Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two specific tasks, hindering a deep model to unify its reasoning capability on multiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can improve the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a large-scale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 proving problems. Each proving problem is annotated with a multi-step proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the annotated program sequence for calculation problems. Naturally, we also present a unified multi-task Geometric Transformer framework, Geoformer, to tackle calculation and proving problems simultaneously in the form of sequence generation, which finally shows the reasoning ability can be improved on both two tasks by unifying formulation. Furthermore, we propose a Mathematical Expression Pretraining (MEP) method that aims to predict the mathematical expressions in the problem solution, thus improving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geoformer obtains state-of-the-art performance by outperforming task-specific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.

This paper presents the development of an AI-based language learning platform Revita. It is a freely available intelligent online tutor, developed to support learners of multiple languages, from low-intermediate to advanced levels. It has been in pilot use by hundreds of students at several universities, whose feedback and needs are shaping the development. One of the main emerging features of Revita is the introduction of a system of linguistic constructs as the representation of domain knowledge. The system of constructs is developed in close collaboration with experts in language teaching. Constructs define the types of exercises, the content of the feedback, and enable the detailed modeling and evaluation of learning progress.

Neural architecture search (NAS) has brought significant progress in recent image recognition tasks. Most existing NAS methods apply restricted search spaces, which limits the upper-bound performance of searched models. To address this issue, we propose a new search space named MobileNet3-MT. By reducing human-prior knowledge in omni dimensions of networks, MobileNet3-MT accommodates more potential candidates. For searching in this challenging search space, we present an efficient Multi-trial Evolution-based NAS method termed MENAS. Specifically, we accelerate the evolutionary search process by gradually pruning models in the population. Each model is trained with an early stop and replaced by its Lottery Tickets (the explored optimal pruned network).In this way, the full training pipeline of cumbersome networks is prevented and more efficient networks are automatically generated. Extensive experimental results on ImageNet-1K, CIFAR-10, and CIFAR-100 demonstrate that MENAS achieves state-of-the-art performance.

Current math word problem (MWP) solvers are usually Seq2Seq models trained by the (one-problem; one-solution) pairs, each of which is made of a problem description and a solution showing reasoning flow to get the correct answer. However, one MWP problem naturally has multiple solution equations. The training of an MWP solver with (one-problem; one-solution) pairs excludes other correct solutions, and thus limits the generalizability of the MWP solver. One feasible solution to this limitation is to augment multiple solutions to a given problem. However, it is difficult to collect diverse and accurate augment solutions through human efforts. In this paper, we design a new training framework for an MWP solver by introducing a solution buffer and a solution discriminator. The buffer includes solutions generated by an MWP solver to encourage the training data diversity. The discriminator controls the quality of buffered solutions to participate in training. Our framework is flexibly applicable to a wide setting of fully, semi-weakly and weakly supervised training for all Seq2Seq MWP solvers. We conduct extensive experiments on a benchmark dataset Math23k and a new dataset named Weak12k, and show that our framework improves the performance of various MWP solvers under different settings by generating correct and diverse solutions.

End-to-end autonomous driving provides a feasible way to automatically maximize overall driving system performance by directly mapping the raw pixels from a front-facing camera to control signals. Recent advanced methods construct a latent world model to map the high dimensional observations into compact latent space. However, the latent states embedded by the world model proposed in previous works may contain a large amount of task-irrelevant information, resulting in low sampling efficiency and poor robustness to input perturbations. Meanwhile, the training data distribution is usually unbalanced, and the learned policy is hard to cope with the corner cases during the driving process. To solve the above challenges, we present a semantic masked recurrent world model (SEM2), which introduces a latent filter to extract key task-relevant features and reconstruct a semantic mask via the filtered features, and is trained with a multi-source data sampler, which aggregates common data and multiple corner case data in a single batch, to balance the data distribution. Extensive experiments on CARLA show that our method outperforms the state-of-the-art approaches in terms of sample efficiency and robustness to input permutations.

Given that rich information is hidden behind ubiquitous numbers in text, numerical reasoning over text should be an essential skill of AI systems. To derive precise equations to solve numerical reasoning problems, previous work focused on modeling the structures of equations, and has proposed various structured decoders. Though structure modeling proves to be effective, these structured decoders construct a single equation in a pre-defined autoregressive order, potentially placing an unnecessary restriction on how a model should grasp the reasoning process. Intuitively, humans may have numerous pieces of thoughts popping up in no pre-defined order; thoughts are not limited to the problem at hand, and can even be concerned with other related problems. By comparing diverse thoughts and chaining relevant pieces, humans are less prone to errors. In this paper, we take this inspiration and propose CANTOR, a numerical reasoner that models reasoning steps using a directed acyclic graph where we produce diverse reasoning steps simultaneously without pre-defined decoding dependencies, and compare and chain relevant ones to reach a solution. Extensive experiments demonstrated the effectiveness of CANTOR under both fully-supervised and weakly-supervised settings.

Abstract: Motivated by recent developments in optical switching and reconfigurable network design, we study dynamic binary search trees (BSTs) in the matching model. In the classical dynamic BST model, the cost of both link traversal and basic reconfiguration (rotation) is O(1). However, in the matching model, the BST is defined by two optical switches (that represent two matchings in an abstract way), and each switch (or matching) reconfiguration cost is α while a link traversal cost is still O(1). In this work, we propose Arithmetic BST (A-BST), a simple dynamic BST algorithm that is based on dynamic Shannon-Fano-Elias coding, and show that A-BST is statically optimal for sequences of length Ω(nαlogα) where n is the number of nodes (keys) in the tree. Abstract: The dynamic optimality conjecture, postulating the existence of an O(1)-competitive online algorithm for binary search trees (BSTs), is among the most fundamental open problems in dynamic data structures.

It has been a long-standing dream to design artificial agents that explore their environment efficiently via intrinsic motivation, similar to how children perform curious free play. Despite recent advances in intrinsically motivated reinforcement learning (RL), sample-efficient exploration in object manipulation scenarios remains a significant challenge as most of the relevant information lies in the sparse agent-object and object-object interactions. In this paper, we propose to use structured world models to incorporate relational inductive biases in the control loop to achieve sample-efficient and interaction-rich exploration in compositional multi-object environments. By planning for future novelty inside structured world models, our method generates free-play behavior that starts to interact with objects early on and develops more complex behavior over time. Instead of using models only to compute intrinsic rewards, as commonly done, our method showcases that the self-reinforcing cycle between good models and good exploration also opens up another avenue: zero-shot generalization to downstream tasks via model-based planning. After the entirely intrinsic task-agnostic exploration phase, our method solves challenging downstream tasks such as stacking, flipping, pick & place, and throwing that generalizes to unseen numbers and arrangements of objects without any additional training.

Recent work has shown that asking language models to generate reasoning steps improves performance on many reasoning tasks. When moving beyond prompting, this raises the question of how we should supervise such models: outcome-based approaches which supervise the final result, or process-based approaches which supervise the reasoning process itself? Differences between these approaches might naturally be expected not just in final-answer errors but also in reasoning errors, which can be difficult to detect and are problematic in many real-world domains such as education. We run the first comprehensive comparison between process- and outcome-based approaches trained on a natural language task, GSM8K. We find that pure outcome-based supervision produces similar final-answer error rates with less label supervision. However, for correct reasoning steps we find it necessary to use process-based supervision or supervision from learned reward models that emulate process-based feedback. In total, we improve the previous best results from 16.8% $\to$ 12.7% final-answer error and 14.0% $\to$ 3.4% reasoning error among final-answer-correct solutions.

Semantic communication is viewed as a revolutionary paradigm that can potentially transform how we design and operate wireless communication systems. However, despite a recent surge of research activities in this area, the research landscape remains limited. In this tutorial, we present the first rigorous vision of a scalable end-to-end semantic communication network that is founded on novel concepts from artificial intelligence (AI), causal reasoning, and communication theory. We first discuss how the design of semantic communication networks requires a move from data-driven networks towards knowledge-driven ones. Subsequently, we highlight the necessity of creating semantic representations of data that satisfy the key properties of minimalism, generalizability, and efficiency so as to do more with less. We then explain how those representations can form the basis a so-called semantic language. By using semantic representation and languages, we show that the traditional transmitter and receiver now become a teacher and apprentice. Then, we define the concept of reasoning by investigating the fundamentals of causal representation learning and their role in designing semantic communication networks. We demonstrate that reasoning faculties are majorly characterized by the ability to capture causal and associational relationships in datastreams. For such reasoning-driven networks, we propose novel and essential semantic communication metrics that include new "reasoning capacity" measures that could go beyond Shannon's bound to capture the convergence of computing and communication. Finally, we explain how semantic communications can be scaled to large-scale networks (6G and beyond). In a nutshell, we expect this tutorial to provide a comprehensive reference on how to properly build, analyze, and deploy future semantic communication networks.