Mathematical Reasoning

Counterfactual reasoning a fundamental aspect of human cognition involves contemplating alternatives to established facts or past events significantly enhancing our abilities in planning and decision-making. In light of the advancements in current multi-modal large language models we explore their effectiveness in counterfactual reasoning. To facilitate this investigation we introduce a novel dataset C-VQA specifically designed to examine the counterfactual reasoning capabilities of modern multi-modal large language models. This dataset is constructed by infusing original questions with counterfactual presuppositions spanning various types such as numerical and boolean queries. It encompasses a mix of real and synthetic data representing a wide range of difficulty levels. Our thorough evaluations of contemporary vision-language models using this dataset have revealed substantial performance drops with some models showing up to a 40% decrease highlighting a significant gap between current models and human-like vision reasoning capabilities. We hope our dataset will serve as a vital benchmark for evaluating the counterfactual reasoning capabilities of models. Code and dataset are publicly available at https://bzhao.me/C-VQA/.

Solving complex visual tasks such as "Who invented the musical instrument on the right?" involves a composition of skills: understanding space recognizing instruments and also retrieving prior knowledge. Recent work shows promise by decomposing such tasks using a large language model (LLM) into an executable program that invokes specialized vision models. However generated programs are error-prone: they omit necessary steps include spurious ones and are unable to recover when the specialized models give incorrect outputs. Moreover they require loading multiple models incurring high latency and computation costs. We propose Visual Program Distillation (VPD) an instruction-tuning framework that produces a vision-language model (VLM) capable of solving complex visual tasks with a single forward pass. VPD distills the reasoning ability of LLMs by using them to sample multiple candidate programs which are then executed and verified to identify the correct one. It translates each correct program into a language description of the reasoning steps which are then distilled into a VLM. Extensive experiments show that VPD improves the VLM's ability to count understand spatial relations and reason compositionally. Our VPD-trained PaLI-X outperforms all prior VLMs achieving state-of-the-art performance across complex vision tasks including MMBench OK-VQA A-OKVQA TallyQA POPE and Hateful Memes. An evaluation with human annotators also confirms that VPD improves model response factuality and consistency. Finally experiments on content moderation demonstrate that VPD is also helpful for adaptation to real-world applications with limited data.

Understanding data visualizations like charts and plots requires reasoning about both visual elements and numerics. Although strong in extractive questions current chart visual question answering (chart VQA) models suffer on complex reasoning questions. In this work we address the lack of reasoning ability by data augmentation. We leverage Large Language Models (LLMs) which have shown to have strong reasoning ability as an automatic data annotator that generates question-answer annotations for chart images. The key innovation in our method lies in the Synthesize Step-by-Step strategy: our LLM-based data generator learns to decompose the complex question into step-by-step sub-questions (rationales) which are then used to derive the final answer using external tools i.e. Python. This step-wise generation procedure is trained on synthetic data generated using a template-based QA generation pipeline. Experimental results highlight the significance of the proposed step-by-step generation. By training with the LLM-augmented data (LAMENDA) we significantly enhance the chart VQA models achieving the state-of-the-art accuracy on the ChartQA and PlotQA datasets. In particular our approach improves the accuracy of the previous state-of-the-art approach from 38% to 54% on the human-written questions in the ChartQA dataset which needs strong reasoning. We hope our work underscores the potential of synthetic data and encourages further exploration of data augmentation using LLMs for reasoning-heavy tasks.

Generalized Category Discovery (GCD) aims to identify a mix of known and novel categories within unlabeled data sets providing a more realistic setting for image recognition. Essentially GCD needs to remember existing patterns thoroughly to recognize novel categories. Recent state-of-the-art method SimGCD transfers the knowledge from known-class data to the learning of novel classes through debiased learning. However some patterns are catastrophically forgot during adaptation and thus lead to poor performance in novel categories classification. To address this issue we propose a novel learning approach LegoGCD which is seamlessly integrated into previous methods to enhance the discrimination of novel classes while maintaining performance on previously encountered known classes. Specifically we design two types of techniques termed as \underline L ocal \underline E ntropy Re\underline g ularization (LER) and Dual-views Kullback-Leibler divergence c\underline o nstraint (DKL). The LER optimizes the distribution of potential known class samples in unlabeled data thus ensuring the preservation of knowledge related to known categories while learning novel classes. Meanwhile DKL introduces Kullback-Leibler divergence to encourage the model to produce a similar prediction distribution of two view samples from the same image. In this way it successfully avoids mismatched prediction and generates more reliable potential known class samples simultaneously. Extensive experiments validate that the proposed LegoGCD effectively addresses the known category forgetting issue across all datasets e.g. delivering a 7.74% and 2.51% accuracy boost on known and novel classes in CUB respectively. Our code is available at: https://github.com/Cliffia123/LegoGCD.

While large multimodal models (LMMs) have achieved remarkable progress generating pixel-level masks for image reasoning tasks involving multiple open-world targets remains a challenge. To bridge this gap we introduce PixelLM an effective and efficient LMM for pixel-level reasoning and understanding. Central to PixelLM are a novel lightweight pixel decoder and a comprehensive segmentation codebook. The decoder efficiently produces masks from the hidden embeddings of the codebook tokens which encode detailed target-relevant information. With this design PixelLM harmonizes with the structure of popular LMMs and avoids the need for additional costly segmentation models. Furthermore we propose a token fusion method to enhance the model's ability to differentiate between multiple targets leading to substantially improved mask quality. To advance research in this area we construct MUSE a high-quality multi-target reasoning segmentation benchmark. PixelLM excels across various pixel-level image reasoning and understanding tasks outperforming well-established methods in multiple benchmarks including MUSE and multi-referring segmentation. Comprehensive ablations confirm the efficacy of each proposed component. All code models and datasets will be publicly available.

This paper addresses the task of video question answering (videoQA) via a decomposed multi-stage modular reasoning framework. Previous modular methods have shown promise with a single planning stage ungrounded in visual content. However through a simple and effective baseline we find that such systems can lead to brittle behavior in practice for challenging videoQA settings. Thus unlike traditional single-stage planning methods we propose a multi-stage system consisting of an event parser a grounding stage and a final reasoning stage in conjunction with an external memory. All stages are training-free and performed using few-shot prompting of large models creating interpretable intermediate outputs at each stage. By decomposing the underlying planning and task complexity our method MoReVQA improves over prior work on standard videoQA benchmarks (NExT-QA iVQA EgoSchema and ActivityNet-QA) with state-of-the-art results and extensions to related tasks (grounded videoQA paragraph captioning).

Recovering the 3D scene geometry from a single view is a fundamental yet ill-posed problem in computer vision. While classical depth estimation methods infer only a 2.5D scene representation limited to the image plane recent approaches based on radiance fields reconstruct a full 3D representation. However these methods still struggle with occluded regions since inferring geometry without visual observation requires (i) semantic knowledge of the surroundings and (ii) reasoning about spatial context. We propose KYN a novel method for single-view scene reconstruction that reasons about semantic and spatial context to predict each point's density. We introduce a vision-language modulation module to enrich point features with fine-grained semantic information. We aggregate point representations across the scene through a language-guided spatial attention mechanism to yield per-point density predictions aware of the 3D semantic context. We show that KYN improves 3D shape recovery compared to predicting density for each 3D point in isolation. We achieve state-of-the-art results in scene and object reconstruction on KITTI-360 and show improved zero-shot generalization compared to prior work. Project page: https://ruili3.github.io/kyn

Social relations have substantial impacts on the potential trajectories of each individual. Modeling these dynamics has been a central solution for more precise and accurate trajectory forecasting. However previous works ignore the importance of `social depth' meaning the influences flowing from different degrees of social relations. In this work we propose HighGraph a graph-based pedestrian relational reasoning method that captures the higher-order dynamics of social interactions. First we construct a collision-aware relation graph based on the agents' observed trajectories. Upon this graph structure we build our core module that aggregates the agent features from diverse social distances. As a result the network is able to model complex social relations thereby yielding more accurate and socially acceptable trajectories. Our HighGraph is a plug-and-play module that can be easily applied to any current trajectory predictors. Extensive experiments with ETH/UCY and SDD datasets demonstrate that our HighGraph noticeably improves the previous state-of-the-art baselines both quantitatively and qualitatively.

In this paper we explore a novel challenging generation task i.e. Handwritten Mathematical Expression Generation (HMEG) from symbolic sequences. Since symbolic sequences are naturally graph-structured data we formulate HMEG as a graph-to-image (G2I) generation problem. Unlike the generation of natural images HMEG requires critic layout clarity for synthesizing correct and recognizable formulas but has no real masks available to supervise the learning process. To alleviate this challenge we propose a novel end-to-end G2I generation pipeline (i.e. graph - layout - mask - image) which requires no real masks or nondifferentiable alignment between layouts and masks. Technically to boost the capacity of predicting detailed relations among adjacent symbols we propose a Less-is-More (LiM) learning strategy. In addition we design a differentiable layout refinement module which maps bounding boxes to pixel-level soft masks so as to further alleviate ambiguous layout areas. Our whole model including layout prediction mask refinement and image generation can be jointly optimized in an end-to-end manner. Experimental results show that our model can generate high-quality HME images and outperforms previous generative methods. Besides a series of ablations study demonstrate effectiveness of the proposed techniques. Finally we validate that our generated images promisingly boosts the performance of HME recognition models through data augmentation. Our code and results are available at: https://github.com/AiArt-HDU/HMEG.

Geometry Problem Solving has drawn growing attention recently due to its application prospects in intelligent education field. However existing methods are still inadequate to meet the needs of practical application suffering from the following limitations: 1) explainability is not ensured which is essential in real teaching scenarios; 2) the small scale and incomplete annotation of existing datasets make it hard for model to comprehend geometric knowledge. To tackle the above problems we propose a novel method called Explainable Geometry Problem Solving (E-GPS). E-GPS first parses the geometric diagram and problem text into unified formal language representations. Then the answer and explainable reasoning and solving steps are obtained by a Top-Down Problem Solver (TD-PS) which innovatively solves the problem from the target and focuses on what is needed. To alleviate the data issues a Bottom-Up Problem Generator (BU-PG) is devised to augment the data set with various well-annotated constructed geometry problems. It enables us to train an enhanced theorem predictor with a better grasp of theorem knowledge which further improves the efficiency of TD-PS. Extensive experiments demonstrate that E-GPS maintains comparable solving performances with fewer steps and provides outstanding explainability.

Sampling from the posterior distribution in latent diffusion models for inverse problems is computationally challenging. Existing methods often rely on Tweedie's first-order moments that tend to induce biased results. Second-order approximations are computationally prohibitive making standard reverse diffusion processes intractable for posterior sampling. This paper presents Second-order Tweedie sampler from Surrogate Loss (STSL) a novel sampler offering efficiency comparable to first-order Tweedie while enabling tractable reverse processes using second-order approximation. Theoretical results reveal that our approach utilizing for the trace of the Hessian with only O(1) compute establishes a lower bound through a surrogate loss and enables a tractable reverse process. We show STSL outperforms SoTA solvers PSLD and P2L by reducing neural function evaluations by 4X and 8X respectively while enhancing sampling quality on FFHQ ImageNet and COCO benchmarks. Moreover STSL extends to text guided image editing and mitigates residual distortions in corrupted images. To our best knowledge this is the first work to offer an efficient second order approximation for solving inverse problems using latent diffusion and editing real world images with corruptions.

Binary neural networks utilize 1-bit quantized weights and activations to reduce both the model's storage demands and computational burden. However advanced binary architectures still incorporate millions of inefficient and nonhardware-friendly full-precision multiplication operations. A&B BNN is proposed to directly remove part of the multiplication operations in a traditional BNN and replace the rest with an equal number of bit operations introducing the mask layer and the quantized RPReLU structure based on the normalizer-free network architecture. The mask layer can be removed during inference by leveraging the intrinsic characteristics of BNN with straightforward mathematical transformations to avoid the associated multiplication operations. The quantized RPReLU structure enables more efficient bit operations by constraining its slope to be integer powers of 2. Experimental results achieved 92.30% 69.35% and 66.89% on the CIFAR-10 CIFAR-100 and ImageNet datasets respectively which are competitive with the state-of-the-art. Ablation studies have verified the efficacy of the quantized RPReLU structure leading to a 1.14% enhancement on the ImageNet compared to using a fixed slope RLeakyReLU. The proposed add&bit-operation-only BNN offers an innovative approach for hardware-friendly network architecture.