the rendered panoramic views provide richer information compared to monocular observations since the reconstructed feature field integrates historical observations. We opt for a 3DGS-based feature field as it permits us to directly convert a point cloud into Gaussians without training. This choice allows us to concentrate on the core navigation task without diverting attention to scene reconstruction.
+
+Specifically, at time step  $t$ , we utilize MobileSAM[51] to extract a feature map  $f_{t}^{r} \in \mathbb{R}^{C \times H \times W}$  for the monocular RGB observation  $r_t$ . Using downsampled depth image  $d_t$ , the feature map  $f_{t}^{r}$  is mapped to 3D world position through the camera pose and intrinsics, resulting in a point cloud where each point is associated with color and feature information. To transform the point cloud into a feature-based 3DGS [53], we transfer the attributes of the points to Gaussians. Each Gaussian has six attributes: coordinates, color, scale, rotation, opacity, and feature. We migrate the coordi
+
+![](images/2ca813ef62bb940fb9f64f950908d18cf3e51b84564938abfdc7ef3bfecc8fd5.jpg)  
+Figure 3. The overall framework of our method. We process observed RGB-D images to update the feature field for rendering panoramic feature maps and a BEV map, which are then processed by our Implicit Partial Completion(IPC) module and BEV-based waypoint predictor. Their predictions are fed into mapper and planner to predict a sub-goal. The robot moves toward this sub-goal or only rotates to achieve Uncertainty-aware Active Perception(UAP) based on its prediction uncertainty.
+
+nates, color, and feature directly from the point cloud while setting the remaining attributes to fixed values. This allows us to treat 3DGS as a point cloud rendering method rather than its conventional use for scene reconstruction. This simple method provides acceptable rendering quality without the need for training.
+
+# 3.4. BEV-based Waypiont Prediction
+
+Panoramic VLN models are predominantly designed using topological maps for global planning and backtracking[11, 14, 34]. These approaches typically rely on a waypoint predictor to estimate the coordinates of nearby waypoints for constructing such maps[3, 21]. While these predictors are built upon panoramic depth images, we present a waypoint predictor for the monocular setting that utilizes a top-down view feature map (BEV feature) to accomplish this, where the BEV can be directly derived from the feature field.
+
+As illustrated in Figure 3, the BEV feature is extracted from the feature field. To generate this map, we position the camera considerably higher above the agent and render an agent-centric BEV feature map  $f_{t}^{b} \in \mathbb{R}^{C \times 192 \times 192}$ . Each pixel in the BEV map corresponds to a  $5cm \times 5cm$  regions. To avoid occlusions caused by ceilings, we filter out Gaussians located more than 1 meter above the agent's height before rendering. The resulting BEV feature map is fed into the waypoint predictor composed of two U-Nets: the first U-Net completes the BEV feature map, while the second predicts a heatmap representing potential waypoints. Using Non-Maximum Suppression (NMS), discrete waypoints relative to the agent are extracted from the heatmap and converted to world coordinates via the agent's pose. These coordinates are then used to update the topological map from  $\mathcal{M}_{t-1}$  to  $\mathcal{M}_{t}$  shown in Figure 2.
+
+The waypoint predictor is trained independently using a heatmap loss [54], with the same dataset as previous works [21, 50]. Additionally, an inpainting loss is applied to ensure the completeness of the BEV feature map. For more implementation details, please refer to the Appendix.
+
+![](images/abf87501f2f1ac5e7857e4127843dae17d5e3381b1e614388452d65bc95e5cd9.jpg)  
+Figure 4. Training MAE on incomplete rendered feature map. The rendered incomplete feature map is randomly masked and input to the view encoder. Then the output is processed by the following decoder to reconstruct the full feature map.
+
+# 3.5. Implicit Partial Completion Module
+
+The feature fields rendered using 3DGS are often incomplete, particularly in unobserved areas (e.g., regions behind the agent), as demonstrated in Figure 4. For instance, unobserved structures such as stairs are rendered as black areas. To address this limitation, we propose an implicit partial completion module that leverages contextual relationships to infer representations of missing regions and extract comprehensive features from these partially incomplete views.
+
+To infer features for missing regions, we leverage the MAE framework[18], which operates on partial features. The MAE view encoder takes rendered partial feature maps as input and generates corresponding latent representations. These latent features are then decoded to reconstruct complete feature maps, guided by the auxiliary loss inspired by MAE. Through this reconstruction-based training paradigm, the decoder learns to predict full feature maps from partial inputs, enabling the view encoder to implicitly infer missing visual information.
+
+Formally, the 3DGS rendered partial feature maps denoted as  $\{f_{t,i}^{m}\}_{i = 1}^{12}$  that corresponding to 12 orientations, with a 30-degree angle between adjacent directions. Given the rendered  $i_{th}$  feature map  $f_{t,i}^{m}$ , we convert it to tokens like ViT[12]. These tokens undergo random masking (set to zero) and, along with an additional [CLS] token, are processed by a transformer-based view encoder. The encoded
+
+tokens are subsequently decoded by another transformer to reconstruct the complete feature map. We train the completion encoder and decoder using the following reconstruction loss:
+
+$$
+\mathcal {L} _ {m a e} = \frac {1}{| \mathcal {S} |} \sum_ {x \in \mathcal {S}} \| x - x ^ {g t} \| ^ {2}, \tag {1}
+$$
+
+where  $S$  denotes the set of predicted masked tokens,  $x$  represents reconstructed tokens and  $x^{gt}$  corresponds to the ground truth tokens. We follow [18] to exclude non-masked patches from the loss computation. Notably, the reconstruction process covers both randomly masked patches and rendered black areas. Upon training completion, the [CLS] token is used to serve as the global representation  $f_{i}^{v}$  of the input feature map. For the rendered 12 views, we extract this global feature for each of them and obtain  $\{f_{t,i}^{v}\}_{i = 1}^{12}$ . To maintain consistency with standard panoramic VLN training protocols that typically employ CLIP features, we also align  $f_{t,i}^{v}$  to CLIP feature by maximizing feature similarity and minimizing distance:
+
+$$
+\mathcal {L} _ {c l i p} = 1 - \frac {f ^ {v} \cdot f ^ {c l i p}}{\| f ^ {v} \| \| f ^ {c l i p} \|} + \| f ^ {v} - f ^ {c l i p} \| _ {2} ^ {2} + \| f ^ {v} - f ^ {c l i p} \| _ {1}, \tag {2}
+$$
+
+$f^{clip}$  is the corresponding CLIP feature. We omit script  $t, i$  here for clarity.
+
+# 3.6. Mapping and Planning
+
+With rendered panoramic features  $\{f_{t,i}^{v}\}_{i = 1}^{12}$  and predicted waypoints at each step, we construct a topological map and perform decision planning, following the general VLN models [3, 11, 21, 34] (see Section 3.1). Specifically, topological map  $\mathcal{M}_{t - 1}$  is updated by these predicted features and waypoints to produce  $\mathcal{M}_t$ . Subsequently, the planner predicts an node  $a_{t}$  guided by the instruction  $\mathcal{I}$ :
+
+$$
+p _ {t} = \operatorname {P l a n n e r} (\mathcal {I}, \mathcal {M} _ {t}), \tag {3}
+$$
+
+$$
+a _ {t} = \arg \max  p _ {t}.
+$$
+
+Here,  $p_t$  is predicted probabilities and  $a_t$  corresponds to a node on  $\mathcal{M}_t$  and serves as a sub-goal for the navigation. The planner is trained using the ground-truth next node  $a_t^*$  by minimizing the cross-entropy loss at each step. The overall loss for the planner is defined as follows:
+
+$$
+\mathcal {L} _ {\text {p l a n n e r}} = \frac {1}{T} \sum_ {t = 1} ^ {T} \mathrm {C E} \left(p _ {t}, a _ {t} ^ {*}\right). \tag {4}
+$$
+
+$T$  is the total planning step and CE is cross entropy loss.
+
+# 3.7. Uncertainty-aware Active Perception
+
+Predictions made by the planner may be compromised, as the implicit partial completion module cannot retrieve information from entirely unobserved directions. To alleviate
+
+this, we draw inspiration from human navigation and propose leveraging the agent's subjective perspective through a simple yet effective active perception strategy. This strategy enables the agent to actively acquire visual observations when uncertain about its decisions. We focus on two key challenges: determining when to look, which involves identifying the steps for the agent to gather observations, and where to look, which involves selecting a informative direction for more visual observations.
+
+(1) When to look? The agent should gather more information when it finds its prediction unreliable, as additional information have potential to improve prediction accuracy. We assess the reliability of a prediction by considering two conditions: directional novelty and low confidence. When both conditions are satisfied, the agent decides to gather more visual information. Directional novelty is defined as a direction pointing towards a previously unobserved sector, specifically any orientation outside the  $\pm 30^{\circ}$  range of already viewed directions at current node. Low confidence is determined by thresholding the class-normalized entropy:  $H_{norm} = H(p) / \log N > \tau$ , where  $H(p)$  is the entropy of prediction  $p_t$  and  $N$  is the number of candidates. Threshold  $\tau$  is a hyper-parameter. This normalization enables stable thresholding across varying class numbers.
+
+(2) Where to Look? When deciding to acquire additional visual information, we choose to have the agent look toward the orientation of the predicted node. Ideally, the optimal direction would be that of the ground truth(GT) next node. However, during inference, we cannot obtain this GT direction. Our strategy is to utilize the direction of the model-predicted node instead. This approach remains informative as the prediction model has been trained under the supervision of ground truth data.
+
+Our solution to these questions culminates in the simple Uncertainty-aware Active Perception(UAP) strategy: the agent rotates to where the model-predicted node is when it is uncertain about its prediction. This inserts a checking step in the traditional combined rotate-then-move action, as depicted in Fig.3. The checking step enables the agent to determine whether to move forward or plan again(i.e. replan) with acquired visual information in the rotation. Replan may occur several times until the agent makes a certain decision or every view is observed.
+
+# 4. Experiments
+
+# 4.1. Setups
+
+We evaluate our approach on the R2R-CE[27] and RxR-CE[29] datasets in simulated environments.
+
+R2R-CE is a dataset based on MP3D[7] using Habitat simulator[42]. It includes 5,611 trajectories divided into train, validation seen, validation unseen, and test unseen splits. Each trajectory has 3 English instructions, with an
+
+average length of 9.89 meters and average instruction length of 32 words. The camera's FOV is 90 degrees.
+
+RxR-CE is a larger multilingual VLN dataset containing 126K instructions in English, Hindi, and Telugu. It includes diverse trajectories in terms of length (the average is 15 meters), which is more challenging in continuous environments. The camera's FOV for RxR-CE is 63 degrees.
+
+Evaluation Metrics. We adopt standard metrics for evaluating the agent's performance in VLN, including Navigation Error(NE), Success Rate(SR), SR given the Oracle stop policy(OSR), Success rate weighted by normalized inverse Path Length(SPL[4]), the normalized DTW distance between the agent's trajectory and ground truth path, nDTW weighted by success rate(sDTW[23]).
+
+Training of each module. The proposed BEV-based waypoint predictor (in Section 3.4) and implicit partial completion module (in Section 3.5) are trained independently before the overall navigation framework pipeline. Specifically, for training the BEV-based waypoint predictor, we randomly navigate between nodes in the graph, collecting rendered BEV features and their corresponding ground truth(GT) waypoint labels, following the methodology of prior works[21, 50], to train the predictor. We train the implicit partial completion module using the samples collected from the MP3D Simulator[7, 42]. To prevent information leakage, we exclude data from the MP3D unseen and test splits. We also include HM3D dataset[40] data, following prior works [49, 50], to enhance generalization.
+
+Implementation Details. All models are trained with AdamW[33] optimizer. Scale of Gaussians is  $2.5\mathrm{cm}$ , with opacity 1 and no rotation. MAE mask ratio is set to 0.5. For the R2R dataset, the planning model is trained on two NVIDIA 3090 GPUs for  $10^{4}$  iterations, with batch size 4 per GPU, requiring approximately 2 days. The learning rate is initialized at  $5 \times 10^{-6}$  and follows a cosine decay schedule. During training, the planning model is initialized with weights pre-trained on panoramic setting. For the RxR dataset, the planning model is similarly trained for  $2 \times 10^{4}$  iterations with learning rate  $5 \times 10^{-6}$  on 4 NVIDIA 3090 GPUs with batch size 2 per GPU, taking about 6 days.
+
+# 4.2. Ablation Study
+
+To evaluate the effectiveness of each module, we conduct ablation studies. Row 1 represents the baseline model, which is our proposed 3DGS-based navigation framework excluding the Implicit Partial Completion(IPC) module and the Uncertainty-Aware Active Perception(UAP) strategy. Row 2 incorporates the UAP strategy, while Row 3 adds the IPC module. Row 4 corresponds to the full model.
+
+Comparing Row 1 with Row 2, the  $1.7\%$  success rate improvement confirms the effectiveness of our active perception strategy. Further analysis of Row 1 versus Row 3
+
+<table><tr><td>IPC</td><td>UAP</td><td>NE↓</td><td>OSR↑</td><td>SR↑</td><td>SPL↑</td></tr><tr><td></td><td></td><td>4.83</td><td>59.1</td><td>51.1</td><td>41.7</td></tr><tr><td></td><td>✓</td><td>4.87</td><td>59.8</td><td>52.8</td><td>43.2</td></tr><tr><td>✓</td><td></td><td>4.70</td><td>60.7</td><td>54.0</td><td>44.4</td></tr><tr><td>✓</td><td>✓</td><td>4.61</td><td>62.4</td><td>54.8</td><td>44.4</td></tr></table>
+
+reveals the critical role of the IPC module: its  $2.9\%$  performance gain demonstrates it extracts comprehensive representation from partially rendered feature maps. When integrating both UAP and IPC (Row 4), the full model achieves optimal performance across key metrics, notably  $+3.7\%$  success rate. This synergy arises because the two components address information incompleteness in complementary ways: the UAP strategy proactively reduces significant incompleteness through active perception, while the IPC module implicitly enhances understanding of incomplete observations via implicit completion.
+
+Discussion. Our framework employs a different backbone (MobileSAM), 3DGS-based feature field, and BEV-based waypoint predictor, distinguishing it from 3DFF, which uses CLIP, NeRF-based feature field, and semantic-map-based waypoint predictor. Even without IPC and UAP modules, our baseline outperforms it. These may be due to better feature field and BEV-based waypoint predictor that don't rely on high-accuracy semantic segmentation. However, our main focus is on solving information incompleteness, so we skip detailed analysis of these components.
+
+# 4.3. Comparison With Other VLN Methods
+
+Table 1. Ablation study.  
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">Obs</td><td colspan="4">Val Unseen</td><td colspan="4">Test Unseen</td></tr><tr><td>NE↓</td><td>OSR↑</td><td>SR↑</td><td>SPL↑</td><td>NE↓</td><td>OSR↑</td><td>SR↑</td><td>SPL↑</td></tr><tr><td>ETPNav[3]</td><td>P</td><td>4.71</td><td>65</td><td>57</td><td>49</td><td>5.12</td><td>63</td><td>55</td><td>48</td></tr><tr><td>BEVBert[2]</td><td>P</td><td>4.57</td><td>67</td><td>59</td><td>50</td><td>4.70</td><td>67</td><td>59</td><td>50</td></tr><tr><td>PRET[34]</td><td>P</td><td>4.58</td><td>66</td><td>59</td><td>49</td><td>4.74</td><td>62</td><td>56</td><td>47</td></tr><tr><td>CM2[15]</td><td>M</td><td>7.02</td><td>41.5</td><td>34.3</td><td>27.6</td><td>7.74</td><td>39</td><td>32</td><td>24</td></tr><tr><td>WS-MGMap[9]</td><td>M</td><td>6.28</td><td>47.6</td><td>38.9</td><td>34.3</td><td>7.11</td><td>45</td><td>35</td><td>28</td></tr><tr><td>NaVid[52]</td><td>M</td><td>5.47</td><td>49.1</td><td>37.4</td><td>35.9</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>3DFF[50]</td><td>M</td><td>5.95</td><td>55.8</td><td>44.9</td><td>30.4</td><td>6.24</td><td>54.4</td><td>43.7</td><td>28.9</td></tr><tr><td>g3D-LF[46]</td><td>M</td><td>5.70</td><td>59.5</td><td>47.2</td><td>34.6</td><td>6.00</td><td>57.5</td><td>46.3</td><td>32.2</td></tr><tr><td>Ours</td><td>M</td><td>4.61</td><td>62.4</td><td>54.8</td><td>44.4</td><td>4.97</td><td>60.5</td><td>53.6</td><td>44.9</td></tr></table>
+
+Table 2. Evaluation on R2R dataset. Obs indicates the observation type. P means panoramic observation and M indicate monocular observation.
+
+Comparison on R2R-CE. Table 2 compares our approach with previous VLN methods. Our model, built upon the PRET panoramic planning model, outperforms all other monocular approaches. Specifically, our method achieves a success rate approximately  $10\%$  higher than the 3DFF model. We also significantly outperform g3D-LF, suggesting that improving the feature field alone is insufficient for monocular observations, as information incompleteness remains a more critical issue. Importantly, our approach significantly narrows the performance gap between monocular
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">Obs</td><td colspan="5">Val Unseen</td></tr><tr><td>NE↓</td><td>OSR↑</td><td>SR↑</td><td>SPL↑</td><td>sDTW↑</td></tr><tr><td>PRET[3]</td><td>P</td><td>5.81</td><td>60.0</td><td>52.5</td><td>43.9</td><td>42.7</td></tr><tr><td>ETPNav[3]</td><td>P</td><td>5.64</td><td>-</td><td>54.8</td><td>44.8</td><td>45.3</td></tr><tr><td>HNR[49]</td><td>P</td><td>5.51</td><td>-</td><td>56.4</td><td>46.7</td><td>47.2</td></tr><tr><td>CM²[15]</td><td>M</td><td>8.98</td><td>25.3</td><td>14.4</td><td>9.2</td><td>-</td></tr><tr><td>WS-MGMap[9]</td><td>M</td><td>9.83</td><td>29.8</td><td>15.0</td><td>12.1</td><td>-</td></tr><tr><td>NaVid[52]</td><td>M</td><td>8.41</td><td>34.5</td><td>23.8</td><td>12.2</td><td>-</td></tr><tr><td>3DFF[50]</td><td>M</td><td>8.79</td><td>36.7</td><td>25.5</td><td>18.1</td><td>-</td></tr><tr><td>Ours</td><td>M</td><td>8.29</td><td>37.7</td><td>31.8</td><td>26.8</td><td>25.2</td></tr></table>
+
+and panoramic models, reducing it from  $12\%$  to  $4\%$  in terms of success rate on the val unseen split.
+
+Comparison on RxR-CE. Table 3 presents the performance comparison on the RxR-CE dataset. Our proposed monoVLN outperforms all previous monocular-based methods. Specifically, our method improves  $6\%$  on the success rate compared to previous monocular-based SOTA methods, indicating that the information incompleteness is also a critical challenge on RxR-CE dataset. Results on R2R-CE and RxR-CE demonstrate the effectiveness of our method on different benchmarks.
+
+# 4.4. Design Choices of Each Module.
+
+Table 3. Evaluation on RxR-CE dataset.  
+
+<table><tr><td></td><td>NE↓</td><td>OSR↑</td><td>SR↑</td><td>SPL↑</td></tr><tr><td>(1)</td><td>5.98</td><td>48.2</td><td>40.8</td><td>32.3</td></tr><tr><td>(2)</td><td>4.60</td><td>60.1</td><td>53.0</td><td>43.8</td></tr><tr><td>(3)</td><td>4.70</td><td>60.7</td><td>54.0</td><td>44.4</td></tr></table>
+
+How to incorporate the reconstruction auxiliary task in IPC module? The MAE view encoder is designed to achieve feature completion (Eq.1) and alignment with CLIP features (Eq.2). To this end, we explore three integration strategies for training: reconstruction-only, joint training, and pretrain-then-finetune. As demonstrated in Table 4, the exclusion of reconstruction during the training process results in substantially diminished performance metrics. The absence of CLIP alignment results in the lowest performance, primarily because the planning model is pretrained solely with CLIP features. Through the integration of both reconstruction and clip alignment during the view encoder training phase, we observe a marked improvement in model performance. Moreover, pretraining with reconstruction loss followed by finetuning with CLIP alignment produces the best results, achieving a  $1\%$  improvement in success rate compared to joint training. Based on these empirical results, we adopt the pretrain-then-finetune paradigm in all other experiments.
+
+Comprehensive study of our active perception strategy.
+
+We evaluate the effectiveness of our Uncertainty-Aware Ac
+
+Table 4. Different ways to incorporate the reconstruction task. (1) Training with reconstruction loss (in Eq.1) only. (2) Training with joint CLIP aligning loss (in Eq.2) and reconstruction loss. (3) Pretrain with reconstruction then finetune with CLIP alignment.  
+
+<table><tr><td>Methods</td><td>initial rotation</td><td>NE↓</td><td>OSR↑</td><td>SR↑</td><td>SPL↑</td><td>num steps↓</td></tr><tr><td>w/o UAP</td><td></td><td>5.77</td><td>51.9</td><td>45.6</td><td>35.1</td><td>108</td></tr><tr><td>ours</td><td></td><td>5.43</td><td>56.5</td><td>48.7</td><td>35.4</td><td>153</td></tr><tr><td>rotate 360</td><td>✓</td><td>4.76</td><td>60.9</td><td>54.2</td><td>45.4</td><td>287</td></tr><tr><td>random view</td><td>✓</td><td>4.64</td><td>62.1</td><td>54.2</td><td>44.2</td><td>127</td></tr><tr><td>w/o UAP</td><td>✓</td><td>4.70</td><td>60.7</td><td>54.0</td><td>44.4</td><td>117</td></tr><tr><td>ours</td><td>✓</td><td>4.61</td><td>62.4</td><td>54.8</td><td>44.4</td><td>128</td></tr></table>
+
+Table 5. Effectiveness of our Active Perception Strategy.
+
+tive Perception(UAP) strategy, both with and without initial rotation, in Table 5. The initial rotation refers to the agent performing a 360-degree rotation before navigation, as implemented in 3DFF [50]. As shown, the first two rows (without initial rotation) demonstrate a significant improvement in success rate with our active perception strategy, achieving a  $3.1\%$  absolute gain. To ensure a fair comparison, we also test the setup with initial rotation<sup>1</sup>. Rows 5 and 6 of the table reveal that the UAP strategy still enhances the success rate, albeit by a smaller margin of  $0.8\%$ . This reduced gain can be attributed to the diminished incompleteness in the rendered views when the initial rotation is performed. Under this experimental setup, we further explore the performance of the approach that involves a 360-degree rotation at every step in Row 3 and acquires a random view observation within the UAP strategy in Row 4. Notably, our UAP strategy outperforms the 360-degree rotation approach in terms of the success rate. The reason behind this is that panoramic views obtained through continuous 360-degree rotations may introduce redundant information. In contrast, our method is designed to selectively collect data only when uncertainty is detected, enabling it to focus on capturing the most relevant details. Moreover, our approach exhibits remarkable efficiency in terms of navigation steps. It significantly reduces the number of extra steps, from 170 in the 360-degree rotation approach to only 11, which further demonstrates the superiority of our UAP strategy.
+
+Impact of entropy threshold in UAP. We investigate the optimal entropy threshold for the UAP strategy. As depicted in Figure 5, we train the model by utilizing a range of entropy thresholds, considering scenarios both with and without an initial rotation. A higher entropy threshold leads to a reduction in the frequency of replanning. This, in turn, results in a decrease in the number of navigation steps and model forward passes. When the threshold equals 1, no replanning occurs, equivalent to the baseline without UAP. In the scenario with an initial rotation, the optimal entropy threshold is 0.75, which is slightly larger than the optimal threshold of 0.5 in the scenario without an initial rotation. The underlying reason for this difference is that the 360 - degree rotation at the onset of navigation provides a more comprehensive panoramic understanding.
+
+![](images/a14cd0b75c63fae45b2ff27e9392d5076517326bb110f2d2e518bd772ae668ce.jpg)
+
+![](images/1b0c8794e0d497623ef8e838eb54fae4b3f297ca909d30a3d5813188fb6a45c4.jpg)  
+Figure 5. Success rate under different entropy threshold with or without initial rotation.
+
+Discussion. Our experiments imply that monocular VLN can match panoramic performance with improved methods, and current panoramic methods can be further enhanced. As illustrated in Table 5, performing a full 360-degree rotation at each step does not yield the highest success rate. Moreover, according to Figure 5, the best performance is not attained when the maximum amount of visual information is collected at a threshold of 0. This suggests that current panoramic agents can be enhanced by eliminating redundant observations, thus revealing a promising direction for improving VLN agents.
+
+# 4.5. Visualization
+
+![](images/719c0faae5b1d17fef21d5f146f38f8af3e4d8c115060bab37cfc04207ae78d7.jpg)  
+Figure 6. Visualization of completed feature maps in unseen environments. The feature map is visualized by PCA like DINOv2[37]. Baseline is the rendered feature map whereas ours is feature map completed by MAE decoder.
+
+We visualize the rendered feature maps in unseen environments in Figure 6. As shown, compared with baseline, our pretrained module can reconstruct small background regions(e.g., row 2, the ceiling) and completes large black areas such as stairs and floors, even though these areas were not observed. Meanwhile, our approach not only reconstructs missing feature maps but also refines those that are blurry or noisy. For instance, in row 1, the rendered feature maps exhibit significant noise, whereas the refined versions are cleaner and more closely aligned with the ground truth, thereby reducing the reliance on high-quality feature fields.
+
+Instruction: Walk out the room and turn right, move forward a bit and turn left, walk towards the corner and turn right, stop there.
+
+![](images/9a5192520f45f5a32cc9f877dcb0c3a510128badd54dfb4f1c13015b82159073.jpg)  
+Figure 7. Real world Example.
+
+<table><tr><td>GPU</td><td>backbone</td><td>waypoint</td><td>view</td><td>planner</td><td>total</td></tr><tr><td>4060</td><td>89ms</td><td>140ms</td><td>146ms</td><td>8ms</td><td>383ms</td></tr><tr><td>3090</td><td>31ms</td><td>27ms</td><td>99ms</td><td>10ms</td><td>167ms</td></tr></table>
+
+Table 6. Inference time on different GPUs. Backbone is MobileSAM's forward time. Waypoint includes BEV rendering and prediction time. View covers panoramic rendering and encoding time. Planner is VLN model forward time.
+
+# 4.6. Properties of Our Method.
+
+Fast Inference. Our model is efficient and achieves fast inference. We show the inference time of each module in Table 6. On 3090, our model's inference is significantly faster than g3D-LF[46], which is running at more than 330ms on 4090. On 4060, the total inference time is 383ms, comparable to g3D-LF on 4090. The planner inference time on 4060 is smaller than 3090, this accounts for 4060's higher clock speed, making it faster on small model inference.
+
+Deployable on Real-world Robot. We deploy our model on Turtlebot4. The inference is done on a laptop with RTX 4060 GPU. As depicted in Figure 7, with given instruction, our model can navigate following it with monocular observation. We find a dataset bias that substantially degrades performance upon deployment. We provide more details in supplementary materials.
+
+# 5. Conclusions
+
+We propose a novel 3DGS-based vision and language navigaiton framework with monocular observation. We tackle the information incompleteness challenge by implicitly completing partial feature maps. We also design a simple uncertainty-aware active perception strategy to gather more visual information to mitigate the challenge. Our experiments imply monocular VLN can match panoramic performance with improved methods.
+
+Limitations and future work. The generalization of our proposed monoVLN to real-world (e.g., our lab) deployment is limited due to the domain gap between the training data from the simulator and real-world scenarios. This limitation will be addressed in our future work.
+
+# Acknowledgments
+
+This work was supported partially by NSFC (No. 62206315, 92470202, U21A20471), Guangdong NSF Project (No. 2024A1515010101, No. 2023B1515040025), Guangdong Key Research and Development Program (No.2024B0101040004), Guangzhou Basic and Applied Basic Research Scheme (No. 2024A04J4067).
+
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+# $\pi$ -AVAS: Can Physics-Integrated Audio-Visual Modeling Boost Neural Acoustic Synthesis?
+
+Susan Liang, Chao Huang, Yunlong Tang, Zeliang Zhang, Chenliang Xu  
+University of Rochester
+
+# Abstract
+
+The Audio-Visual Acoustic Synthesis (AVAS) task aims to model realistic audio propagation behavior within a specific visual scene. Prior works often rely on sparse image representations to guide acoustic synthesis. However, we argue that this approach is insufficient to capture the intricate physical properties of the environment and may struggle with generalization across diverse scenes. In this work, we review the limitations of existing pipelines and address the research question: Can we leverage physical audio-visual associations to enhance neural acoustic synthesis? We introduce Physics-Integrated Audio-Visual Acoustic Synthesis (PI-AVAS or  $\pi$ -AVAS), a novel framework designed with two key objectives. i) Generalization: We develop a vision-guided audio simulation framework that leverages physics-based sound propagation. By explicitly modeling vision-grounded geometry and sound rays, our approach achieves robust performance across diverse visual environments. ii) Realism: While simulation-based approaches offer generalizability, they often compromise on realism. To mitigate this, we incorporate a second stage for data-centric refinement, where we propose a flow matching-based audio refinement model to narrow the gap between simulation and real-world audio-visual scenes. Extensive experiments demonstrate the effectiveness and robustness of our method. We achieve state-of-the-art performance on the RWAVS-Gen, RWAVS, and RAF datasets. Additionally, we show that our approach can be seamlessly integrated with existing methods to significantly improve their performance.
+
+# 1. Introduction
+
+The audio-visual acoustic synthesis task, as introduced by Chen et al. [6] and Liang et al. [21], aims to generate realistic binaural audio for new speaking and listening positions based on vision data. This task presents unique challenges, including synthesizing realistic binaural audio and achieving novel-view synthesis. Various approaches have been proposed to address this problem [6, 9, 21, 22, 26, 43]. NAF [26] simulates sound propagation within a scene us
+
+![](images/daf58c8a33a6bdb268f452ec066e2fa8d87a5c64ecd9b42a20ce2054efd080ce.jpg)  
+Geometry-Based Audio Simulation
+
+![](images/0840dc61c346dcaf56f71b816ff62ee5f445a7d085e478fceb37eccb2023ddaa.jpg)  
+Realism:  
+Generalization:  
+Figure 1. An intuitive comparison between audio simulation approaches, neural rendering approaches, and our  $\pi$ -AVAS. Physics-based approaches generalize well but lack realism, while neural rendering produces high-quality results but struggles with novel sound sources. Our two-stage method achieves both realism and generalization using the physics-based sound simulation and audio refinement model.
+
+![](images/f7011286854e098e7b9124a2c220cf943d5d20103457b0fe34eb05009bd0311e.jpg)  
+Vision-Informed Neural Rendering
+
+![](images/ff3a52588a9b3383a3e82d5a8eec0e1e0c09bec481917488cb5890f706fe6f93.jpg)  
+Realism  
+Generalization  
+×
+
+![](images/6b5d10af15e4e0e852a282b5f7c4bbfe6d07f0ec83e40cda254f4dc1e8741939.jpg)  
+Ours (two stages)  
+Realism:
+
+![](images/bd33174e51765f0005e27aae565dbce962a8f65dec7551beb8df4874edfc30d7.jpg)  
+Generalization:  
+#
+
+ing a local feature grid and an implicit decoder. INRAS [43] divides sound modeling into a three-stage implicit neural field. Chen et al. [6] present a vision-conditioned audio transformation network to synthesize audio for new listening positions. Liang et al. [21] design a NeRF-like system to jointly render audio and visual content.
+
+While these methods produce plausible results for fixed sound sources, they struggle to generalize to novel sound sources due to inadequate modeling of sound propagation. Sound propagation is influenced by various environmental factors, including the positions of the sound emitter and receiver, the room geometry, and the material properties of surfaces. The complex interactions among these physical properties impact the propagation behavior in a given environment. To address these factors, existing methods typically learn from sparse images implicitly within neural networks. Although this implicit modeling of visual information can support audio synthesis, it falls short of accurately capturing the necessary physical properties that govern sound propagation. In other words, the limited image-audio pairs do not provide sufficient information to infer the
+
+complete room geometry and scene layout. Consequently, these models experience significant performance degradation when confronted with novel sound sources.
+
+Recognizing the limitations of implicit learning approaches in capturing physical audio-visual associations, we investigate the question: Can we leverage explicit physical priors in audio-visual modeling to bridge this gap? In this paper, we propose a novel two-stage method to address this challenge. In the first stage, we design a vision-guided sound simulation framework that improves generalization for novel emitter and receiver positions. We begin by reconstructing a 3D mesh environment from a set of images using NeRF [29] or Gaussian Splitting [18]. This scene mesh effectively captures the geometry and structure of the environment, which are critical factors influencing sound propagation. For a given sound source and receiver pair, we model sound propagation within the mesh scene by treating sound as a ray [36]. This physics-based simulation approach enables robust generalization to new positions, even in complex environments.
+
+While explicit modeling of scenes from visual input provides a significant advantage in generalization, it falls short of achieving realistic audio rendering [4, 46] for several reasons. (1) The material properties of each bounce surface, such as absorption, scattering, and transmission, are not fully considered. (2) The simulation traces only a limited number of sound rays due to computational restrictions, and low-frequency values are imprecise. (3) Background noise effects are not modeled. To address these issues, we propose our second stage to enhance the realism of the simulated sound. We utilize a conditional flow matching model [25, 47] to refine the coarsely simulated sound. With the powerful generative capability of flow-matching models, we can effectively correct errors from the first stage. An intuitive comparison between traditional audio simulation methods, neural rendering approaches, and our proposed method is presented in Fig. 1.
+
+We conduct extensive experiments on three real-world datasets: RWAVS-Gen, RWAVS [21], and RAF [9] datasets. RWAVS-Gen and RWAVS datasets measure the waveform sound generation quality, and the RAF dataset assesses the room impulse response rendering performance. The experimental results demonstrate that our method exhibits strong generalization and can be readily applied to novel sound sources. We also show that our method can be integrated into existing approaches to improve their generalization performance. In conclusion, our contributions are as follows:
+
+- We introduce a novel physics-integrated audio-visual acoustic synthesis framework to generate realistic audio content at novel positions based on visual information.  
+- We propose a vision-guided audio simulation method to enhance generalization for novel sources and listeners.  
+- We design a flow matching-based audio refinement model
+
+to bridge the gap between simulation sounds and realworld recordings.
+
+- Our experiments highlight the limitations of existing approaches, demonstrate the advantages of our method, and show the applicability of our model.
+
+# 2. Related Work
+
+Our work is closely related to areas such as vision-informed audio generation and flow matching models. We discuss each area and related work in the following section.
+
+# 2.1. Vision-Informed Audio Generation
+
+Vision-informed audio generation focuses on synthesizing audio based on visual inputs like images, videos, meshes, and poses. Many studies propose neural network-based audio generation pipelines [5, 6, 12, 15, 21, 23, 26, 27, 32, 33, 43, 52]. For instance, 2.5D Visual Sound [12] employs a U-Net [34] to synthesize binaural audio conditioned on an image, while Chen et al. [5] introduce a cross-modal transformer [49] to generate audio that matches room acoustics informed by an image. Some researchers have also developed video-guided audio generation methods, such as Diff Foley [27], and Movie Gen [32], which produce synchronized audio by considering temporal cues in videos.
+
+Another key area of vision-informed audio generation is pose-conditioned audio rendering, which is the focus of this paper. Inspired by Neural Radiance Field (NeRF) [29], several works [1, 2, 6, 7, 11, 14, 20, 21, 26, 33, 43] explore novel-pose audio synthesis by learning an audio field. Chen et al. [6] introduce a CNN-based network for transforming audio to synthesize sound at novel poses, while Liang et al. [21] design a NeRF-like system to jointly generate audio and visual content conditioned on poses. Although these pose-conditioned approaches generate plausible results for fixed sound sources, they face challenges with novel sound sources. In comparison, our method can easily render sound for new sources, thanks to our vision-guided audio simulation approach with physics integration.
+
+# 2.2. Flow Matching Models
+
+Deriving from Continuous Normalizing Flows (CNFs) [8], Lipman et al. [25] introduce Flow Matching to train CNFs in a simulation-free manner. Flow Matching, especially Optimal Transport Flow Matching [28], models the transformation between noise and data samples in a simpler and more efficient way than diffusion models [13, 41], leading to more stable training and better performance. Tong et al. [47] extend Flow Matching to arbitrary distribution transformations, including probability paths between different data distributions [24]. Inspired by this, we treat our simulated audio as one distribution and the target binaural audio as another distribution and use Flow Matching to refine
+
+![](images/d918661a929b644072d77b3eeeede2abdde240ac7ac37ceb5eb2e1a8b85d1344.jpg)  
+Figure 2. Overview of our approach. Our framework  $\pi$ -AVAS consists of two stages: the vision-guided audio simulation and the audio refinement with flow matching. In the first stage, we conduct 3D scene reconstruction and simulate sound propagation between a speaker and a listener in the mesh scene. In the second stage, we refine the coarsely simulated sound with a flow matching model, enhancing the quality of the synthesized sound.
+
+the simulation results. The audio refinement network effectively corrects simulation errors from the first stage.
+
+# 3. Method
+
+Our method aims to boost the performance of audio-visual acoustic synthesis models for novel sound sources. We design a novel Physics-Integrated Audio-Visual Acoustic Synthesis model (PI-AVAS or  $\pi$ -AVAS) with two stages. In the first stage (Sec. 3.1), we introduce a vision-guided audio simulation approach that integrates the physical properties of sound propagation. In the second stage (Sec. 3.2), we propose a conditional flow matching model that refines the prediction results from the first stage, improving the quality of audio generation. Additionally, we introduce a data augmentation strategy in Sec. 3.3 to facilitate model training. The complete pipeline is illustrated in Fig. 2.
+
+# 3.1. Vision-Guided Audio Simulation
+
+To enhance the generalization for audio sources and receivers in novel positions, we design a vision-guided audio simulation framework.
+
+3D Scene Mesh Extraction. We aim to reconstruct meshes of an audio-visual scene from input images in the first step (see the second subfigure in Fig. 2). Given a set of images and their corresponding camera poses, we utilize Neural Radiance Field (NeRF) [29, 45] or 3D Gaussian Splatting [18] to learn a neural representation of the given environment. Then, we convert the NeRF model weights or Gaussian points to 3D point clouds, which are a more compatible data format. Once the point clouds are reconstructed, we use Poisson surface reconstruction [17] to generate meshes of the audio-visual scene. Empirically, we do not observe a noticeable difference between the reconstructed 3D meshes of NeRF and Gaussian Splattings. We leave a detailed comparison between NeRF, Gaussian Splatting, and traditional Structure-from-Motion approaches [38] for future work, as
+
+this is not the main focus of our paper.
+
+Physics-Integrated Sound Simulation. After we generate the meshes of an audio-visual scene, we can simulate the audio propagation between arbitrary sound emitters and sound receivers in this scene (see the third subfigure in Fig. 2).
+
+Specifically, for a pair of sound source tx and sound receiver rx, we treat the sound emitted by the source  $x_{\mathrm{tx}} \in \mathbb{R}^n$  ( $n$  is the audio length) as a collection of rays, tracing each ray's interaction with the room's meshes [3, 40]. We denote the energy received at the receiver from the transmitter as  $E(\mathrm{tx} \to \mathrm{rx})$ , from which we omit the time delay variable for simplicity. We model both direct propagation and indirect reflection to calculate the received energy:
+
+$$
+E (\mathrm {t x} \rightarrow \mathrm {r x}) = \underbrace {E _ {\mathrm {d}} (\mathrm {t x} \rightarrow \mathrm {r x})} _ {\text {D i r e c t p r o p a g a t i o n}} + \underbrace {E _ {\mathrm {i d}} (\mathrm {t x} \rightarrow \mathrm {r x})} _ {\text {I n d i r e c t r e f l e c t i o n}}. \tag {1}
+$$
+
+$E_{\mathrm{d}}(\mathrm{tx}\rightarrow \mathrm{rx})$  is the energy of direct propagation and  $E_{\mathrm{id}}(\mathrm{tx}\rightarrow \mathrm{rx})$  is the reflected energy defined as
+
+$$
+\begin{array}{l} E _ {\mathrm {i d}} (\mathrm {t x} \rightarrow \mathrm {r x}) = \int_ {\Omega} \underbrace {E (\omega \rightarrow \mathrm {t x})} _ {\text {E n e r g y}} \underbrace {G (\omega \leftrightarrow \mathrm {t x})} _ {\text {G e o m e t r y}} \tag {2} \\ \underbrace {\rho (\omega \to \mathrm {t x} \to \mathrm {r x})} _ {\text {M a t e r i a l p r o p e r t y}} * \underbrace {M (\omega \leftrightarrow \mathrm {t x})} _ {\text {S c e n e s i z e}} d \omega , \\ \end{array}
+$$
+
+where  $\Omega$  is the entire mesh space,  $\omega$  is an area of  $\Omega$ ,  $M(\omega \leftrightarrow \mathrm{tx})$  measures energy absorption and time delay,  $G(\omega \leftrightarrow \mathrm{tx})$  means the energy dispersion and occlusion during sound propagation,  $\rho (\omega \rightarrow \mathrm{tx}\rightarrow \mathrm{rx})$  represents the acoustic property of each bounce surface, and the asterisk  $*$  is the convolution operation.
+
+Eq. (1) can be converted to an infinite sum of integrals and solved with the Neumann series expansion [19]. We then calculate the impulse response based on the accumulated energy  $E$  and convolve that with the sound source to generate the simulated sound. To improve the realism of the
+
+![](images/66b43decdf3557187bcec57ae8d343862841938cbf62358d3575a251e8631ca1.jpg)  
+Figure 3. Visualization of the audio refinement process with the flow matching model. The flow matching model learns a vector field that gradually transforms a simulated sound  $x_{\mathrm{sim}}$  to a ground-truth sound  $x_{\mathrm{rx}}$ .
+
+simulated sound, we also apply the Head-Related Transfer Function (HRTF) to generate binaural audio  $x_{\mathrm{sim}} \in \mathbb{R}^{2 \times n}$  based on the listener's head direction. Because it is challenging to estimate material property solely based on visual information [10, 39], we assign default material coefficients to all surfaces.
+
+So far, we simulate sound propagation between the sound source and the receiver using visual information obtained from a set of images. Since this approach integrates the physical properties of sound propagation, it generalizes well to novel sound sources and listeners.
+
+# 3.2. Audio Refinement With Flow Matching
+
+Although the vision-guided audio simulation approach offers robustness for novel poses, there is a noticeable fidelity gap between simulated and recorded sounds [4, 46] as mentioned in the introduction section, e.g., the material property is not correctly modeled. Therefore, we introduce our second stage to further enhance the quality of the generated sound  $x_{\mathrm{sim}}$ . We propose a flow matching model to refine and improve the simulated audio. We illustrate the audio refinement process with the flow matching model in Fig. 3. Flow Matching Formula. Specifically, we treat the simulated sound  $x_{\mathrm{sim}} \in \mathbb{R}^{2 \times n}$  as one data distribution  $\mathcal{N}(x|x_{\mathrm{sim}}, \sigma^2 I)$  and the recorded sound (ground-truth sound)  $x_{\mathrm{rx}} \in \mathbb{R}^{2 \times n}$  as another data distribution  $\mathcal{N}(x|x_{\mathrm{rx}}, \sigma^2 I)$ , where  $\sigma$  is a predefined standard deviation. We model the sound refinement process as a transfer between these two distributions. We design the following time-dependent probability path  $p_t: [0,1] \times \mathbb{R}^n \to \mathbb{R}_{>0}$ :
+
+$$
+p _ {t} (x) = \mathcal {N} (x | t x _ {\mathrm {r x}} + (1 - t) x _ {\mathrm {s i m}}, \sigma^ {2} I), \tag {3}
+$$
+
+where  $p_0(x) = \mathcal{N}(x|x_{\mathrm{sim}},\sigma^2 I)$ ,  $p_1(x) = \mathcal{N}(x|x_{\mathrm{rx}},\sigma^2 I)$ , and time step  $t\in [0,1]$ . We define the time-dependent flow  $\psi_t(x):[0,1]\times \mathbb{R}^n\to \mathbb{R}^n$  as follows:
+
+$$
+\psi_ {t} (x) = t x _ {\mathrm {r x}} + (1 - t) x _ {\mathrm {s i m}} + \sigma \epsilon , \tag {4}
+$$
+
+where  $\epsilon$  is sampled from a standard Gaussian distribution  $\mathcal{N}(0,I)$ . According to the definition of vector fields, we can derive the vector field  $v_{t}:[0,1]\times \mathbb{R}^{n}\to \mathbb{R}^{n}$  using the flow defined in Eq. (4):
+
+$$
+v _ {t} \left(\psi_ {t} (x)\right) = \frac {d}{d t} \psi_ {t} (x) = x _ {\mathrm {r x}} - x _ {\mathrm {s i m}}. \tag {5}
+$$
+
+Then we train a deep neural network  $u_{t}(\psi_{t}(x), x_{\mathrm{tx}}, p; \theta)$  to fit the vector field defined in Eq. (5), where  $\theta$  is the trainable parameters of a neural network,  $x_{\mathrm{tx}}$  is the source sound, and  $p$  is the pose information of sound source tx and listener rx. The training objective is
+
+$$
+\mathcal {L} _ {\mathrm {F M}} (\theta) = \mathbb {E} _ {q _ {0} (x), q _ {1} (x), t} \| u _ {t} \left(\psi_ {t} (x), x _ {\mathrm {t x}}, p; \theta\right) - \left(x _ {\mathrm {r x}} - x _ {\mathrm {s i m}}\right) \| ^ {2}. \tag {6}
+$$
+
+We provide pseudo-code for training the audio refinement model in the appendix. In our experiments, we use Short-time Fourier transform (STFT) to transform both the target  $x_{\mathrm{rx}} - x_{\mathrm{sim}}$  and predicted  $u_{t}(\psi_{t}(x),x_{\mathrm{tx}},p;\theta)$  vector fields from a time space to a time-frequency space and calculate the L2 distance as the training loss.
+
+After training, we utilize the network for audio refinement. Given a simulated sound  $x_{\mathrm{sim}}$ , we generate an enhanced sound  $x_{\mathrm{rx}}$  by solving the ordinary differential equation:
+
+$$
+\frac {d}{d t} \psi_ {t} (x) = u _ {t} \left(\psi_ {t} (x), x _ {\mathrm {t x}}, p; \theta\right), \tag {7}
+$$
+
+$$
+\psi_ {0} (x) = x _ {\mathrm {s i m}}.
+$$
+
+The solution  $\psi_{1}(x)$  is the synthesized binaural audio. In this paper, we study one first-order solver (Euler solver) and two second-order solvers (Midpoint solver and Heun solver). We compare different solvers and provide the pseudo-code of inference in the appendix.
+
+Audio Refinement Network. In Fig. 4 (a), we show the architecture of our network that is designed to approximate the vector field  $v_{t}(x)$ . Given an intermediate sound  $\psi_t(x)$  sampled from Eq. (4), we concatenate it with the source sound  $x_{\mathrm{tx}}$  emitted by the loudspeaker. The concatenated sound is first fed to a two-layer convolutional encoder to enrich the channel dimension and then passed to a stack of multi-scale gated convolution blocks. To condition the vector field prediction on the source and listener's poses  $p$  and time step  $t$ , we first project them into a high-frequency space using Random Gaussian Fourier Embedding (RGFE) [44], followed by MLPs. The resulting embeddings form the flow matching conditions  $c$ , which are then passed to the multi-scale gated convolution blocks. Each multi-scale gated convolution block uses condition  $c$  to adjust the sound features  $f_{i-1}$  and predicts the next sound features  $f_{i}$  and a skip feature  $s_i$ . Finally, we combine all
+
+![](images/600c5c581329fc367796877f3351b7f5e56e5e68e4d997fe633778bb1aa50e13.jpg)  
+(a) Audio Refinement Network
+
+![](images/368b291e12eeb875aefdab13bbe5e2c2f131d7451660f0f36084ab1698ffd467.jpg)  
+(b) Multi-Scale Gated Convolution Block
+
+skip features  $\{s_0,s_1,\ldots ,s_{L - 1}\}$  together, where  $L$  is the number of blocks, and use a two-layer convolutional decoder to predict the vector field  $u_{t}$ .
+
+We present our multi-scale gated convolution block in Fig. 4 (b). Inspired by WaveNet [48] and ViGAS [6], we design a gate operator to filter and control intermediate features. Given a feature  $f_{i-1}$  from the previous block, we utilize dilated convolution layers (D-Conv) to learn meaningful features  $D_1(f_{i-1})$  and  $D_2(f_{i-1})$ , where  $D_1$  and  $D_2$  are dilated convolution layers. We also use pointwise convolution layers (P-Conv) to extract condition features  $P_1(c)$  and  $P_2(c)$ , where  $P_1$  and  $P_2$  are pointwise convolution layers. We apply the gated operator using the following equation:
+
+$$
+y = \tanh  \left(D _ {1} \left(f _ {i - 1}\right) + P _ {1} (c)\right) \otimes \sigma \left(D _ {2} \left(f _ {i - 1}\right) + P _ {2} (c)\right), \tag {8}
+$$
+
+where  $\otimes$  means Hadamard product.
+
+Then we feed  $y$  through a pointwise convolution layer to form the residual and add it to the input feature  $f_{i - 1}$  to generate the new feature  $f_{i}$ . We feed  $y$  through another pointwise convolution layer to generate a skip feature  $s_i$ . Since we gradually increase the dilation size of each block, we name it the multi-scale gated convolution block.
+
+# 3.3. Data Augmentation
+
+Data scarcity presents a challenge when we train audiovisual acoustic synthesis models, as each scene is typically recorded in a 10 to 20-minute video. This yields only 600 to 1200 samples (at 1 fps) per scene for training. To facilitate training, we propose a data augmentation strategy (see Fig. 5). Given that the video captures continuous camera movement, we approximate the camera's entire trajectory by interpolating between discrete training poses (shown as orange poses in the figure). We then shift each training pose randomly along this trajectory by up to one second forward or backward. These shifted positions serve as augmented
+
+![](images/c6fb163afc1466f0313466e4373ab6985a0ee8d893f7a3d86237119796df763d.jpg)  
+Figure 4. Model architecture. (a) shows the audio refinement network. Given an intermediate sound  $\psi_t(x)$  and a source sound  $x_{\mathrm{tx}}$ , we concatenate them and pass them through an encoder followed by a series of multi-scale gated convolution blocks. We use timestep  $t$  and pose  $p$  as conditions by encoding them with RGFE and MLPs. All skip features  $s_i$  are gathered and used to predict the vector field  $u_t$ . (b) illustrates the multi-scale gated convolution block. We design a gate operator to filter and control the intermediate features  $f_i$ .  
+Figure 5. Data augmentation. We randomly shift each training pose, represented in orange, along the interpolated camera trajectory by up to one second forward or backward. The shifted poses, shown in blue, serve as augmented poses to aid in model training.
+
+poses (blue poses), and we pair them with temporally corresponding audio clips as augmented sound samples.
+
+# 4. Experiments
+
+# 4.1. Generalization Evaluation
+
+We first evaluate the generalization ability of various methods to novel sound sources.
+
+Experiment Setup. We use the Real-World Audio-Visual Scene (RWAVS) dataset [21] to benchmark our method. The RWAVS dataset captures multimodal data, including the source position, camera poses, mono source sounds, and binaural received sounds for each scene. The dataset captures data from diverse environments, such as offices, multi-room houses, apartments, and outdoor spaces. For each scene, the original RWAVS dataset contains multiple videos with varying sound source locations. To examine generalization issues in existing approaches, we design a
+
+Table 1. Quantitative comparison with state-of-the-art methods on the RWAVS-Gen dataset using the generalization evaluation setup. We also show the inference speed and the model size of all methods. We highlight the best result in bold.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">Office</td><td colspan="2">House</td><td colspan="2">Apartment</td><td colspan="2">Outdoors</td><td colspan="2">Overall</td><td rowspan="2">Speed (ms)</td><td rowspan="2">Size (MB)</td></tr><tr><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td></tr><tr><td>INRAS [43]</td><td>2.126</td><td>0.182</td><td>3.605</td><td>0.220</td><td>4.535</td><td>0.232</td><td>2.058</td><td>0.157</td><td>3.081</td><td>0.198</td><td>2.9</td><td>0.79</td></tr><tr><td>NAF [26]</td><td>2.275</td><td>0.181</td><td>2.873</td><td>0.186</td><td>4.878</td><td>0.231</td><td>1.575</td><td>0.135</td><td>2.900</td><td>0.183</td><td>4.6</td><td>0.74</td></tr><tr><td>ViGAS [6]</td><td>2.137</td><td>0.183</td><td>3.878</td><td>0.213</td><td>3.946</td><td>0.221</td><td>1.967</td><td>0.154</td><td>2.982</td><td>0.193</td><td>12.8</td><td>9.72</td></tr><tr><td>AV-NeRF [21]</td><td>2.086</td><td>0.180</td><td>3.759</td><td>0.221</td><td>4.520</td><td>0.230</td><td>2.308</td><td>0.165</td><td>3.168</td><td>0.199</td><td>2.1</td><td>3.04</td></tr><tr><td>π-AVAS (Ours)</td><td>1.856</td><td>0.163</td><td>1.946</td><td>0.140</td><td>3.898</td><td>0.209</td><td>1.326</td><td>0.125</td><td>2.257</td><td>0.159</td><td>10.4</td><td>5.62</td></tr></table>
+
+![](images/0986ecf767b2d770c8dd08fff549ec6ac79ba92cbdea7f96cee2d65a8cb4fdf3.jpg)  
+Figure 6. Visualization of synthesized binaural sounds for novel sound sources and listeners.
+
+new evaluation setup: in each environment, we select one video as training data, with the remaining videos used for evaluation. This setup allows us to effectively assess how well existing methods generalize to new sound source locations within the same environment. We present an example in the appendix. We denote this new benchmark as RWAVS-Gen to distinguish it from the original RWAVS benchmark.
+
+Following AV-NeRF [21], we select NAF [26], INRAS [43], ViGAS [6], and AV-NeRF as our baselines. NAF models sound propagation within a scene by using a local feature grid and an implicit decoder. INRAS disentangles sound modeling through a three-stage implicit neural field. ViGAS predicts sound at a new location by leveraging audio-visual features from source viewpoints. AV-NeRF constructs a multi-modal neural field to condition audio modeling on 3D visual scene context.
+
+We choose magnitude distance (MAG) [51] and envelope distance (ENV) [30] metrics to evaluate audio quality following RWAVS [21].
+
+Quantitative Results. We compare our model with existing approaches on the RWAVS-Gen dataset and report their generalization performance in Tab. 1. All methods show better audio rendering performance in the office and the outdoor scenes while causing worse audio generation in the house and apartment scenes because the office is a classic shoebox environment with four parallel walls and the outdoor scene is an open space without occlusion. Our model achieves the best performance across all four environments, achieving the lowest metric losses, with 2.257 MAG and 0.159 ENV. This demonstrates the strong robustness and
+
+generalization capability of our physics-integrated model to novel sound sources.
+
+Inference Speed. We test the inference speed of different models to render one second of binaural audio with one RTX 4090 GPU and report the results in the rightmost column in Tab. 1. Since our approach involves audio simulation (2.1ms) and requires 4 steps to complete flow matching estimation (8.3ms), it is slower than some methods that directly output sound. However, (1) our approach still meets the real-time requirement (16.7ms for 60 FPS and 33.3ms for 30 FPS), meaning it causes no noticeable delay in real-world audio applications. (2) There are many successful works we can use to reduce inference time without performance degradation, such as consistency models [42] and adversarial diffusion distillation [35]. If we reduce the number of steps to 1, our method needs only 4.2 ms for inference.
+
+Qualitative Comparison. We visualize the generated sounds of different approaches in Fig. 6 for an intuitive comparison. As depicted, existing methods encounter challenges when applied to novel sound sources, resulting in inaccurate sound volume. In contrast, our physics-based approach effectively considers the changes in sound source locations and accurately produces binaural audio.
+
+# 4.2. Standard Evaluation
+
+We then compare the rendering performance of our  $\pi$ -AVAS model with other methods using standard benchmarks.
+
+Experiment Setup. We use the original RWAVS and Real Acoustic Field (RAF) datasets to benchmark our approach. For the RWAVS dataset, we make no modification to the benchmark and use the original setup to test our model. The RAF dataset is a real-world room impulse response dataset that densely captures real room acoustic data. It provides impulse response signals of an office environment in two conditions: empty and furnished. It allows to study the difference in acoustic fields introduced by furniture.
+
+Besides the baselines used in the RWAVS-Gen experiment, we include state-of-the-art approaches on RWAVS and RAF datasets to augment our experiment. AV-GS [1] introduces an audio-visual Gaussian Splitting method that explicitly represents a scene for acoustic synthesis. SOAF [11] designs an occlusion-aware acoustic field. AVR [20] utilizes the volume rendering technique to generate acoustic impulse responses.
+
+Table 2. Quantitative comparison with state-of-the-art methods on the original RWAVS dataset. We highlight the best-performing result in bold and underline the second-best result.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">Office</td><td colspan="2">House</td><td colspan="2">Apartment</td><td colspan="2">Outdoors</td><td colspan="2">Overall</td></tr><tr><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td></tr><tr><td>Mono-Mono</td><td>9.269</td><td>0.411</td><td>11.889</td><td>0.424</td><td>15.120</td><td>0.474</td><td>13.957</td><td>0.470</td><td>12.559</td><td>0.445</td></tr><tr><td>Mono-Energy</td><td>1.536</td><td>0.142</td><td>4.307</td><td>0.180</td><td>3.911</td><td>0.192</td><td>1.634</td><td>0.127</td><td>2.847</td><td>0.160</td></tr><tr><td>Stereo-Energy</td><td>1.511</td><td>0.139</td><td>4.301</td><td>0.180</td><td>3.895</td><td>0.191</td><td>1.612</td><td>0.124</td><td>2.830</td><td>0.159</td></tr><tr><td>INRAS [43]</td><td>1.405</td><td>0.141</td><td>3.511</td><td>0.182</td><td>3.421</td><td>0.201</td><td>1.502</td><td>0.130</td><td>2.460</td><td>0.164</td></tr><tr><td>NAF [26]</td><td>1.244</td><td>0.137</td><td>3.259</td><td>0.178</td><td>3.345</td><td>0.193</td><td>1.284</td><td>0.121</td><td>2.283</td><td>0.157</td></tr><tr><td>ViGAS [6]</td><td>1.049</td><td>0.132</td><td>2.502</td><td>0.161</td><td>2.600</td><td>0.187</td><td>1.169</td><td>0.121</td><td>1.830</td><td>0.150</td></tr><tr><td>AV-NeRF [21]</td><td>0.930</td><td>0.129</td><td>2.009</td><td>0.155</td><td>2.230</td><td>0.184</td><td>0.845</td><td>0.111</td><td>1.504</td><td>0.145</td></tr><tr><td>AV-GS [1]</td><td>0.861</td><td>0.124</td><td>1.970</td><td>0.152</td><td>2.031</td><td>0.177</td><td>0.791</td><td>0.107</td><td>1.417</td><td>0.140</td></tr><tr><td>SOAF [11]</td><td>0.828</td><td>0.126</td><td>1.951</td><td>0.153</td><td>2.097</td><td>0.182</td><td>0.770</td><td>0.109</td><td>1.411</td><td>0.142</td></tr><tr><td>π-AVAS (Ours)</td><td>0.674</td><td>0.109</td><td>1.992</td><td>0.149</td><td>2.041</td><td>0.173</td><td>0.785</td><td>0.106</td><td>1.373</td><td>0.134</td></tr></table>
+
+Table 3. Quantitative comparison with state-of-the-art methods on the RAF dataset. We highlight the best-performing result in bold and underline the second-best result.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="6">RAF-Furnished</td><td colspan="6">RAF-Empty</td></tr><tr><td>T60↓</td><td>C50↓</td><td>EDT↓</td><td>Amp.↓</td><td>Phase↓</td><td>Env.↓</td><td>T60↓</td><td>C50↓</td><td>EDT↓</td><td>Amp.↓</td><td>Phase↓</td><td>Env.↓</td></tr><tr><td>AAC-nearest</td><td>13.0</td><td>3.41</td><td>73.5</td><td>1.09</td><td>1.60</td><td>4.83</td><td>13.0</td><td>3.41</td><td>73.3</td><td>1.09</td><td>1.60</td><td>4.83</td></tr><tr><td>AAC-linear</td><td>12.4</td><td>3.65</td><td>90.2</td><td>0.99</td><td>1.60</td><td>3.81</td><td>13.1</td><td>3.25</td><td>71.5</td><td>1.10</td><td>1.59</td><td>5.22</td></tr><tr><td>Opus-nearest</td><td>14.4</td><td>3.78</td><td>80.3</td><td>1.19</td><td>1.60</td><td>5.35</td><td>13.3</td><td>4.25</td><td>100.6</td><td>1.16</td><td>1.59</td><td>4.58</td></tr><tr><td>Opus-linear</td><td>13.1</td><td>3.55</td><td>77.8</td><td>1.47</td><td>1.60</td><td>5.74</td><td>12.7</td><td>3.94</td><td>95.5</td><td>0.95</td><td>1.59</td><td>4.26</td></tr><tr><td>NAF [26]</td><td>7.1</td><td>0.98</td><td>20.6</td><td>0.93</td><td>1.62</td><td>5.34</td><td>8.0</td><td>1.22</td><td>26.3</td><td>0.85</td><td>1.62</td><td>4.67</td></tr><tr><td>INRAS [43]</td><td>6.9</td><td>1.08</td><td>21.4</td><td>0.96</td><td>1.62</td><td>6.43</td><td>7.6</td><td>1.21</td><td>25.8</td><td>0.88</td><td>1.62</td><td>4.72</td></tr><tr><td>AVR [20]</td><td>5.0</td><td>0.95</td><td>17.9</td><td>0.75</td><td>1.58</td><td>4.52</td><td>5.5</td><td>1.04</td><td>23.3</td><td>0.67</td><td>1.58</td><td>3.96</td></tr><tr><td>π-AVAS (Ours)</td><td>4.8</td><td>0.81</td><td>16.3</td><td>0.24</td><td>1.58</td><td>4.95</td><td>5.0</td><td>0.91</td><td>19.3</td><td>0.26</td><td>1.56</td><td>4.42</td></tr></table>
+
+We use MAG and ENV metrics to measure performance on the RWAVS dataset. Following AVR [20], we choose T60, C50, EDT, Amplitude (Amp.), Phase, and Envelope (Env.) to assess performance on the RAF dataset. T60, C50, and EDT are the most important metrics for measuring impulse response quality by analyzing energy decay. Amplitude and Phase metrics evaluate the impulse response in the time-frequency domain. The Envelope metric evaluates the impulse response in the time domain.
+
+RWAVS Results. As shown in Tab. 2, we compare our method with existing baselines on the original RWAVS dataset. Mono-Mono, Mono-Energy, and Stereo-Energy are non-learnable methods that generate binaural audio by scaling mono audio using estimated energy values. Other methods are neural network-based approaches, such as AVGS [1] and SOAF [11]. Our approach outperforms both non-learnable and learnable approaches, setting new state-of-the-art performance on the RWAVS dataset. The results demonstrate that our  $\pi$ -AVAS model achieves plausible novel-view audio synthesis quality.
+
+RAF Results. We present our  $\pi$ -AVAS's performance on the RAF dataset in Tab. 3. AAC [16] and Opus [50] are traditional audio encoding methods. "Nearest" and "linear" refer to different interpolation modes. AVR [20] is the state-of-the-art method on this dataset. Our method surpasses
+
+AVR on most metrics and performs on par with it on the Envelope metric. Considering that AVR takes 24 hours to converge while our model trains in 5 hours, our  $\pi$ -AVAS exhibits a better trade-off between training time and impulse response generation quality.
+
+# 4.3. Applicability Of Our Simulation Method
+
+The generalization capability of our method is empowered by our first stage, the vision-guided audio simulation module (Sec. 3.1). We find that this module not only improves the performance of our flow matching model but can also be applied to existing neural synthesis approaches to enhance their generalization ability. By replacing their input source audio with our simulated audio, we integrate our vision-guided audio simulation module into their framework. Experiment results shown in Tab. 4 demonstrate the applicability of our approach, with overall performance improvements across most methods. For example, we improve the MAG metric of the AV-NeRF model by 0.772 and reduce the ENV loss by 0.036.
+
+# 4.4. Ablation Studies
+
+We provide a thorough ablation study using the RWAVS-Gen dataset, with results shown in Tab. 5.
+
+Table 4. Applicability of our method. We apply our simulation method to other approaches to improve their generalization ability (denoted as "w/ sim"). We conduct experiments on the RWAVS-Gen dataset. The performance improvement is marked with a green triangle  $\triangledown$ .  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">Office</td><td colspan="2">House</td><td colspan="2">Apartment</td><td colspan="2">Outdoors</td><td colspan="2">Overall</td></tr><tr><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td></tr><tr><td>INRAS [43]</td><td>2.126</td><td>0.182</td><td>3.605</td><td>0.220</td><td>4.535</td><td>0.232</td><td>2.058</td><td>0.157</td><td>3.081</td><td>0.198</td></tr><tr><td>w/ sim</td><td>2.125</td><td>0.179</td><td>2.329</td><td>0.157</td><td>4.907</td><td>0.246</td><td>1.691</td><td>0.136</td><td>2.763 (▼ 0.318)</td><td>0.180 (▼ 0.018)</td></tr><tr><td>NAF [26]</td><td>2.275</td><td>0.181</td><td>2.873</td><td>0.186</td><td>4.878</td><td>0.231</td><td>1.575</td><td>0.135</td><td>2.900</td><td>0.183</td></tr><tr><td>w/ sim</td><td>2.203</td><td>0.184</td><td>2.214</td><td>0.154</td><td>4.925</td><td>0.241</td><td>1.556</td><td>0.131</td><td>2.724 (▼ 0.176)</td><td>0.178 (▼ 0.050)</td></tr><tr><td>ViGAS [6]</td><td>2.137</td><td>0.183</td><td>3.878</td><td>0.213</td><td>3.946</td><td>0.221</td><td>1.967</td><td>0.154</td><td>2.982</td><td>0.193</td></tr><tr><td>w/ sim</td><td>2.074</td><td>0.173</td><td>2.317</td><td>0.137</td><td>3.683</td><td>0.206</td><td>1.679</td><td>0.135</td><td>2.438 (▼ 0.544)</td><td>0.163 (▼ 0.030)</td></tr><tr><td>AV-NeRF [21]</td><td>2.086</td><td>0.180</td><td>3.759</td><td>0.221</td><td>4.520</td><td>0.230</td><td>2.308</td><td>0.165</td><td>3.168</td><td>0.199</td></tr><tr><td>w/ sim</td><td>2.014</td><td>0.174</td><td>1.946</td><td>0.136</td><td>4.374</td><td>0.221</td><td>1.250</td><td>0.122</td><td>2.396 (▼ 0.772)</td><td>0.163 (▼ 0.036)</td></tr></table>
+
+Table 5. Ablation Studies. We conduct a comprehensive ablation study to verify the effectiveness of our proposed method. The term "pra+HRTF" refers to substituting our vision-guided acoustic simulation approach with pyroomacoustics and HRTF. "Regression" denotes training our audio refinement convolutional network without the flow matching loss.  
+
+<table><tr><td></td><td colspan="2">Methods</td><td colspan="2">Office</td><td colspan="2">House</td><td colspan="2">Apartment</td><td colspan="2">Outdoors</td><td colspan="2">Overall</td></tr><tr><td>Simulation</td><td>Refinement</td><td>Augmentation</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td><td>MAG↓</td><td>ENV↓</td></tr><tr><td>pra[37]+HRTF[31]</td><td></td><td></td><td>4.259</td><td>0.226</td><td>5.264</td><td>0.227</td><td>8.762</td><td>0.288</td><td>3.454</td><td>0.203</td><td>5.435</td><td>0.236</td></tr><tr><td>✓</td><td></td><td></td><td>2.609</td><td>0.186</td><td>2.753</td><td>0.170</td><td>7.360</td><td>0.268</td><td>3.031</td><td>0.177</td><td>3.938</td><td>0.200</td></tr><tr><td></td><td>Regression</td><td></td><td>1.904</td><td>0.167</td><td>3.826</td><td>0.204</td><td>4.033</td><td>0.219</td><td>1.612</td><td>0.143</td><td>2.844</td><td>0.183</td></tr><tr><td></td><td>✓</td><td></td><td>1.880</td><td>0.166</td><td>3.144</td><td>0.198</td><td>4.209</td><td>0.207</td><td>1.577</td><td>0.138</td><td>2.702</td><td>0.177</td></tr><tr><td>✓</td><td>✓</td><td></td><td>1.856</td><td>0.163</td><td>2.191</td><td>0.148</td><td>3.898</td><td>0.209</td><td>1.496</td><td>0.134</td><td>2.360</td><td>0.164</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>2.002</td><td>0.169</td><td>1.946</td><td>0.140</td><td>4.071</td><td>0.220</td><td>1.326</td><td>0.125</td><td>2.336</td><td>0.164</td></tr></table>
+
+Vision-Guided Audio Simulation. First, we test the importance of our vision-guided audio simulation module (Sec. 3.1). We use pyroomacoustics [37] plus HRTF [31] as a baseline, which does not incorporate vision information. In this setup, we create a shoebox environment and use pyroomacoustics to estimate the room impulse response. We convolve the impulse response and the input audio to render mono audio at the target location. We then apply HRTF to generate binaural audio. Compared with this baseline, our module consistently outperforms it (see the first and the second rows), showing the importance of vision information in audio simulation.
+
+Audio Refinement Network. We proceed to evaluate our second stage — the audio refinement flow matching model (see Sec. 3.2). To establish a baseline, we remove the flow matching training objective from the second stage and train the audio refinement network with a regression loss function, labeled as "Regression" in the table. By incorporating the flow matching training objective, we achieve more precise audio refinement performance (compare the third and fourth rows). We hypothesize that the flow matching formula decomposes the challenging one-step estimation into several simpler steps, thereby progressively refining the simulated sound. By combining our first and second stages (see the fifth row), we achieve improved performance beyond either stage alone, demonstrating (1) the realism limitations of simulation-only approaches, (2) the generaliza
+
+tion challenges of neural rendering-only methods, and (3) the advantages of our two-stage approach.
+
+Augmentation Strategy. We also assess the impact of our data augmentation strategy (refer to the last row). By enhancing the audio refinement training with additional data, we achieve lower metric losses for both house and outdoor scenes; however, we observe no improvement for office and apartment scenes. Consequently, we apply data augmentation only to house and outdoor scenes.
+
+# 5. Conclusion
+
+In this paper, we study the limitations of existing approaches to the audio-visual acoustic synthesis problem. We design a two-stage, physics-integrated audio-visual acoustic synthesis framework to enhance both realism and generalization capabilities. The first stage of our framework is a vision-guided audio simulation module, followed by a flow-matching-based audio refinement module. To mitigate data scarcity in this task, we also propose a data augmentation strategy. Experimental results show the effectiveness of our proposed approach, achieving new state-of-the-art results on the RWAVS-Gen, RWAVS, and RAF datasets. We further show how our physics-integrated method improves existing approaches in terms of generalization.
+
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+# $p$ -MoD: Building Mixture-of-Depths MLLMs via Progressive Ratio Decay
+
+Jun Zhang $^{1,\ast}$ , Desen Meng $^{1,\ast}$ , Zhengming Zhang $^{2}$ , Zhenpeng Huang $^{1}$ , Tao Wu $^{1}$ , Limin Wang $^{1,3,\text{图}}$ ,  $^{1}$ State Key Laboratory for Novel Software Technology, Nanjing University  $^{2}$ China Mobile Research Institute  $^{3}$ Shanghai AI Lab https://github.com/MCG-NJU/p-MoD
+
+# Abstract
+
+Despite the remarkable performance of multimodal large language models (MLLMs) across diverse tasks, the substantial training and inference costs impede their advancement. In this paper, we propose  $p$ -MoD, an efficient MLLM architecture that significantly reduces training and inference costs while maintaining model performance. The majority of computation in MLLMs stems from the overwhelming volume of vision tokens processed by the transformer-based LLM. Accordingly, we leverage the Mixture-of-Depths (MoD) mechanism, where each LLM layer selects essential vision tokens to process while skipping redundant ones. However, integrating MoD into MLLMs is non-trivial. To address the challenges of training and inference stability as well as limited training data, we adapt the MoD module with two novel designs: tanh-gated weight normalization (TanhNorm) and symmetric token reweighting (STRing). Moreover, we observe that vision tokens exhibit higher redundancy in deeper layers and thus design a progressive ratio decay (PRD) strategy, which gradually reduces the token retention ratio layer by layer, employing a shifted cosine schedule. This crucial design fully unleashes the potential of MoD, significantly boosting the efficiency and performance of our models. Extensive experiments on two baseline models across 15 benchmarks show that our model matches or even surpasses the performance of corresponding baselines, while requiring only  $55.6\%$  TFLOPs and  $53.7\%$  KV cache storage during inference, and  $77.7\%$  GPU hours during training.
+
+# 1. Introduction
+
+Recently, both academia and industry have witnessed the rapid development of multimodal large language models (MLLMs) [1, 14, 24, 46, 47, 51, 55], which have demonstrated exceptional performance across various vision-language understanding tasks. Pioneering works in this field [8, 27, 29, 59] focused on processing single low-resolution image inputs. Subsequently, to meet the di
+
+![](images/d1b1aa3e3fd4303dfca5301dd74caf0d4cc0a96ee2835f148deef0bd9588aa08.jpg)  
+Figure 1. Comparison with the LLaVA-NeXT [28] baseline. Our model demonstrates comparable performance with the baseline model on 15 benchmarks across various domains, with  $46.3\%$  fewer KV cache storage and  $44.4\%$  fewer TFLOPs during inference.
+
+verse demands of real-world applications, increasing efforts have broadened the forms of visual inputs that MLLMs can support, including multiple high-resolution images and videos [6, 24, 45, 47, 55].
+
+Current state-of-the-art MLLMs handle high-resolution images either by dividing the original image into multiple slices [6, 28, 55] which are independently processed by the vision encoder, or by using a stronger vision encoder with improved positional encoding which can process any image at its native resolution [1, 31, 47]. Consequently, when processing multiple high-resolution images or videos, the number of vision tokens increases dramatically, proportional to the number of pixels and the number of images or video frames. The overwhelming volume of vision tokens processed by the transformer-based LLM results in explosion of computational costs, which severely hampers further de
+
+velopment and broader application of MLLMs. Designing more efficient MLLM architectures with minimal performance degradation has thus become an urgent challenge for the community.
+
+Previous efforts primarily focus on compressing vision tokens before the LLM, either in the Vision Encoder or the multimodal projector [2, 6, 12, 38, 39, 42, 49, 50, 55, 56]. These approaches force the LLM to handle heavily compressed vision information, overlooking the fact that the LLM, with its enormous model capacity, has the potential to compress the vision tokens by itself within the transformer layer.
+
+In this paper, we focus on optimizing computation efficiency of MLLMs within the transformer layers of the LLM. We propose to build efficient MLLMs with Mixture-Depths (MoD) [41] mechanism, which selects the most important and informative vision tokens to be processed by each transformer layer, while skipping redundant ones to improve efficiency. However, integrating MoD mechanism into MLLMs is non-trivial and entails several significant challenges.
+
+First, different from training an MoD-based LLM from scratch, integrating MoD mechanism into a pre-trained vanilla LLM during multimodal training poses a substantial risk of disrupting the language abilities of the original LLM. To address this, we design tanh-gated weight normalization (TanhNorm), which not only ensures proper initialization of the newly added MoD module, but also enhances training stability and performance. It also mitigates numerical stability issues during inference.
+
+Second, MLLMs are trained on multimodal data [28] that are several orders of magnitude smaller in scale compared to the text data used for training MoD-based LLMs [41]. We enhance the MoD mechanism with symmetric token reweighting (STRing) module which fully leverage the language supervision signals during training, enabling MoD modules to learn to accurately assess token importance even with limited training data.
+
+Thanks to these two enhancements, our upgraded MoD layers can be seamlessly applied to MLLMs. However, we argue that setting a fixed ratio of retained tokens across different MoD layers [41] is a suboptimal design choice under multimodal scenario, as the degree of redundancy in vision tokens should vary across layers. We conducted a series of exploratory experiments by adjusting the ratio of different layers in our MoD-based MLLM, which demonstrate that vision tokens exhibit higher redundancy in deeper layers. Accordingly, we propose a progressive ratio decay (PRD) strategy, which follows a shifted cosine schedule to gradually reduce the token retention ratio layer by layer. Trained with this strategy, our model significantly outperforms models that use a constant retention ratio across all layers under the same computation budget.
+
+Building upon the above innovations, we present our model,  $p$ -MoD, Mixture-of-Depth MLLMs equipped with our progressive ratio decay strategy and upgraded MoD layers (i.e.  $p$ -MoD layers). Extensive experiments validate the effectiveness of our proposed model. As shown in Figure 1, across 15 benchmarks spanning various domains, our model matches or even outperforms the strong LLaVA-NeXT [28] baseline, with only  $55.6\%$  TFLOPs and  $53.7\%$  KV cache storage during inference, and  $77.7\%$  GPU hours during training.
+
+# 2. Related Work
+
+Building Efficient LLMs. Considerable efforts have been made to build efficient LLMs. One representative approach is the Mixture of Experts (MoE) mechanism [7, 9, 19, 22, 43, 60], where a router directs each token to different MLP experts of the transformer block. MoE models achieve faster training and inference speeds compared to dense models of the same size, but at the cost of lower performance. The more recently proposed Mixture of Depths (MoD) [41] module assigns weights to tokens and processes only a portion of highest-weighted tokens, skipping lower-weighted tokens to save computation. MoD-based LLMs demonstrate strong performance under limited compute budgets. In this paper, we propose to build more efficient MLLMs by upgrading MoD with several innovative improvements.
+
+Building Efficient MLLMs. The main computational burden in MLLMs arises from the large number of vision tokens that the LLM must process. Previous works mainly focused on compressing vision tokens before they enter the LLM via convolution [6, 55], pooling [38, 50], query-based modules [2, 16] or token merging [3, 15, 25, 42, 49]. However, reducing vision-related computation within the LLM layers is less explored. LLaVolta [4] speeds up MLLM training by performing naive average pooling operation in intermediate LLM layers. FastV [5] and some subsequent works [13, 15, 17, 48, 57] improve MLLMs' efficiency by compressing vision tokens in intermediate transformer layers based on attention scores. However, these methods neglect the fact that tokens compressed in early layers might be crucial in deeper layers, potentially leading to performance degradation. In contrast, we utilize MoD for learnable layerwise vision token selection, improving model efficiency while avoiding potential performance loss caused by token dropping.
+
+# 3. Method
+
+In this section, we introduce our  $p$ -MoD model. As illustrated in Figure 2, our model consists of  $p$ -MoD layers which upgrades MoD architecture with tanh-gated weight
+
+![](images/80337e718331e5f93657a206491ff59e82eb53f78545271a4ea9cedba4120f7e.jpg)  
+Figure 2. Overview of  $p$ -MoD. Middle: Our efficient MLLM model which consists of  $p$ -MoD layers. Each layer independently selects important vision tokens to process while skipping redundant ones. The proportion of selected tokens for layer  $i$  is specified by the token retention ratio  $R_{i}$ . For simplicity, the vision encoder and connector are omitted. Left: Detailed architecture of  $p$ -MoD layers. Given the input tokens, the weight predictor first assigns weights to each token. The top  $R_{i} \%$  of tokens with highest weights are selected and processed by the transformer layer, while the rest of the tokens are skipped. The weights are normalized by TanhNorm module, and then both the selected and skipped tokens are symmetrically scaled by their corresponding weights in our STRing module. Right: Our crucial design is the progressive ratio decay (PRD) strategy, which gradually reduces the token retention ratio  $R_{i}$  layer by layer, following a shifted cos schedule.
+
+normalization(TanhNorm) and symmetric token reweighting(STRing). Our crucial design is the progressive ratio decay(PRD) strategy which controls the token retention ratio across different layers. In the following sections, we first revisit MoD briefly and then explain each component of our  $p$ -MoD model in detail.
+
+# 3.1. Revisiting Mixture-of-Depths
+
+The MoD layer consists of a weight predictor and a vanilla transformer layer. It assigns weights for each input token using the weight predictor and then selects the top  $R\%$  tokens with the highest weights to be processed by the transformer layer. Formally, given an MoD layer  $M$  with a token retention ratio  $R$ , a transformer layer  $T$ , and a linear weight predictor, the input tokens  $X \in \mathbb{R}^{n \times d}$  is first passed through the linear predictor to generate a set of weights:
+
+$$
+w = \operatorname {L i n e a r} (X) \in \mathbb {R} ^ {n}, \tag {1}
+$$
+
+with  $n$  denoting the sequence length and  $d$  denoting the embedding dimension.
+
+Then, we compute the  $R$ -th percentile of the router weights, denoted as  $P_{R}(w)$ . Tokens with weights larger than  $P_{R}(w)$  will be selected to be processed by the transformer layer  $T$  while other tokens are skipped in this layer, which guarantees only  $n \times R\%$  tokens are processed. The
+
+calculation process of an MoD layer can be formulated as:
+
+$$
+X _ {i} ^ {\prime} = \left\{ \begin{array}{l l} w _ {i} T \left(X _ {i}\right) + T \left(X _ {i}\right), & \text {i f} \quad w _ {i} > P _ {R} (w) \\ X _ {i}, & \text {i f} \quad w _ {i} \leq P _ {R} (w) \end{array} . \right. \tag {2}
+$$
+
+Notably, after being processed by the transformer layer, the selected tokens are then scaled by their corresponding weights. In this way, the weight predictor is engaged into the gradient path, enabling its parameters to be updated by backpropagation. We term this process token reweighting.
+
+In the original MoD module designed for LLMs [41],  $X$  represents text tokens. In our multimodal scenario,  $X$  represents vision tokens. We only apply MoD on vision tokens as they occupy the main computation load and exhibit high redundancy in LLM layers.
+
+# 3.2. Adapting Mixture-of-Depths Module
+
+Different from training MoD-based LLMs from scratch, integrating MoD into MLLMs presents several challenges. The insertion of new MoD modules into pre-trained LLMs can lead to instability during training and inference. The relatively small amount of multimodal data may not be sufficient to train the MoD modules. In this section, we introduce two enhancements to the MoD module to address these challenges.
+
+![](images/3d66317e841ddbfb43f3d5a1cbced070092b38fdf35c097a32a66cad744e0471.jpg)  
+Figure 3. Exploratory experiments on vision token redundancy.
+
+![](images/5f3ab454e65eb73904ca4d5c42b254d5f427df310a75e8f871b2dc3625b93ccd.jpg)  
+(a) Illustration of our exploratory experiment setup. Our baseline MoD model is trained with a token retention ratio of  $70\%$  for all layers. We divide the layers into three groups: shallow, middle, and deep. In each set of experiments, we decrease the token retention ratio  $(R\%)$  in a specific group of layers.  
+(b) Results of our exploratory experiments. Performance drops more slowly when the token retention ratio of deeper layers is decreased, indicating that vision tokens are more redundant in deeper layers. This inspires us to progressively reduce the token retention ratio layer by layer.
+
+# 3.2.1. Tanh-gated Weight Normalization
+
+The original MoD mechanism [41] is designed for training MoD-based LLMs from scratch. In our multimodal training scenario, we need to insert new MoD modules into a pre-trained vanilla LLM. One common approach is alternate training [58], where only the newly inserted modules are trained in the first stage, and all modules are simultaneously trained in the second stage. However, this approach is not suitable for MoD, as the MoD modules scale the tokens by their weights during the token reweighting process, and the subsequent frozen LLM layers are unable to handle scaled tokens. Our experiments show consistent results that training the MoD modules while freezing the LLM layers fails to converge. Consequently, the only feasible method is to directly address the challenge: inserting the MoD modules into the LLM and training both of them simultaneously.
+
+To address this challenge, we design tanh-gated weight normalization (TanhNorm), which employs a normalization function  $f(w) = \alpha \tanh(w)$  to normalize the predicted weights before token reweighting. After applying TanhNorm to MoD, Equation 2 can be reformulated as:
+
+$$
+X _ {i} ^ {\prime} = \left\{ \begin{array}{l l} \alpha \tanh  (w _ {i}) T (X _ {i}) \\ + T (X _ {i}), & \text {i f} w _ {i} > P _ {R} (w) \\ X _ {i}, & \text {i f} w _ {i} \leq P _ {R} (w) \end{array} \right.. \tag {3}
+$$
+
+Here  $\alpha$  is a hyper-parameter which controls the range of the normalized weights. Although simple, our TanhNorm ensures: (1) the normalized weight distribution is zero-centered, (2) the range(variance) of the weight distribution can be easily controlled by adjusting the gating factor  $\alpha$ . These properties offer the following benefits:
+
+- The normalized weights are closely around zero at the start of training, which ensures proper training initialization by keeping the LLM intact after inserting MoD modules.  
+- The zero-centered weight distribution reduced the risk that some tokens are repetitively scaled by positive(or negative) weights in all MoD layers. This ensures training stability and mitigates numerical stability issues during inference.
+
+Both of the above benefits contribute to improved model performance. We validate the effectiveness of  $\mathrm{TanhNorm}$  in Section 4.3.
+
+# 3.2.2. Symmetric Token Reweighting
+
+Compared to the text data used for training MoD-based LLMs, MLLMs are trained on multimodal data [28] that are several orders of magnitude smaller in scale. It is challenging to train a weight predictor (the only learnable part in the MoD module) to accurately and robustly assess the importance of vision tokens and assign corresponding weights.
+
+As stated in Section 3.1, the gradient of the weight predictor module stems from the token reweighting process. The original MoD performs token reweighting only on selected tokens as in Equation 2. In this way, the language supervision signals only supervise the weight predictor to assign high weights to the selected tokens, while the process of predicting weights for the skipped tokens is not supervised (i.e. no gradient).
+
+To fully leverage the limited training data, we enhance the MoD mechanism by symmetrically applying the token reweighting process to both selected and skipped tokens. With our symmetric token reweighting (STRing) module,
+
+<table><tr><td>Model</td><td>Inference TFLOPs ↓</td><td>Inference KV cache ↓</td><td>Doc VQA</td><td>Chart QA</td><td>Text VQA</td><td>Info VQA</td><td>RW QA</td><td>G QA</td><td>OK VQA</td><td>PO PE</td><td>AI 2D</td><td>SE ED</td><td>AVG</td></tr><tr><td>LLaVA-v1.5</td><td>8.38</td><td>100%</td><td>28.1</td><td>18.2</td><td>46.0</td><td>25.8</td><td>55.6</td><td>61.9</td><td>53.4</td><td>85.9</td><td>55.2</td><td>66.2</td><td>49.6</td></tr><tr><td>+p-MoD</td><td>4.92(-41.3%)</td><td>53.7%</td><td>27.6</td><td>16.8</td><td>44.8</td><td>26.8</td><td>55.7</td><td>62.2</td><td>56.0</td><td>85.5</td><td>56.2</td><td>66.5</td><td>49.8</td></tr><tr><td>LLaVA-NeXT</td><td>39.46</td><td>100%</td><td>70.1</td><td>61.6</td><td>62.7</td><td>34.7</td><td>57.6</td><td>63.5</td><td>54.0</td><td>87.2</td><td>64.0</td><td>68.9</td><td>62.4</td></tr><tr><td>+p-MoD</td><td>21.94(-44.4%)</td><td>53.7%</td><td>70.0</td><td>61.8</td><td>60.5</td><td>34.1</td><td>57.6</td><td>63.3</td><td>55.1</td><td>86.8</td><td>65.1</td><td>69.0</td><td>62.3</td></tr></table>
+
+Table 1. Comparison with baseline models on 10 benchmarks. Our models (marked in gray) achieves comparable or even better performance compared to baseline models, with only  $55.6\%$  TFLOPs and  $53.7\%$  KV cache storage during inference. All models are of 7B parameter scale.  
+
+<table><tr><td>Model</td><td>S QA</td><td>MM B</td><td>MM MU</td><td>VQA v2</td><td>MM E</td><td>AVG</td></tr><tr><td>LLaVA-v1.5</td><td>69.7</td><td>64.1</td><td>36.6</td><td>76.6</td><td>1506.8</td><td>64.5</td></tr><tr><td>+ p-MoD</td><td>69.3</td><td>65.4</td><td>36.3</td><td>76.9</td><td>1482.8</td><td>64.4</td></tr><tr><td>LLaVA-NeXT</td><td>69.7</td><td>67.5</td><td>35.3</td><td>79.3</td><td>1519.3</td><td>65.6</td></tr><tr><td>+ p-MoD</td><td>71.0</td><td>67.3</td><td>36.0</td><td>78.8</td><td>1495.5</td><td>65.6</td></tr></table>
+
+Table 2. Comparison with baseline models on more benchmarks. Our  $p$ -MoD models (marked in gray) matches the performance of corresponding baseline models. SQA stands for ScienceQA-IMG. All models are 7B in size.  
+
+<table><tr><td>Model</td><td>Doc VQA</td><td>Chart QA</td><td>Text VQA</td><td>G QA</td><td>SE ED</td><td>MM B</td><td>AVG</td></tr><tr><td>vanilla MoD</td><td>61.1</td><td>54.0</td><td>55.8</td><td>61.8</td><td>66.9</td><td>63.1</td><td>60.4</td></tr><tr><td>+ TanhNorm</td><td>61.8</td><td>54.5</td><td>56.4</td><td>62.5</td><td>67.1</td><td>65.9</td><td>61.4</td></tr><tr><td>+ STRing</td><td>65.7</td><td>58.4</td><td>59.3</td><td>63.0</td><td>67.1</td><td>66.8</td><td>63.4</td></tr><tr><td>+ PRD</td><td>70.0</td><td>61.8</td><td>60.5</td><td>63.3</td><td>69.0</td><td>67.3</td><td>65.3</td></tr></table>
+
+Table 3. Ablation study on our proposed innovations. Under fair comparison, all of our proposed modules (TanhNorm, STRing, and PRD) significantly improve model performance without any computational overhead, making indispensable contributions to the strong performance of our final model (marked in gray).
+
+Equation 3 can be further modified as:
+
+$$
+X _ {i} ^ {\prime} = \left\{ \begin{array}{c c c c} \alpha \tanh  (w _ {i}) T (X _ {i}) & & \\ + T (X _ {i}), & \text {i f} & w _ {i} > P _ {R} (w) & . \\ \alpha \tanh  (w _ {i}) X _ {i} + X _ {i}, & \text {i f} & w _ {i} \leq P _ {R} (w) \end{array} \right.
+$$
+
+In this way, the MoD module can fully leverage the language supervision signals during training and learn to accurately assess token importance with limited training data.
+
+# 3.3. Progressive Ratio Decay
+
+After upgrading MoD with TannahNorm and STRing modules, we are able to successfully train MoD-based MLLMs. However, the performance-efficiency trade-off exhibited by the model is far from satisfactory. When the token retention ratio is set below  $70\%$ , the model's performance deteriorates sharply.
+
+Original MoD-based LLMs [41] adopt a fixed token retention ratio across all MoD layers. This strategy assumes that the tokens have the same degree of redundancy in different layers. We argue that this assumption does not hold in the multimodal scenario. Under the effect of self-attention in every transformer layer, vision tokens gradually aggregate information from each other and text tokens gather relevant information from vision tokens. Therefore, vision tokens are expected to become increasingly redundant in deeper layers.
+
+To validate our hypothesis, we conduct a series of exploratory experiments on our MoD-based MLLM trained with a token retention ratio of  $70\%$  across all layers. As
+
+shown in Figure 3a, we first divide the layers into several groups: shallow, middle, and deep layers. In each set of experiment, we gradually decrease the token retention ratio  $(\mathbb{R}\%)$  in a specific group of layers while keeping the other layers unchanged, and evaluate the model under this customized inference setting. The results in Figure 3b strongly support our hypothesis: performance drops more slowly when the token retention ratio of deeper layers is decreased. This suggests that vision tokens exhibit higher redundancy in deeper layers, which is consistent with observations in previous works [5, 57].
+
+Accordingly, we design a progressive ratio decay (PRD) strategy. As shown on the right side of Figure 2, PRD gradually reduces the token retention ratio layer by layer, following a shifted cosine schedule. Suppose the model has  $L$  layers, the token retention ratio for the  $l$ -th layer is formulated as:
+
+$$
+R _ {l} = \frac {1}{2} \cos \frac {\pi l}{L} + \beta , \quad l = 1, 2, \dots , L. \tag {5}
+$$
+
+Here  $\beta$  is a shift factor, which can be used to flexibly control the overall computational cost of the model by vertically shifting the cosine decay curve.
+
+Experiments in Section 4.3 demonstrates that our  $p$ -MoD model with PRD strategy significantly outperforms models that use a constant retention ratio under the same computation budget. It also outperforms other kinds of ratio schedulers.
+
+<table><tr><td colspan="2">Ratio Scheduler</td><td>Decay</td><td>Progressive</td><td>Doc VQA</td><td>Chart QA</td><td>Text VQA</td><td>G QA</td><td>SE ED</td><td>MM B</td><td>AVG</td></tr><tr><td colspan="2">Constant</td><td>X</td><td>X</td><td>58.0</td><td>51.6</td><td>56.1</td><td>62.1</td><td>64.5</td><td>62.8</td><td>59.2</td></tr><tr><td colspan="2">Interleaved</td><td>X</td><td>X</td><td>60.3</td><td>54.8</td><td>57.0</td><td>62.3</td><td>65.3</td><td>62.1</td><td>60.3</td></tr><tr><td colspan="2">Stepped</td><td>✓</td><td>X</td><td>67.2</td><td>61.2</td><td>59.4</td><td>63.5</td><td>68.4</td><td>66.1</td><td>64.3</td></tr><tr><td rowspan="2">PRD</td><td>Linear</td><td rowspan="2">✓</td><td rowspan="2">✓</td><td>69.3</td><td>60.4</td><td>60.5</td><td>63.8</td><td>68.0</td><td>66.7</td><td>64.8</td></tr><tr><td>Cosine</td><td>70.0</td><td>61.8</td><td>60.5</td><td>63.3</td><td>69.0</td><td>67.3</td><td>65.3</td></tr></table>
+
+![](images/1d05030f79188807c403f900b9fb3ffaedcde34542d0ca190aea54791e2aa4f4.jpg)  
+Figure 4. Illustration of different ratio schedule functions in Table 4.
+
+Table 4. Ablation on different token retention ratio schedules. Our default model is marked in gray.  
+
+<table><tr><td>Model</td><td>Token Compression Ratio ↓</td><td>Infer. TFLOPs</td><td>Doc VQA</td><td>Chart QA</td><td>Text VQA</td><td>Info VQA</td><td>RW QA</td><td>GQA</td><td>SQA</td><td>MM MU</td><td>PO PE</td><td>AI 2D</td><td>VQA v2</td><td>SE ED</td><td>AVG</td></tr><tr><td>LLaVA-NeXT</td><td>100%</td><td>39.46</td><td>70.1</td><td>61.6</td><td>62.7</td><td>34.7</td><td>57.6</td><td>63.5</td><td>69.7</td><td>35.3</td><td>87.2</td><td>64.0</td><td>79.3</td><td>68.9</td><td>62.9</td></tr><tr><td>+MQT [16]</td><td>50.2%</td><td>19.86</td><td>49.9</td><td>44.0</td><td>53.5</td><td>29.8</td><td>53.5</td><td>62.3</td><td>69.1</td><td>36.1</td><td>85.8</td><td>64.0</td><td>77.2</td><td>65.8</td><td>57.6</td></tr><tr><td>+LLaVolta [4]</td><td>53.1%</td><td>21.30</td><td>66.6</td><td>58.8</td><td>60.1</td><td>33.2</td><td>56.9</td><td>63.7</td><td>70.2</td><td>36.7</td><td>86.3</td><td>65.3</td><td>78.6</td><td>68.5</td><td>62.0</td></tr><tr><td>+FastV [5]</td><td>53.1%</td><td>22.73</td><td>65.9</td><td>58.2</td><td>62.2</td><td>33.0</td><td>55.6</td><td>62.4</td><td>69.9</td><td>35.6</td><td>84.5</td><td>63.6</td><td>78.7</td><td>68.2</td><td>61.5</td></tr><tr><td>+p-MoD</td><td>53.7%</td><td>21.94</td><td>70.0</td><td>61.8</td><td>60.5</td><td>34.1</td><td>57.6</td><td>63.3</td><td>71.0</td><td>36.0</td><td>86.8</td><td>65.1</td><td>78.8</td><td>69.0</td><td>62.8</td></tr></table>
+
+Table 5. Comparison with other vision token compression methods.  $p$ -MoD significantly outperforms other compression methods, achieving the best performance on most benchmarks and the best average performance. All models are of 7B parameter scale. Results on 13B models are demonstrated in Table 8.
+
+# 4. Experiment
+
+# 4.1. Setups
+
+Models. To evaluate the effectiveness of  $p$ -MoD, we select two representative open-source MLLMs: LLaVA-1.5 [27] and LLaVA-NeXT [28], as the baseline models in our experiments. LLaVA-1.5 resizes input images to the fixed resolution which aligns with the training setup of its CLIP [40] vision encoder, encoding an image into 576 tokens. LLaVA-NeXT divides high-resolution images into multiple slices which are independently processed by the vision encoder. This strategy enhances the visual perception capabilities, but also leads to a significantly larger number of vision tokens (up to 2880) and much higher computation costs.
+
+Training Recipe. Our  $p$ -MoD models follow the two-stage training recipe of the baselines. In the pre-training stage, the MLP connector is trained on image caption data. In the fine-tuning stage,  $p$ -MoD modules are insert into the LLM and updated together with the connector and the LLM.
+
+Benchmarks. We conduct comprehensive experiments across 15 benchmarks: VQAv2 [11], GQA [18], OK-VQA [34], AI2D [21] and ScienceQA-IMG [32] are traditional visual question answering benchmarks; DocVQA [36], TextVQA [44], ChartQA [35] and InfographicVQA [37] focus on fine-grained visual question answering; POPE [26] evaluates hallucination in MLLMs; SEED-Bench (Image) [23], RealWorldQA, MME [10], MMBench [30] and MMMU [53] are comprehensive benchmarks tailored for MLLMs. To ensure our results
+
+can be conveniently reproduced, we evaluate our model on all these benchmarks with the lmms-eval [54] evaluation framework.
+
+Evaluation Metrics. In addition to performance on benchmarks, we present various metrics that reflect training and inference efficiency. We report TFLOPs which measures the inference computation complexity, and the KV cache storage which constitutes the main memory bottleneck during inference. Furthermore, we measure GPU hours consumed during training, along with inference latency.
+
+# 4.2. Main Results
+
+We integrate  $p$ -MoD with LLaVA-1.5 and LLaVA-NeXT baseline models and conduct comprehensive evaluation across 15 benchmarks, which measures comprehensive abilities of MLLMs across various aspects. The results are shown in Table 1 and Table 2. Both  $p$ -MoD-LLaVv1.5 and  $p$ -MoD-LLaVA-NeXT achieve comparable or even better performance across all benchmarks compared to their baseline models, with significant savings in inference TFLOPs and inference KV cache savings.
+
+In Table 1, it is noteworthy that text-rich and graph-based benchmarks like DocVQA, ChartQA, TextVQA, and InfoVQA require fine-grained visual perception and reasoning abilities. Models can only given a correct answer when they successfully identify answer-related regions that occupy only small portions of the entire image. Remarkably,  $p$ -MoD-LLaVA-NeXT achieves negligible performance drop on DocVQA and InfoVQA, and even gains  $0.2\%$  accuracy on ChartQA with substantial improvements
+
+in time and memory efficiency.
+
+The above results indicate that our approach substantially improves efficiency while maintaining performance.
+
+# 4.3. Ablation Study
+
+Effectiveness of proposed innovations. We conduct ablation in Table 3 to demonstrate the effectiveness of our proposed innovations. All experiments in the table are conducted under the same computational cost. TanhNorm, STRing and PRD all significantly enhance model performance, making indispensable contributions to the strong performance of our final  $p$ -MoD model.
+
+Progressive Ratio Decay. Based on the exploratory experiments in Section 3.3, we conclude that vision tokens exhibit higher redundancy in deeper layers, and design the progressive ratio decay strategy with shifted cosine schedule.
+
+To further validate this conclusion and the effectiveness of PRD, we experiment with four other schedule functions which control the token retention ratio for each LLM layer. As illustrated in Figure 4, the functions include: (1) a constant function that uses the same ratio for all layers, (2) an interleaved function which interleaves a vanilla transformer layer and an MoD layer with low ratio, which is adopted in the original MoD paper [41], (3) a stepped decay function, (4) a linear decay function. To ensure a fair comparison, we fix the average retention ratios across all layers at approximately  $54\%$ . Based on the results demonstrated in Table 4, we can draw the following conclusions:
+
+- The non-decaying functions (i.e. constant and interleaved) significantly underperform the decaying functions. This result strongly supports our conclusion that vision tokens exhibit higher redundancy in deeper layers.  
+- Our progressively decayed PRD functions (i.e. cosine and linear) notably outperforms the discontinuous stepped decay function, and the cosine function achieves the best results. This proves the effectiveness of our shifted cosine schedule.
+
+Tanh-gated Weight Normalization. To validate the effectiveness of  $\mathrm{TanhNorm}$ , we compare different weight normalization methods in Table 6. First, we verify that using no weight normalization module will result in overflow during training, as shown in the first row (details are explained in appendix). Then, we validate the effectiveness of the two important properties of  $\mathrm{TanhNorm}$  stated in Section 3.2.1: (1) the normalized weight distribution is zero-centered, (2) the range(variance) of the weight distribution can be easily controlled by adjusting the gating factor  $\alpha$ .
+
+For the first property, we design two experiments with the Softmax function, a standard normalization function that is not zero-centered. Specifically, we experiment with the vanilla softmax function  $f(w) = \alpha \cdot \text{Softmax}(w), \alpha = 0.2$ , and a shifted softmax function  $f(w) = \alpha \cdot \text{Softmax}(w) + b, \alpha = 0.4, b = -0.2$  which
+
+<table><tr><td>Norm
+Type</td><td>Doc
+VQA</td><td>Chart
+QA</td><td>Text
+VQA</td><td>G
+QA</td><td>SE
+ED</td><td>MM
+B</td><td>AVG</td></tr><tr><td>-</td><td colspan="6">OVERFLOW</td><td>-</td></tr><tr><td>Softmax</td><td>63.9</td><td>57.6</td><td>57.9</td><td>62.7</td><td>68.2</td><td>67.0</td><td>62.9</td></tr><tr><td>Shifted softmax</td><td>62.5</td><td>57.0</td><td>57.3</td><td>62.9</td><td>68.3</td><td>66.4</td><td>62.4</td></tr><tr><td>TanhNorm(α=1)</td><td colspan="6">OVERFLOW</td><td>-</td></tr><tr><td>TanhNorm(α=0.2)</td><td>70.0</td><td>61.8</td><td>60.5</td><td>63.3</td><td>69.0</td><td>67.3</td><td>65.3</td></tr></table>
+
+Table 6. Ablation on tanh-gated weight normalization. Our default model is marked in gray. The rows with no performance reported indicates that the corresponding experiment faces overflow issue during training or inference.
+
+has the same range as our  $\mathrm{TanhNorm}$  function  $f(w) = \alpha \tanh (w),\alpha = 0.2$
+
+Comparing the last row of Table 6 with the second and third rows, we verify that  $\mathrm{TanhNorm}$  significantly outperforms the vanilla softmax function and the shifted softmax function. It proves that being zero-centered is key to  $\mathrm{TanhNorm}$ 's strong performance. The shifted softmax function, despite having the same range as  $\mathrm{TanhNorm}$ , results in worse performance due to the lack of zero-centered property.
+
+For the second property, we experiment with a naive choice of the gating factor  $\alpha$  by setting it to 1, which can be interpreted as no gating is applied. As shown in the fourth row of Table 6, this experiment results in the overflow problem during inference. This validates the importance of controlling the gating factor  $\alpha$  to guarantee training and inference stability.
+
+# 4.4. Comparison with Related Works
+
+In Table 5, we compare  $p$ -MoD with several strong token compression methods. MQT [16] employs a query transformer to compress vision tokens. LLaVolta [4] performs average pooling in intermediate LLM layers, achieving remarkable results despite its simplicity. FastV [5] drops vision tokens in intermediate LLM layers based on the attention score from text tokens.  $p$ -MoD significantly outperforms other compression methods, achieving the best performance on most benchmarks and the best average performance.
+
+# 4.5. Efficiency-Performance Trade-off
+
+Thanks to the shifted cosine schedule used by PRD in Section 3.3 to control the token retention ratio across all layers, we can change the shift factor  $\beta$  to control the overall computational cost of the model. In this way, we can train and deploy  $p$ -MoD models under different performance-efficiency trade-offs based on our actual needs.
+
+To showcase the versatility of our approach, we conducted experiments with  $\beta = 0.3, 0.4, 0.5$ , respectively. The results are presented in Table 7. Our default  $p$ -MoD
+
+<table><tr><td rowspan="2">Model</td><td colspan="4">Efficiency</td><td colspan="7">Benchmark</td></tr><tr><td>Training GPU hours ↓</td><td>Inference TFLOPs ↓</td><td>Inference Latency (ms) ↓</td><td>Inference KV cache storage ↓</td><td>Doc VQA</td><td>Chart QA</td><td>Text VQA</td><td>G QA</td><td>SE ED</td><td>MM B</td><td>AVG</td></tr><tr><td>LLaVA-NeXT-7B</td><td>560</td><td>39.46</td><td>519.1</td><td>100%</td><td>70.1</td><td>61.6</td><td>62.7</td><td>63.5</td><td>68.9</td><td>67.5</td><td>65.7</td></tr><tr><td>p-MoD-0.3</td><td>403 (-28.0%)</td><td>17.78 (-54.9%)</td><td>326.7 (-37.1%)</td><td>42.3%</td><td>65.5</td><td>57.8</td><td>58.1</td><td>63.1</td><td>68.6</td><td>67.0</td><td>63.4</td></tr><tr><td>p-MoD-0.4</td><td>415 (-25.9%)</td><td>19.56 (-50.4%)</td><td>347.1 (-33.1%)</td><td>47.5%</td><td>66.5</td><td>59.6</td><td>58.4</td><td>63.8</td><td>68.5</td><td>66.6</td><td>63.9</td></tr><tr><td>p-MoD-0.5</td><td>435 (-22.3%)</td><td>21.94 (-44.4%)</td><td>368.0 (-29.1%)</td><td>53.7%</td><td>70.0</td><td>61.8</td><td>60.5</td><td>63.3</td><td>69.0</td><td>67.3</td><td>65.3</td></tr></table>
+
+Table 7. The Efficiency-Performance trade-off experiments. To showcase the versatility of our approach, we conducted experiments with  $\beta = 0.3, 0.4, 0.5$ , respectively. Inference latency is measured on TextVQA dataset.
+
+![](images/c5ddfab8b80d5dafd9c3b8aefb1a2c7c611ec59196be0f36552f40090a5b53f3.jpg)  
+layer 11
+
+![](images/776af6911f614c325a5e3edb7f4c992dd43d696d661b7ce56307e9c5caf4be1f.jpg)  
+layer 16
+
+![](images/6af051c2f639d9efe19d01c87def112116974df56d7eebaee277c4c8bbb74d37.jpg)  
+layer 21
+
+![](images/28805ef3a563275838b3a1fe5a6fbb5f708b2e97adbe53de5888ffca936a3486.jpg)  
+layer 26
+
+![](images/b7ae22df1f018e5a3b1c0ff91927bb5b8949ff8b77b7963146162d776de70693.jpg)  
+layer 11
+
+![](images/0a939700d20d873e0e4816c7257fbe974d375e8f06c25b72f03a319eb5c8f5c8.jpg)  
+layer 16
+
+![](images/6954fff18735dc6c051dd7b67116ba7b79285f859a01f399245063a0c7c57b3e.jpg)  
+layer 21  
+Figure 5. Visualization of tokens selected by different  $p$ -MoD layers. The selected tokens are colored in red. Please zoom in for a clearer view. As the number of selected tokens gradually decreases in deeper layers (due to PRD strategy), the model gradually concentrates on vision tokens corresponding to regions with rich semantic information.
+
+![](images/f78a7d03cdb3804349c8ffd4e009bfbdda21b768640a9066c24c185dc75bc695.jpg)  
+layer 26
+
+model with  $\beta = 0.5$  reduced training GPU hours by  $22.3\%$ , inference TFLOPs by  $44.4\%$ , inference latency by  $29.1\%$ , and KV cache storage by  $46.3\%$ . Using a lower  $\beta$  can further improve efficiency, with an acceptable performance drop.
+
+# 4.6. Visualization: Which tokens are selected?
+
+In Figure 5, we visualize the tokens selected by  $p$ -MoD-LLaVA-NeXT at different layers. Guided by the PRD strategy, the number of tokens processed by the MoD layers gradually decreases layer by layer. It can be observed that the selected vision tokens progressively concentrate on key regions in the image with rich semantic information. For the upper row of images in Figure 5, the selected tokens gradually converge to those corresponding to text, drawings, and the person on the right. Tokens corresponding to the white background are skipped in deep layers. In the lower row of images in Figure 5, the selected tokens
+
+gradually converge towards the artifact and the measurement markings on the ruler. These results indicate that our model effectively compresses visual information by selecting the informative tokens, enabling it to maintain performance while significantly reducing training and inference costs.
+
+# 5. Conclusion and Future Work
+
+In this paper, we explore building efficient MLLMs by adapting the Mixture-of-Depths mechanism. Our proposed model, termed  $p$ -MoD, features three key designs: tanh-gated weight normalization, symmetric token reweighting module, and the progressive ratio decay strategy. Our model achieves comparable or even superior results to the baseline models on a diverse set of 15 benchmarks, with substantial improvements on training and inference efficiency. We hope  $p$ -MoD can serve as a strong and efficient baseline for future research on developing efficient MLLMs.
+
+Acknowledgements. This work is supported by the National Key R&D Program of China (No. 2022ZD0160900), Jiangsu Frontier Technology Research and Development Program (No. BF2024076), the Collaborative Innovation Center of Novel Software Technology and Industrialization, and Nanjing University-China Mobile Communications Group Co., Ltd. Joint Institute.
+
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+# Why LVLMs Are More Prone to Hallucinations in Longer Responses: The Role of Context
+
+Ge Zheng $^{1,2*}$  Jiaye Qian $^{2*}$  Jiajin Tang $^{2}$  Sibei Yang $^{1\dagger}$
+
+$^{1}$ School of Computer Science and Engineering, Sun Yat-sen University  $^{2}$ ShanghaiTech University
+
+Project Page: https://github.com/SooLab/HalTrapper
+
+# Abstract
+
+Large Vision-Language Models (LVLMs) have made significant progress in recent years but are also prone to hallucination issues. They exhibit more hallucinations in longer, free-form responses, often attributed to accumulated uncertainties. In this paper, we ask: Does increased hallucination result solely from length-induced errors, or is there a deeper underlying mechanism? After a series of preliminary experiments and findings, we suggest that the risk of hallucinations is not caused by length itself but by the increased reliance on context for coherence and completeness in longer responses. Building on these insights, we propose a novel "induce-detect-suppress" framework that actively induces hallucinations through deliberately designed contexts, leverages induced instances for early detection of high-risk cases, and ultimately suppresses potential object-level hallucinations during actual decoding. Our approach achieves consistent, significant improvements across all benchmarks, demonstrating its efficacy. The strong detection and improved hallucination mitigation not only validate our framework but, more importantly, re-validate our hypothesis on context. Rather than solely pursuing performance gains, this study aims to provide new insights and serves as a first step toward a deeper exploration of hallucinations in LVLMs' longer responses.
+
+# 1. Introduction
+
+Recently, Large Vision-Language Models (LVLMs) [3, 7, 8, 12, 18, 48, 98] have made significant strides in developing general-purpose foundation models, achieving new, unprecedented capabilities. These models facilitate dynamic, context-driven interactions centered on the image content through open-ended conversations with users, given the input image and user instructions. Their impressive generative capabilities allow them to address various traditional
+
+![](images/19e28f9336ad5e136fafd6188f913f1d7f12479e2a453cb896aff2db720fda91.jpg)  
+Figure 1. Left: Our three main findings and the three steps of our HalTrapper method. Right: The distribution of hallucination locations detected by our HalTrapper is close to the true distribution of hallucinations, indicating that our method, to some extent, captures the essence of LVLM hallucinations.
+
+vision tasks [5, 20, 34, 35, 38, 49, 56, 58, 63-65, 88, 95, 96, 99, 100] within a unified framework and seamlessly handle more comprehensive tasks [15, 16, 23, 51, 60, 79, 86, 93] that require world knowledge and complex reasoning, such as visual question answering [2, 26, 59, 62], video-based reasoning [6, 9, 37, 41] and mathematical reasoning [54, 74]. However, LVLMs also grapple with the hallucination issue [27, 57, 92, 97], a serious and well-recognized challenge in deploying them in real-world scenarios [21, 36, 45, 52], due to their propensity for erroneous generation.
+
+Hallucination in LVLMs specifically refers to the discrepancy between the generated textual responses and the actual visual content and user instruction received, resulting in the production of irrelevant or non-existent objects, attributes, and other details. Various approaches have been proposed to reduce hallucinations, including filtering more reliable training data [46, 90, 97] or using specialized contrastive training materials [28] to re-fine-tune the model, thereby minimizing factually incorrect outputs. Rather than relying on costly, data-intensive solutions, recent approaches propose training-free strategies, such as
+
+contrastive decoding to contrastive model responses with their error-prone versions [31, 33, 76], rolling back uncertain outputs [25], or enhancing attention to visual content [50]. This has significantly mitigated the hallucination phenomenon, particularly in answering visual questions and identifying specific object hallucinations. However, most of these efforts primarily focus on short responses, while hallucinations in long-form generation remains underexplored.
+
+In this paper, we explore a seemingly straightforward—even widely taken for granted—phenomenon: LVLMs are more prone to hallucinations in longer, freeform textual responses compared to shorter answers. As shown in Fig. 1, the frequency of hallucinated objects correlates with their position in the output token sequence, with a higher likelihood of appearing at later positions. Previous work [97] has also observed similar phenomena, simply attributing the issue to autoregressive text generation, where increasing length leads to accumulated hallucinations and greater uncertainties. However, beneath the intuitive manifestation of length (like an iceberg), deeper factors (beneath the surface) have yet to receive adequate attention: Is the increased hallucination merely a result of the cumulative errors due to length itself, or does it arise from a deeper underlying mechanism?
+
+Motivated by this, this paper presents the first and preliminary attempt to explore the underlying factors through a three-step analysis approach:
+
+- Phenomenon discovery to propose hypotheses (Sec. 3).  
+- Preliminary statistics to analyze hypotheses (Sec. 4).  
+- Hypothesis application to detect and mitigate hallucinations, thereby re-validating it (Sec. 5).
+
+Phenomenon Discovery: Context may be a potential factor. Since free-form textual responses lack a predefined answer set or clear response forms, LVLMs rely heavily on context, including user instructions, visual input, and especially prior textual outputs. Consequently, we investigate the effect of context (see Sec. 3), specifically by modifying either the image or text context and observing marked shifts in the distribution of the hallucination-length curve, which indicates that hallucinations appear at earlier positions.
+
+Hypothesis Analysis: Contextual coherence and completeness induce hallucinations. Based on this observation, we hypothesize that contextual cues influence hallucinations along two key dimensions:
+
+- Contextual coherence drives LVLMs to maintain consistency with prior outputs while avoiding redundancy through distinct generation. The former focuses attention on contextual image content, while the latter shifts it to new information, potentially leading to dispersed attention, confusion, and hallucinations (see Sec. 4.1). Non-hallucinated tokens exhibit clear, focused attention, whereas hallucinated tokens show dispersed patterns. Notably, hallucinated tokens share highly similar attention
+
+distributions (see Fig. 3), suggesting LVLMs may be forced to attend to the same ungrounded, fragmented regions when balancing contextual and distinct content fails.
+
+- Contextual completeness requires responses to incorporate comprehensive content while maintaining a logically coherent linguistic structure. However, when available recognized content is insufficient, LVLMs may employ contextual extrapolation as a compensatory strategy, potentially leading to hallucinated outputs (see Sec. 4.2). As contextual completeness increases, hallucinations tend to appear earlier in the response (see Fig. 4). Furthermore, contextual extrapolation seems to follow inherently fixed patterns, with different sets of prompts repeatedly generating overlapping hallucinated tokens.
+
+Application and Re-validation. To further validate the hypotheses, we propose HalTrapper—a novel "induce-detect-suppress" framework that directly induces hallucinations by applying the two hypotheses, leverages the induced instances to detect high-risk cases early to nip them in the bud, and ultimately suppress potential hallucinations during the actual decoding stage.
+
+- Induction: (1) Imposing new, coherent outputs on an already complete response induces intra-response hallucinations. (2) Explicitly guiding imagination both based on and beyond recognized objects induces external expansion hallucinations.  
+- Detection: (1) Building on our coherence findings in Fig. 3, we identify hallucinations by analyzing attention similarity with induced intra-response hallucinations. (2) Building on our completeness findings in Fig. 4, we collect potential hallucinations by identifying objects that frequently appear under different imagination prompts. (3) Interestingly, our detection results align with the original hallucination distribution in Fig. 1, suggesting that context-induced and detected hallucinations mirror those seemingly driven by length, re-validating context is one of the potential factors beneath the iceberg of length.  
+- Suppression: Given the detected potential hallucinations, we can directly suppress their likelihood to mitigate hallucinations. Inspired by contrastive decoding [31, 32, 76], we innovatively treat detected hallucinated objects as contrastive context tokens to their probability in the contrastive branch, thereby reducing their likelihood in the original decoding branches.
+
+To sum up, our contributions are as follows:
+
+- We are the first to explore the underlying factors beneath the intuitive length-hallucination correlations, and identify context as the potential factor.  
+- We introduce a novel hypothesis based on coherence and completeness, and validate it through statistical analysis, hallucination detection, and suppression.  
+- Our exploration reveals novel insights, including the sim
+
+ilarity in image attention patterns of hallucinated objects and the repetition of hallucinations across prompts.
+
+- Building on the hypothesis, we propose a novel "inducedetect-suppress" framework, which re-validates our hypothesis while achieving competitive performance on public benchmarks.
+
+# 2. Related Work
+
+# 2.1. Large Vision-Language Models
+
+The success of large language models (LLMs) [1, 4, 13, 71] establishes the foundation for the development of large visual-language models (LVLMs) [3, 17, 47, 98]. Recent approaches typically adopt a unified framework, where a pre-trained visual encoder extracts visual features, which are then mapped to the LLM embedding space via either linear layers [12, 47] or Q-Former [3, 17, 98], and subsequently processed with text inputs. While LVLMs demonstrate remarkable capabilities in visual understanding [2, 10, 14, 26, 43, 55, 59, 61, 67–69, 80–85, 94] and reasoning tasks [29, 53, 89] through supervised fine-tuning [22, 24, 42, 47, 91], hallucinations remains a prominent challenge [33, 40, 57, 97]. Existing studies [19, 30, 70, 77] on the internal mechanisms of LVLMs have yet to provide a thorough explanation of the nature of hallucinations, particularly in long-form responses. This work sheds light on hallucinations in long-form generation in LVLMs.
+
+# 2.2. Hallucinations in LVLMs
+
+Unlike hallucination in LLMs, which refers to the generation of factually incorrect or meaningless content, hallucinations in LVLMs are more concerned with discrepancies between the generated content and the provided visual inputs. Early studies [40, 57] adapt the definition of hallucinations from the captioning task to the context of LVLMs. Subsequent research [25, 32, 46, 97] conduct preliminary analyses of hallucinations, investigating factors such as language priors [32, 46], co-occurrence patterns [32, 97], uncertainty [97], and positional dependencies [97].
+
+Several approaches [25, 28, 31, 32, 46, 50, 76, 87, 90, 97] are proposed to mitigate hallucinations in LVLMs through training. These methods include curating high-quality training datasets [97], integrating specialized contrastive training signals [28], and employing revisor models designed to correct hallucinated outputs [46, 87]. In contrast, other studies [25, 31, 32, 50, 76] explore training-free strategies as alternatives to resource-intensive training approaches. VCD [32] introduces the contrastive decoding (CD) [39] method to suppress hallucinations, gaining significant attention in the field. Subsequent methods [31, 50, 76] further design various contrastive conditions to induce hallucinations from new perspectives. Additionally, OPERA [25] identifies the overreliance on knowledge aggregation posi
+
+tions within the text attention mechanism as a key cause of hallucinations and suggests a rollback strategy to address this issue. Furthermore, PAI [50] strengthens the impact of image attention on model outputs, effectively reducing hallucinations.
+
+# 3. Is Context a Deeper Underlying Factor?
+
+In this section, we conduct exploratory experiments to investigate the underlying factor influencing hallucination beyond generation length. We first introduce PoScore to represent hallucination positions and reproduce the widely recognized phenomenon that hallucinations tend to occur in longer responses (Sec. 3.1). Subsequently, we modify either image or text context and analyze their effects on hallucination distribution, thereby identifying context as a potential underlying factor (Sec. 3.2).
+
+Default Experimental Settings. Our default experimental setup (in Sec. 3 and Sec. 4) evaluates the LLaVA v1.5 7B [47], Qwen VL Chat [3], and MiniGPT-4 [98] on a randomly sampled set of 500 COCO [44] images for statistical analysis. Additional experimental details are presented in Appendix A.
+
+# 3.1. Hallucinations Linked to Length.
+
+When leveraging LVLMs for dialogue or question-answering tasks, a notable phenomenon is that hallucinations tend to occur more frequently in the later positions of the response. To quantitatively analyze this phenomenon, we define the relative position score for each generated object as follows, consistent with previous work [97]:
+
+$$
+\operatorname {P o S c o r e} _ {s, i} = \frac {\operatorname {I n d e x} \left(o _ {s , i}\right)}{N _ {s}} \tag {1}
+$$
+
+where  $o_{s,i}$  denotes the  $i^{th}$  object in the response of the  $s^{th}$  sample, and  $N_{s}$  represents the length of the  $s^{th}$  sample. We visualize the PoScore distributions for hallucinated and non-hallucinated objects for the LLaVA model in Fig. 1, with additional results from other models provided in Fig. 7 in Appendix. The results reveal a marked increase in the frequency of hallucinations as the response lengthens, aligning with findings from previous studies [78, 97].
+
+# 3.2. Hallucinations Beyond Length.
+
+Moving beyond these prior observations, we delve deeper by posing a critical question: Is the increased hallucination merely a result of the cumulative errors due to length itself, or does it arise from a deeper underlying mechanism? In light of the critical role that context plays in free-form responses, we design the following two context modification strategies and analyze the changes in hallucination positions (PoScore) to investigate the effect of context:
+
+![](images/aef323b2cc227a52c852fbde021f5e108f2ed0788997ac9b4bbc058b971ec02a.jpg)  
+Figure 2. Statistical analysis of hallucination positions under context modifications. Both cropping the image and enriching the prompt lead to earlier hallucination occurrences.
+
+- Crop the image input into centered squares, retaining approximately one-third of the original area, and re-annote accordingly.  
+- Enrich the text input by adding two sentences that describe the image, and then prompt to describe other details.
+
+The results in Fig. 2 show that hallucinations tend to occur earlier in the generation process across both settings, challenging the widely held belief that they are more likely to appear in the later stages. These findings underscore the complexity of hallucinations, revealing that context plays a significant role in their occurrence, rather than attributing them solely to generation length.
+
+# 4. Coherence and Completeness
+
+This section delve into the mechanisms through which context influences hallucinations by employing a hypothesis-verification framework. Our analysis focuses on two key aspects: contextual coherence (Sec. 4.1) and contextual completeness (Sec. 4.2). Finally, we link back to text and image manipulation experiments in Sec. 3.2, providing explanations with these factors (Sec. 4.3).
+
+# 4.1. Coherence: Avoidance of Internal Repetition
+
+Contextual coherence drives the model to maintain consistency with previous outputs while avoiding redundant repetition of both the input and prior content. Based on this, we propose and validate a hypothesis on hallucination occurrence.
+
+Hypothesis. The two aspects of contextual coherence in image attention are conflicting: attention is required to focus on relevant regions for consistency with previous outputs, while also shifting to new areas to avoid repetition. This tension leads to dispersed attention and hallucinations.
+
+Experimental settings. To validate our hypothesis, we analyze both individual attention and pairwise attention comparisons. Specifically, we analyze the image attention maps of hallucinated objects  $\mathcal{H}$  and non-hallucinated objects  $\mathcal{N}$ , with representative results shown in Fig. 3 (right). Addi
+
+![](images/315c81e7cf8431ed411a65a08f7687bad7e3b51b3f095e4ed4eb44ecec51896a.jpg)  
+Figure 3. Statistical analysis related to contextual coherence. Within the same caption, hallucinated object pairs exhibit higher attention similarity scores than non-hallucinated pairs.
+
+tionally, we quantify the intra-set attention similarity of objects within the same response, denoted by  $S_{\mathcal{H}}$  and  $S_{\mathcal{N}}$ , as follows:
+
+$$
+S _ {\mathcal {H}} = \left\{\operatorname {s i m} \left(A _ {s, i}, A _ {s, j}\right) \mid o _ {s, i}, o _ {s, j} \in \mathcal {H} \right\}, \tag {2}
+$$
+
+$$
+S _ {\mathcal {N}} = \left\{\operatorname {s i m} \left(A _ {s, i}, A _ {s, j}\right) \mid o _ {s, i}, o _ {s, j} \in \mathcal {N} \right\}
+$$
+
+where  $A_{s,i}$  and  $A_{s,j}$  represent the image attention maps of the  $i^{th}$  and  $j^{th}$  objects in the response for the  $s^{th}$  image, and  $\mathrm{sim}(\cdot ,\cdot)$  denotes the cosine similarity function. Fig. 3 (left) illustrates the distributions of  $S_{\mathcal{H}}$  and  $S_{\mathcal{N}}$ .
+
+Results. Qualitative analysis (right panel of Fig. 3) indicates that when the model successfully identifies real objects, it concentrates on the relevant regions. Conversely, if the model fails to recognize a novel object, its attention disperses and distracting information, leading to hallucinations. Quantitative results (left panel of Fig. 3) show a clear difference between the distributions of  $S_{\mathcal{H}}$  and  $S_{\mathcal{N}}$ . Specifically, hallucinated objects exhibit higher attention similarity, while real objects show lower values. This further indicates that hallucinated objects typically manifest diffuse, noisy attention patterns, making attention similarity a robust metric for their detection.
+
+# 4.2. Completeness: External Extrapolation
+
+Contextual completeness comprises two key dimensions: the informational dimension, which demands a thorough and comprehensive response, and the structural dimension, which ensures the response is logically coherent and grammatically sound. Building on this, we propose the following hypotheses regarding the occurrence mechanism and inherent tendency of hallucination.
+
+Hypothesis. (a) Occurrence: When a response includes correctly identified objects but remains incomplete in informative or structural aspect, the model compensates by ex
+
+![](images/e079918b105aff38e8a0ec9b10fc78e774377596d91eae82cc89062df5e4e77c.jpg)
+
+![](images/303cbd00fd7678906836349eb6c563c0dc708f82e31b68e783ad1e0c516d540a.jpg)  
+Figure 4. Statistical analysis related to contextual completeness: (a) Hallucination positions shift progressively earlier as more image information is included in the prompts. (b) Similar hallucinations consistently recur across varied prompts for the same image.
+
+panding imagined details, i.e., hallucinations. (b) Tendency: These hallucinations from external extrapolation rely on multimodal context, particularly visual inputs.
+
+Experimental settings. We conduct two separate experiments for validation as follows:
+
+(a) We validate the role of completeness by analyzing its correlation with hallucination positions. Specifically, we extend text manipulation experiment in Sec. 3.2 by incrementally adding image descriptions to the prompt and visualizing the average PoScore in Fig. 4(a).  
+(b) We further investigate the consistency and image-related properties of hallucinated objects across different prompts. Specifically, we apply five prompts to each image and compute the proportion of repeated hallucinated objects. Formally, let  $\mathcal{H}_{s_k}$  represent the set of hallucinated objects generated by the  $k^{th}$  prompt for the  $s^{th}$  sample, with the complete hallucination set given by  $\mathcal{H}_s = \bigcup_{k=1}^5 \mathcal{H}_{s_k}$ . We count the occurrence of each hallucinated object  $h \in \mathcal{H}_s$  as  $c_s(h) = \sum_{k=1}^5 \mathbb{1}(h \in \mathcal{H}_{s_k})$ , where  $\mathbb{1}$  is the indicator function. Then we calculate  $N(k)$ , the number of hallucinated objects that appear  $k \in [1,2,3,4,5]$  times over all samples, along with its proportion  $R(k)$  shown in Fig. 4(b):
+
+$$
+\begin{array}{l} N (k) = \sum_ {s} \sum_ {\substack {h \in \mathcal {H} _ {s} \\ N (1)}} k \cdot \mathbb {1} \left(c _ {s} (h) = k\right), \tag{3} \\ R (k) = \frac {N (k)}{\sum_ {k = 1} ^ {5} N (k)} \\ \end{array}
+$$
+
+Results. (a) The results in Fig. 4(a) indicate that as more enriched sentences are incorporated, leading to a more comprehensive context, hallucinations occur at earlier positions. This is because the diminishing content available for generation makes it increasingly challenging for LVLMs to accurately identify details for a complete and coherent response.
+
+(b) The proportion presented in Fig. 4(b) demonstrate that all models exhibit a high degree of repetitiveness in hallucinated objects, with objects appearing in only one response accounting for merely  $30\%$  on average. Given the variations in both questions and preceding responses, the repeated hallucinated objects are often closely tied to the image context, aligning with our qualitative analysis in Appendix E.
+
+# 4.3. Link Back to Phenomenon in Sec. 2.2
+
+Explaining Text Manipulation Experiments. Revisiting the text manipulation experiments, we find that contextual coherence and completeness provides an intuitive explanation for this behavior. When additional descriptions of real objects are incorporated, the model tends to avoid redundancy and maintain coherence, thereby reducing the number of objects to describe. Consequently, the model turns to uncertain or unverified objects more quickly to ensure completeness, leading to earlier hallucinations.
+
+Explaining Image Manipulation Experiments. Contextual completeness offers a compelling explanation for the image manipulation experiments. Similarly, cropping images systematically reduces the number of recognizable objects, forcing the model to hallucinate earlier in order to maintain contextual completeness.
+
+# 5. Re-Validation via Detection and Suppression
+
+To rigorously validate our hypothesis, we extend the findings from Section 4 to practical application of hallucination detection and suppression. Specifically, we propose HalTrapper, which introduces a novel "induce-detect-suppress" strategy (see Fig. 5). The induce-detect stages leverage Internal Grounding (IG) and External Expansion (EE) techniques for hallucination detection (Sec. 5.1), and can be easily adapted with Contrastive Contextual Decoding (CCD) for suppression (Sec. 5.2).
+
+# 5.1. Hallucination Induction-Detection
+
+# 5.1.1. Internal Grounding
+
+In Sec. 4.1, we demonstrate that the attention similarity between paired objects serves as an effective indicator for distinguishing hallucinated pairs from non-hallucinated ones. Building on this insight, we propose the Internal Grounding (IG) method, which adopts an induce-then-detect paradigm to detect hallucinated objects in model responses.
+
+Induction. A key component of IG is the selection of reference objects, which serve as anchors for similarity computation. Instead of using naturally generated objects, we induce the model to generate additional objects following the initial response, which are more prone to hallucination. Specifically, given an input image and the model's initial response, we replace the EOS token in the generated output with an additional cue, "There is also". Since the initial responses inherently covers a considerable number of
+
+![](images/09f50547f09bdaa3aaf2d94edb40b0e9ec43d3c0724036ec44aadc4745eedb1c.jpg)  
+Figure 5. Overview of HalTrapper: It consists of two branches leveraging coherence and completeness insights. One generates captions with an appended "There is also" prompt to induce potential hallucinated objects, detected via high attention similarity between caption and induced tokens. The other prompts the LVLM to imagine surrounded content beyond the image to identify consistent hallucinations. With detected hallucinated objects, HalTrapper further suppresses hallucinations through Contrastive Contextual Decoding.
+
+the identified objects, when completeness is compromised, the model tends to externally extrapolate to compensate, thereby restoring completeness (see Sec. 4.2). The resulting object serves as the reference object and is denoted as  $\sigma_{\mathrm{s}}^{\mathrm{ref}}$  for the  $s^{th}$  sample.
+
+Detection. We then compute the attention similarity scores IGScore between the induced hallucinated objects  $o_s^{ref}$  and the preceding objects, filtering out potential hallucination candidates  $S_{IG}$  with high similarity:
+
+$$
+\operatorname {I G S c o r e} _ {s, i} = \operatorname {s i m} \left(A _ {s} ^ {r e f}, A _ {s, i}\right) \tag {4}
+$$
+
+$$
+S _ {I G} = \left\{o _ {s, i} \mid \operatorname {I G S c o r e} _ {s, i} > \theta_ {I G} \right\}
+$$
+
+where  $\theta_{IG}$  denotes the threshold. Notably, the proposed method remains robust even when the reference object is real, as the similarity scores between non-hallucinated objects are typically low, effectively preventing real objects from being misclassified as hallucinations.
+
+# 5.1.2. External Expansion
+
+Another observation is that hallucinated objects exhibit consistency across identical visual inputs (Sec. 4.2). Based on this property, we propose the External Expansion (EE) method, explicitly inducing the imagination related to the image, treating them as detected potential hallucinations.
+
+Induction. Considering that hallucinations from external extrapolation rely on image context, we first prompt with "Please imagine what object might be outside the frame" to induce image-related associations and capture potential hallucinations. However, directly extracting hallucinated objects from the response leads to false positives, as the model might imagine objects present in the image. To address this, we design a reason-then-imagine prompt to filter out such existing objects (see Appendix C.2). It explicitly guides the model in distinguishing between recognized objects and imagined ones. Furthermore, it utilizes reliable intermediate steps to enable context-driven reasoning, thereby improving response fidelity.
+
+Detection. We introduce EEScore, based on the principle that an object's presence in the imagination set improves the
+
+likelihood of it being perceived as a hallucination, while its presence in the reason set reduces this likelihood. Specifically, we define the imagination set and the reason set at direction  $d \in \mathcal{D}$  as  $S_{I,d}$  and  $S_{R,d}$ , respectively. The final set of potential hallucinations is formulated as follows:
+
+$$
+\operatorname {E E S c o r e} _ {s, i} = \sum_ {d \in \mathcal {D}} \left[ \mathbb {1} \left(o _ {s, i} \in S _ {I, d}\right) - \mathbb {1} \left(o _ {s, i} \in S _ {R, d}\right) \right] \tag {5}
+$$
+
+$$
+S _ {E E} = \left\{o _ {s, i} \mid \operatorname {E E S c o r e} _ {s, i} > \theta_ {E E} \right\}
+$$
+
+Finally, we combine the potential hallucinations detected by the IG and EE methods as follows:
+
+$$
+S _ {\text {i n d u c t i o n}} = S _ {I G} \cup S _ {E E} \tag {6}
+$$
+
+# 5.2. Hallucination Suppression
+
+Preliminaries. Let  $\theta$  denote the parameters of an LVLM. Given an input image  $v$  and a text prompt  $x$ , the model autogressively generates a response  $y$  of length  $L$ . Formally, the decoding process can be formulated as follows:
+
+$$
+p _ {\theta} (y | v, x) = \prod_ {i = 1} ^ {L} p _ {\theta} \left(y _ {i} | v, x, y _ {<   i}\right) \tag {7}
+$$
+
+where  $y_{i}$  and  $y_{<i}$  represent the token at position  $i$  and preceding tokens before position  $i$ , respectively, and  $p_{\theta}(y_i|v,x,y_{<i}) \propto \exp \log \mathrm{it}_{\theta}(y_i|v,x,y_{<i})$  denotes the conditional probability distribution of the next token  $y_{i}$  given the preceding tokens  $y_{<i}$ .
+
+Based on this formulation, we introduce contrastive decoding (CD), originally proposed by [39]. CD utilizes an amateur model as a contrastive reference to optimize the decoding objectives while maintaining plausibility constraint. Recently, [31, 32, 76] apply CD to LVLMs, leveraging hallucination-amplifying branches as contrastive signals to mitigate hallucinations. Specifically, the CD process, with the new model  $\theta^{\prime}$  as the contrastive branch and all other in
+
+<table><tr><td>Model</td><td>Metric</td><td>AUROC</td><td>TPR5%FPR</td><td>F1max</td><td>Acc.</td></tr><tr><td rowspan="6">LLaVA v1.5</td><td>PoScore</td><td>70.7</td><td>4.3</td><td>38.3</td><td>70.7</td></tr><tr><td>Top Logit</td><td>64.0</td><td>13.0</td><td>32.2</td><td>61.9</td></tr><tr><td>Logits&#x27;Entropy</td><td>67.7</td><td>16.6</td><td>36.6</td><td>71.4</td></tr><tr><td>Image Attn. Ratio</td><td>44.9</td><td>6.0</td><td>27.3</td><td>32.0</td></tr><tr><td>IG Score</td><td>82.3</td><td>43.3</td><td>54.8</td><td>86.3</td></tr><tr><td>EE Score</td><td>77.5</td><td>-</td><td>46.1</td><td>72.9</td></tr><tr><td rowspan="6">MiniGPT 4</td><td>PoScore</td><td>70.5</td><td>12.2</td><td>35.4</td><td>66.2</td></tr><tr><td>Top Logit</td><td>65.6</td><td>22.9</td><td>37.0</td><td>76.5</td></tr><tr><td>Logits&#x27;Entropy</td><td>65.5</td><td>22.1</td><td>35.3</td><td>75.9</td></tr><tr><td>Image Attn. Ratio</td><td>64.3</td><td>7.7</td><td>31.9</td><td>57.9</td></tr><tr><td>IG Score</td><td>76.6</td><td>34.0</td><td>48.6</td><td>80.7</td></tr><tr><td>EE Score</td><td>60.5</td><td>-</td><td>30.0</td><td>46.5</td></tr><tr><td rowspan="6">Qwen VL</td><td>PoScore</td><td>71.1</td><td>4.8</td><td>34.4</td><td>65.8</td></tr><tr><td>Top Logit</td><td>71.5</td><td>19.6</td><td>36.1</td><td>77.7</td></tr><tr><td>Logits&#x27;Entropy</td><td>70.7</td><td>23.3</td><td>36.6</td><td>73.9</td></tr><tr><td>Image Attn. Ratio</td><td>57.3</td><td>6.8</td><td>26.9</td><td>41.4</td></tr><tr><td>IG Score</td><td>76.2</td><td>33.3</td><td>43.8</td><td>84.6</td></tr><tr><td>EE Score</td><td>81.3</td><td>-</td><td>46.3</td><td>73.0</td></tr></table>
+
+Table 1. Quantitative results for hallucination detection. The best performances within each setting are bolded.
+
+puts unchanged, is expressed as follows:
+
+$$
+\begin{array}{l} p _ {c d} \left(y _ {i} \mid v, x, y _ {<   i}\right) = \operatorname {s o f t m a x} [ (1 + \alpha) \operatorname {l o g i t} _ {\theta} \left(y _ {i} \mid v, x, y _ {<   i}\right) \\ - \alpha \operatorname {l o g i t} _ {\theta^ {\prime}} \left(y _ {i} | v, x, y _ {<   i}\right) ] \tag {8} \\ \end{array}
+$$
+
+where  $p_{\theta^{\prime}}(x_i|v,x,y_{< i})\propto \exp \log \mathrm{it}_{\theta^{\prime}}(x_i|v,x,y_{< i})$  . It also employs a truncation of the probability distribution following [32].
+
+Contrastive Contextual Decoding (CCD). Building on the previously introduced induce-detect stages, a simple CD-based extension CCD enables hallucination suppression. Unlike previous CD methods, CCD explicitly integrates a prior for potential hallucination objects, aiming to reduce their likelihood in response. Specifically, we encode potential hallucinated objects as text tokens, referred to as Contrastive Contextual Tokens (CCT)  $x_{cct}$ . We then concatenate CCT with the image input to construct a contrastive branch, with model parameters and other inputs unchanged. The CCD process can be formally expressed as follows:
+
+$$
+p _ {c c d} \left(y _ {i} \mid v, x, y _ {<   i}\right) = \prod_ {i = 1} ^ {L} p _ {c c d} \left(y _ {i} \mid v, x _ {c c t}, x, y _ {<   i}\right) \tag {9}
+$$
+
+We then detail the modifications applied to the CD process as follows:
+
+$$
+\begin{array}{l} p _ {c c d} \left(y _ {i} \mid v, x _ {c c t}, x, y _ {<   i}\right) = \\ \operatorname {s o f t m a x} \left[ (1 + \alpha) \log \mathrm {i t} _ {\theta} \left(y _ {i} \mid v, x, y _ {<   i}\right) \right. \tag {10} \\ - \alpha \operatorname {l o g i t} _ {\theta} \left(y _ {i} | v, x, x _ {c c t}, y _ {<   i}\right) ] \\ \end{array}
+$$
+
+By treating CCT tokens as complementary to image content, the model naturally increases the likelihood of potential hallucinated objects and their associated terms in the contrastive branch, thereby effectively reducing their occurrence in the final generation.
+
+# 6. Experiments
+
+Datasets and Benchmarks. To demonstrate the effectiveness of our HalTrapper, we use images from COCO [44]
+
+![](images/a644c3cd01cf746cf86bf98b749df0ac51045305877b4da68e25e8ebb686f6fb.jpg)  
+Figure 6. Comparison between the positional distribution of hallucinations detected by our method and the overall hallucination distribution, demonstrating a high degree of alignment.
+
+and AMBER [72] datasets. Detailed descriptions can be found in the Appendix C.1.
+
+Base Models. We select LLaVA v1.5 7B [47], MiniGPT-4 [98], and Qwen VL Chat [3] as our main baselines for our study. We also evaluate more recent models Qwen2 VL 7B [75] and Janus Pro 7B [11] on AMBER, which has higher annotation qualities.
+
+Implementation Details. For all experiments, the maximum number of newly generated tokens is set to 512. Following prior mainstream studies on CD [32, 76], we adapt  $\alpha = 1.0$  and  $\beta = 0.1$ . See Appendix C.3 and C.4 for details on CCT construction and more hyperparameters.
+
+# 6.1. Detection
+
+Metrics. Inspired by [66], we adapt AUROC (Area Under the ROC Curve) and TPR@5%FPR (the True Positive Rate at 5% False Positive Rate) as our primary metrics for hallucination detection. AUROC quantifies the model's overall discriminative ability across all classification thresholds, while TPR@5%FPR is suitable for scenarios with strict requirements on the false positive rate. We also report the F1 Score and Accuracy at the threshold that maximizes the F1. Baseline Methods. For each generated object  $o_{s,i}$ , we first employ PoScore [97] as a basic metric. We also propose two uncertainty-based metrics: Top Logit and Logits' Entropy. The Top Logit is the maximum value of the logits when generating  $o_{s,i}$ , while Logits' Entropy refers to the entropy of the logits at that moment. Additionally, we employ an Attention-based metric called the Image Attention Ratio, defined as the ratio of the model's attention score on the image to its total attention score when generating  $o_{s,i}$ .
+
+Results. The quantitative results of hallucination detection are presented in Table 1. As shown, our approach demonstrates significant improvements across all evaluation settings. For IG, in terms of the AUROC metric, our method outperforms the best baseline PoScore by  $5\% - 12\%$ . This indicates that our method enhances performance across the entire classification curve. Considering that our IG method originates from within the model, this indicates that the model indeed exhibits significant similar attention pat
+
+<table><tr><td rowspan="2">Decoding</td><td rowspan="2">Method</td><td colspan="6">LLaVA v1.5 7B [47]</td></tr><tr><td>CS↓</td><td>CI↓</td><td>Prec.</td><td>Recall</td><td>F1</td><td>Len</td></tr><tr><td rowspan="5">Greedy</td><td>ICD [76]</td><td>51.4</td><td>14.7</td><td>73.4</td><td>81.0</td><td>77.0</td><td>102.1</td></tr><tr><td>CODE [31]</td><td>50.0</td><td>13.7</td><td>75.8</td><td>76.9</td><td>76.4</td><td>88.3</td></tr><tr><td>Vanilla</td><td>52.2</td><td>14.6</td><td>73.7</td><td>80.3</td><td>76.9</td><td>100.8</td></tr><tr><td>Ours</td><td>41.6</td><td>11.9</td><td>78.7</td><td>80.1</td><td>79.4</td><td>100.0</td></tr><tr><td></td><td>10.6↓</td><td>2.7↓</td><td>5.0↑</td><td>0.2↓</td><td>2.5↑</td><td></td></tr><tr><td rowspan="6">Nucleus</td><td>VCD [32]</td><td>58.2</td><td>16.9</td><td>70.8</td><td>78.8</td><td>74.6</td><td>103.2</td></tr><tr><td>ICD [76]</td><td>55.0</td><td>16.5</td><td>70.9</td><td>77.9</td><td>74.2</td><td>102.1</td></tr><tr><td>CODE</td><td>54.2</td><td>16.4</td><td>72.3</td><td>76.2</td><td>74.2</td><td>91.6</td></tr><tr><td>Vanilla</td><td>58.6</td><td>18.8</td><td>68.1</td><td>76.4</td><td>72.0</td><td>105.2</td></tr><tr><td>Ours</td><td>48.6</td><td>14.5</td><td>74.6</td><td>77.7</td><td>76.1</td><td>100.9</td></tr><tr><td></td><td>10.0↓</td><td>4.3↓</td><td>6.5↑</td><td>1.3↓</td><td>4.1↑</td><td></td></tr><tr><td rowspan="4">Beam Search</td><td>OPERA [25]</td><td>53.6</td><td>15.7</td><td>72.4</td><td>77.6</td><td>74.9</td><td>98.8</td></tr><tr><td>Vanilla</td><td>55.6</td><td>15.8</td><td>72.8</td><td>81.0</td><td>76.7</td><td>104.2</td></tr><tr><td>Ours</td><td>45.2</td><td>12.1</td><td>78.9</td><td>81.2</td><td>80.0</td><td>101.8</td></tr><tr><td></td><td>10.4↓</td><td>3.7↓</td><td>6.1↑</td><td>0.2↓</td><td>3.3↑</td><td></td></tr></table>
+
+tern in certain hallucination scenarios. Additionally, for TPR@5%FPR, our method improves by at least  $10\%$  compared to the baselines. This highlights the substantial potential of the EE metric in inducing hallucinations. Given that MiniGPT 4 is trained only on the image interface, its ability to follow instructions is relatively limited, which may account for the lack of improvement in the EE metric.
+
+We also visualized the qualitative results of hallucination positions distribution detected by our method, with the overall distribution of hallucination positions, as shown in Fig. 6. It demonstrates that our method accurately captures the hallucination distribution, closely aligning with the overall pattern observed in captions. This further indicates that although we claim that our method is designed for long-text scenarios, its effectiveness is not merely dependent on the length of the generated text. Instead, our approach effectively captures an intrinsic mechanism underlying LVLM hallucinations, which is beyond text length. Therefore, our study not only validates the applicability of our method but also provides a new perspective for understanding the formation mechanism of LVLM hallucinations.
+
+# 6.2. Suppression
+
+Metrics. CHAIR [57] is commonly used to quantify hallucinations in model-generated captions based on COCO. Besides CHAIR, we also report several classic metrics, including Precision, Recall, F1, and the average length of the captions. For AMBER [72], following the approach outlined in their paper, we report CHAIR, Cover, Hal, and Cog. As we primarily focus on long context scenarios, we conduct full evaluations only on its generative subset and reported the results accordingly. We also conduct experiments on POPE and GPT-4o, please refer to the Appendix D.2 and D.4.
+
+Baseline Methods. We compare our HalTrapper with VCD [32], ICD [76], CODE [31], and OPERA [25].
+
+CHAIR Evaluation. As shown in Tables 2 and 3. HalTrapper significantly reduces CHAIR while maintaining Recall
+
+Table 2. Results on CHAIR. Lower  $\mathrm{CHAIR}_S$ ,  $\mathrm{CHAIR}_I$ , and higher precision, recall and F1 indicate fewer hallucinations. The best performances within each setting are bolded.  
+
+<table><tr><td rowspan="2">Decoding</td><td rowspan="2">Method</td><td colspan="3">MiniGPT 4 [98]</td><td colspan="3">Qwen VL Chat [3]</td></tr><tr><td>CS↓</td><td>CI↓</td><td>Prec.</td><td>CS↓</td><td>CI↓</td><td>Prec.</td></tr><tr><td rowspan="4">Greedy</td><td>Vanilla</td><td>39.6</td><td>14.7</td><td>76.6</td><td>43.4</td><td>13.5</td><td>75.8</td></tr><tr><td>ICD [76]</td><td>42.6</td><td>14.7</td><td>76.3</td><td>50.4</td><td>14.4</td><td>73.7</td></tr><tr><td>CODE [31]</td><td>32.8</td><td>13.6</td><td>81.2</td><td>40.4</td><td>12.5</td><td>78.9</td></tr><tr><td>Ours</td><td>28.6</td><td>10.7</td><td>83.1</td><td>38.6</td><td>10.2</td><td>80.9</td></tr><tr><td rowspan="5">Nucleus</td><td>Vanilla</td><td>37.2</td><td>14.6</td><td>77.1</td><td>44.8</td><td>13.6</td><td>76.3</td></tr><tr><td>VCD [32]</td><td>39.6</td><td>14.9</td><td>76.6</td><td>47.4</td><td>14.1</td><td>74.3</td></tr><tr><td>ICD</td><td>41.4</td><td>14.9</td><td>76.1</td><td>52.6</td><td>15.0</td><td>73.0</td></tr><tr><td>CODE [31]</td><td>36.6</td><td>14.0</td><td>79.5</td><td>43.6</td><td>14.5</td><td>75.4</td></tr><tr><td>Ours</td><td>29.0</td><td>11.5</td><td>82.1</td><td>42.4</td><td>11.3</td><td>79.3</td></tr><tr><td rowspan="3">Beam Search</td><td>Vanilla</td><td>38.8</td><td>13.8</td><td>78.0</td><td>41.4</td><td>11.6</td><td>79.0</td></tr><tr><td>OPERA [25]</td><td>43.0</td><td>14.9</td><td>75.8</td><td>42.8</td><td>12.5</td><td>76.9</td></tr><tr><td>Ours</td><td>37.6</td><td>13.7</td><td>78.3</td><td>34.2</td><td>9.7</td><td>82.7</td></tr></table>
+
+Table 3. More results on CHAIR with MiniGPT-4 and Qwen VL.  
+
+<table><tr><td>Model / Method</td><td>CHAIR↓</td><td>Cover↑</td><td>Hal↓</td><td>Cog↓</td></tr><tr><td>LLaVA v1.5 7B [47]</td><td>11.2</td><td>50.2</td><td>47.9</td><td>4.6</td></tr><tr><td>+ VCD [32]</td><td>8.9</td><td>51.2</td><td>38.1</td><td>4.4</td></tr><tr><td>+ ICD [76]</td><td>8.6</td><td>51.1</td><td>37.3</td><td>3.9</td></tr><tr><td>+ CODE [31]</td><td>9.0</td><td>51.1</td><td>39.5</td><td>4.3</td></tr><tr><td>+ Ours</td><td>8.0 (3.2↓)</td><td>51.5 (1.3↑)</td><td>36.3 (11.6↓)</td><td>3.8 (0.8↓)</td></tr><tr><td>Qwen2 VL [75]</td><td>6.6</td><td>71.8</td><td>50.3</td><td>4.6</td></tr><tr><td>+ VCD</td><td>7.3</td><td>70.6</td><td>53.2</td><td>4.6</td></tr><tr><td>+ ICD</td><td>8.2</td><td>74.9</td><td>74.9</td><td>9.1</td></tr><tr><td>+ CODE</td><td>7.6</td><td>71.6</td><td>56.3</td><td>5.1</td></tr><tr><td>+ Ours</td><td>5.6 (1.0↓)</td><td>70.9</td><td>46.1 (4.2↓)</td><td>3.8 (0.8↓)</td></tr><tr><td>Janus Pro 7B [11]</td><td>6.3</td><td>65.6</td><td>37.5</td><td>2.0</td></tr><tr><td>+ VCD</td><td>5.5</td><td>66.2</td><td>32.5</td><td>2.1</td></tr><tr><td>+ ICD</td><td>6.1</td><td>67.1</td><td>36.3</td><td>2.5</td></tr><tr><td>+ CODE</td><td>6.0</td><td>65.3</td><td>33.6</td><td>1.6</td></tr><tr><td>+ Ours</td><td>5.4 (0.9↓)</td><td>66.5 (0.9↑)</td><td>32.7 (4.8↓)</td><td>1.8 (0.2↓)</td></tr></table>
+
+Table 4. Results on AMBER [73] generative task.  $\downarrow$  indicates lower is better.
+
+with minimal negative impact. Across all experiments on  $\mathrm{CHAIR}_S$  and  $\mathrm{CHAIR}_I$ , HalTrapper achieves significant improvements. Notably, in Table 2, our approach consistently improves  $\mathrm{CHAIR}_S$  by over  $10\%$  and  $\mathrm{CHAIR}_I$  by  $2.5\%$ . This demonstrates that the hallucination candidates identified by our IG and EE metrics are of high quality, enabling the inclusion of a large number of hallucinated objects while minimizing the presence of non-hallucinated ones. This, in turn, provides validation of the effectiveness of our IG and EE metrics in detecting hallucinations, further highlighting the universality and practical significance of our findings.
+
+AMBER Evaluation. As shown in the Table 4, HalTrapper continues to demonstrate performance improvements on latest models. Ablation Study. See Appendix D.1 for more details on the ablation study.
+
+# 7. Conclusion
+
+In this paper, we propose a novel method for eliminating hallucinations in Large Vision-Language Models through two mechanisms: external spatial expansion and internal visual grounding. Our HalTrapper introduces a simple, zero-shot hallucination detection and suppression technique that achieves significant improvements across all benchmarks, with no additional training required. Our approach consistently delivers substantial improvements across all benchmarks, validating its effectiveness.
+
+Acknowledgment. This work is supported by the National Natural Science Foundation of China (No.62206174).
+
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