We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?

Visual mathematical reasoning, as a fundamental visual reasoning ability, has received widespread attention from the Large Multimodal Models (LMMs) community. Existing benchmarks, such as MathVista and MathVerse, focus more on the result-oriented performance but neglect the underlying principles in knowledge acquisition and generalization. Inspired by human-like mathematical reasoning, we introduce WE-MATH, the first benchmark specifically designed to explore the problem-solving principles beyond end-to-end performance. We meticulously collect and categorize 6.5K visual math problems, spanning 67 hierarchical knowledge concepts and five layers of knowledge granularity. We decompose composite problems into sub-problems according to the required knowledge concepts and introduce a novel four-dimensional metric, namely Insufficient Knowledge (IK), Inadequate Generalization (IG), Complete Mastery (CM), and Rote Memorization (RM), to hierarchically assess inherent issues in LMMs' reasoning process. With WE-MATH, we conduct a thorough evaluation of existing LMMs in visual mathematical reasoning and reveal a negative correlation between solving steps and problem-specific performance. We confirm the IK issue of LMMs can be effectively improved via knowledge augmentation strategies. More notably, the primary challenge of GPT-4o has significantly transitioned from IK to IG, establishing it as the first LMM advancing towards the knowledge generalization stage. In contrast, other LMMs exhibit a marked inclination towards Rote Memorization - they correctly solve composite problems involving multiple knowledge concepts yet fail to answer sub-problems. We anticipate that WE-MATH will open new pathways for advancements in visual mathematical reasoning for LMMs. The WE-MATH data and evaluation code are available at https://github.com/We-Math/We-Math.

Waveflow: Enforcing boundary conditions in smooth normalizing flows with application to fermionic wave functions

In this paper, we introduce four main novelties: First, we present a new way of handling the topology problem of normalizing flows. Second, we describe a technique to enforce certain classes of boundary conditions onto normalizing flows. Third, we introduce the I-Spline bijection, which, similar to previous work, leverages splines but, in contrast to those works, can be made arbitrarily often differentiable. And finally, we use these techniques to create Waveflow, an Ansatz for the one-space-dimensional multi-particle fermionic wave functions in real space based on normalizing flows, that can be efficiently trained with Variational Quantum Monte Carlo without the need for MCMC nor estimation of a normalization constant. To enforce the necessary anti-symmetry of fermionic wave functions, we train the normalizing flow only on the fundamental domain of the permutation group, which effectively reduces it to a boundary value problem.

SELFIES and the future of molecular string representations

Artificial intelligence (AI) and machine learning (ML) are expanding in popularity for broad applications to challenging tasks in chemistry and materials science. Examples include the prediction of properties, the discovery of new reaction pathways, or the design of new molecules. The machine needs to read and write fluently in a chemical language for each of these tasks. Strings are a common tool to represent molecular graphs, and the most popular molecular string representation, SMILES, has powered cheminformatics since the late 1980s. However, in the context of AI and ML in chemistry, SMILES has several shortcomings -- most pertinently, most combinations of symbols lead to invalid results with no valid chemical interpretation. To overcome this issue, a new language for molecules was introduced in 2020 that guarantees 100\% robustness: SELFIES (SELF-referencIng Embedded Strings). SELFIES has since simplified and enabled numerous new applications in chemistry. In this manuscript, we look to the future and discuss molecular string representations, along with their respective opportunities and challenges. We propose 16 concrete Future Projects for robust molecular representations. These involve the extension toward new chemical domains, exciting questions at the interface of AI and robust languages and interpretability for both humans and machines. We hope that these proposals will inspire several follow-up works exploiting the full potential of molecular string representations for the future of AI in chemistry and materials science.

Towards Domain Generalization in Object Detection

Despite the striking performance achieved by modern detectors when training and test data are sampled from the same or similar distribution, the generalization ability of detectors under unknown distribution shifts remains hardly studied. Recently several works discussed the detectors' adaptation ability to a specific target domain which are not readily applicable in real-world applications since detectors may encounter various environments or situations while pre-collecting all of them before training is inconceivable. In this paper, we study the critical problem, domain generalization in object detection (DGOD), where detectors are trained with source domains and evaluated on unknown target domains. To thoroughly evaluate detectors under unknown distribution shifts, we formulate the DGOD problem and propose a comprehensive evaluation benchmark to fill the vacancy. Moreover, we propose a novel method named Region Aware Proposal reweighTing (RAPT) to eliminate dependence within RoI features. Extensive experiments demonstrate that current DG methods fail to address the DGOD problem and our method outperforms other state-of-the-art counterparts.

Spatial-Scale Aligned Network for Fine-Grained Recognition

Existing approaches for fine-grained visual recognition focus on learning marginal region-based representations while neglecting the spatial and scale misalignments, leading to inferior performance. In this paper, we propose the spatial-scale aligned network (SSANET) and implicitly address misalignments during the recognition process. Especially, SSANET consists of 1) a self-supervised proposal mining formula with Morphological Alignment Constraints; 2) a discriminative scale mining (DSM) module, which exploits the feature pyramid via a circulant matrix, and provides the Fourier solver for fast scale alignments; 3) an oriented pooling (OP) module, that performs the pooling operation in several pre-defined orientations. Each orientation defines one kind of spatial alignment, and the network automatically determines which is the optimal alignments through learning. With the proposed two modules, our algorithm can automatically determine the accurate local proposal regions and generate more robust target representations being invariant to various appearance variances. Extensive experiments verify that SSANET is competent at learning better spatial-scale invariant target representations, yielding superior performance on the fine-grained recognition task on several benchmarks.

ROI Pooled Correlation Filters for Visual Tracking

The ROI (region-of-interest) based pooling method performs pooling operations on the cropped ROI regions for various samples and has shown great success in the object detection methods. It compresses the model size while preserving the localization accuracy, thus it is useful in the visual tracking field. Though being effective, the ROI-based pooling operation is not yet considered in the correlation filter formula. In this paper, we propose a novel ROI pooled correlation filter (RPCF) algorithm for robust visual tracking. Through mathematical derivations, we show that the ROI-based pooling can be equivalently achieved by enforcing additional constraints on the learned filter weights, which makes the ROI-based pooling feasible on the virtual circular samples. Besides, we develop an efficient joint training formula for the proposed correlation filter algorithm, and derive the Fourier solvers for efficient model training. Finally, we evaluate our RPCF tracker on OTB-2013, OTB-2015 and VOT-2017 benchmark datasets. Experimental results show that our tracker performs favourably against other state-of-the-art trackers.

Learning Spatial-Aware Regressions for Visual Tracking

In this paper, we analyze the spatial information of deep features, and propose two complementary regressions for robust visual tracking. First, we propose a kernelized ridge regression model wherein the kernel value is defined as the weighted sum of similarity scores of all pairs of patches between two samples. We show that this model can be formulated as a neural network and thus can be efficiently solved. Second, we propose a fully convolutional neural network with spatially regularized kernels, through which the filter kernel corresponding to each output channel is forced to focus on a specific region of the target. Distance transform pooling is further exploited to determine the effectiveness of each output channel of the convolution layer. The outputs from the kernelized ridge regression model and the fully convolutional neural network are combined to obtain the ultimate response. Experimental results on two benchmark datasets validate the effectiveness of the proposed method.

Correlation Tracking via Joint Discrimination and Reliability Learning

For visual tracking, an ideal filter learned by the correlation filter (CF) method should take both discrimination and reliability information. However, existing attempts usually focus on the former one while pay less attention to reliability learning. This may make the learned filter be dominated by the unexpected salient regions on the feature map, thereby resulting in model degradation. To address this issue, we propose a novel CF-based optimization problem to jointly model the discrimination and reliability information. First, we treat the filter as the element-wise product of a base filter and a reliability term. The base filter is aimed to learn the discrimination information between the target and backgrounds, and the reliability term encourages the final filter to focus on more reliable regions. Second, we introduce a local response consistency regular term to emphasize equal contributions of different regions and avoid the tracker being dominated by unreliable regions. The proposed optimization problem can be solved using the alternating direction method and speeded up in the Fourier domain. We conduct extensive experiments on the OTB-2013, OTB-2015 and VOT-2016 datasets to evaluate the proposed tracker. Experimental results show that our tracker performs favorably against other state-of-the-art trackers.

Towards Software Development For Social Robotics Systems

In this paper we introduce the core results of the project on software development for social robotics systems. The usability of maintenance and control features is crucial for many kinds of systems, but in the case of social robotics we also have to take into account that (1) the humanoid robot physically interacts with humans, (2) the conversation with children might have different requirements in comparison to the conversation with adults. The results of our work were implement for the humanoid PAL REEM robot, but their core ideas can be applied for other types of humanoid robots. We developed a web-based solution that supports the management of robot-guided tours, provides recommendations for the users as well as allows for a visual analysis of the data on previous tours.