Learning From Mistakes Makes LLM Better Reasoner

Large language models (LLMs) recently exhibited remarkable reasoning capabilities on solving math problems. To further improve this capability, this work proposes Learning from Mistakes (LeMa), akin to human learning processes. Consider a human student who failed to solve a math problem, he will learn from what mistake he has made and how to correct it. Mimicking this error-driven learning process, LeMa fine-tunes LLMs on mistake-correction data pairs generated by GPT-4. Specifically, we first collect inaccurate reasoning paths from various LLMs and then employ GPT-4 as a "corrector" to (1) identify the mistake step, (2) explain the reason for the mistake, and (3) correct the mistake and generate the final answer. Experimental results demonstrate the effectiveness of LeMa: across five backbone LLMs and two mathematical reasoning tasks, LeMa consistently improves the performance compared with fine-tuning on CoT data alone. Impressively, LeMa can also benefit specialized LLMs such as WizardMath and MetaMath, achieving 85.4% pass@1 accuracy on GSM8K and 27.1% on MATH. This surpasses the SOTA performance achieved by non-execution open-source models on these challenging tasks. Our code, data and models will be publicly available at https://github.com/microsoft/LEMA.

FFINet: Future Feedback Interaction Network for Motion Forecasting

Motion forecasting plays a crucial role in autonomous driving, with the aim of predicting the future reasonable motions of traffic agents. Most existing methods mainly model the historical interactions between agents and the environment, and predict multi-modal trajectories in a feedforward process, ignoring potential trajectory changes caused by future interactions between agents. In this paper, we propose a novel Future Feedback Interaction Network (FFINet) to aggregate features the current observations and potential future interactions for trajectory prediction. Firstly, we employ different spatial-temporal encoders to embed the decomposed position vectors and the current position of each scene, providing rich features for the subsequent cross-temporal aggregation. Secondly, the relative interaction and cross-temporal aggregation strategies are sequentially adopted to integrate features in the current fusion module, observation interaction module, future feedback module and global fusion module, in which the future feedback module can enable the understanding of pre-action by feeding the influence of preview information to feedforward prediction. Thirdly, the comprehensive interaction features are further fed into final predictor to generate the joint predicted trajectories of multiple agents. Extensive experimental results show that our FFINet achieves the state-of-the-art performance on Argoverse 1 and Argoverse 2 motion forecasting benchmarks.

Closing the Gap Between the Upper Bound and the Lower Bound of Adam's Iteration Complexity

Recently, Arjevani et al. [1] established a lower bound of iteration complexity for the first-order optimization under an $L$-smooth condition and a bounded noise variance assumption. However, a thorough review of existing literature on Adam's convergence reveals a noticeable gap: none of them meet the above lower bound. In this paper, we close the gap by deriving a new convergence guarantee of Adam, with only an $L$-smooth condition and a bounded noise variance assumption. Our results remain valid across a broad spectrum of hyperparameters. Especially with properly chosen hyperparameters, we derive an upper bound of the iteration complexity of Adam and show that it meets the lower bound for first-order optimizers. To the best of our knowledge, this is the first to establish such a tight upper bound for Adam's convergence. Our proof utilizes novel techniques to handle the entanglement between momentum and adaptive learning rate and to convert the first-order term in the Descent Lemma to the gradient norm, which may be of independent interest.

G2-MonoDepth: A General Framework of Generalized Depth Inference from Monocular RGB+X Data

Monocular depth inference is a fundamental problem for scene perception of robots. Specific robots may be equipped with a camera plus an optional depth sensor of any type and located in various scenes of different scales, whereas recent advances derived multiple individual sub-tasks. It leads to additional burdens to fine-tune models for specific robots and thereby high-cost customization in large-scale industrialization. This paper investigates a unified task of monocular depth inference, which infers high-quality depth maps from all kinds of input raw data from various robots in unseen scenes. A basic benchmark G2-MonoDepth is developed for this task, which comprises four components: (a) a unified data representation RGB+X to accommodate RGB plus raw depth with diverse scene scale/semantics, depth sparsity ([0%, 100%]) and errors (holes/noises/blurs), (b) a novel unified loss to adapt to diverse depth sparsity/errors of input raw data and diverse scales of output scenes, (c) an improved network to well propagate diverse scene scales from input to output, and (d) a data augmentation pipeline to simulate all types of real artifacts in raw depth maps for training. G2-MonoDepth is applied in three sub-tasks including depth estimation, depth completion with different sparsity, and depth enhancement in unseen scenes, and it always outperforms SOTA baselines on both real-world data and synthetic data.

Language-driven Open-Vocabulary Keypoint Detection for Animal Body and Face

Current approaches for image-based keypoint detection on animal (including human) body and face are limited to specific keypoints and species. We address the limitation by proposing the Open-Vocabulary Keypoint Detection (OVKD) task. It aims to use text prompts to localize arbitrary keypoints of any species. To accomplish this objective, we propose Open-Vocabulary Keypoint Detection with Semantic-feature Matching (KDSM), which utilizes both vision and language models to harness the relationship between text and vision and thus achieve keypoint detection through associating text prompt with relevant keypoint features. Additionally, KDSM integrates domain distribution matrix matching and some special designs to reinforce the relationship between language and vision, thereby improving the model's generalizability and performance. Extensive experiments show that our proposed components bring significant performance improvements, and our overall method achieves impressive results in OVKD. Remarkably, our method outperforms the state-of-the-art few-shot keypoint detection methods using a zero-shot fashion. We will make the source code publicly accessible.

Adaptive Spatio-Temporal Voxels Based Trajectory Planning for Autonomous Driving in Highway Traffic Flow

Trajectory planning is crucial for the safe driving of autonomous vehicles in highway traffic flow. Currently, some advanced trajectory planning methods utilize spatio-temporal voxels to construct feasible regions and then convert trajectory planning into optimization problem solving based on the feasible regions. However, these feasible region construction methods cannot adapt to the changes in dynamic environments, making them difficult to apply in complex traffic flow. In this paper, we propose a trajectory planning method based on adaptive spatio-temporal voxels which improves the construction of feasible regions and trajectory optimization while maintaining the quadratic programming form. The method can adjust feasible regions and trajectory planning according to real-time traffic flow and environmental changes, realizing vehicles to drive safely in complex traffic flow. The proposed method has been tested in both open-loop and closed-loop environments, and the test results show that our method outperforms the current planning methods.

Long-Term Dynamic Window Approach for Kinodynamic Local Planning in Static and Crowd Environments

Local planning for a differential wheeled robot is designed to generate kinodynamic feasible actions that guide the robot to a goal position along the navigation path while avoiding obstacles. Reactive, predictive, and learning-based methods are widely used in local planning. However, few of them can fit static and crowd environments while satisfying kinodynamic constraints simultaneously. To solve this problem, we propose a novel local planning method. The method applies a long-term dynamic window approach to generate an initial trajectory and then optimizes it with graph optimization. The method can plan actions under the robot's kinodynamic constraints in real time while allowing the generated actions to be safer and more jitterless. Experimental results show that the proposed method adapts well to crowd and static environments and outperforms most SOTA approaches.

M-OFDFT: Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learning

Orbital-free density functional theory (OFDFT) is a quantum chemistry formulation that has a lower cost scaling than the prevailing Kohn-Sham DFT, which is increasingly desired for contemporary molecular research. However, its accuracy is limited by the kinetic energy density functional, which is notoriously hard to approximate for non-periodic molecular systems. In this work, we propose M-OFDFT, an OFDFT approach capable of solving molecular systems using a deep-learning functional model. We build the essential nonlocality into the model, which is made affordable by the concise density representation as expansion coefficients under an atomic basis. With techniques to address unconventional learning challenges therein, M-OFDFT achieves a comparable accuracy with Kohn-Sham DFT on a wide range of molecules untouched by OFDFT before. More attractively, M-OFDFT extrapolates well to molecules much larger than those in training, which unleashes the appealing scaling for studying large molecules including proteins, representing an advancement of the accuracy-efficiency trade-off frontier in quantum chemistry.

Generalization error bounds for iterative learning algorithms with bounded updates

This paper explores the generalization characteristics of iterative learning algorithms with bounded updates for non-convex loss functions, employing information-theoretic techniques. Our key contribution is a novel bound for the generalization error of these algorithms with bounded updates, extending beyond the scope of previous works that only focused on Stochastic Gradient Descent (SGD). Our approach introduces two main novelties: 1) we reformulate the mutual information as the uncertainty of updates, providing a new perspective, and 2) instead of using the chaining rule of mutual information, we employ a variance decomposition technique to decompose information across iterations, allowing for a simpler surrogate process. We analyze our generalization bound under various settings and demonstrate improved bounds when the model dimension increases at the same rate as the number of training data samples. To bridge the gap between theory and practice, we also examine the previously observed scaling behavior in large language models. Ultimately, our work takes a further step for developing practical generalization theories.

How does representation impact in-context learning: A exploration on a synthetic task

In-context learning, i.e., learning from in-context samples, is an impressive ability of Transformer. However, the mechanism driving the in-context learning is not yet fully understood. In this study, we aim to investigate from an underexplored perspective of representation learning. The representation is more complex for in-context learning senario, where the representation can be impacted by both model weights and in-context samples. We refer the above two conceptually aspects of representation as in-weight component and in-context component, respectively. To study how the two components affect in-context learning capabilities, we construct a novel synthetic task, making it possible to device two probes, in-weights probe and in-context probe, to evaluate the two components, respectively. We demonstrate that the goodness of in-context component is highly related to the in-context learning performance, which indicates the entanglement between in-context learning and representation learning. Furthermore, we find that a good in-weights component can actually benefit the learning of the in-context component, indicating that in-weights learning should be the foundation of in-context learning. To further understand the the in-context learning mechanism and importance of the in-weights component, we proof by construction that a simple Transformer, which uses pattern matching and copy-past mechanism to perform in-context learning, can match the in-context learning performance with more complex, best tuned Transformer under the perfect in-weights component assumption. In short, those discoveries from representation learning perspective shed light on new approaches to improve the in-context capacity.