DSRF: A Dynamic and Scalable Reasoning Framework for Solving RPMs
Authors: Chengtai Li
Yuting He
Jianfeng Ren
Ruibin Bai
Yitian Zhao
Xudong Jiang
Venue: NeurIPS 2025 poster ()
Keywords: Abstract Visual Reasoning
Knowledge Representation
Knowledge Reasoning
Primary area: neuroscience_and_cognitive_science
TL;DR: A Dynamic and Scalable Reasoning Framework for Solving RPMs

Abstract: Abstract Visual Reasoning (AVR) entails discerning latent patterns in visual data and inferring underlying rules. Existing solutions often lack scalability and adaptability, as deep architectures tend to overfit training data, and static neural networks fail to dynamically capture diverse rules. To tackle the challenges, we propose a Dynamic and Scalable Reasoning Framework (DSRF) that greatly enhances the reasoning ability by widening the network instead of deepening it, and dynamically adjusting the reasoning network to better fit novel samples instead of a static network. Specifically, we design a Multi-View Reasoning Pyramid (MVRP) to capture complex rules through layered reasoning to focus features at each view on distinct combinations of attributes, widening the reasoning network to cover more attribute combinations analogous to complex reasoning rules. Additionally, we propose a Dynamic Domain-Contrast Prediction (DDCP) block to handle varying task-specific relationships dynamically by introducing a Gram matrix to model feature distributions, and a gate matrix to capture subtle domain differences between context and target features. Extensive experiments on six AVR tasks demonstrate DSRF’s superior performance, achieving state-of-the-art results under various settings. Code is available here: https://github.com/UNNCRoxLi/DSRF.

DSRF: A Dynamic and Scalable Reasoning Framework for Solving RPMs
Chengtai Li Yuting Hel.3
Jianfeng 1.4+ Ruibin Bai Yitian Zhao? Xudong Jiang"
'The Digital Port Technologies Lab, School of Computer Science, University of Nottingham Ningbo China
Cixi Institute of Biomedical Engineering,
Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences
4 Beacons Excellence Research and Innovation Institute, University of Nottingham Ningbo China
$ School of Electrical and Electronic Engineering, Nanyang Technological University
{scxc12, scxyh2, jianfeng ren, ruibin. bai bnottnnntnn edu cn yitian, zhao@nimte ac. en, exdjiangentu, edu.sg
Abstract
Abstract Visual Reasoning (AVR) entails discerning latent patterns in visual data and inferring underlying rules. Existing solutions often lack scalability and adapt- ability, as deep architectures tend to overfit training data, and static neural networks fail dynamically capture diverse rules. To tackle the challenges, Dynamic and Scalable Reasoning Framework (DSRF) that greatly enhances the reasoning ability by widening the network instead of deepening and dynami- cally adjusting the reasoning network to better fit novel samples instead of static network. Specifically, we design a Multi- View Reasoning Pyramid (MVRP) capture complex rules through layered reasoning to focus features each view on distinct combinations of attributes, widening the reasoning network cover more attribute combinations analogous complex reasoning rules. Addition- Prediction (DDCP) block to handle
propose a
ally, we propose Dynamic varying task-specific relationships dynamically by introducing Gram matrix model feature distributions, and a gate matrix to capture subtle domain differences between context and target features. Extensive experiments on six AVR tasks demonstrate DSRF's superior performance, achieving state-of of-the-art results under various settings. Code is available here: https//ghhubboom/NNNCooo....
Introduction
Abstract Visual Reasoning (AVR) aims to identify latent patterns from visual clues and then derive underlying rules [ It has been widely used for human IQ tests 2 Recently, AVR has become common benchmark for evaluating the reasoning ability of LLMS 315 Among various AVR tasks, Raven's Progressive Matrices (RPMs) are most popular 6-10), where the question a 2x3 or 3x3 image matrix, with each row/column following a common rule and the bottom-right slot to be filled in. RPMs reduce language and cultural barriers by creating rules using symbols and geometric shapes, requiring pure reasoning ability without relying on prior knowledge.
is typically
"Coreesonniig Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Dynomic Domatn-Commie Controst Prediction
Gate
DDCP
GARB
C Ovtputt
MRM
Input
Aggregation
Scalable
DDCP MRM
DDCP
Goted Attention
Reasoning Block
MRM
Output
Aggregation
DDCP MRM
DDCP
DDCP
DDCP
MRM
MRM
MRM
Scalable
Multi-View Mapping
Input Visual Feature
Figure 1: The DSRF is scalable, it maps high-level abstract visual features into multiple views and extracts complex rule from these views through a layered pyramid, and it is dynamic, as each DDCP equipped with various dynamic mechanisms capture task-specific rules within each view.
Existing RPM solvers module to encode visual features and a reasoning module to capture underlying rules. Reasoning modules are often built from shallow networks, which are much smaller than perception modules, greatly limiting their reasoning ability. As the visual features extracted from AVR tasks are rather abstract, and the reasoning rules are often concise and intuitive, stacking deep reasoning modules may increase the risk of overfitting [18]. Recently, a deeper reasoning network is introduced by incorporating reasoning blocks at multiple perceptive fields and aggregating the reasoning results from multiple layers [19]. However, shallow visual features lack the information needed for effective reasoning. The lack of scalability of reasoning networks compared to the well-established scalability in visual perception networks greatly limits the ability of existing RPM solvers.
often establish relations between images through a perception
To tackle this challenge, we propose Multi View Reasoning Pyramid (MVRP), scalable layered reasoning pyramid. As shown in Fig. [ the multi-view mapping enables the model to easily scale up to cover more attribute combinations analog to reasoning rules. In addition, rules in RPMs are often human-understandall potentially overfit the training data. Furthermore, images often contain a huge number of feasible rules across diverse attributes, e.g., Shape, Size, Position, Color, and Number 6 20). To effectively capture these rules, instead of deepening the network, the proposed MVRP focuses on widening the network to model more complex rules.
concise and intuitive. Deep reasoner in existing models [1] 19 may
often employ static reasoning networks built from convolutional neural networks (CNNs) multi-layer perceptrons (MLPs), in which static filters and network weights are derived from the training data and faithfully applied novel test samples, expecting minimum domain shift. These static reasoning modules greatly limit their adaptability to task-specific demands in novel application scenarios. Thus, critical design dynamic task-adaptive mechanism to flexibly handle diverse rule sets in novel test scenarios.
Another challenge is that previous methods 9 15
To dynamically model underlying relations and strengthen reasoning ability over tremendous rules, we propose a Dynamic Contratt Prediction (DDCP) block, with three dynamic aspects in network design. The gating mechanism DDCP, helping the network adapt to various input features and automatically highlight relevant features for rule construction. 2) Dynamic modeling of domain differences by a novel Gated Attention Reasoning Block (GARB). Gram matrix derived from self-correlatio is designed to model the distribution of context features and another for target features. The GARB dynamically contrasts the domain difference in three aspects, and it is in turn applied to highlight the context features for better constructing the rules. As shown in [21, the GARB allows our model to flexibly adjust parameters following the input, thereby improving its ability to handle varying conditions. 3) Dynamic gating in GARB for highlighting domain difference. The

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domain difference is complex and diverse, in which irrelevant features may mislead the reasoning process. The dynamic gate highlights the domain difference related context features and target features, adaptively focusing on relevant features for establishing the underlying rules.
Our contributions can be summarized follows: 1) The proposed Dynamic and Scalable Reasoning Framework (DSRF) solves RPMs in scalable and dynamic manner. 2) The proposed MVRP well captures complex rules through a layered reasoning pyramid, which could scale up the network casily by mapping high-dimensional features into different views. 3) The proposed DDCP greatly enhances the generalization capability of the reasoning networks through dynamic domain modeling and dynamic gating designed in GARB. 4) Extensive results on six AVR datasets show that DSRF significantly outperforms state-of of-the--rt models and generalizes well on novel tasks.
2 Related Work
Abstract Visual Reasoning has recently attracted growing research interests. In particular, a lot of efforts have been made to enhance the reasoning capabilities of large language models 3 4
AVR tasks can be broadly categorized
follows []) 1) RPM tasks challenging the subject to
identify the right answer according to the underlying rules in a question panel, including RAVEN [6]
I-RAVEE (8, RAVEN-FAIR [9) PGM (7). Unicode [IO], and many others g 91. 2) Same-different
tasks such as SVRT 22 to discern similarities and differences according to underlying rules. Recently, it is extended to the CVR task (0 and MC²R task [T.. where models must identify one or more outliers from a group of images. 3) Other research directions in AVR, e.g., Bongard Problems [23 consisting of abstract shapes and rules for assessing reasoning methods in scenarios with limited samples; Arithmetic Visual Reasoning (4 combining numerical understanding with visual elements; Relations Game 25 centered on detecting explicit spatial-relations rules among objects in images.
AVR models often consist of a perception module and a reasoning module. As most AVR tasks are built from regular shapes, relatively shallow networks are often employed in AVR models, e.g. RelBase (12), MRNet [9], PredRNet [15), AlgebraicMR [13) and SCAR (17. Recently, in view of excellence of transformers in capturing the long-range global interaction, HCV-ARR 14, DRNet [6] and HP2 AI [19 incorporate both transformer branch and CNN branch to enhance visual features.
Traditionally, AVR models are often designed capture the row- and/or column- similarities using addition, subtraction, and dot product operations, e.g., MRNett 99. DRNet [6] and HCV-
ARR [14] or establish the weights for images to model the underlying relations 1 13 17 Recent
works focus on embedding the abstract rules into the reasoning network through a "predict-and-
verify" paradigm [15 19 18). Despite the rapid developments, existing AVR models often lack the
scalability to boost their reasoning capability, e-g., both MRNet (9) and HCV-ARR (14 focus on capturing row and column similarities, leading to shallow reasoning network that greatly restricts the scalability. Recently, PredRNet [15] and HP AI [99 scale the network by stacking the reasoning blocks, their models have the problem of overfitting after stacking just four reasoning blocks. The lack of scalability greatly hinders the development of more general and more powerful reasoning models, Furthermore, existing models such as PredRNet [15]. POL [18), DBCR (26.. DARR [27] and HP?AI AI [19] often fit a static reasoning network to underlying rules, limiting the reasoning ability and generalizing poor on novel data. In this work, we propose DSRF to tackle the challenge of dynamically and comprehensively reasoning over complex rules in an easily scalable manner.
3 Proposed DSRF
3.1 Overview of Proposed DSRF
Formally, the RPM problem is defined (Q; A). where Q is the question matrix, typically consisting 3 or 2x3 3 images of size H x W excluding the last slot, and A is the set of candidate answers. We take the most popular AVR task, the RAVEN problem [6] of 3 x images as an example, where Q = {Q1, Q2................... Q } and A- = {A1, A2.... As}. The target is to select one image from A to fill in the missing slot of the question panel, ý = Re, (Pe,((Q A); Op): O,), where ÿ is the predicted answer, Re, (-) and (.) are the reasoning module and perception module, respectively.
The overview of DSRF shown in Fig. 2 We utilize four ResNet blocks [5] as the perception module. Other backbones can also be applied as shown in Sec. 4.3 For scalable reasoning, the
3

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proposed MVRP incorporates layered pyramid to encapsulate the composition structure of complex rules, and multi-view mapping to provide convenient mechanism map features into different views, easily widening the network to cover tremendous complex rules. To handle the domain
Abstract Visual Images
Layer
Qa
F F4 Fs P4 F4 F
F1 F2 P P4 Ps P
DDCP
0
Co
Fx F F
Fy Fg P.
Question Panel
CNN Gate
MRM
(A
Linror
Lineor
CWN
GELU
Answer Panel
Share webshh
Alia Liinee
Self-Attentionn
Perception
GARB
GARB
Pa
FFM
QUA
Group Embedding
Fx
GARB
Shortcut
Classifier
DDCP
MRM
F9
M
F 19
View
DDCP
MRM
P
Multi-view Mapping
L
Layer
Figure 2: Overview proposed DSRF-Small. Visual features are mapped into multiple views, and DDCP block highlights the domain differences and dynamically encapsulates the underlying rules through GARBs in each view. The MRM explores rule combinations across different levels of granularity. All the views fused and passed to the next pyramid level, progressively refining rules.
drift between context and target images, DDCP block is designed in each view, where GARB encapsulates the abstract rules under the "predict-anddverrft"" paradigm [18, and highlight the domain difference through dynamic gating and dynamic domain contrast. Additionally, convolution gate [28) is designed to dynamically highlight the most relevant rules in a view. To better comprehend complex rules, a multi- gualiiigranulrrttyy rule mixer (MRM) is designed to explore rule combinations through channel-wise, tosen-wise, sample-wise and row-wise feature mixing.
3.2 Vueti-View Reasoning Pyramid
The MVRP is structured as a layered reasoning pyramid, where each layer employs multi-head mechanism map the features into different views, each representing different group attributes. As a result, different views focus on distinct combinations of attributes, and complex rules can be constructed layer-by-layer through the reasoning pyramid. More importantly, by mapping into more views, the proposed method can easily enlarge the network to capture rich rules. Specifically, consider layer in the pyramid with H/ views, the mapping M is defined as,
Multi Vieli Mapping:
(Vi. V ... = M(X), X T V E.TxC
where X represents the input features of layer I and V/ represents the h-th view of layer 1, T is the token size, Cd and 5h denote the number of channels at layer I and the h-th view, respectively.
Reasoning Pyramid: The layered pyramid built from multi-view features aims to encapsulate the complex reasoning rules. Formally, denote F (-) as the function of DDCP for the h-th view at layer I, which dynamically analyzes the domain difference between context and target features in each view. Denote (.) as the function of MRM, which investigates rule combinations via multi-granular feature mixing. The output features for the h-th view the 1-th layer are obtained as,
V
FLA (FLh (V/))- MRM
We aggregate the features from all views for layer as P' = D W V. where W represents the weight matrix for the h-th view at layer 1. By aggregating the multi-view features, the model captures a rich set of rule combinations from different views. Then, as the features pass through consecutive layers, the model gradually improves its understanding of complex rules.

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Learnable
Weights
CNN
CWN
Downsample
F
P4P9
CNN
CNN
Linen
Concat
22
F
Dot Product
CNN
MWN
Hadomard
Figure 3: Block diagram of GARB. Techniques including Gram matrix for modeling feature distribu- tion, learnable weights, gating mechanism and attention mechanism enhance dynamic reasoning.
Discussion of Scalability: Deep networks, while powerful, prone overfitting
29
Typically as abstract rules are concise and intuitively defined for reasoning tasks, deep reasoning networks may easily overfit [9]. Instead of common practice of deepening the network in visual recognition, the MVRP expands the network by scaling the number of views to encompass a broad of attribute combinations. As shown later in the experiments, the model generalizes better on Out-Of- Of-Distributiin (OOD) settings and reasons better over the complex rules in many datasets.
Specifically, design three pyramids with small, medium and large configurations, with pyramid structure of "2-1", "4-2-1", and "8-4-1", where each number represents the number of views in each layer. This progressive increase of views enables scalability by covering attributes. As shown experiments, all three models, DSRF-S, DSRF-M, and DSRF-L, achieve excellent reasoning accuracy across various settings different datasets. The large model DSRF-L performs best without overfitting, but at a higher computational cost.
combinations of
3.3 Dynamic Domain-Contras Prediction Block
The proposed DDCP block is built on the "predict-and-verity" paradigm [8]. Given features {Fr R RT'x" xc ji= for the three images, we treat the first two Fi, F2 as the context and F3 as the target, the goal is to derive a prediction function R that minimizes the prediction error, F. F3 R(F,, F2).
arg min R
F3 R(F,,
By doing so, R could progressively capture the underlying rules. Fig, 2 shows that Gated Attention Reasoning Block (GARB) serves as the core reasoning module, which leverages self-correlation to model the distributions of context and target features for dynamic reasoning. Note that for RAVEN problems (6. the same reasoning network R(-) is applied across three rows to ensure the rule consistency. Inspired by [28), to further highlight the critical rule information, we employ convolutional gate as shown Fig. to selectively emphasize relevant features while suppressing noisy irrelevant rules. As result, DDCP enhances the model's adaptability and generalization by allowing dynamic rule hypothesis and validation, effectively handling complex and diverse rule sets.
3.4 Gated Attention Reasoning Block
The proposed GARB is the core reasoning module dynamically reason over large number of rules. As shown in Fig. 3 to enhance the dynamic nature of the reasoning module. For illustration, example. We first linearly project the target features and context features as (28)
we resort to the attention mechanism [3 and gate mechanism [3
the first
FI= = FF(ss,,
Fd = =os F2)), === = =" FF
(4)
where F9, Fk and Fa are query, key, and value matrices, respectively, F.. F and Fi are three corresponding linear projections, and Fos is a Down-Sample function.
5

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Following [3], we utilize the Gram matrix derived from the correlattot to model the distribution of context features and target features, and derive the domain-differenn features A E R?*T as,
1 (((W99 @ (F"F*") o oW*) (F*
A
(5)
V
where @ denotes Hadamard product, W and W denote learnable weights, (-) denotes sigmoid function to scale the learnable weights into [0, 1] for learning stability. We use two Gram matrices F9 F and F pa" derived from the self-correlation for modeling the feature domain [35], and hence effectively capture the context and target feature distributions. Moreover, we introduce learnable parameters W and W to be applied on the Gram matrices dynamically highlight the most relevant context and target features, improving efficiency and avoiding overfitting as illustrated in [29]. The domain difference A captures the distinctions between context features and target features, which is applied on F" at a later stage to highlight variations that are essential for distinguishing contextual dependencies from sreget-ppcific characteristics. To further capture finer-grained domain differences between context and target features, we introduce two auxiliary branches A td and And
A
A Oo(FFMM A A o o (F M*),
(6)
where M' E <T and M TRCC" xT are learnable matrices, which helps highlight the important Nomain-differene features relating to F" and F², respectively. a (F)MM) and a (F MD) can be treated as gating matrices. As they depend on the input features, their dynamic nature helps the model to modulate its focus effectively to capture subtle relational patterns specific to each input which would be missed otherwise, as pointed out in (31. Finally, the predicted features F² are obtained as,
F FLincar (( (A
o
(7)
dynamic
dynamic
dynamic
The three terms are all dynamic and adaptable to the inputs so that the model could flexibly adapt to task-specific reasoning rules, thereby equipping it with enhanced reasoning capabilities compared to merely learning static mapping relationships [19.. However, relying solely dynamic parameters may lead to training instability, as the parameters continuously drift. We hence incorporate static linear and convolutional layers to ensure that the features are mapped into a relatively stable space.
3.5 Multi-granularity Rule Mixer
To better establish the reasoning rules, we propose the MRM explore combinations of rules through multi-granular rule mixing, thereby enbancing the feature interaction. Specifically, denote the features after DDCP in the h-th view of layer I as F), To mix F/, on multiple levels of granularity, we first adopt a whisnel-wise mapping Flhh and a token-wise mapping F!th in parallel at the fine-grained feature level capture rule combinations across channels and tokens, respectively,
M = =F + + F (F)).
(8) to further refine
We then apply coarser row-wise mapping Fi.h and sample- wise mapping Fl'h h the rules, yielding an integrated feature map V FCom (F! (Fth (M,))) where the convolution Feom combines these relationships. By utilizing granulrratllrttty mapping, the model refines the complex rules from various perspectives and granularity and hence captures more rule combinations.
4 Experimental Results
4.1 Experiment Settings
DSRF is compared with 16 state-of-ther -fttc-----hhearttt models, WReN (7]. CoPINet (36,, SCL (37. SRAN 8
DCNet (38. MRNet (), HCV-ARR [14, AlgeMR [3], ARII 39] PredRNet [15) STSN 40)
SCAR 17 I. DRNet [66). TRIVR 41I. HI [9 and Slot Abstractors 42 on 6 RPM datasets,
namely RAVEN 6). I-RAVEN 8. RAVEN-FAIR 9. PGM 77. Unicode Analogies (UA) I0] and
RPM-like Video Prediction (RVP) 41. Unless otherwise stated, results of compared methods are obtained using the source codes provided by the authors. We follow the standard evaluation protocol in 6 I The input image size is 80 x 80. No other form of auxiliary supervision is incorporated during training. The Adam optimizer is applied with a learning rate of 1e-3 and weight decay of le-5. The batch size is set to 128. More details are provided in Appendix.

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Table 1: Comparisons RAVENS
6 8
9
Other results obtained from their original papers.
Models
Avg.
O-RVN
I-RVN
RVN-F
MRNet (CVPR'21)
9
82.2
84.0
81.0
81.6
HCV-ARR (AAAI'2)
14
92.2
87.3
93.9
95.4
AlgeMR (3)PR'23)
13
93.5
92.9
93.2
94.3
SCAR (AAA1'24)
[1
93.8
92.8
94.7
93,9
PredRNet (ICML23)
[5
96.5
95.8
96.5
97.1
DRNet (AAA1'2)
[16
97.4
96.9
97.6
97.6
HP? AI (ACM MM'24)
19
98.9
98.8
99.4
98.6
DSRF-S (Ours)
98.7
98.6
98.8
98.8
DSRF-M (Ours)
99.2
99.1
99.4
99.0
DSRF-L (Ours)
99.2
99.1
99.4
99.1
Table 2: Comparison RAVENs under OOD settings 6
8
Train on O-RVN Train on I-RVN Train on RVN-F
Models
Avg.
(G)
(M)
I-RVN
RVN-F
O-RVN RVN-F O-RVN
I-RVN
MRNet (CVPR'21)
75.7
65.8
81.2
76.5
78.6
78.8
73.4
3.58
4.96
HCV-ARR (AAAI23)
14
87.3
79.4
91.9
81.4
89.4
94.1
87.3
8.70
7.72
SCAR (AAA1'24
117
90.7
84.7
95.9
91.9
94.5
91.3
85.6
0.44
0.55
HPa AI (ACM MM'24
19
92.3
87.7
96.9
89.9
94.0
95.3
90.0
12.82
6.38
PredRNet (CMML23)
[5
94.3
89.2
97.9
93.9
97.3
96.2
91.4
2.05
1.28
DSRF-S (Ours)
96.7
95.1
98.5
95.9
98.2
97.3
95.4
10.10
11.64
DSRF-M
97.3
95.6
98.7
97.4
98.7
97.8
95.8
13.92
23.86
DSRF-L (Ours)
97.7
95.9
98.9
97.9
98.9
98.1
96.5
22.10
42.29
4.2
Comparisons with State-of-the-Ae Models
Results on RAVEN Datasets. Tab. presents the results the three RAVEN datasets 6 g
We have following observations. DSRF-S is comparable the previous best performing model, HP [1.. while DSRF-M and DSRF-L consistently outperform it across three datasets [ 8 9 with gain of 0.3% over HP" (19. The performance gain is attributed to the scalability of DSRF that boosts reasoning ability and the dynamic designs that adapt to complex relations. 2) Furthermore, on RVN-F 9. DSRF-L achieves the largest performance gain over HP2 AI [19], reducing the error from 1.4% to 0.9%. highlighting the superiority of DSRF-L in widening the network to capture more complex rules. 3) Lastly, despite being lighter version, DSRF-S attains competitive average accuracy of 98.7% across three datasets 6 g 9. Our DSRF-M and DSRF-L outperform it by 0.5%, contributing an enhanced reasoning ability, while showing no sign of overfitting.
We further conduct Cout-OfDDittrbbuti (OOD) experiments on the three RAVEN datasets 6 8 9 where models are trained on one dataset while evaluated on another. Tab. summarizes the results. We can observe the following. I) Our models consistently and significantly outperforms all compared methods across settings, reaching average accuracies of 96. 7%,, 97.3%, and 97.7% for small, medium, and large models, respectively. Specifically, DSRF-L outperforms the second best model, PredRNet [15), by 3.4% on average. 2) When trained on O-RVN (6] and tested on I-RVN [8), all the compared models perform poorly with accuracies below 90%, showing the defects of static reasoning models in handing domain shift. In contrast, DSRF-L maintains an accuracy of 95.9%, achieving performance gain of 6.7% compared to PredRNet [15]. 3) Across six OOD settings, the proposed models demonstrate minimal accuracy fluctuations, indicating that our models maintain their robustness across different scenarios.
As shown Tab. 2 the DSRF-S requires competitive 10. GFLOPs with 11. 11.64M parameters, while significantly outperforming other methods in accuracy. As the model scales up, despite the increase of GFL.Ps and model parameters, DSRF-M and DSRF-L consistently bring performance gain, indicating that the MVRP could well expand the reasoning network without overfitting.

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Table 3: Comparison results the Unicode Analogy/Unicode Analogy OOD
10
Accuracy (%) on Unicode / Unicode-OOD
Models
Avg.
Arith
Const
Dist3
Prog
Union
MRNet (CVPR'21)
24.3/22.9
25.5/20.9
22.9/23.7
24.4/26.1
27.4/23.5
21.5/20.2
SCAR (AAA1'24)
[7
31.4/23.1
26.6/22.3
34.0/25.0
28.6/24.9
25.9/24.5
41.8/18.9
HCV-ARR (AAAI'23)
14
25.9/24.1
26.8/23.6
25.0/26.4
23.5/26.4
24.2/23.0
30.0/26.6
PredRNet (CMM/22)
15
57.7/27.7
65.5/26.3
51.4/30.7
48.5/32.4
57.6/27.0
65.6/22.3
HP Al (ACM MM244
55.2/30.2
59.4/26.2
50.6/28.8
53.7/34.6
54.2/28.4
58.2/33.0
DSRF-S (Ours)
72.1/34.5
74.4/29.1
61.0/34.3
76.6/37.9
72.8/33.0
75.6/38.2
DSRF-M (Ours)
73.2/35.9
76.5/30.3
61.9/35.6
76.8/38.9
73.6/35,4
77.1/39.5
DSRF-L (Ours)
73.8/37.3
79.4/32.5
61.9/36.4
77.0/39.8
73.7/36.7
77.2/41.2
Table 4: Comparisons on PGM
7
Results of other methods are obtained from their original papers.
Models
Avg.
PGM-N
PGM-I PGM-E
HAP HTP HT HALT HASC
CoPINet (NIPS'19)
56.4
51.2
16.4
WReN (ICML'18
32.4
62.6
64.4
17.2
27.2
41.9
19.0
14.4
12.5
DCNet (ICLR221)
38
68.6
59.7
17.8
SRAN (AAAI'2)
8
71.3
60.1
18.4
MRNet (CVPR'21)
[9]
43.4
93.4
68.1
19.2
38.4
55.3
25.9
30.1
16.9
ARII (NIPS'22)
39
45.5
88.0
72.0
29.0
50.0
64.1
32.1
16.0
12.7
PredRNet (ICML/23)
15
47.8
97.4
70.5
19.7
63.4
67.8
23.4
27.3
13.1
STSN (ICLR'23)
400
98.2
78.5
20.4
HPŻAL (ACM MM'24)
19
99.3
80.0
22.6
Slot Abs.1CMM/224
42
51.9
91.5
91.6
39.3
63.3
78.3
20.4
16.7
14.3
DSRF-S (Ours)
50.9
99.3
82.4
25.2
63.1
75.7
29.3
16.2
16.1
DSRF-M (Ours)
52.7
99.5
84.5
27.4
65.7
78.8
31.3
17.4
16.7
DSRF-L (Ours) (Ours)
54.9
99.8
87.3
31.5
67.7
82.3
34.2
18.9
17.8
Results on Unicode Dataset. We conduct experiments on the UA dataset (10 across five rule types under two settings: 1) Normal setting, where the dataset is randomly divided into training, validation, and test sets; and 2) OOD setting, where all the symbols in the training set do not appear in the The UA dataset [10] provides comprehensive evaluation of conceptual schema across multiple levels of abstraction. The following observations can be made from Tab. 3 1) All three proposed DSRF models significantly and consistently outperform existing methods across five rule types under both settings. Specifically, in the normal setting, the proposed DSRF-L achieves the highest average accuracy of 73.8% demonstrating substantial performance gain of 16. compared to the previous-best model, PredRNet [15]. 2) Under the OOD setting, all models experience significant performance drop due to distribution shifts and unfamiliar data patterns. While most existing models achieve poor accuracies of approximately 25% approaching random guessing, our DSRF-L obtains a significantly higher average accuracy 37.3%, presenting a notable improvement of 7.1% over the previous-best model HP² AI [19), highlighting the robustness of our model by dynamically capturing the domain difference.
Results on PGM Dataset. Then, we benchmark our DSRF models against state-of-the-art models on the PGM dataset 77]. Following [42] experiments are evaluated across eight regimes: neutral (PGM-N), interpolation (PGM-I), extrapolation (PGM-E), held-out attribute pairs (HAP), held-out triple pairs (HTP), held-out triples (HT), held-out attribute line type (HALT), held-out attribute shape color (HASC). The last seven regimes evaluate OOD generalization. (See Appendix B. 1.4 for more details.) The results in Tab, Tab, 4reeeal the following: Both DSRF-M and DSRF-L surpass existing approaches across nearly all regimes. Notably, DSRF-L achieves new state-of-the-. average accuracy of 54.9%, substantially outperforming the previous best result 51 51.9% by Slot Abstractors 42 validating our framework's effectiveness. 2) The performance gains of DSRF become even more pronounced under challenging held-out and transfer regimes such as HAP, HTP, HT and HASC, where DSRF-L reaches 82.3% on HTP and 34.2% on HT, significantly outperforming

---

Table 5: Comparisons RVP dataset 41
Other results obtained from their original papers.
CoPINet [36]
SRAN 8
SCL
37
TRIVR [41]
DSRF-S
DSRF-M
DSRF-L
62.3
63,9
66.3
71.6
85.4
87.7
88.8
Table 6: Ablation of major components of DSRF-M on three RAVEN datasets 6 g
Avg.
O-RVN
I-RVN
RVN-F
w/o DDCP
95.2
94.9
95.1
95.6
w/o GARB
95.9
95.9
95.6
96.3
w/o CNN gate
98.0
97.9
97.8
98.3
w/o dynamic gate
98.0
97.8
98.1
98.2
w/o MRM
98.7
98.7
98.8
98.6
DSRF-M
99.2
99.1
99.4
99.0
all baselines and demonstrating strong domain-difference modeling and compositional generalization. 3) We observe a clear monotonic improvement as we scale the model from DSRF-S to DSRF-M and then to DSRF-L. This is evidenced across all metries: the overall average accuracy sees a steady gain from 50.9% 52.7% and finally to 54.9%. The improvement especially notable in the HTP regime, where performance increases from 75.7% (DSRF-S) to 78.8% (DSRF-M) and reaches 82.3% (DSRF-L). This consistent progression demonstrates that our framework's 's effectiveness scales reliably with increased model capacity.
Results RVP Dataset. Lastly, we evaluate DSRF variants on the RVP dataset [1] for real-world traffic scenarios. RVP is built on the RPM framework, where future frames are predicted from two historical frames sampled every 15 frames, leveraging reasoning patterns learned from other videos. As shown in Tab. 5] our model largely outperforms the second-best model, thanks to the MVRP that enables the integration of more reasoning blocks into the reasoning module, allowing the model to capture more complex and subtle underlying rules in real-world scenarios. In contrast, previous models with simpler reasoning modules struggle to generalize such complex environments.
4.3 Ablation Studies
bllaioon of Major Components. evaluate the major components DSRF, we conduct an ablation study across three RAVEN datasets 66. 8. 9). by systematically removing one component at a time to assess its individual performance contribution. The results are presented in Tab. 6 When removing DDCP and GARB, single convolutional layer is used to replace them. It can be observed that the accuracy on all three datasets will drop significantly removing either DDCP or GARB, i.e., 4.0% for DDCP and 3.3% for GARB, demonstrating their importance in dynamically encapsulating the task-specific rules. Additionally, removing the CNN gate in DDCP or removing the dynamic gate in GARB both leads significant accuracy decline of 1.2%, highlighting their significance in dynamically emphasizing the relevant features while suppressing irrelevant features. Finally, MRM also shows its effectiveness in aggregating features from different levels of granularity.
DSRF as Plug-and- Play Reasoning Module. The proposed DSRF could serve as a aalugandd-llas reasoning module. We replace the original reasoning module of state-of-the-art models, i.e., RM+PM of MRNet (9) ARR of HCV-ARR [4], PRB of PredRNet [15] and PredAI of HP²AI [19], by DSRF-S and DSRF-M respectively, and conduct comparison experiments on the three RAVEN datasets 6 g as shown in Tab. 7 We can observe that DSRF-S and DSRF-M consistently improve performance compared to the original reasoning modules, indicating their robustness and effectiveness in reasoning complex underlying relations. Lastly. DSRF-M consistently outperforms DSRF-S across all four perception modules on all three datasets, indicating the effectiveness of our scalable MVRP in boosting the model's 's reasoning ability.
Lightweight DSRF. The MVRP module enables scalable model efficiency by reducing the channel dimensions of feature mappings per view. This allows the creation of lightweight variants (DSRF-S- Light,
that preserve core reasoning capabilities with significantly reduced parameters

---

Table 7: Replacing reasoning modules by DSRF-S and DSRF-M RAVEN datasets 6 8
Perception
Reasoning
Avg.
O-RVN
I-RVN
RVN-F
RM+PM 9
83.9
84.0
81.0
86.8
MSE
DSRF-S
96.5
96.3
96.7
96.5
DSRF-M
97.1
96.4
96.9
97.9
ARR [14
92.2
87.3
93.9
95.4
HCV 14
DSRF-S
96.9
96.4
96.5
97.9
DSRF-M
97.6
97.5
97.2
98.1
PRB [T5]
96.5
95.8
96.5
97.1
RN-4B 15
DSRF-S
98.7
98.6
98.8
98.8
DSRF-M
99.2
99.1
99.4
99.0
PredAI [9]
98.9
98.8
99.4
98.6
HPALC 19
DSRF-S
99.2
99.1
99.4
99.2
DSRF-M
99.4
99.3
99.5
99.4
Table 8: Ablation of lightweight DSRE-S and DSRF-M on RAVENS 6
and PGM (7].
Avg.
O-RVN I-VVN RVN-F PGM-N PGM-I
PGM-E
(G)
(M)
DSRF-S
83.8
98.7
98.6
98.8
99.3
82.4
25.2
10.10
11.64
DSRF-S-Light
83.5
98.5
98.5
98.6
99.1
81.7
24.8
4.06
4.96
DSRF-M
84.8
99.1
99.4
99.0
99.5
84.5
27.4
13.92
23.86
DSRF-M-Light
84.2
98.8
98.9
98.8
99.3
83.1
26.1
5.11
8.72
Table 9: Ablation of column- wise reasoning ESRF-Mane and DSRF-L the PGM dataset 7
Avg.
PGM-N PGM-I PGM-E HAP
HTP
HT
HALT
HASC
DSRF-M
52.7
99.5
84.5
27.4
65.7
78.8
31.3
17.4
16.7
DSRF-M-RC
55.8
99.7
88.9
35.1
68.9
82.1
34.1
19.1
18.1
DSRF-L
54.9
99.8
87.3
31.5
67.7
82.3
34.2
18.9
17.8
DSRF-L-RC
58.4
99.9
92.1
40.2
71.3
86.7
37.3
19.9
19.4
and GFLOPs. Evaluations on three RAVEN and PGM datasets (Tab. () confirm that these variants maintain competitive accuracy while achieving substantial efficiency gains.
Column-wise reasoning of DSRF. While DSRF's row-wise design efficiently handles standard row-centric RPMs, faces limitations datasets like PGM that emphasize column-wist reasoning. Although weight-sharing across rows allows for implicit column- pattern recognition, we explic- itly enhance this capability by integrating dedicated column-wise DDCP branch. The modularity of the DDCP design permits this seamless extension, enabling explicit fusion of column- wise features with the original row-wise processing. As shown in Tab, 9 the revised models (DSRF-M-RC and DSRF-L-RCC yield significant gains, improving the average reasoning accuracy of DSRF-M from 52.7% to 55.8% and DSRF-L from 54.9 44.9% 58.4%, respectively.
Conclusion
The proposed Dynamic and Scalable Reasoning Framework is designed tackle the challenges of scalability and the dynamic nature of abstract visual reasoning, in order to boost the reasoning ability of our model and generalize it well novel tasks. Specifically, the proposed MVRP tackles the scalability challenges by hierarchically widening the network to capture a broad range of complex rules. In addition, the proposed DDCP blocks enhance the adaptability to diverse rules by dynam- ically highlighting task-specific relationships respective to the domain difference through novel Gated Attention Reasoning Block. Extensive results on six AVR datasets demonstrate that DSRF outperforms state-of-the-ee models different datasets and tasks.
10

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Acknowledgment
This work was supported by Ningbo Science & Technology Bureau under Grant 2023Z138, 2023Z237. 2024Z110 and 2024Z124.
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A Significance of This Research
Abstract Visual Reasoning (AVR) is pivotal yet challenging research in artificial intelligence, focusing on inferring complex abstract rules from visual data [[]. Progress in this field is critical for enhancing machine comprehension and learning capabilities []]. However, recent works [3 indicate that LLMs often fail to comprehend abstract concepts and relationships within images for visual reasoning tasks. Additionally, although multimodal models attempt to integrate visual and linguistic information, they still fall short in complex visual reasoning tasks [43]. Specifically, as stated in [44] in AVR tasks, enhancing the amount of information is more important than enforcing disentangled representations because the amount of information has greater impact on downstream task performance.
The proposed method provides a novel solution to tackle the challenges of existing AVR models on scalability and generalization ability. Specifically, the proposed method leverages the Multi- View Reasoning Pyramid to map high-level visual features into different views, and hierarchically constructs the complex reasoning rules through the layered pyramid, thereby greatly enhancing the scalability of the model. In addition, in contrast to the static reasoning networks in existing models, the proposed Dynamic Domain-Contrast Prediction Block incorporates different mechanisms to dynamically model the underlying rules, including CNN gate to selectively highlight the important reasoning features, and a set of Gated Attention Reasoning Blocks to dynamically reason over a large number of rules. Furthermore, in each GARB, we model the distribution of context features and target features by utilizing Gram matrix, contrast the domain differences through learning parameters, and further modulate its focus to capture subtle relational patterns specific to the inputs by using two gate matrices. As shown in the experiments, our work pushes the edge of abstract visual reasoning, achieving state-of-the-art performance across six benchmark datasets.
B Experimental Settings
B.1 Dataset Description
Table 10: Summary of benchmark datasets.
Datasets
#Samples
#lmages #Attributes
#Relations
O-RVN 6
70K
1.12M
7
4
I-RVN 8
70K
1.12M
4
RVN-F
9
70K
1.12M
7
4
PGM
7
1.42M
22.72M
5
5
UA 10
50K
0.45M
5
RVP
3K
48K
/
B.1.1 Original RAVEN Dataset
The original RAVEN dataset (6 comprises 70,000 question sets, generated by converting sentences derived from an Attributed Stochastic Image Grammar (A-SIG) [5] Each question set consists of eight context images and eight candidate options, resulting in total of 1.12 million images. Each question is defined by five rule-governing attributes such as Number, Position, Type, Size and Color, and two noise attributes such as Uniformity and Orientation. Each attribute follows one of the four rules, namely Constant, Progression, Arithmetic, and Distribute Becebbuteeeeeeee_eeeeeee This design yields an average of 6.29 rules per problem, which significantly higher than the rule complexity in the PGM dataset 77. The RAVEN dataset [6] is evenly divided into seven configurations, i.e., Center, 2x2Grid (2x2G), 3 3Grid (3x3G), Left-Right (L-R), Up-Down (U-D), Ont-ennenter (O-IC), and Ontdd (O-IG), which are generated using three levels from A-SIG (5). The standard 10-fold evaluation protocol (6] is applied, where six folds are used for training, and two folds each for validation and testing. However, as identified in [8 9. there is loophole in the RAVEN dataset, i.e., candidate options in the RAVEN dataset are created by modifying one single attribute from the correct answer, which allows models to easily select the correct answer by identifying common properties among candidates rather than understanding the underlying relational patterns in the context matrix. The samples of RAVEN are shown in Fig.
14

---

Rule:
Rule:
Rule:
Number Position constant
Number Arithmetic
Number / Position Constant
Type Distribute Three
Type Progression
Type : Constant
Size Arithmetic
Size Constant
Size Constant
Color Progression
Color Constant
Color Progression
Figure 4: Three typical samples in RAVEN dataset.
B.1.2 I-RAVEN Dataset
The I-RAVEN dataset g eliminates the vulnerability of the original RAVEN dataset [6, differing in the way of generating negative candidate answers. Specifically, it utilizes Attribute Bisection Tree to generate impartial and balanced candidate options, where each option has exactly three differing attributes from the other through three iterations. This makes the candidate options more indistinguishable without identifying the context matrix, leading to more rigorous and fair evaluation of the models' abstract reasoning capability. Other settings are exactly the same as the original RAVEN dataset [6]. The samples of I-RAVEN are shown in Fig. 5
B.1.3 RAVEN-FAIR Dataset
The RAVEN-FAIR dataset g also addresses the shortcut issue the RAVEN dataset 66] The negative candidates systematically generated by randomly selecting existing option, either negative answer or the correct answer, and modifying one its attributes. This design ensures that the correct answer cannot be selected by only identifying the most common candidate options. Other settings are exactly the same as the original RAVEN dataset [6]. Three samples of RAVEN-FAIR are shown in Fig.
B.1.4 PGM Dataset
The PGM dataset (7) is widely recognized as the first large-scale RPM benchmark to evalu- ate the reasoning ability of deep learning models. It consists of 1.42M question sets, with 1.2M questions for training, 20K for validation, and 200K for testing. Each question set tains 8 context images and candidate images, resulting in a total of 22.72M images. Each matrix in PGM 7 is set of triples, S {[r, o, a]Ir E R, (Progressions on, XOR, OR, AND, Consistent, Union] defines the set of rules, = (Shape, Line] represents the set of objects and A = {Size, Type, Color. Position, Number indicates the set of attributes. The PGM dataset comprises 8 regimes.
O,a A}. where R
Neutral regime (PGM-N): In this regime, both training and test sets can contain any rela- tion-object-atrribute triples. They are disjoint at the pixel level but share identical structural distribu- tions, serving as the bascline for reasoning performance.
15

---

?
Rule:
Rule:
Rule:
Number Position Constant
Number Arithmetic
Position Arithmetic
Type Distribute Three
Type Progression
Type Distribute Three
Size Progression
Size Progression
Size Arithmetic
Color: Distribute__hie Three
Color Arithmetic
Color Progression
Figure 5: Three typical samples in I-RAVEN dataset.
?
Rule:
Rule:
Rule:
Number / Position: Constant
Number / Position : Constant
1. Number Position: Constant
Type Distribute_ Three
Type Distribute_Thereeee Three Constant
2. Type Constant Distribute_ Three
Size Arithmetic
Size Arithmetic
3. Size: Constant
Color: Constant
Color: Arithmetic
4. Color: Arithmetic Distribute_ Three
Figure 6: Three typical samples in CAVEN-FAIR dataset.
Interpolation regime (PGM-I): Training and test sets share the same attribute types, but ordered attributes like color and size use even-indexed values training and odd-indexed values in testing. evaluates the model's 's ability to interpolate within known attribute ranges.
Extrapolation regime (PGM-E): Training samples include the lower half of ordered attribute values, while testing uses the upper half. This regime measures whether the model can extrapolate to unseen attribute ranges beyond the training distribution.
Held-out Attribute Pairs regime (HAP): In this regime, viable attribute pairs are defined, with 16 used for training and 4 held out for testing. While training samples contain each attribute separately,
16

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test samples include both together, assessing compositional generalization to unseen attribute co- occurrences.
Held-out Triple Pairs regime (HTP): In this regime, each structure contains at least two triples, forming 400 viable triple pairs, with 360 used for training and 40 reserved for testing. The held-out pairs never co-occur in training, evaluating the model's ability to generalize to unseen combinations of triple relations.
Held-out Triples regime (HT): In this regime, the 29 unique triples are randomly reserved for testing, ensuring all attribute types represented. These triples appear in training, and every test sample includes at least one, evaluating reasoning over entirely unseen combinations.
Held-out Attribute Line Type regime (HALT):: In this regime, all line-type combinations are excluded from the training data but appear every test sample. It tests the model's structural generalization to unseen line-style and type relations.
Held-out Attribute Shape Color regime (HASC): In this regime, no shape-color combinations included in the training data, but every test sample contains at least one. It evaluates the model's ability generalize compositionally unseen pairings of object shape and color.
Most methods are evaluated on the Neutral regime, where the training and test sets are sampled from the same distribution of the Neutral regime. Other regimes designed assess the model's generalization capability, where the test set contains rules that are excluded from the training and validation sets, leading to rigorous evaluation under Out-Of-Diitribution (OOD) settings. The samples in PGM are shown in Fig.
E
Relation type: shape, AND Attribute type: position
Relation type: shape, consistent union Attribute type: size
Relation type (R): shape, XOR Attribute type (A): type
Figure 7: Three typical samples in PGM dataset.
B.1.5 Unicode Analogies Dataset
The Unicode Analogies (UA) dataset 110 provides a comprehensive framework for representing conceptual schema across multiple levels of abstraction. Each problem is generated by one of the five rule types, i.e. Constant, Progression, Arithmetic,
istrribuiinn. Three, and Union. The UA dataset [00] contains 2500 annotated characters with an average of 2.8 annotated features per character. Following the standard evaluation protocol in [10] 10-fold evaluation used, with seven folds for training, and one fold for validation and two folds for testing. In addition, it introduces complexities by blurring the lines between objects and features, as well as between perception and cognition. Compared to the three RAVEN datasets 6 g 9. the UA dataset [10) poses additional
challenges as requires models to incorporate contextual information solving [10). The samples in Unicode are shown in Fig.
stages of problem
17

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II
M
?
-
A
?
8
O
C
c
D
Problem Type:
Problem Type:
Prablem Type:
arithmetic compoeentttmmmnnttt--tt internalsolid_nens _noshift
constant aspect_ constant_aspect_nont _sppict_noshift
Figure 8: Three typical samples in the Unicode dataset.
B.1.6 RVP Dataset
The RVP dataset is built upon the UA-DETRAC dataset [46), which includes 100 challenging real-world traffic videos captured from 24 locations using Canon EOS 550D camera. These videos represent diverse traffic conditions such as urban highways, intersections, and T-junctions. The original UA-DETRAC dataset contains over 140,000 annotated frames with details like vehicle type, illumination, occlusion, truncation ratio, and bounding boxes. Under the RPM framework, RVP predicts future frame based two historical frames sampled every 15 frames, using reasoning rules derived from other videos. Unlike traditional video prediction tasks, RVP uses non-consecutive frames, making the task more challenging. The goal is select the correct answer from eight candidate frames by analyzing the progression vehicle size and position. The incorrect options are sampled least 15 frames apart from the correct answer avoid trivial clues. In total, the dataset includes 3,000 questions and 48,000 frames, featuring visually complex scenes with multiple vehicles and detailed urban backgrounds. The samples in RVP shown in Fig. 9
?
?
Figure 9: Three typical samples in RVP dataset.
B.2 Detailed Description of Compared Methods
The proposed DSRF is compared with the following state-of- of-the-arttttt methods.
WReN M utilizes a Relation Network to derive the inter-feature relations for solving RPM problems.
CoPINet (36 estimates the probability of each candidate answer by applying contrastive module on top perception module built from ResNet blocks, using the question panel and each candidate the input.
18

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SCL 37
is designed to discover the underlying compositional structure. It consists of three integrated networks: an object network, an attribute network, and relationship network.
SRAN g
employs a hierarchical rule embedding module and a gated embedding fusion module to produce rule embeddings from two row sequences.
DCNet 38
incorporates a rule contrast module and choice contrast module to leverage the intrinsic structure of RPMs, enhancing distinctions among options by comparing latent rules across rows.
MRNet 9 utilizes a multi-resolution convolution layer for visual perception and computes the row similarity as the reasoning strategy.
ARII 39 is framework that learns abstract rule representations through internal inference mecha- nisms, combining a rule encoder, a reasoner, and an internal referrer. It repeatedly applies the same rule different instances achieve comprehensive understanding.
HCV-ARR [4] utilizes mixed model combining convolutional blocks and vision transformer blocks to capture multi-level features from RPM images, and employs attention mechanism to dynamically determine the relations between a row/column of panel images.
AlgeMR 13 includes an object detector to identify discrete entity attributes and uses algebraic methods such as Gröbner bases and ideal containment to solve RPMs as computational problems.
SCAR 17 utilizes a Structure-Aware dynamic Layer (SAL) that enables the processing of AVR tasks with diverse structures by adapting its weights the problem instance.
PredRNet [15]
employs sequential residual convolutional layers to extract high-level visual features from images and utilizes convolutional blocks to identify abstract rules by predicting the target images using the context images.
combines slot attention for object-centric encoding and a transformer for reasoning, scoring each answer by concatenating its slots with context panel slots, and optimizing with both task and reconstruction losses.
STSN 40
DRNet [66] is dual-stream neural network inspired by the two-stream visual processing hypothesis, which achieves strong generalization on RPM benchmarks by integrating spatial and semantic features extract abstract reasoning rules.
TRIVR [4]
a two-stage visual reasoning model that separates perception and reasoning to reflect better the human approach to solve RPM problems. By introducing "2+1" formulation extract explicit reasoning rules from each sample, TRIVR significantly reduces the model complexity and outperforms state-of-the-als methods multiple RPM-like datasets.
HP²AI 19
extracts multi-scale visual features via hierarchical encoder and infers row-wise relations using Predictive Analogy-Inference (PredAI) blocks, focusing on key attributes to solve RPM tasks effectively.
Slot Abstractors 42) integrates blot-based object-centric representations with the scalable, multi- head Transformer architecture. By incorporating strong relational inductive biases, it effectively handles reasoning tasks involving many objects and multiple relations.
B.3 Implementation Details
We strictly follow the standard evaluation protocol outlined in 6 & 10 40
Input images are resized 80 x 80, and datasets are divided into training, validation, and test sets, with the validation set used for hyper-paramete tuning. No additional auxiliary supervision is employed during training. We apply Muon to hidden-layer parameters with dimension least 2 using a learning rate of 3e-3, and Adam to all remaining parameters using a learning rate of le-3, with weight decay set to le-5. The models are trained with a batch size of 128 on an Intel Xeon Silver 4216 CPU with two NVIDIA RTX A5000 GPUs. The code will be released upon the acceptance of this paper.
19

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Table 11: Ablation studies of different reasoning blocks on RAVEN 6
I-RAVEN 8 and RAVEN-
FAIR 99. The proposed GARB significantly improves the reasoning accuracy compared with other reasoning modules.
Accuracy (%) on Different RAVEN Configurations
Datasets
Components
Avg.
Center
2x2G
3x3G
L-R
U-D
O-IC
O-IG
PredAI
97.5
99.9
96.7
92.6
99.9
99.7
99.7
93.8
PRB
98.2
100.0
98.1
94.5
98.2
99.8
99.7
97.4
O-RVN 6
DDCP
99.1
100.0
99.3
96.2
99.9
100.0
99.9
98.2
PredAI
97.3
99.9
96.9
91.8
99.9
99.9
99.7
92.9
PRB
97.9
99.9
98.1
93.5
99.7
99.9
99.9
94.5
I-RVN 8
DDCP
99.4
100.0
99.9
97.6
100.0
99.9
100.0
98.4
PredAI
98.2
99.9
98.1
96.5
99.9
100.0
100.0
93.1
PRB
98.5
100.0
98.7
97.4
99.9
100.0
99.9
93.8
RVN-F 9
DDCP
99.0
100.0
99.8
97.3
100.0
99.9
100.0
96.3
Table 12: Ablation studies of MRM on RAVEN 6 I-RAVEN 8 and RAVEN-FAIR
9 datasets.
Accuracy (%) on Different RAVEN Configurations
Components
Avg.
Center
2x2G
3x3G
L-R
U-D
O-IC
O-IG
MLP
98.7
99.9
98.4
96.1
99.9
99.9
99.9
96.9
I-RVN O-RVN
CNN
98.9
100.0
99.3
95.8
100.0
100.0
99.9
97.1
Attention
98.5
100.0
98.4
95.1
99.9
100.0
99.9
96.4
MRM
99.1
100.0
99.3
96.2
99.9
100.0
99.9
98.2
MLP
98.9
100.0
99.3
95.9
99,9
100.0
99.9
97.2
CNN
99.1
100.0
99.5
96.4
100.0
100.0
100.0
97.9
Attention
98.6
100.0
98.5
95.1
99.9
99.9
99.8
96.7
MRM
99.4
100.0
99.9
97.6
100.0
99.9
100.0
98.4
RVN-F 9
MLP
98.5
100.0
98.9
97.2
99.9
100.0
99.9
93.9
CNN
98.7
100.0
99.2
97.8
99.9
99.9
100.0
94.3
Attention
98.3
99.9
98.5
96.6
100.0
99.9
99.8
93.4
MRM
99.0
100.0
99.8
97.3
100.0
99.9
100.0
96.3
C
More Experimental Results
C.1 More Ablation Results on Three RAVEN Datasets
C.1.1 Ablation of DDCP
DDCP is the main reasoning block in this paper. To evaluate its contributions, we replace it with two previously rest-performing reasoning blocks such as PredAI [19] and PRB [15]. For a fair comparison, we also equip these three reasoning blocks with an additional CNN gate as in DDCP The results are summarized Tab. TT The results highlight the notable performance gain by DDCP, Compared to PredAI [19 and PRB [15), the average improvement is 1.5% and 1.0% respectively across all configurations over three datasets. This indicates that the dynamic structure DDCP effectively captures task-specific information, leading to performance improvements.
C.1.2 Ablation of MRM
The proposed MRM leverages multi-granular rule mixing explore diverse rule combinations, thereby enriching feature interactions. To evaluate its effectiveness, we replace MRM with commonly- used structures for feature mixing, e.g. MLP, CNN and Attention. MLP maps features along single dimension, processing all features uniformly, making it incapable of achieving multi-persppetive understanding, while CNN focuses more on local feature extraction, making challenging to capture global information comprehensively. On the other hand, Attention focuses
the weight
20

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Table 13: Ablation studies of the three branches in GARB on RAVEN 6 I-RAVEN RAVEN-FAIR datasets.
8 and
Accuracy (%) on Different RAVEN Configurations
Components
Avg.
Center
2x2G
3x3G
L-R
U-D
O-IC
O-IG
97.8
99.8
98.2
93.2
99.7
99.9
99.6
94.1
B+C
98.5
100.0
98.4
94.8
99.8
100.0
99.6
97.1
O-RVA
B+T
98.8
100.0
99.1
95.5
100.0
100.0
99.8
97.3
B+C+T
99.1
100.0
99.3
96.2
99.9
100.0
99.9
98.2
I-RVN 8
B
98.1
100.0
98.6
93.7
99.9
99.8
99.7
95.2
B+C
98.6
100.0
98.5
94.8
100.0
100.0
100.0
97.1
B+T
98.9
100.0
99.2
95.6
99.9
100.0
99.8
98.1
B+C+T
99.4
100.0
99.9
97.6
100.0
99.9
100.0
98.4
RVN-F 9
B
98.2
100.0
98.6
96.1
99.9
100,0
99.8
93.6
B+C
98.6
100.0
99.3
96.4
99.9
100.0
100.0
95.1
B+T
98.8
100.0
99.1
97.1
100.0
100.0
99.8
95.9
B+C+T
99.0
100.0
99.8
97.3
100.0
99.9
100.0
96.3
Table 14: Detailed ablation results of major components on RAVEN 6 I-RAVEN 8 and RAVEN- datasets.
FAIR
Accuracy (%)
on Different RAVEN Configurations
Components
Avg.
Center
2x2G
3x3G
L-R
U-D
O-IC
O-IG
w/o DDCP
94.9
99.9
96.7
90.3
98.8
98.8
99.4
80.3
w/o GARB
95.9
100.0
98.2
91.8
99.7
99.5
100.0
82.3
O-RVN
w/o CNN gate
97.9
100.0
98.5
93.7
99.7
99.8
98.9
94.4
w/o dynamic gate
97.8
99.8
98.2
93.2
99.7
99.9
99.6
94.1
w/o MRM
98.7
99.8
98.8
95.5
99.8
99.9
99.5
98.0
DSRF-M
99.1
100.0
99.3
96.2
99.9
100.0
99.9
98.2
w/o DDCP
95.1
100.0
97.7
91.6
99.7
99.8
99.4
77.9
RVN-F I-VN g
w/o GARB
95.6
100.0
98.6
93.0
99.9
99.8
99.6
78.9
w/o CNN gate
97.8
99.8
98.8
93.0
99.9
100.0
99.7
93.5
w/o dynamic gate
98.1
100.0
98.6
93.7
99.9
99.8
99.7
95.2
w/o MRM
98.8
100,0
98.7
95.6
100.0
100.0
99.9
97.7
DSRF-M
99.4
100.0
99.9
97.6
100.0
99.9
100.0
98.4
w/o DDCP
95.6
99.5
95.0
91.3
99.3
99.6
99.3
85.3
w/o GARB
96.3
99.8
95.8
92.3
99.2
99.3
98.7
89.6
w/o CNN gate
98.3
100.0
98.5
95.8
99.8
99.9
99.8
94.4
w/o dynamic gate
98.2
100.0
98.6
96.1
99.9
100.0
99.8
93.6
w/o MRM
98.6
100.0
98.2
96.5
100.0
99.9
99.7
96.3
DSRF-M
99.0
100.0
99.8
97.3
100.0
99.9
100.0
96.3
distribution between features rather than the structured decomposition or reorganization of features. The results are shown Tab.
The proposed MRM showcases its ability to excel in reasoning tasks that involve complex rule com- positions, outperforming static or locally focused methods like MLP and CNN, as well as Attention mechanisms that lack explicit feature decomposition. For relatively simpler configurations such as Center, L-R, U-D, and D-IC, components, including MLP. CNN, and Attention, achieve near- perfect performance, with accuracies close to 100% in many cases. However, for more challenging configurations like 3x3G and O-IG, the proposed MRM consistently outperforms other compared methods. For instance, the RAVEN dataset (6), the proposed MRM achieves an accuracy of 96.2% and 98.2% on 3x3G and D-IG, respectively, significantly outperforming 95. and 96.4%. achieved by the Attention mechanism.
21

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Table 15: Detailed ablation results for the proposed DSRF as plug-and-pla reasoning module on three RAVEN datasets 66
Module
Accuracy (%)
Different RAVEN Configurations
Perception Reasoning
Avg.
Center
2x2G
3x3G
L-R
U-D
O-IC
O-IG
RM+PM
84.0
98.7
72.5
52.3
99.4
99.2
99.6
66.3
MSE
DSRF-S
96.3
100.0
97.7
87.7
99.9
99.8
99.7
89.6
DSRF-M
96.4
99.9
97.7
89.6
100.0
100.0
99.5
88.5
ARR
87.3
99.8
71.4
65.9
99.9
99.8
98.0
76.2
HCV
DSRF-S
96.4
99.9
97.4
88.8
99.6
99.9
99.9
89.1
O-RVA
DSRF-M
97.5
100.0
98.8
93.1
99.9
100.0
99.9
91.0
PRB
95.8
99.8
95.1
87.6
99.2
99.4
99.9
89.4
RN-4B
DSRF-S
98.6
100.0
99.3
96.1
100.0
99.9
99.9
94.9
DSRF-M
99.1
100.0
99.3
96.2
99.9
100.0
99.9
98.2
PredAI
98.8
100.0
98.8
95.3
99.9
99.8
99.9
98.0
HPALC
DSRF-S
99.1
100.0
99.5
96.4
99.8
100.0
100.0
98.4
DSRF-M
99.3
100.0
99.6
97.1
100.0
99.9
100.0
98.4
RM+PM
81.0
99.6
63.4
59.2
98.7
98.3
95.7
51.9
MSE
DSRF-S
96.7
99.8
97.1
92.0
99.6
99.6
99.6
89.2
DSRF-M
96.9
100.0
97.7
90.6
99.8
99.8
99.8
90.9
ARR
93.9
99.9
96.2
75.5
99.4
99.6
99.5
87.3
HCV
DSRF-S
96.5
100.0
99.2
91.5
100.0
99.9
99.8
85.2
ERVN
DSRF-M
97.2
100.0
99.2
94.9
99.9
99.9
99.9
86.7
PRB
96.5
99.9
97.8
91.2
99.7
99.7
99.6
87.7
RN-4B
DSRF-S
98.8
100.0
99.5
96.7
100.0
99.9
99.8
95.8
DSRF-M
99.4
100.0
99.9
97.6
100.0
99.9
100.0
98.4
PredAI
99.4
100.0
99.9
97.4
99.9
100.0
100.0
98.8
HPALC
DSRF-S
99.4
100.0
99.5
98.2
100.0
100.0
100.0
98.5
DSRF-M
99.5
100.0
99.9
98.4
100.0
100.0
100.0
98.5
RM+PM
86.8
97.0
72.7
69.5
98.7
98.9
97.6
73.3
MSE
DSRF-S
96.5
100.0
93.6
89.7
99.1
100.0
99.9
93.4
DSRF-M
97.9
99.9
98.8
92.7
100.0
100.0
99.7
94.1
ARR
95.4
99.8
92.9
87.9
99.8
99.6
99.7
88.5
RVN-F 9
HCV
DSRF-S
97.9
99.8
98.9
93.0
100.0
99.8
99.6
94.3
DSRF-M
98.1
99.9
99.0
94.0
99.8
99.9
99.7
94.8
PRB
97.1
99.8
97.3
92.6
99.7
99.5
99.7
91.2
RN-4B
DSRF-S
98.8
100.0
99.6
96.2
100.0
99.9
100.0
96.2
DSRF-M
99.0
100.0
99.8
97.3
100.0
99.9
100.0
96.3
PredAI
98.6
100.0
99.4
96.9
99.9
99.9
99.7
94.2
HPALC
DSRF-S
99.2
99.9
99.6
97.5
100.0
99.9
99.9
97.8
DSRF-M
99.4
100.0
99.9
98.3
99.9
100.0
99.9
97.8
C.1.3 Ablation of Three Branches in GARB
In Tab. we conduct an ablation study to evaluate the contributions of the three branches in the proposed GARB module: B represents the base branch for fundamental feature extraction, C denotes the context-enhancement branch that emphasizes context features, and T stands for the target-enhancement branch designed to refine target-specific features. The results are summarized in Tab. L3
The results demonstrate clear progressive performance improvement as more branches are integrated. The base branch alone achieves an average accuracy 98.0% over three datasets across different configurations. Adding the context-enhanncmment branch (B+C) improves the average accuracy
22

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Table 16: Comparison with state-of-the-art models on the original RAVEN dataset the original method based on contrasting over candidate answers.
6 denotes that
Acc. ()) on RAVEN Dataset 66
Under In- In-Distribution Settings
Models
Avg.
Center
2x2G
3x3G
L-R
U-D
O-IC
O-IG
$ HCV-ARR (AAAI'3)
13
96.0
99.4
86.9
89.1
99.9
99.9
99.8
96.8
MRNet (CVPR211)
[
96.6
99.9
97.8
91.2
99.7
99.7
99.6
87.7
MRNet (CVPR211)
9
84.0
98.7
72.5
52.3
99.4
99.2
99.6
66.3
HCV-ARR (AAAT23)
14
87.3
99.8
71.4
65.9
99.9
99.8
98.0
76.2
SCAR (AAAT224)
17
92.8
98.7
80.4
92.9
99.1
99.3
98.2
81.2
AlgeMR (CVPR'23)
13
92.9
98.8
91.9
93.1
99.2
99.1
98.2
70.1
PredRNet (ICMI/23)
15
95.8
99.8
95.1
87.6
99.2
99.4
99.9
89.4
HP² AI (ACM MM'24)
19
98.8
100.0
98.8
95.3
99.9
99.8
99.9
98.0
DSRF-S (Ours)
98.6
100.0
99.3
96.1
100.0
99.9
99.9
94.9
DSRF-M (Ours)
99.1
100.0
99.3
96.2
99.9
100.0
99.9
98.2
DSRF-L (Ours)
99.1
100.0
99.3
96.5
99.9
100.0
99.9
98.3
Table 17: Comparison with state-of-the-an models on I-RAVEN g and RAVEN-FAIR 9 datasets.
Acc. () on I-RAVEN /8/AAVEN-FAIL (9]
Datasets Under In- In-Distribution Settings
Models
Avg.
Center
2x2G
3x3G
L-R
U-D
O-IC
O-IG
MRNet (CVPR2Z))
99
81.0/86.8
99.6/97.0
63.4/72.7
59.2/69.5
98.7/98.7
98.3/98.9
95.7/97.6
51.9/73.3
AlgeMR (CVPR'23)
13
93.2/94.3
99.5/99.8
89.6/93.2
89.7/88.0
99.7/99.8
99.5/99.8
99.6/99.9
74.7/79.6
HCV-ARR (AAAT23)
93.9/95.4
99.9/99.8
96.2/92.9
75.5/87.9
99.4/99.8
99.6/99.6
99.5/99.7
87.3/88.5
SCAR (AAA1'2)
[7
94.7/93.9
99.1/98.6
95.7/93.1
80.4/81.3
99.3/99.8
99.3/99.8
98.2/99.3
91.2/85.7
PredRNet (ICM)22))
15
96.5/97.1
99 99.9/99.8
97.8/97.3
91.2/92.6
99.7/99.7
99.7/99.5
99.6/99.7
87.7/91.2
HP Al MM124)
19
99.4/98.6
100.0/100.0
99.99994
97.4/96.9
99.9/99.9
100.0/99.9
100.0/99.7
98.8/94.2
DSRF-S (Oun))
98.8/98.8 8 100.0/100.0
99.5/99.6 96.7/96.2 2
100.0/100.0
99.9/99.9 9
99, 9/100000.0
8598/
DSRF-M (Ours)
99. 4/.9999
100.0/100.0
99.9/99.8
97. 97.6/97.3
100.0/100.0
99. 9/99/9
100.0/100.0
98 4/96.3
DSRF-L (Durs)
99.4/99.1
100.0/100.0 99.9/99.8 97.6/97.4
99.9/100.0
100,0/100,0
99.9/100.0
98.8/96.5
to 98.6%, highlighting the benefit of incorporating contextual features. Incorporating the target- enhancement branch (B+T) provides a more significant boost, achieving an average accuracy of 98.8%, indicating the importance of (B+C+T) achieves the highest average accuracy of 99.2%, demonstrating the complementary strengths of the three branches and their effectiveness in capturing task-specific information for enhanced reasoning performance.
adjustments. Finally, the full three-branch structure
C.1.4 Detailed Ablation of Major Components
In Tab. 5 of the manuscript, we summarize the ablation study of the major components on the three RAVEN datasets 6 g 9 Now, we present the detailed ablation study results in Tab. 14, showcasing the contributions of key components, including DDCP, GARB, CNN gate, dynamic gate, and MRM. As shown in Tab. 14] we observe that for simpler configurations such as Center, L-R, and U-D on all three datasets, our method achieves an accuracy of 100% in most cases even when some of our components are removed. However, for more challenging configurations such 2x2G, 3x3G, and O-IG, removing specific components leads to significant performance drops, particularly those related to dynamic reasoning. For example, for O-IG on the RAVEN dataset [6], removing the DDCP module results in a sharp decline from 98. 98.2% to 80.3%, highlighting the importance of DDCP in dynamically identifying and contrasting features. Similarly, for 3x3G on the RAVEN-FAT dataset [9] removing the dynamic gate reduces accuracy from 97.3% to 96.1 %, demonstrating the critical role of dynamic adaptability for handling complex rules.
C.1.5 Detailed Results of DSRF as Plug-and-PHy Reasoning Module
Due to the page limit, we only summarize the average performance for DSRF serving as a plug- and-play reasoning module across different configurations in Tab. 6 of the manuscript. Here,
23

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Table 18: Comparison with state-of-the-art models under OOD settings on three RAVEN datasets 6
Avg.
Center
2x2G
3x3G
L-R
U-D
O-IC
O-IG
Models
Training on RAVEN (6]
while testing on I-RAVEN
8 /RAVEN-FAIR 9 Datasets
MRNett (CVPR221)
9
65.8/81.2 1.2
86 8/96.1
40.3/58.9
35.3/54.3
87.2/99.3
86. 16.1/98.9 9
88.4/97.6
36. 36.7/63.3
HCV-ARR (MAII2))
14
79,4/91.9
99. 99.4/99.9
54.6/84,1
51.2/80.4
98.9/99,7
98.7/99.4 4
96.3/99.5
60.4/80.2
SCAR (AAA120
17
84.7/95.9
99.8/99.9
65.5/95.1
59.4/86.6
99.7/99.8
99.8/99.8
99,9/99.6
68.6/90.3
HP AT (ACM MM
19
87.7/96.9
100.0/100.0
72.1/93.7
63.1/91.4
100.0/99.9
100.0/99.9
99.9/99.9
78. 78.2/93.2
PredRNet (CMM/25)
15
89.2/97.9
100.0/100.0
75.4/95.4
68.8/94.9
100.0/99.9
99,9/99.9
100.0/99.9
80.9/95.1
DSRF-S (Ours)
95.1/98.5
100,0/100.0
91.3/99.5
80.9/95.2
100.0/100.0
100.0/99.9
100.0/100.0
93.7/95.1
DSRF-M (Ours)
95.6/98.7
100.0/100.0
91.9/99.7
82,5/96.2
100.0/100.0
100.0/100.0
100.0/100.0
94.5/95.2
DSRF-L. (Ours)
95.9/98.9
100.0/100.0
92.5/99.9 84.0/96.9
100.0/100.0
100.0/100.0
99.9/100.0
95.2/95.8
Training on I-RAVEN (8) while testing on RAVEN 6 /RAVEN-FAIR 9 Datasets
MRNet (CVPR'21)
9
76.5/78.6
58.7/98.5
60.7/58.5 47. 17.6/48.2
95.7/96.3
96.3/97.4
91.9/96.9 9
44. 44.3/54.2
HCV-ARR (AAAI23)
14
81.4/89.4
99.7/98.9
61.7/79.9
49.5/69.8
98. 8/98.3
98,9/98.9
98.1/98.5
63. 63.3/81.3
IPP AT MMC20
19
89,9/94.0
99.2/99.5
77.2/86.6
14.1/83.0
99.9/100.0
99.7/100.00
99.8/99.9
79.5/89.4 4
SCAR (AAA120
17
91.9/94.5
99.1/99.9
84.8/87.8
82.4/83.9
99.6/99.9
99.5/99.8
99.6 99,6/99.9
78.6/90.1
PredRNet (CML223)
[5
93,9/97.3
99.3/99.4
93.9/97.3
84.1/93.0
99.6/99.9
99,5/99.7
99.4/100.0
DSRF-S (Ours)
95,9/98.2 2
100.0/100.0
96.3/98.2 87 6/6//.7
99 8/18000000
100.0/100.0
99 69999
87.9/95.0 0
DSRF-M (Our))
97.4/98.7
100.0/100.0
86.8/97.5 92.3/95.7
99.9/100.0
100.0/100.0
99.6/99.9
93.4/98.0
DSRF-L (Ours)
97.9/98.9
100.0/100.0
97.6/98.5 93.7/96.6 100.0/100.0
100.0/99.9
99.9/100.0
94.3/97.4
Training on RAVEN-FAIR (9] while testing on RAVEN
6 /IRRAVEN [ Datasets
MRNet (CMPR'21)
9
78.8/73.4
93.9/91.1 1
61.3/53.5
49.2/41.3
93. 1/891
92, 9
95.9/89.1 I
66. 16605
SCAR (AAA120
17
91.3/85.6
98 98.4/98.3
84.3/64.3
73.6/51.5
99.4/99.4 4
99.4/99.3
99.0/99.4 4
84.8/87.3
HCV-ARR (AAAI2))
14
94.1/87.3
99.1/98.8
88,5/68.5
79.4/56.2
99.7/99.4
99.5/99.5
99.2/99.5
93.1/89.1
HP (ACM)
19
95.3/90.0
99.2/99.7
90.3/72.9
84.9/65.7
9998/
99.5/99.7
99.3/99.9
94.1/92.8
PredRNet (CMB223
96.2911.4
99.6/100.0
97.4/86.5
88.9/68.3
99.6/100.0
99. 99.1/99.4
99 99.6/99.8
89.7/86.3
DSRF-S (Ouns)
97.3/95.4
99.9/99.9
98.1/96.0
90.8/82.3
99.6/100.0
99.6/100.0
99.6/99.9
93.8/90.4
DSRF-M (Ours)
97.8/95.8
100.0/100.0
97.9/96.9
93.3/82.7
99.9/100.0
99.9/100.0
99.8/100.0
9/98/
D-L (Qurs)
98.1/96.5
100.0/100.0
98.1/97.7
94.9/88.9
99.9/99.9
100.0/99.9
99.9/99.9
93.7/89.5
supplement the detailed evaluation results on all configurations in Tab. [5] For most configurations, the proposed method demonstrates significant performance gains when combined with different visual perception modules. Specifically, for casier configurations such as Center, L-R, U-D, and O-IC, our reasoning module. when combined with certain perception modules, achieves perfect reasoning with 100% accuracy. For more challenging configurations like 3x3G, O-IG, and 2x2G, our reasoning module also delivers significant improvements. For example, on the 3x3G configuration, DSRF-M achieves 97.1% accuracy with HPALC [9] on the RAVEN dataset 6. a substantial enhancement compared to the 52.3% achieved by MSE with RM+PM 9
C.2 Detailed Results on Three RAVEN Datasets Under In-Distribution Settings
In Tab. of the manuscript, we summarize the comparison results on the three RAVENS over all configurations. Here, we supplement the results for all configurations RAVEN 6). I-RAVEN (8) and RAVEN-FAIR g datasets. Detailed results on three RAVEN datasets are presented in Tab. 16 and Tab. 17 From these two tables, we can observe the following. 1) When the shorteut in RAVEN is not leveraged, MRNet 9 and HCV-ARR (44 both experience a notable performance drop. In contrast, the proposed DSRF-L achieves the highest average accuracy of 99. 1% without relying on the shortcut, demonstrating the superiority of its reasoning capability. 2) On simple configurations, such as Center, 2x2G, L-R, U-D, and O-IC, our three methods all comprehensively understand the underlying rules, achieving accuracies exceeding 99.0% across three RAVEN datasets (6 8, 9. 3) However, on challenging configurations such as 3 3x3G, all compared methods perform relatively poorly. In contrast, the proposed DSRF-L obtains the highest average accuracies of 96.5%, 97. 97.6%, and 97.4% on RAVEN 6 I-RAVEN 8 and RAVEN-FAIR (9) respectively, improving the second- best model HP² AI 19 by 1.2% 0.2% and 0.5%. These results demonstrate the robustness and effectiveness of the model's dynamic reasoning ability. 4) On the challenging O-IG configuration, the proposed DSRF-L obtains the largest performance gain over the second-best model HP2 AI [19 by 2.3% on the RAVEN-FAIR dataset 19. This highlights the reasoning ability of the DDCP to dynamically encapsulate complex relational patterns.
24

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C.3 Detailed Results on Three RAVEN Datasets Under Out-Of-Distribation Settings
We report the comparison results on the three RAVEN datasets 6 under OOD settings in Tab. of the manuscript. Here, we supplement the results on different configurations to show the model's generalization ability to transfer knowledge across different settings, where the model trained on one dataset while tested on the other two. Detailed results under OOI) settings are presented in Tab. [8] From this table, we can observe the following. 1) Our three models consistently and significantly outperform all existing models across almost all configurations under all OOD settings. 2) The proposed DSRF-L exhibits consistent performance across 7 configurations, demonstrating accuracy fluctuations of 16.0% and 4.2% under RAVEN OOD setting, 6.3% and 3.4% under I-RAVEN OOD setting, and 6.3% and 11.15 % under RAVEN-FAIR OOD setting. Specifically, considering RAVEN OOD setting where the accuracy fluctuations are the highest, our DSRF-L still outperforms the second-best model PredRNet [15] with 15.2% and 0.9% reduction in accuracy fluctuation, illustrating the robustness of our models across diverse testing configurations.
D Failure Case Analysis
Fig. 10 presents failure cases to visually illustrate the benefit of our method, in contrast to PredR- Net's [1]]. In Case 1, PredRNet [15] overfits the RAVEN dataset 66 by selecting the most common option from the answer panels, where eight objects have varying colors, failing to derive the un- derlying abstract rules, whereas DSRF-M effectively identifies the correct answer by capturing the rule-based patterns dynamically, In Case 2, the task involves complex rule combinations, making it challenging for Pred 115 static "predict-and" verify" approach to reason about the correct solution. In contrast, DSRF-M leverages dynamic attention mechanisms to focus on the layout structure, enabling it to reason and select the correct answer. Case also represents a more complex problem due to the combination of multiple rules, which results in significantly challenging task. The proposed DSRF could solve it but PredRNet [15] cannot.
In Cases 4, 5, and 6, both methods fail to select the correct answer. In particular, Case 4 and Case 5 both involve highly complex layouts, where it is challenging to precisely derive the intricate arrangement of objects. In Case 6, there are two irrelevant attributes Position and Type that may confuse both models. Indeed, reasoning over complex layout and being robust to irrelevant attributes are remaining challenges, which are worth to further explore in future.
E Limitation
Although the Multi- View Reasoning Pyramid (MVRP) enables scalable and structured reasoning by mapping features into multiple views, the current implementation adopts manually predefined number of views per layer (e.g., "2-1", "4-2-1", "8-4-1"). While these settings have shown strong performance across benchmarks, they may not be optimal for all tasks. Automatically discovering the number and composition of views could further improve the model's adaptability. In particular, different problem types may benefit from different view granularities, and one- one-size-fits-lle design might limit the model's flcxibility in some scenarios. Additionally, for certain complex tasks, fine- grained hierarchical view configurations could be beneficial but have not yet been explored in the current framework. Investigating how view configurations interact with rule complexity would provide valuable insights for future enhancements.
F Summary of Network Architecture
We provide the detailed architecture of our proposed DDCP in Tab. 19 MRM in Tab. 20 and core component GARB in Tab. 21, For readability, we do not include batch normalization, layer normalization, dropout layer and activation functions in the structure. For example, F(8, 32, 3, 25) represents feature with a group size of 8, 32 channels, context features in row, and token size of 25. The group size is 8 because we concatenate 8 answer images with the question panel. Additionally, before transforming into multiple heads in GARB, our features are three-dimensional, such as F(8, 25, 32), which represents batch size of 8, token size of 25, and 32 channels. More details will be provided in our released code upon the paper acceptance.
25

---

Case
Case 2
Case 3
o8
O-RVN I-VV
Out: I-RW
RVN-F D-VVN
Number: Distribution
Constant
Constant
Position:
Constant
Position: Constant
Type: Constant
Type: Distribution Three
Type: Constant
Size: Distribution Three
Size: Constant
Size: Distribution Three
Color: Distribution Three
Color: Constant
Color: Progression
Number: Constant
Position: Distribution Three
Type: Constant
Constant
Case 4
Case 5
Case 6
O-RVN > HRVN
[-RV RVN-F
RVN-F + O-RWN
Number: Constant
Nunber: Constant
Progression
Position:
Position: NA
Type: Distribution Three
Type: Constant
Type:
Size: Constane
Size: NA
Size: Progression
Color: Distribution Three
Color: Progression
Color: Distribution Three
Choice DSRF-M
Choice PredRNet
Correct
Figure 10: Failure cases RAVEN datasets under OOD settings. The choices of DSRF-M and
PredRNet 15 are compared.
26

---

Table 19: Detailed network architecture of the proposed DDCP, with the number of parameter channels a, the kernel size 3. To better illustrate the CNN gate, denote the G as the gate matrix.
Function
Operations
Input
Output
Permute
F(8, 32, 25)
F(8, 25,
Lincar(a=64)
F(8, 9, 25, 32)
F(8, 9, 25, 64)
Split
F(8, 9, 25, 64)
F(8, 25, 32)
&G(8, 9, 25,
Permute
F(8, 9, 25, 32)
F(8, 9,,9, 25)
Split
F(8, 32, 9,25)
F(8, 32, 25)
Reason Row
GARB(o=322
F(8, 3,
F(8, 32,
Reason 2nd Row
GARB(o=32)
32,
F(8, 32,
Reason 3rd Row
GARB(a=322)
F(8, 32, 25)
F(8, 32,
Concat
F(8, 32, 25)x3
F(8, 32,9, 9,2))
Permute
F(8, 32, 9, 25)
F(8, 9, 25, 32)
CNN Gate
Conv2d(a=36,, (=(3,
G(8, 9, 25, 32)
G(8, 36, 25, 32)
Conv2d(a=9,, (=33, 3))
G(8, 36, 25, 32)
G(8, 9, 25)
Linear(a=32)
G(8, 9, 25, 32)
G(8, 9, 25,
Hadamard Product
F(8, 9, 25, 32)&G(8, 9, 25, 32)
F(8, 22)
Permute
F(8, 9, 25, 32)
F(8, 32. 9,25)
Conv2d(a=128, (3,3, 3))
F(8, 32, 9, 25)
F(8, 128, 9,25)
Conv2d(a=32, B=33
F(8, 128, 95)
F(8, 32, 95)
Residual
Add
F(8, 32, 9, 25)
F(8, 32, 9, 25)
Table 20: Detailed network architecture of the proposed MRM. a denotes the number of channels. To illustrate the parallel structure in the model, we denote the feature for the channel-wise linear map as C and the feature for the token-wise linear map as T.
Function
Operations
Input
Output
Token- wise Map
Linear(a=25)
F(8, 32, 25)
T(8, 32, 25)
Permute
T(8, 32, 9, 25)
T(8. 9, 22,
Permute
F(8, 32, 95)
F(8, 25,
Channel-wise Map
Linear(a=32))
F(8, 9, 25,
C(8, 9, 25,
Add
T(8, 25, 32)&C(8 9, 32)
F(8, 25,
Reshape&Permute
F(8, 25,32)
F(8, 25, 32,
Row-wise Map
Linear(a=3)
F(8, 25, 32,
F(8, 25,,
Reshape&Permute
F(8, 25, 3,
F(8, 25,
Sample-wise Map
Linear(a=9)
F(8, 25, 25,
F(8, 2(8,25,
Permute
F(8, 25, 32,9)
F(8, 32,9,255
Conv2d(a=128, (=(3, 3))
F(8, 32, 9,2
F(8, 128, 9.25)
Conv2d(a=32, (=(3, 3))
F(8, 128, 9, 25)
F(8, 3,,9,
Residual
Add
F(8. 32, 9, 25)x2
F(8. 32, 9, 25)
27

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Table 21: Detailed network architecture of the proposed GARB, with the number of parameter channels a, the kernel size B. W is the learnable matrix. GQ and GK denote the two Gram matrices. DGQ and DGK are Q-wise and K-wise dynamic gates. DQ and DK represent two enhanced features after dynamic gates. the domain difference. is the prediction error.
Function
Operations
Input
Output
Split
F(8, 32, 25)
F(8, 32, 2, 25)
&F(8, 32, 1,)
Downsample
Conv2d(o=32, B=(2, 1)) F(8, 32, 2, 25)
F(8, 32, 1,25)
Q Generation
Reshape&Permutte
F(8, 1,)
F(8, 22)
K Generation
Reshape&Permutte
F(8, 32, 25)
F(8, 22)
V Generation
Pesmate&Perrmute
F(8, 122
F(8, 22)
Q Mapping
Linear(a=32)
F(8, 22)
Q(8, 25, 32)
K Mapping
Linear(a=32)
F(8, 22)
K(8, 25,
Mapping
Linear(a=32)
F(8, 25,
V(8, 22)
Q Multi-head
Reshape&Permiie
Q(8, 25, 32)
Q88. 8, 25,
K Multi-head
Reshape&
K(8, 25, 32)
K(8, 8, 25. 4)
V Multi-head
Reshape&Permute
V(8, 25, 32)
V(8, 8, 25.
Basic Branch
Gram GQ
Dot Product
Q(8, 8, 25, 4)&Q(8, 8, 25,
GQ(8, 8, 25, 25)
Gram GK
Dot Product
K(8, 8, 25, 4)&K(88 8, 25,
GK(8. 8, 25)
GQ Highlight
Hadamard Product
GQ(8, 8, 25, 25) W(8, 25, 25)
GQ(8, 8, 25,25)
GK Highlight
Hadamard Product
GK(8, 8, 25, 25)& 25,
GK(8, 8, 25,25)
Difference
Minus
GQ(8, 8, 25, 25)&GK(8, 8,25, 25) D(8, 8, 25. 25)
Conv2d(o=32,$=6333)
D(8. 8, 25, 25)
D(8. 32, 25, 25)
Conv2d(==8,B=033)
D(8, 32, 25, 25)
D(8, 8, 25, 25)
Context-enhanced Branch
DGK Dynamic Gate Dot Product
K(8, 8, 25, 4)8 8, 25,
DGK(8, 8, 25, 25)
DK Highlight
Hadamard Product
D(8, 8, 25, 25)&DG 8, 25, 25) DK(8, 8, 25, 25)
(3nv2d((=32,8=3333)) DK(8, 8, 25, 25) (onv2d(==8,3=63)
DK(8. 32, 25, 25)
DK(8, 32, 25, 25)
DK(8, 8, 25, 25)
Target-enhanced Branch
DGQ Dynamic Gate Dot Product
Q(8. 8, 25, 4(8, 8, 25, 4)
DGQ(8, 8, 25, 25)
DQ Highlight
Hadamard Product
D(8, 8, 25, 25)&DGQ(8, 8, 25, 25) DQ(8, 8, 25, 25)
DQ(8, 8, 25, 25) (0nv2d(==32,3=33333 8o
DQ(8, 32, 25, 25)
DQ(8, 32, 25, 25)
DQ(8, 8, 25, 25)
Plus
D&DK&DQ(8, 8, 25, 25)x3 D(8. 8, 25, V 25,
D(8, 8, 25, 25)
Dot Product
F(8, 8, 25, 4)
Prediction
Permate
F(8, 8, 25, 4)
F(8, 22)
Linear(a=32)
F(8, 25, 32)
F(8, 25,
Reshape& Permute Permute
F(8, 25, 32)
F(8, 32, 25)
Error
Minus
F(8, 32, 1, 25)&F(8 32, 1, 25)
E(8, 32, 25)
Concat
F(8, 32, 2, 25)& 32, 15)
F(8. 32, 3, 25)
28

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Reviews:
[{"review_id": "FiUf7dMSWv", "reviewer": "Reviewer_Bup5", "summary": "The paper proposes a new reasoning framework, called dynamic and scalable reasoning framework (DSRF) for solving abstract visual reasoning problems, specially Raven’s Progressive matrices (RPMs). DSRF consists of blocks like multi-view reasoning pyramid to widen the network to capture more attribute combinations, dynamic domain contrast prediction block to dynamically capture rules with the help of a gated attention reasoning block. Finally a multi-granularity rule mixing block is proposed to capture different combinations of rules from different perspectives. Through extensive results on six RPM benchmarks, including one involving real world traffic prediction, the authors demonstrate the effectiveness of the framework. The authors also demonstrate that DSRF outperforms other methods under different OOD settings and can be used to replace the reasoning module of other models.", "questions": "1. How sample-efficient is DSRF? Can the authors evaluate on ART [1] /SVRT [2] tasks, where sample efficiency can be systematically evaluated?\n\n2. Is the model trained using the standard scoring mechanism used in RPMs, where for each answer choice a score is obtained which is used to compute cross entropy loss?\n\n3. How important is the multi-view reasoning pyramid to the overall performance?\n\n4. Given that the MRM module seems the least significant component, its not clear to me how the different mixings are important. Perhaps some ablations targeting those could be helpful and also some additional information about how these mixings are done. \n\n[1] - Webb, T. W., Sinha, I., and Cohen, J. D. Emergent symbols through binding in external memory. In 9th International Conference on Learning Representations, ICLR, 2021.\n\n[2] - Vaishnav, M. and Serre, T. Gamr: A guided attention model for (visual) reasoning. In 11th International Conference on Learning Representations, ICLR, 2023", "limitations": "Discussed in appendix, would be good to have a summarized version in the main paper.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The paper is well written.\n2. Proposed a new reasoning framework DSRF for RPMs, consisting of blocks like multi-view reasoning pyramid, dynamic domain contrast prediction, multi-granularity rule mixer targeting different aspects relevant for abstract visual reasoning.\n3. Extensive results on six benchmarks (including real-world images) demonstrate its effectiveness. \nDSRF can also be used to replace the reasoning frameworks of other models, to further improve their performance on RPM benchmarks. \n\n\nWeaknesses:\n\n1. The authors don’t compare with ARII [1] and Slot-Abstractor [2] for the PGM which especially outperforms other methods on OOD generalization regimes, and it seems both of them achieve higher scores than DSRF on extrapolation. Also it would be valuable to evaluate DSRF on other OOD generalization regimes in the PGM dataset like Heldout shape color, Heldout line type, Heldout triples etc some of which are more difficult than the extrapolation regime.\n\n2. Given that operations within DSRF extract rules by processing the RPMs rowwise, it seems this framework won’t be able to capture any rules columnwise.\n\n[1] - Zhang, W., Liu, X. and Song, S., 2022. Learning robust rule representations for abstract reasoning via internal inferences. Advances in Neural Information Processing Systems, 35, pp.33550-33562\n\n[2] - Mondal, S.S., Cohen, J.D. and Webb, T.W., 2024. Slot abstractors: Toward scalable abstract visual reasoning. arXiv preprint arXiv:2403.03458", "was_revised": true, "final_justification": "The authors' rebuttal has addressed my concerns and questions, so I raised my score.", "rebuttal": "**W1. Comparison on PGM OOD regimes** \n\nFollowing your comments, we have evaluated DSRF-M and DSRF-L on all PGM tasks, including PGM-H.O.P (Held-out Attribute Pairs), PGM-H.O.TP (Held-out Triple Pairs), PGM-H.O.T (Held-out Triples), PGM-H.O.LT (Held-out Line-Type) and PGM-H.O.SC (Held-out Shape-Color) settings, each testing the model’s ability to generalize to novel combinations of attributes, unseen pairs or individual triples, and new attribute-object pairings. \n\n| | PGM-N | PGM-I | PGM-E | PGM-H.O.P | PGM-H.O.TP | PGM-H.O.T | PGM-H.O.LT | PGM-H.O.SC |\n| -| - | - | -| - | -| -| -| -|\n| ARII [a] | 88.0  | 72.0  | 29.0  | 50.0 | 64.1| 32.1| 16.0 | 12.7 |\n| Slot-Abstractor [b] | 91.5  | 91.6  | 39.3  | 63.3  | 78.3  | 20.4 | 16.7 | 14.3  |\n| DSRF-M | 99.5  | 84.5  | 27.4  | 65.7 | 78.8 | 31.3  | 17.4  | 16.7  |\n| DSRF-L | 99.8  | 87.3  | 31.5  | 67.7 | 82.3 | 34.2  | 18.9       | 17.8   |\n\nTable A. Comparisons on PGM OOD regimes.  \n\n \nAs noted by the reviewer, DSRF underperforms Slot-Abstractor [b] in Interpolation and Extrapolation tasks. This is mainly because DSRF adopts a more general reasoning paradigm without accessing attribute labels, while Slot-Abstractor [b] utilizes these attribute labels to model continuous attribute variations effectively. \n\nOn other OOD settings, DSRF consistently outperforms ARII [a] and Slot-Abstractor [b]. This is mainly because these settings involve more complex rule-attribute compositions, where DSRF's dynamic and modular design enables stronger generalization beyond fixed attribute-slot mappings. \n\nDSRF-L surpasses ARII [a] in all PGM tasks and Slot-Abstractor [b] in 6/8 tasks, while DSRF-M outperforms ARII [a] in 7/8 tasks and Slot-Abstractor [b] in 6/8 tasks. These results demonstrate their superior performance in PGM OOD tasks. \n\nWe will include these experimental results in the final manuscript. \n\n \n\n**W2: Handling column-wise rule** \n\nThank you for your insightful comments. We respond to your comments as follows. \n\n- Intuitions for modelling row-wise rules only. \n\nDSRF focuses on row-wise rules only as most datasets such as RAVEN [18], I-RAVEN [7], RAVEN-FAIR [8] only implement row-wise rules. We prioritized efficiency by focusing on row-wise reasoning, which suffices for most RPM tasks but admittedly limits the model. \n\n- Not explicitly but implicitly model column-wise rules. \n\n- While DSRF does not explicitly model column-wise rules, column-wise reasoning emerges implicitly through the shared weight architecture across rows. As the same DDCP module is applied to all rows, it encourages the model to learn generalizable patterns that may also align along columns, allowing the model to partially capture column-wise regularities. \n\n- In all the datasets we evaluated, only PGM [6] implements column-wise rules. By utilizing row-wise DDCP only, DSRF performs excellently on PGM, as shown in Table 4. \n\n- Incorporating column-wise DDCP. \n\nFollowing your comments, we extend the framework by adding a column-wise DDCP reasoning branch, whose outputs are fused with the row-wise DDCP to enhance rule representation. The DDCP’s modular design enables easy adaptation for column-wise processing. \n\nWe evaluate this extension on PGM as shown below, where DSRF-M-RC/DSRF-L-RC denote the DSRF-M/DSRF-L variants utilizing both row-wise and column-wise DDCPs. By adding column-wise DDCPs, the performance significantly improves. \n\n \n\n|           | PGM-N | PGM-I | PGM-E | PGM-H.O.P | PGM-H.O.TP | PGM-H.O.T | PGM-H.O.LT | PGM-H.O.SC |\n| -- | - | --| ----- | --------- | ---------- | --------- | ---------- | ---------- |\n| DSRF-M    | 99.5  | 84.5  | 27.4  | 65.7      | 78.8       | 31.3      | 17.4       | 16.7       |\n| DSRF-M-RC | 99.7  | 88.9  | 35.1  | 68.9      | 82.1       | 34.1      | 19.1       | 18.1       |\n| DSRF-L    | 99.8  | 87.3  | 31.5  | 67.7      | 82.3       | 34.2      | 18.9       | 17.8       |\n| DSRF-L-RC | 99.9  | 92.1  | 40.2  | 71.3      | 86.7       | 37.3      | 19.9       | 19.4       |\n\nTable B: Results for DSRF-M-RC and DSRF-L-RC on PGM. \n\n \n\nWe will revise these results and related discussions in the final manuscript. \n\n \n\n[a] Webb, T. W., Sinha, I., and Cohen, J. D. Emergent symbols through binding in external memory. In ICLR, 2021. \n\n[b] Vaishnav, M. and Serre, T. GAMR: A guided attention model for (visual) reasoning. In ICLR, 2023. \n\n \n\n**Q1: Evaluating** **sample-efficient of DSRF** **on SVRT** \n\nFollowing your comments, we conducted experiments on the SVRT dataset using 500, 1k, 5k, and 10k training samples respectively, following GAMR [b]. This evaluation provides a controlled setting to assess generalization under limited data. The results are summarized below (left: same-different tasks/right: spatial related tasks). DSRF achieves strong performance across various SVRT tasks, even when trained with limited samples such as 500 samples per task. The results demonstrate its ability to learn abstract visual rules efficiently. \n\n|   | ResNet-50 [c] | RN [6] | ESBN [a] | Atten-ResNet [d] | GAMR [b] | DSRF-M |\n| - | - | - | - | - | - | - |\n| SVRT-500 | 54/85 | 53/85  | 58/64    | 63/95  | 78/98  | 86/100 |\n| SVRT-1k  | 57/96  | 58/90  | 58/64    | 69/98    | 83/99  | 92/100 |\n| SVRT-5k  | 78/100  | 68/97  | 63/68    | 88/100  | 94/100 | 98/100 |\n| SVRT-10k | 84/100  | 75/97  | 67/67    | 92/100  | 95/100 | 99/100 |\n\nTable C. Sample efficiency analysis on the SVRT dataset. \n\n \n\nWe will add this sample efficiency analysis into the in the final manuscript and the supplementary materials accompanying the publication. \n\n \n\n[c] He, Kaiming, et al. \"Deep residual learning for image recognition.\" *CVPR*, 2016. \n\n[d] Vaishnav, Mohit, et al. \"Understanding the computational demands underlying visual reasoning.\" *Neural Computation* 34.5 (2022): 1075-1099. \n\n \n\n**Q2: Standard scoring mechanisms****?** \n\nYes, our model uses the standard RPM scoring mechanism, consistent with PredRNet [13] and many other models [12, 17]. We apply binary cross-entropy loss over the scores of the eight answer choices, which is functionally equivalent to Softmax with cross-entropy loss under the condition of single-choice questions. \n\n \n\n**Q3: Importance of multi-view reasoning pyramid** \n\nMulti-view reasoning pyramid serves as the foundational architecture of our framework, enabling its scalable design and robust performance. By utilizing different number of views, we design three pyramids with small, medium and large configurations, with a pyramid structure of “2-1”, “4-2-1”, and “8-4-1”, where each number represents the number of views in each layer. Combined with the dynamic reasoning capability enabled by DDCP and its core module, GARB, our DSRF demonstrates strong scalability. Notably, larger model variants do not overfit the training data but instead achieve consistent performance improvements across diverse benchmarks, as evidenced by the progressive improvements from DSRF-S to DSRF-M and, and from DSRF-M to DSRF-L in Tables 1–3 of the manuscript. The reviewer may refer to the reply to W2/Q2 of Reviewer Yeks for a more comprehensive comparison of DSRF variants across datasets. Due to space limit, we omit here.  \n\n \n\n**Q4. Ablation of different mixings in MRM and more** \n\nThank you for your thoughtful suggestions. We respond to your comments as follows. \n\n- **Ablation of different mixings in MRM** \n\nFollowing your comments, we have added the ablation of different mixings in MRM, a 3-layers MLP (MLP), two channel-wise 2D convolution layers (CNN), and a self-attention block [e] on O-RVN, I-RVN and RVN-F datasets, as summarized below. \n\n|   | O-RVN | I-RVN | RVN-F |\n| -| - | - | -|\n| w/o MRM | 98.7  | 98.8  | 98.6  |\n| MLP | 98.8  | 98.9  | 98.6  |\n| CNN | 99.0  | 99.2  | 98.8  |\n| Self-Attention | 98.8  | 99.0  | 98.8  |\n| MRM   | 99.1  | 99.4  | 99.0  |\n\nTable D. Ablation of different mixings in MRM. \n\n \n\nThe results show that alternative mixings exhibit inferior accuracy compared to the MRM, confirming that our multi-granularity mixing architecture more effectively captures diverse rule interactions. While the improvement is relatively modest compared to other novel architectural components like MVRP and DDCP, the gains persist across dataset while maintaining practical relevance. \n\n \n\n[e] Vaswani, Ashish, et al. \"Attention is all you need.\" *NeurIPS*, 2017. \n\n \n\n- **Additional information on mixings in MRM** \n\nMRM enhances rule composition by performing feature mixing across multiple levels of granularity, including channel-wise, token-wise, row-wise, and sample-wise projections. \n\n- Specifically, the channel-wise mixing is implemented through a linear projection that is applied along the channel dimension, capturing interactions across feature channels and enabling the model to refine semantic dimensions associated with specific attributes. \n\n- For the token-wise mixing, each spatial token is projected using a shared MLP, modelling intra-view spatial relationships and allowing the network to process localized rule patterns within the view. \n\n- For the sample-wise mixing, all tokens within a view are aggregated into a global representation and passed through a linear projection layer, providing global context for each sample and supporting top-down rule verification. \n\n- For the row-wise mixing, features from different matrix rows within a sample are aligned through a linear projection, capturing structural relations such as progression or repetition along the row axis that commonly exist in RPM problems. \n\nThese mixing operations capture interactions across different dimensions of the reasoning space, enabling the model to refine and combine partial rule patterns extracted from individual views. \n\n \nWe will add these results and discussions in the final manuscript and the supplementary materials accompanying the publication. \n\n \nWe trust this rebuttal has comprehensively addressed your concerns. Should any additional questions arise, we would be pleased to provide further clarification."}, {"review_id": "d0sPhFr0E7", "reviewer": "Reviewer_UTPG", "summary": "This paper proposes DSRF, a new abstract visual reasoning framework to address the limitations of scalability and adaptability in existing models. The proposed MVRP module maps visual features into multiple views to capture complex reasoning rules. The DDCP module introduces a dynamic attention mechanism, enabling the reasoning network to adaptively handle abstract rules in various tasks. Experiments conducted on six AVR datasets demonstrate that DSRF achieves SOTA accuracy on these datasets, exhibiting outperforming abstract visual reasoning ability.", "questions": "1. Has DSRF been evaluated under held-out settings of PGM or RAVEN?\n\n2. Can we apply DSRF to non-matrix abstract visual reasoning tasks, such as the Bongard Problems?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths\n\nThe paper proposes novel modules with both scalability and adaptability. MVRP expands the space of representable abstract rules by constructing multiple views from representations, allowing it to model a wide range of compositional rules. DDCP can dynamically attend to domain differences in flexibly adapt to task-specific abstract rules. The experimental section is thorough, and the results show that DSRF achieves SOTA performance across the six abstract visual reasoning datasets.\n\nWeaknesses\n\n1. While the proposed modules enhance model capacity, they may introduce additional computational overhead. The paper does not provide a quantitative analysis of model efficiency, such as inference speed or memory consumption, nor does it compare the number of model parameters across the compared models.\n\n2. The data efficiency and training data requirements of DSRF are not discussed. A discussion on how the model performs under limited training data would be valuable.\n\n3. There is ambiguity in the paper’s definition of OOD evaluation. If the differences among I-RVN, O-RVN, and RVN-F lie solely in the provided options, while the attributes and rules remain unchanged, then these settings may not constitute true OOD tests. Since existing methods have achieved strong performance on datasets like RAVEN, the performance of DSRF on unseen rule-attribute combinations is critical.\n\n4. The definitions of Θp and Θr are missing in Line 107.", "was_revised": true, "final_justification": "The authors' responses have addressed my concerns about computational efficiency and OOD evaluation. They have reported additional results to show the model's performance on OOD configurations. So I maintained the original score.", "rebuttal": "**W1: Computational complexity Analysis** \n\nThe reviewer may overlook the model complexity analysis in the last two columns of Table 2, and the associated discussions at Line 233-236 in Sec. 4.2, where we reported GFLOPs and model size (M) of compared models. One of our key contributions is to introduce a scalable design to boost the reasoning capability of our models. As shown in Table 2, our DSRF-S, DSRF-M and DSRF-L outperform all the compared models. Through systematic model scaling, we demonstrate progressive improvements in reasoning capability across the DSRF architecture variants (S→M→L), validating the effectiveness of our scalable design paradigm. \n\n \n\n**W2: Data efficiency** \n\nThank you for your comments. Following your comments, we conducted experiments on the SVRT dataset using 500, 1k, 5k, and 10k training samples respectively, following GAMR [b]. This evaluation provides a controlled setting to assess generalization under limited data. The results are summarized below (left: same-different tasks/right: spatial related tasks). DSRF achieves strong performance across various SVRT tasks, even when trained with limited samples such as 500 samples per task. The results demonstrate its ability to learn abstract visual rules efficiently. \n\n \n\n|          | ResNet-50 [c] | RN [6] | ESBN [a] | Atten-ResNet [d] | GAMR [b] | DSRF-M |\n| -------- | ------------- | ------ | -------- | ---------------- | -------- | ------ |\n| SVRT-500 | 54/85         | 53/85  | 58/64    | 63/95            | 78/98    | 86/100 |\n| SVRT-1k  | 57/96         | 58/90  | 58/64    | 69/98            | 83/99    | 92/100 |\n| SVRT-5k  | 78/100        | 68/97  | 63/68    | 88/100           | 94/100   | 98/100 |\n| SVRT-10k | 84/100        | 75/97  | 67/67    | 92/100           | 95/100   | 99/100 |\n\nTable A. Sample efficiency analysis on the SVRT dataset. \n\n \n\nWe will add this data efficiency analysis into the in the final manuscript and the supplementary materials accompanying the publication. \n\n \n\n[a] Webb, T. W., Sinha, I., and Cohen, J. D. Emergent symbols through binding in external memory. In ICLR, 2021. \n\n[b] Vaishnav, M. and Serre, T. Gamr: A guided attention model for (visual) reasoning. In ICLR, 2023. \n\n[c] He, Kaiming, et al. \"Deep residual learning for image recognition.\" *CVPR,* 2016. \n\n[d] Vaishnav, Mohit, et al. \"Understanding the computational demands underlying visual reasoning.\" *Neural Computation* 34.5 (2022): 1075-1099. \n\n \n\n**W3: Ambiguity in OOD evaluation** \n\nThank you for your comments. We would like to clarify that OOD (Out-of-Distribution) may refer to different levels of distribution shift. \n\n- **Distribution shifts due to novel rule-attribute combinations on PGM and Unicode datasets****.** \n\n- We have conducted experiments on OOD settings on Unicode Analogy [9], where all the symbols in the training set do not appear in the test set. The results are reported in Table 3 and the related discussions can be found at Line 237-250. \n\n- In addition, we have conducted experiments on OOD settings on PGM [6], Interpolation that evaluates generalization to intermediate attribute values, and Extrapolation that tests the model’s ability to reason beyond the observed attribute range. The results are reported in Table 4 and the related discussions can be found at Line 251-260. \n\n- Furthermore, we provide the experimental results on held-out settings of PGM in the table below, *i.e.*, PGM-H.O.P (Held-out Attribute Pairs), PGM-H.O.TP (Held-out Triple Pairs), PGM-H.O.T (Held-out Triples), PGM-H.O.LT (Held-out Line-Type) and PGM-H.O.SC (Held-out Shape-Color) settings, each testing the model’s ability to generalize to novel combinations of attributes, unseen pairs or individual triples, and new attribute-object pairings absent during training. Our models perform best across almost all settings. \n\n|                     | PGM-N | PGM-I | PGM-E | PGM-H.O.P | PGM-H.O.TP | PGM-H.O.T | PGM-H.O.LT | PGM-H.O.SC |\n| ------------------- | ----- | ----- | ----- | --------- | ---------- | --------- | ---------- | ---------- |\n| ARII [a]            | 88.0  | 72.0  | 29.0  | 50.0      | 64.1       | 32.1      | 16.0       | 12.7       |\n| Slot-Abstractor [b] | 91.5  | 91.6  | 39.3  | 63.3      | 78.3       | 20.4      | 16.7       | 14.3       |\n| DSRF-M              | 99.5  | 84.5  | 27.4  | 65.7      | 78.8       | 31.3      | 17.4       | 16.7       |\n| DSRF-L              | 99.8  | 87.3  | 31.5  | 67.7      | 82.3       | 34.2      | 18.9       | 17.8       |\n\nTable B. Comparisons on PGM OOD regimes. \n\n \n\n- Distribution shifts due to novel samples on RAVENs \n\nThe OOD settings across I-RVN, O-RVN, and RVN-FAIR involve shifts in image distributions and answer choice generation strategies, testing novel samples while the underlying rule-attribute combinations remain largely consistent. Under these OOD settings, our DSRFs significantly outperforms compared methods, as shown in Table 2. \n\n \n\nWe acknowledge that the OOD settings in PGM [6] and Unicode [9] are more challenging than OOD settings on RAVENs. Nevertheless, our model demonstrates strong performance under these OOD regimes, as reported in Tables 3 and 4, showing that DSRF is capable of generalizing beyond memorized rule structures and adapting to new reasoning patterns. \n\n \n\nWe acknowledge the current ambiguity in defining out-of-distribution (OOD) evaluation settings. For the final version, we will rigorously specify the OOD criteria for each benchmark (RAVENs [7,8,18], PGM [6], and Unicode [9]), explicitly delineating their distinct characteristics. \n\n \n\n**Q1: Has DSRF been evaluated under held-out settings of PGM or RAVEN?** \n\nIn the original manuscript, we evaluate DSRF under two OOD settings of the PGM dataset: Interpolation and Extrapolation. Following your suggestion, we have additionally provided results on **held-out settings of PGM** [6] as shown in the reply to W3 above. To our best knowledge, no held-out settings were defined for RAVENs [7, 8, 18]. \n\n \n\n**Q2: Non-matrix abstract visual reasoning such as Bongard problem** \n\nYes, the core components of DSRF are general and can be adapted to other forms of abstract visual reasoning, including non-matrix tasks like the Bongard problems. \n\n- **Adaptation to Bongard Problems** \n\nSpecifically, the DDCP block only requires a set of context-target pairs and does not rely on any fixed spatial layout. Similarly, the MVRP can be applied to grouped features based on visual attributes rather than grid positions. To adapt DSRF to Bongard problems, one may treat the positive or negative example sets as a separate context-to-target reasoning branch and apply DDCP to extract the reasoning patterns. \n\n- **Evaluation of** **Bongard problems** \n\nFollowing your comments, we add the experimental results of DSRF on Bongard-OpenWorld [c]. \n\n \n\n|      | GPT-4 [d] | SNAIL [e] | DSRF-S | DSRF-M | DSRF-L |\n| ---- | --------- | --------- | ------ | ------ | ------ |\n| Acc. | 63.3      | 64.0      | 64.3   | 65.2   | 66.1   |\n\n**Table C.** Comparisons on **Bongard problems****.** \n\n \n\nThe results of GPT-4 [d] and SNAIL [e] are obtained from [c]. We evaluate DSRFs following the same evaluation protocol [c]. DSRFs outperform the compared methods on Bongard problems, even the large language model like GPT-4 [d]. \n\n \n\nWe will update the results and the related discussions in the final manuscript. \n\n \n\n[c] Wu, Rujie, et al. \"Bongard-openworld: Few-shot reasoning for free-form visual concepts in the real world.\" arXiv preprint arXiv:2310.10207 (2023). \n\n[d] Bubeck, Sébastien, et al. \"Sparks of artificial general intelligence: Early experiments with gpt-4.\" arXiv preprint arXiv:2303.12712 (2023). \n\n[e] Mishra, Nikhil, et al. \"A Simple Neural Attentive Meta-Learner.\" ICLR 2018."}, {"review_id": "74BV3Vs37J", "reviewer": "Reviewer_UaAG", "summary": "The core breakthrough of DSRF is to solve the static architecture defects of HP²AI and other models through width expansion (MVRP) and dynamic domain adaptation (DDCP), and significantly improve the performance in OOD scenarios and complex rule tasks, but at a higher computational cost.", "questions": "1. In Table 4 and Table 5, how does the DSRF-S model perform? \n2. In ablation experiments, how much accuracy loss will be caused by the alternative scheme of DDCP Gram matrix (such as covariance matrix) ?", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strength\n\n1. The experiments contains many baselines and datasets.\n\n2. The author analyzes the failed cases in the appendix.\n\nWeakness\n\n1. Although many models have been compared in the experiment, there are few models (10M~25M) with the same size as DSRF-S or DSRF-M as the baseline. Therefore, it is difficult to conclude that the improvement of model capability is due to the author's special model design method or the growth of model parameters.\n\n2. In terms of computing efficiency, it is a pity that the lightweight scheme was not discussed.", "was_revised": false, "final_justification": "", "rebuttal": "**W1: Performance gain from model design or model growth****?** \n\nThank you for your insightful comments. The two principal design objectives of this work, as emphasized in the title, are dynamic adaptability and scalability. Specifically, we aim to develop a scalable abstract visual reasoning framework while effectively tackling the challenge of overfitting. \n\n- **Simply stacking reasoning modules would lead to overfitting** \n\nAs noted in the original PredRNet [13] and HPAI [17] studies, stacking deep reasoning modules frequently induces overfitting, despite aiming to enhance reasoning through additional blocks. \n\n| PredRNet [13]     | O-RVN     | I-RVN     | RVN-F     |\n| ----------------- | --------- | --------- | --------- |\n| K=1               | 94.6      | 95.0      | 95.8      |\n| K=2               | 95.5      | 96.4      | 96.5      |\n| K=3               | 95.8      | 97.1      | 96.5      |\n| K=4               | 96.0      | 96.8      | 94.8      |\n| **HPAI** **[17]** | **O-RVN** | **I-RVN** | **RVN-F** |\n| K=1               | 98.1      | 98.6      | 98.3      |\n| K=2               | 98.4      | 99.1      | 98.3      |\n| K=3               | 98.8      | 99.4      | 98.6      |\n| K=4               | 98.0      | 99.0      | 98.2      |\n\nTable A. Experimental results of stacking K reasoning blocks in PredRNet [13] and HPAI [17]. \n\nAs shown above, both PredRNet [13] and HPAI [17] exhibit performance saturation or marginal degradation beyond three blocks, revealing inherent scalability constraints and depth-induced overfitting tendencies. These observations align with our motivation to pursue horizontal scalability through multi-view decomposition rather than relying on deeper stacking. \n\n- **Our scaled-up models maintain generalization** \n\nAs shown in Tables 1–3, scaled-up models (DSRF-M/L) consistently outperform smaller variants (DSRF-S/M) on both RAVEN [7,8,18] and Unicode [9] benchmarks. We acknowledge that DSRF falls within a relatively large parameter range (10M–40M), but our scaled-up architectures successfully learn latent rule representations while preserving robust generalization capabilities across diverse task distributions. \n\nThis robustness is attributed to the novel architecture of MVRP, DDCP and MRM. Each view is processed independently through modular DDCP–MRM branches, which mitigates overfitting by encouraging localized, attribute-sensitive reasoning. The DDCP block promotes relational comparisons instead of direct memorization, while the MVRP introduces compositional constraints that prevent the model from relying on shortcut patterns. Together, these mechanisms guide the model to learn transferable rule structures, allowing larger variants to benefit from increased capacity without overfitting. \n\n- **Ablation shows the effectiveness of designed modules.** \n\nTo assess the individual contribution of our core modules, we provide detailed ablation studies in Table 6. The ablations show that removing designed components leads to substantial performance degradation, even under the same model scale. In addition, in Table 7, we show that replacing the reasoning module of state-of-the-art models by DSRF-S and DSRF-M significantly improves the reasoning accuracy. All these ablations support our claim that the improvement of performance comes from the proposed design rather than simply growing models. \n\n \n\nWe will further clarify this point in the final manuscript and provide more justifications.  \n\n \n\n**W2: Lightweight scheme of DSRF** \n\nThank you for your insightful comments. Although the original manuscript did not specifically investigate lightweight implementations, our framework inherently supports efficient deployment through its modular architecture, enabling straightforward adaptation to resource-constrained scenarios. \n\n- **Lightweight scheme by adjusting MVRP hyperparameters.** \n\nIn particular, the MVRP allows for controlling the channel dimensions of feature mappings within each view. By decreasing the dimensionality of each mapped view, the model can be scaled down to more lightweight variants with lower memory and FLOPs, while still maintaining core reasoning capabilities. \n\n- **Results of lightweight DSRFs** \n\nBy reducing the channel dimensions of each view by half, we can construct a lightweight variant of DSRF-S and DSRF-M, denoted as DSRF-S-Light and DSRF-M-Light. We conduct comparison experiments on three RAVEN datasets and three PGM settings (PGM-N, PGM-I, PGM-E). The lightweight variants achieve substantial reductions in model size and computational cost (GFLOPs) while maintaining reasonable accuracy. \n\n \n\n|              | O-RVN | I-RVN | RVN-F | PGM-N | PGM-I | PGM-E | GFLOPs | Model Size (M) |\n| ------------ | ----- | ----- | ----- | ----- | ----- | ----- | ------ | -------------- |\n| DSRF-S-Light | 98.5  | 98.5  | 98.6  | 99.1  | 81.7  | 24.8  | 4.06   | 4.96           |\n| DSRF-S       | 98.7  | 98.6  | 98.8  | 99.3  | 82.4  | 25.2  | 10.10  | 11.64          |\n| DSRF-M-Light | 98.8  | 98.9  | 98.8  | 99.3  | 83.1  | 26.1  | 5.11   | 8.72           |\n| DSRF-M       | 99.1  | 99.4  | 99.0  | 99.5  | 84.5  | 27.4  | 13.92  | 23.86          |\n\nTable B. Comparisons with lightweight DSRFs. \n\n \n\nWe will supplement the lightweight schemes and related experimental results in the final manuscript and the supplementary materials accompanying the publication.  \n\n \n\n**Q1**: **In Table 4 and Table 5, how does the DSRF-S model perform?** \n\nWe supplement the results of DSRF-S as follows. \n\n|        | PGM-N | PGM-I | PGM-E | RVP  |\n| ------ | ----- | ----- | ----- | ---- |\n| DSRF-S | 99.3  | 82.4  | 25.2  | 85.4 |\n| DSRF-M | 99.5  | 84.5  | 27.4  | 87.7 |\n\nTable C. Evaluation of DSRF-S and DSRF-M on PGM [6] and RVP [37] datasets. \n\n \n\nWhile DSRF-S demonstrates inferior performance relative to DSRF-M, it maintains competitive advantages over alternative baseline models, consistent with our expectations. \n\n \n\n**Q2: Performance loss by replacing DDCP Gram matrix** **with an alternative scheme** \n\nThank you for the question. We conduct additional ablation experiments where the Gram matrix in DDCP is replaced with a covariance matrix. This modification results in a performance drop of approximately 0.4% on three RAVEN datasets and 0.6% on three PGM settings (PGM-N, PGM-I, PGM-E), indicating that the Gram matrix is more effective than the covariance matrix. \n\n \n\n|                 | O-RVN | I-RVN | RVN-F | PGM-N | PGM-I | PGM-E |\n| --------------- | ----- | ----- | ----- | ----- | ----- | ----- |\n| DDCP-Gram       | 99.1  | 99.4  | 99.0  | 99.5  | 84.5  | 27.4  |\n| DDCP-Covariance | 98.8  | 99.0  | 98.6  | 99.4  | 83.6  | 26.8  |\n\nTable D Comparisons between Gram matrix and covariance matrix in DDCP. \n\n \n\nWe will supplement this ablation in the supplementary materials accompanying the publication."}, {"review_id": "8U4yoBaElt", "reviewer": "Reviewer_Yeks", "summary": "The paper presents a framework called the Dynamic and Scalable Reasoning Framework (DSRF) aimed at solving Raven’s Progressive Matrices (RPMs), a benchmark for abstract visual reasoning (AVR). The core contributions of the paper lie in two main components: the Multi-View Reasoning Pyramid (MVRP), which enables the model to scale by expanding the network across multiple views to capture complex attribute combinations, and the Dynamic Domain-Contrast Prediction (DDCP) block, which utilizes a gating mechanism and Gram matrices to dynamically handle domain shifts and task-specific relationships. The authors argue that DSRF addresses key challenges in AVR, particularly scalability and adaptability, by widening the network rather than deepening it. Extensive experiments on six AVR tasks demonstrate DSRF’s superior performance over state-of-the-art models in various settings.", "questions": "1.The author claims that each view in the MVRP focuses on distinct attribute combinations. How is this enforced or encouraged during training? Is there any orthogonality loss, entropy regularization, or clustering analysis to show that views specialize on different features?\n\n2.The scalability of DSRF is presented as a strength, yet the performance improvement from DSRF-M to DSRF-L is marginal given the increase in computational cost. Can the authors provide more analysis or visualization to justify whether the scalability is practically meaningful?\n\n3.The argument that deeper reasoning networks tend to overfit is used as a central motivation for the proposed framework. However, no empirical evidence is provided to support this claim. For example, what happens to performance when increasing the depth of a PredRNet or HP2AI baseline beyond 4 blocks?\n\n4.Including results from representative LLMs on AVR would strengthen the empirical evaluation and provide a clearer comparison.\n\n5.The paper introduces MVRP, DDCP, and GARB as hierarchically organized components, yet presents them under the same heading level. Could the authors clarify their structural relationships more explicitly, perhaps by adjusting the heading hierarchy to better reflect their conceptual roles?", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n1.Competitive Performance: The proposed DSRF consistently outperforms prior methods, including recent state-of-the-art models, with noticeable margins, especially in challenging OOD settings.\n\n2.Modularity and Transferability: The fact that DSRF can be plugged into different perception backbones and still improve performance shows the potential generality and applicability of the method.\n\nWeaknesses:\n\n1.Limited Novelty: Much of the underlying technology, such as the pyramid structure and gated attention mechanisms, relies on well-established deep learning techniques. While the combination of these methods is valid, the novelty of the contributions remains relatively limited. The paper does not provide sufficient groundbreaking innovations to distinguish it from other recent works in AVR.\n\n2.Insufficient analysis of scalability: While the scalability claim is central to the paper, the marginal performance gain from DSRF-M to DSRF-L is relatively small (e.g., 97.3% to 97.7% in Table 2), despite a considerable increase in FLOPs and parameters. The paper lacks a deeper justification of this trade-off and whether the scalability is truly meaningful in practice.\n\n3.Unsubstantiated Overfitting Claim: The authors argue that stacking deep reasoning modules in existing models often leads to overfitting. However, no experimental evidence or quantitative comparison is provided to support this claim.\n\n4.Lack of Comparison with LLMs: Although the authors state that AVR has become a standard benchmark for evaluating the reasoning capabilities of large language models (LLMs), the experimental section does not include any comparison with such models. This omission weakens the paper’s claim regarding the effectiveness and competitiveness of DSRF in the broader context of reasoning benchmarks.\n\n5.Inconsistent Structural Presentation: The proposed framework introduces MVRP, DDCP, and GARB as distinct module levels, yet presents them under the same heading tier in the paper’s organization. This parallel presentation of conceptually hierarchical components may lead to confusion about their structural relationships and respective roles within the architecture.", "was_revised": true, "final_justification": "After reviewing the authors' rebuttal, I find that they have addressed several of my key concerns, particularly regarding the scalability analysis, specialization of views in MVRP, and the empirical evidence for their claims about overfitting in deeper reasoning networks. The additional clarifications and supplementary results, including comparisons to representative LLMs, have strengthened the empirical evaluation and reinforced the practical relevance of the proposed framework. While some aspects of novelty remain incremental, the methodological integration is well-motivated and demonstrates consistent and competitive performance across diverse AVR tasks. Given these clarifications and the solid experimental results, I now view this as a technically sound and valuable contribution to the AVR community, and I recommend acceptance.", "rebuttal": "**W1: While combination is valid, novelty remains relatively limited.** \n\nWhile our framework builds upon certain established deep learning components, its core design is fundamentally different from prior architectures. \n\n- **MVRP differs significantly from spatial pyramids.** \n\nMVRP diverges from spatial or scale-based architectures prevalent in vision models [a,b]. It adopts a *channel-wise hierarchical organization*, where each view represents a distinct feature space. This design integrates DDCPs for dynamic reasoning adjustments based on context–target contrasts and MRM for progressive rule integration. Together, they form a *hierarchical reasoning framework* that explicitly mirrors compositional structure of latent rules. Our DSRF systematically enumerates rule combinations in a *principled and scalable* manner, enabling comprehensive coverage of complex attribute interactions while maintaining generalizability. \n\n- **DDCP enables dynamic reasoning.** \n\nDDCP enables dynamic reasoning behaviors by modeling context-target differences via gated attention guided by Gram matrices. This design allows the model to adapt its reasoning pathway based on specific context–target configuration of each sample, rather than relying on static mappings. DDCP learns dynamic mappings that continuously adapt to evolving context-target relationships, enabling robust generalization under distribution shift and novel rule configurations. \n\n- **DSRF: Novel** **dynamic and scalable reasoning framework** \n\nThe integration of MVRP, DDCP and MRM forms a novel dynamic and scalable framework to reason for complex abstract rules. Moreover, it is adaptive and generalizable, as evidenced in OOD experiments on RAVENs [7, 8, 18], Unicode [9] and PGM [6] in Table 2-4, setting our approach apart from existing static or handcrafted reasoning strategies in abstract visual reasoning. \n\n \n\nWe believe DSRF provides a principled and extensible framework for scaling up reasoning capacity without overfitting. We will emphasize these distinctions more clearly in the final version. \n\n \n\n[a] Lin, Tsung-Yi, et al. \"Feature pyramid networks for object detection.\" CVPR, 2017. \n\n[b] Yang, Guoyu, et al. \"Asymptotic feature pyramid network for labeling pixels and regions.\" TCSVT, 34(9), 2024: 7820-7829. \n\n \n\n**W2/Q2: Scalability analysis** \n\nThank you for the insightful question. \n\n- Performance saturation in scaling DSRF \n\nThe relatively small gain in Table 2, from 97.3% to 97.7%, is primarily due to the ceiling effect, where top-performing models all achieve high accuracy on RAVENs. Notably, DSRF-S significantly boosts the previously best-performing model, PredRNet [13], from 94.3% to 96.7%, while DSRF-M and DSRF-L further improve to 97.3% and 97.7%, all three significantly outperforming baselines despite the ceiling effect and demonstrating monotonically increasing gains by scaling. \n\n- Consistent performance gains by scaling up DSRFs \n\nTable A compares DSRF-S, DSRF-M and DSRF-L on all 6 RPM datasets. We added the held-out settings of PGM, *i.e.*, PGM-H.O.P (Held-out Attribute Pairs), PGM-H.O.TP (Held-out Triple Pairs), PGM-H.O.T (Held-out Triples), PGM-H.O.LT (Held-out Line-Type) and PGM-H.O.SC (Held-out Shape-Color) settings, each testing the model’s ability to generalize to novel combinations of attributes, unseen pairs or individual triples, and new attribute-object pairings. \n\nScaling up DSRF yields consistent and substantial gains across all scenarios. Notably, under more challenging OOD settings on Unicode [9] and PGM [6], we observe more pronounced improvements, demonstrating that scalability becomes increasingly valuable when the reasoning task is more complex and the domain shift is substantial. \n\n|   |  | DSRF-S | DSRF-M | DSRF-L |\n| - | -| -| -| - |\n| RAVENs [7, 8, 18]  | O-RVN | 98.6   | 99.1   | 99.1   |\n|| I-RVN   | 98.8 | 99.4   | 99.4   |\n|| RVN-F   | 98.8  | 99.0   | 99.1   |\n| RAVENs OOD [7, 8, 18] | O-RVN -> I-RVN | 95.1   | 95.6   | 95.9   |\n|| O-RVN -> RVN-F  | 98.5   | 98.7   | 98.9   |\n|| I-RVN -> O-RVN  | 95.9  | 97.4   | 97.9   |\n|| I-RVN -> RVN-F | 98.2   | 98.7   | 98.9   | \n|| RVN-F -> O-RVN | 97.3 | 97.8   | 98.1   | \n|| RVN-F -> I-RVN  | 95.4  | 95.8   | 96.5   |\n| Unicode [9]   |  | 72.1  | 73.2   | 73.8   |\n| Unicode OOD [9]  | | 34.5   | 35.9   | 37.3   |\n| PGM [6]    | PGM-N | 99.3   | 99.5   | 99.8   |\n|| PGM-I    | 82.4  | 84.5   | 87.3   | \n|| PGM-E    | 25.2 | 27.4   | 31.5   | \n|| PGM-H.O.P    | 63.1 | 65.7   | 67.7   | \n|| PGM-H.O.TP    | 75.7 | 78.8   | 82.3   | \n|| PGM-H.O.T  | 29.3  | 31.3   | 34.2   | \n|| PGM-H.O.LT    | 16.2  | 17.4   | 18.9   | \n|| PGM-H.O.SC    | 16.1  | 16.7   | 17.8   | \n| RVP [37]     |    | 85.4   | 87.7   | 88.8   |\n\nTable A. Comparisons between DSRF-S, DSRF-M, DSRF-L on 6 RPM datasets. \n\n \n\n- Performance-complexity tradeoff analysis. \n\nWhile model scaling yields diminishing returns where near-optimal performance has already been achieved, it remains crucial for tackling harder OOD challenges. As evidenced above, scaled models exhibit enhanced capability in handling more complex cases, advancing toward developing more generalizable AI systems. \n\n- Practical meaning of scalability. \n\nPrevious models typically scale reasoning capacity by stacking reasoning blocks, but generalize poorly [13, 17]. Our goal is not merely to increase model size, but more importantly to **expand reasoning capacity in a structured way while avoiding overfitting**. Specifically, the MVRP increases coverage of compositional rules by distributing reasoning across multiple attribute-based views. The DDCP adapts to varying rule distributions and focuses on relevant context-target differences. These mechanisms systematically scale reasoning capacity and effectively capture the latent rules present in training data while maintaining strong generalization on OOD samples, enabling the model to handle increasingly diverse and difficult reasoning scenarios. \n\n \n\nWe will add more scalability analysis in the final manuscript. \n\n \n\n**W3/Q3: Unsubstantiated overfitting claim:** \n\nAs noted in PredRNet [13] and HPAI [17], stacking reasoning modules often induces overfitting. \n\n| PredRNet [13]  | O-RVN | I-RVN | RVN-F |\n| - | - | - | - | \n|K=1  | 94.6 |  95.0 | 95.8  | \n| K=2  | 95.5 | 96.4  | 96.5  | \n| K=3  | 95.8 | 97.1  | 96.5  | \n| K=4  | 96.0 | 96.8  | 94.8  | \n|**HPAI [17]**  | **O-RVN** | **I-RVN** | **RVN-F**|\n| K=1 | 98.1 | 98.6  | 98.3  |\n| K=2 | 98.4 | 99.1  | 98.3  |\n| K=3 | 98.8 | 99.4  | 98.6  |\n| K=4 | 98.0 | 99.0  | 98.2  | \n\nTable B. Ablation of the number of reasoning blocks K in PredRNet [13] and HPAI [17]. \n\nBoth PredRNet [13] and HPAI [17] exhibit performance saturation or marginal degradation beyond three blocks, revealing inherent scalability constraints and depth-induced overfitting tendencies. These observations align with our motivation to pursue horizontal scalability through multi-view decomposition rather than relying on deep stacking. \n\nWe will further clarify this in the final manuscript. \n\n \n\n**W4/Q4: Lack of comparison with LLMs:** \n\nIn literature, researchers have applied LLMs for AVR tasks [c]. Table C compares DSRF-M with recent LLMs on RAVEN [18], reported by Apple [c]. LLMs exhibit near-chance performance on RAVEN, while dedicated AVR models like DSRF achieve almost perfect performance. \n\n \n\n|   | GPT-4V | Gemini Pro | QWen-VL-Max | LLaVA-1.5-13B | LLaVA-1.6-34B | DSRF-M |\n| - | -| - | - | - | - | -|\n| RAVEN [18] | 0.12  | 0.11| 0.10| 0.10  | 0.10 | 0.99   |\n\nTable C. Comparison to LLMs on RAVEN [18]. \n\n[c] Zhang, Yizhe, et al. \"How Far Are We from Intelligent Visual Deductive Reasoning?.\" ICLR 2024 Workshop: How Far Are We From AGI. \n\n \n\n**W5/Q5: Inconsistent structural presentation****.** \n\nWe will revise the manuscript following your comments. \n\n \n\n**Q1: Each view in MVRP** **captures distinct attribute combinations****?** \n\nThank you for the insightful question. \n\n- **Channel-wise decomposition facilitates feature disentanglement [b]** \n\nAlthough we do not impose explicit constraints such as orthogonality loss or entropy regularization, our model encourages view specialization implicitly through the multi-head view mapping in MVRP. Each view divides the global feature representation into attribute-relevant subspaces. Prior studies have shown that channel-wise decomposition can facilitate feature disentanglement and attribute grouping [d]. We allocate dedicated reasoning branch to each view, allowing different views to attend to different relational patterns. In addition, the subsequent DDCP modules adaptively extract localized reasoning patterns within each view, further reinforcing specialization across views during training. \n\nFollowing your comments, we ablate the case that we add an orthogonality loss as shown in Table D. This results in no performance improvement and may even lead to a slight accuracy drop due to minor conflicts between multiple loss terms. \n\n|  | RAVEN | I-RAVEN | RAVEN-FAIR |\n| - | - | - | - |\n| DSRF-M  | 99.1  | 99.4 | 99.0  |\n| +Orthogonality Loss | 98.9  | 99.2 | 98.9 |\n\nTable D. Comparison to adding orthogonality loss. \n\n \n\n- **Clustering analysis** \n\nSince figures can’t be reported during rebuttal, we compute cosine similarity between the four views' feature maps in DSRF-M's first layer, following [e]. The results in Table E indicate low interview similarity, supporting the emergence of view-wise specialization. \n\n| Sim(v1, v2) | Sim(v1, v3) | Sim(v1, v4) | Sim(v2, v3) | Sim(v2, v4) | Sim(v3, v4) |\n| - | - | - | - | -| - |\n| -0.06 | 0.06  | -0.08  | 0.03 | -0.03 | 0.01 |\n\nTable E. Feature similarity across views. \n\nWe will include t-SNE clustering analysis in the final manuscript to show that each view captures different aspects of the input. \n\n[d] Hu, J., Shen, L., & Sun, G. Squeeze-and-excitation networks. CVPR, 2018, pp. 7132–7141. \n\n[e] Zhao, Wenliang, et al. \"Towards interpretable deep metric learning with structural matching.\" ICCV, 2021."}]

Author rebuttal:

Meta-review: The paper received all borderline accepts post-rebuttal. The AC, unfamiliar with the subfield, reviewed all materials and recommends acceptance as a poster due to reviewer consensus (Bup5, UTPG, UaAG, Yeks) and score increases from Bup5 and Yeks. Please incorporate promised revisions in the camera-ready version.
Decision: Accept (poster)