Math-PUMA: Progressive Upward Multimodal Alignment to Enhance Mathematical Reasoning

Multimodal Large Language Models (MLLMs) excel in solving text-based mathematical problems, but they struggle with mathematical diagrams since they are primarily trained on natural scene images. For humans, visual aids generally enhance problem-solving, but MLLMs perform worse as information shifts from textual to visual modality. This decline is mainly due to their shortcomings in aligning images and text. To tackle aforementioned challenges, we propose Math-PUMA, a methodology focused on Progressive Upward Multimodal Alignment. This approach is designed to improve the mathematical reasoning skills of MLLMs through a three-stage training process, with the second stage being the critical alignment stage. We first enhance the language model's mathematical reasoning capabilities with extensive set of textual mathematical problems. We then construct a multimodal dataset with varying degrees of textual and visual information, creating data pairs by presenting each problem in at least two forms. By leveraging the Kullback-Leibler (KL) divergence of next-token prediction distributions to align visual and textual modalities, consistent problem-solving abilities are ensured. Finally, we utilize multimodal instruction tuning for MLLMs with high-quality multimodal data. Experimental results on multiple mathematical reasoning benchmarks demonstrate that the MLLMs trained with Math-PUMA surpass most open-source MLLMs. Our approach effectively narrows the performance gap for problems presented in different modalities.

Sparse Graph Learning with Eigen-gap for Spectral Filter Training in Graph Convolutional Networks

It is now known that the expressive power of graph convolutional neural nets (GCN) does not grow infinitely with the number of layers. Instead, the GCN output approaches a subspace spanned by the first eigenvector of the normalized graph Laplacian matrix with the convergence rate characterized by the "eigen-gap": the difference between the Laplacian's first two distinct eigenvalues. To promote a deeper GCN architecture with sufficient expressiveness, in this paper, given an empirical covariance matrix $\bar{C}$ computed from observable data, we learn a sparse graph Laplacian matrix $L$ closest to $\bar{C}^{-1}$ while maintaining a desirable eigen-gap that slows down convergence. Specifically, we first define a sparse graph learning problem with constraints on the first eigenvector (the most common signal) and the eigen-gap. We solve the corresponding dual problem greedily, where a locally optimal eigen-pair is computed one at a time via a fast approximation of a semi-definite programming (SDP) formulation. The computed $L$ with the desired eigen-gap is normalized spectrally and used for supervised training of GCN for a targeted task. Experiments show that our proposal produced deeper GCNs and smaller errors compared to a competing scheme without explicit eigen-gap optimization.

Towards Geometry Guided Neural Relighting with Flash Photography

Previous image based relighting methods require capturing multiple images to acquire high frequency lighting effect under different lighting conditions, which needs nontrivial effort and may be unrealistic in certain practical use scenarios. While such approaches rely entirely on cleverly sampling the color images under different lighting conditions, little has been done to utilize geometric information that crucially influences the high-frequency features in the images, such as glossy highlight and cast shadow. We therefore propose a framework for image relighting from a single flash photograph with its corresponding depth map using deep learning. By incorporating the depth map, our approach is able to extrapolate realistic high-frequency effects under novel lighting via geometry guided image decomposition from the flashlight image, and predict the cast shadow map from the shadow-encoding transformed depth map. Moreover, the single-image based setup greatly simplifies the data capture process. We experimentally validate the advantage of our geometry guided approach over state-of-the-art image-based approaches in intrinsic image decomposition and image relighting, and also demonstrate our performance on real mobile phone photo examples.

A Self-Attention Joint Model for Spoken Language Understanding in Situational Dialog Applications

Spoken language understanding (SLU) acts as a critical component in goal-oriented dialog systems. It typically involves identifying the speakers intent and extracting semantic slots from user utterances, which are known as intent detection (ID) and slot filling (SF). SLU problem has been intensively investigated in recent years. However, these methods just constrain SF results grammatically, solve ID and SF independently, or do not fully utilize the mutual impact of the two tasks. This paper proposes a multi-head self-attention joint model with a conditional random field (CRF) layer and a prior mask. The experiments show the effectiveness of our model, as compared with state-of-the-art models. Meanwhile, online education in China has made great progress in the last few years. But there are few intelligent educational dialog applications for students to learn foreign languages. Hence, we design an intelligent dialog robot equipped with different scenario settings to help students learn communication skills.

Deep Surface Normal Estimation with Hierarchical RGB-D Fusion

The growing availability of commodity RGB-D cameras has boosted the applications in the field of scene understanding. However, as a fundamental scene understanding task, surface normal estimation from RGB-D data lacks thorough investigation. In this paper, a hierarchical fusion network with adaptive feature re-weighting is proposed for surface normal estimation from a single RGB-D image. Specifically, the features from color image and depth are successively integrated at multiple scales to ensure global surface smoothness while preserving visually salient details. Meanwhile, the depth features are re-weighted with a confidence map estimated from depth before merging into the color branch to avoid artifacts caused by input depth corruption. Additionally, a hybrid multi-scale loss function is designed to learn accurate normal estimation given noisy ground-truth dataset. Extensive experimental results validate the effectiveness of the fusion strategy and the loss design, outperforming state-of-the-art normal estimation schemes.

Deep Graph Laplacian Regularization

We propose to combine the robustness merit of model-based approaches and the learning power of data-driven approaches for image restoration. Specifically, by integrating graph Laplacian regularization as a trainable module into a deep learning framework, we are less susceptible to overfitting than pure CNN-based approaches, achieving higher robustness to small dataset and cross-domain denoising. First, a sparse neighborhood graph is built from the output of a convolutional neural network (CNN). Then the image is restored by solving an unconstrained quadratic programming problem, using a corresponding graph Laplacian regularizer as a prior term. The proposed restoration pipeline is fully differentiable and hence can be end-to-end trained. Experimental results demonstrate that our work avoids overfitting given small training data. It is also endowed with strong cross-domain generalization power, outperforming the state-of-the-art approaches by remarkable margin.

3D Point Cloud Denoising using Graph Laplacian Regularization of a Low Dimensional Manifold Model

3D point cloud - a new signal representation of volumetric objects - is a discrete collection of triples marking exterior object surface locations in 3D space. Conventional imperfect acquisition processes of 3D point cloud - e.g., stereo-matching from multiple viewpoint images or depth data acquired directly from active light sensors - imply non-negligible noise in the data. In this paper, we adopt a previously proposed low-dimensional manifold model for the surface patches in the point cloud and seek self-similar patches to denoise them simultaneously using the patch manifold prior. Due to discrete observations of the patches on the manifold, we approximate the manifold dimension computation defined in the continuous domain with a patch-based graph Laplacian regularizer and propose a new discrete patch distance measure to quantify the similarity between two same-sized surface patches for graph construction that is robust to noise. We show that our graph Laplacian regularizer has a natural graph spectral interpretation, and has desirable numerical stability properties via eigenanalysis. Extensive simulation results show that our proposed denoising scheme can outperform state-of-the-art methods in objective metrics and can better preserve visually salient structural features like edges.

Zoom and Learn: Generalizing Deep Stereo Matching to Novel Domains

Despite the recent success of stereo matching with convolutional neural networks (CNNs), it remains arduous to generalize a pre-trained deep stereo model to a novel domain. A major difficulty is to collect accurate ground-truth disparities for stereo pairs in the target domain. In this work, we propose a self-adaptation approach for CNN training, utilizing both synthetic training data (with ground-truth disparities) and stereo pairs in the new domain (without ground-truths). Our method is driven by two empirical observations. By feeding real stereo pairs of different domains to stereo models pre-trained with synthetic data, we see that: i) a pre-trained model does not generalize well to the new domain, producing artifacts at boundaries and ill-posed regions; however, ii) feeding an up-sampled stereo pair leads to a disparity map with extra details. To avoid i) while exploiting ii), we formulate an iterative optimization problem with graph Laplacian regularization. At each iteration, the CNN adapts itself better to the new domain: we let the CNN learn its own higher-resolution output; at the meanwhile, a graph Laplacian regularization is imposed to discriminatively keep the desired edges while smoothing out the artifacts. We demonstrate the effectiveness of our method in two domains: daily scenes collected by smartphone cameras, and street views captured in a driving car.