数学推理

We present VISPROG, a neuro-symbolic approach to solving complex and compositional visual tasks given natural language instructions. VISPROG avoids the need for any task-specific training. Instead, it uses the in-context learning ability of large language models to generate python-like modular programs, which are then executed to get both the solution and a comprehensive and interpretable rationale. Each line of the generated program may invoke one of several off-the-shelf computer vision models, image processing routines, or python functions to produce intermediate outputs that may be consumed by subsequent parts of the program. We demonstrate the flexibility of VISPROG on 4 diverse tasks - compositional visual question answering, zero-shot reasoning on image pairs, factual knowledge object tagging, and language-guided image editing. We believe neuro-symbolic approaches like VISPROG are an exciting avenue to easily and effectively expand the scope of AI systems to serve the long tail of complex tasks that people may wish to perform.

Visual Question Answering (VQA) models often perform poorly on out-of-distribution data and struggle on domain generalization. Due to the multi-modal nature of this task, multiple factors of variation are intertwined, making generalization difficult to analyze. This motivates us to introduce a virtual benchmark, Super-CLEVR, where different factors in VQA domain shifts can be isolated in order that their effects can be studied independently. Four factors are considered: visual complexity, question redundancy, concept distribution and concept compositionality. With controllably generated data, Super-CLEVR enables us to test VQA methods in situations where the test data differs from the training data along each of these axes. We study four existing methods, including two neural symbolic methods NSCL and NSVQA, and two non-symbolic methods FiLM and mDETR; and our proposed method, probabilistic NSVQA (P-NSVQA), which extends NSVQA with uncertainty reasoning. P-NSVQA outperforms other methods on three of the four domain shift factors. Our results suggest that disentangling reasoning and perception, combined with probabilistic uncertainty, form a strong VQA model that is more robust to domain shifts. The dataset and code are released at https://github.com/Lizw14/Super-CLEVR.

We consider the problem of solving LP relaxations of MAP-MRF inference problems, and in particular the method proposed recently in (Swoboda, Kolmogorov 2019; Kolmogorov, Pock 2021). As a key computational subroutine, it uses a variant of the Frank-Wolfe (FW) method to minimize a smooth convex function over a combinatorial polytope. We propose an efficient implementation of this subproutine based on in-face Frank-Wolfe directions, introduced in (Freund et al. 2017) in a different context. More generally, we define an abstract data structure for a combinatorial subproblem that enables in-face FW directions, and describe its specialization for tree-structured MAP-MRF inference subproblems. Experimental results indicate that the resulting method is the current state-of-art LP solver for some classes of problems. Our code is available at pub.ist.ac.at/ vnk/papers/IN-FACE-FW.html.

Post-training quantization (PTQ) is widely regarded as one of the most efficient compression methods practically, benefitting from its data privacy and low computation costs. We argue that an overlooked problem of oscillation is in the PTQ methods. In this paper, we take the initiative to explore and present a theoretical proof to explain why such a problem is essential in PTQ. And then, we try to solve this problem by introducing a principled and generalized framework theoretically. In particular, we first formulate the oscillation in PTQ and prove the problem is caused by the difference in module capacity. To this end, we define the module capacity (ModCap) under data-dependent and data-free scenarios, where the differentials between adjacent modules are used to measure the degree of oscillation. The problem is then solved by selecting top-k differentials, in which the corresponding modules are jointly optimized and quantized. Extensive experiments demonstrate that our method successfully reduces the performance drop and is generalized to different neural networks and PTQ methods. For example, with 2/4 bit ResNet-50 quantization, our method surpasses the previous state-of-the-art method by 1.9%. It becomes more significant on small model quantization, e.g. surpasses BRECQ method by 6.61% on MobileNetV2*0.5.

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers, acting as the prior of the distribution, while the information of the forward model can be granted at the sampling stage. Nonetheless, as the generative process remains in the same high dimensional (i.e. identical to data dimension) space, the models have not been extended to 3D inverse problems due to the extremely high memory and computational cost. In this paper, we combine the ideas from the conventional model-based iterative reconstruction with the modern diffusion models, which leads to a highly effective method for solving 3D medical image reconstruction tasks such as sparse-view tomography, limited angle tomography, compressed sensing MRI from pre-trained 2D diffusion models. In essence, we propose to augment the 2D diffusion prior with a model-based prior in the remaining direction at test time, such that one can achieve coherent reconstructions across all dimensions. Our method can be run in a single commodity GPU, and establishes the new state-of-the-art, showing that the proposed method can perform reconstructions of high fidelity and accuracy even in the most extreme cases (e.g. 2-view 3D tomography). We further reveal that the generalization capacity of the proposed method is surprisingly high, and can be used to reconstruct volumes that are entirely different from the training dataset. Code available: https://github.com/HJ-harry/DiffusionMBIR

One of the classical multi-view geometry problems is the so called P3P problem, where the absolute pose of a calibrated camera is determined from three 2D-to-3D correspondences. Since these solvers form a critical component of many vision systems (e.g. in localization and Structure-from-Motion), there have been significant effort in developing faster and more stable algorithms. While the current state-of-the-art solvers are both extremely fast and stable, there still exist configurations where they break down. In this paper we algebraically formulate the problem as finding the intersection of two conics. With this formulation we are able to analytically characterize the real roots of the polynomial system and employ a tailored solution strategy for each problem instance. The result is a fast and completely stable solver, that is able to correctly solve cases where competing methods fail. Our experimental evaluation shows that we outperform the current state-of-the-art methods both in terms of speed and success rate.

Humans have the innate capability to answer diverse questions, which is rooted in the natural ability to correlate different concepts based on their semantic relationships and decompose difficult problems into sub-tasks. On the contrary, existing visual reasoning methods assume training samples that capture every possible object and reasoning problem, and rely on black-boxed models that commonly exploit statistical priors. They have yet to develop the capability to address novel objects or spurious biases in real-world scenarios, and also fall short of interpreting the rationales behind their decisions. Inspired by humans' reasoning of the visual world, we tackle the aforementioned challenges from a compositional perspective, and propose an integral framework consisting of a principled object factorization method and a novel neural module network. Our factorization method decomposes objects based on their key characteristics, and automatically derives prototypes that represent a wide range of objects. With these prototypes encoding important semantics, the proposed network then correlates objects by measuring their similarity on a common semantic space and makes decisions with a compositional reasoning process. It is capable of answering questions with diverse objects regardless of their availability during training, and overcoming the issues of biased question-answer distributions. In addition to the enhanced generalizability, our framework also provides an interpretable interface for understanding the decision-making process of models. Our code is available at https://github.com/szzexpoi/POEM.

The rapid advances in Vision Transformer (ViT) refresh the state-of-the-art performances in various vision tasks, overshadowing the conventional CNN-based models. This ignites a few recent striking-back research in the CNN world showing that pure CNN models can achieve as good performance as ViT models when carefully tuned. While encouraging, designing such high-performance CNN models is challenging, requiring non-trivial prior knowledge of network design. To this end, a novel framework termed Mathematical Architecture Design for Deep CNN (DeepMAD) is proposed to design high-performance CNN models in a principled way. In DeepMAD, a CNN network is modeled as an information processing system whose expressiveness and effectiveness can be analytically formulated by their structural parameters. Then a constrained mathematical programming (MP) problem is proposed to optimize these structural parameters. The MP problem can be easily solved by off-the-shelf MP solvers on CPUs with a small memory footprint. In addition, DeepMAD is a pure mathematical framework: no GPU or training data is required during network design. The superiority of DeepMAD is validated on multiple large-scale computer vision benchmark datasets. Notably on ImageNet-1k, only using conventional convolutional layers, DeepMAD achieves 0.7% and 1.5% higher top-1 accuracy than ConvNeXt and Swin on Tiny level, and 0.8% and 0.9% higher on Small level.

We introduce algebraic machine reasoning, a new reasoning framework that is well-suited for abstract reasoning. Effectively, algebraic machine reasoning reduces the difficult process of novel problem-solving to routine algebraic computation. The fundamental algebraic objects of interest are the ideals of some suitably initialized polynomial ring. We shall explain how solving Raven's Progressive Matrices (RPMs) can be realized as computational problems in algebra, which combine various well-known algebraic subroutines that include: Computing the Grobner basis of an ideal, checking for ideal containment, etc. Crucially, the additional algebraic structure satisfied by ideals allows for more operations on ideals beyond set-theoretic operations. Our algebraic machine reasoning framework is not only able to select the correct answer from a given answer set, but also able to generate the correct answer with only the question matrix given. Experiments on the I-RAVEN dataset yield an overall 93.2% accuracy, which significantly outperforms the current state-of-the-art accuracy of 77.0% and exceeds human performance at 84.4% accuracy.

Building benchmarks to systemically analyze different capabilities of video question answering (VideoQA) models is challenging yet crucial. Existing benchmarks often use non-compositional simple questions and suffer from language biases, making it difficult to diagnose model weaknesses incisively. A recent benchmark AGQA poses a promising paradigm to generate QA pairs automatically from pre-annotated scene graphs, enabling it to measure diverse reasoning abilities with granular control. However, its questions have limitations in reasoning about the fine-grained semantics in videos as such information is absent in its scene graphs. To this end, we present ANetQA, a large-scale benchmark that supports fine-grained compositional reasoning over the challenging untrimmed videos from ActivityNet. Similar to AGQA, the QA pairs in ANetQA are automatically generated from annotated video scene graphs. The fine-grained properties of ANetQA are reflected in the following: (i) untrimmed videos with fine-grained semantics; (ii) spatio-temporal scene graphs with fine-grained taxonomies; and (iii) diverse questions generated from fine-grained templates. ANetQA attains 1.4 billion unbalanced and 13.4 million balanced QA pairs, which is an order of magnitude larger than AGQA with a similar number of videos. Comprehensive experiments are performed for state-of-the-art methods. The best model achieves 44.5% accuracy while human performance tops out at 84.5%, leaving sufficient room for improvement.