A.1 Prototype-based Graph Information Bottleneck - Eq. 4 From Eq. 3, the GIB objective is: min We perform ablation studies to examine the effectiveness of our model (i.e., PGIB and PGIB In Figure 7, the " with all " setting represents our final model that includes all the components. We conduct experiments on graph classification using different readout functions for PGIB. We illustrate the reasoning process on two datasets, i.e., MUT AG and BA2Motif, in Figure 8. PGIB Then, PGIB computes the "points contributed" to predicting each class by multiplying the similarity We have conducted additional qualitative analysis. It is crucial that the prototypes not only contain key structural information from the input graph but also ensure a certain level of diversity since each class is represented by multiple prototypes. Its goal is to make the masked subgraph's prediction as close as possible to the original graph, which helps to detect substructures significant

To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps.

Improving the reasoning capabilities of large language models (LLMs) has attracted considerable interest. Recent approaches primarily focus on improving the reasoning process to yield a more precise final answer.

Existing work in prototype-based image classification uses a this looks like that'' reasoning process, which dissects a test image by finding prototypical parts and combining evidence from these prototypes to make a final classification. However, all of the existing prototypical part-based image classifiers provide only one-to-one comparisons, where a single training image patch serves as a prototype to compare with a part of our test image. With these single-image comparisons, it can often be difficult to identify the underlying concept being compared (e.g., is it comparing the color or the shape?''). Our proposed method modifies the architecture of prototype-based networks to instead learn prototypical concepts which are visualized using multiple image patches. Having multiple visualizations of the same prototype allows us to more easily identify the concept captured by that prototype (e.g., the test image and the related training patches are all the same shade of blue''), and allows our model to create richer, more interpretable visual explanations. Our experiments show that our ``this looks like those'' reasoning process can be applied as a modification to a wide range of existing prototypical image classification networks while achieving comparable accuracy on benchmark datasets.

While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate reasoning steps can inadvertently introduce hallucinations and accumulated errors, thereby limiting models' ability to solve complex reasoning tasks. Inspired by how humans engage in careful and meticulous deductive logical reasoning processes to solve tasks, we seek to enable language models to perform explicit and rigorous deductive reasoning, and also ensure the trustworthiness of their reasoning process through self-verification. However, directly verifying the validity of an entire deductive reasoning process is challenging, even with advanced models like ChatGPT. In light of this, we propose to decompose a reasoning verification process into a series of step-by-step subprocesses, each only receiving their necessary context and premises. To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps. It also empowers language models to carry out reasoning self-verification in a step-by-step manner. By integrating this verification process into each deductive reasoning stage, we significantly enhance the rigor and trustfulness of generated reasoning steps. Along this process, we also improve the answer correctness on complex reasoning tasks.

Navigation guided by natural language instructions presents a challenging reasoning problem for instruction followers. Natural language instructions typically identify only a few high-level decisions and landmarks rather than complete low-level motor behaviors; much of the missing information must be inferred based on perceptual context. In machine learning settings, this is doubly challenging: it is difficult to collect enough annotated data to enable learning of this reasoning process from scratch, and also difficult to implement the reasoning process using generic sequence models. Here we describe an approach to vision-and-language navigation that addresses both these issues with an embedded speaker model. We use this speaker model to (1) synthesize new instructions for data augmentation and to (2) implement pragmatic reasoning, which evaluates how well candidate action sequences explain an instruction. Both steps are supported by a panoramic action space that reflects the granularity of human-generated instructions. Experiments show that all three components of this approach---speaker-driven data augmentation, pragmatic reasoning and panoramic action space---dramatically improve the performance of a baseline instruction follower, more than doubling the success rate over the best existing approach on a standard benchmark.

Is dynamics prediction indispensable for physical reasoning? If so, what kind of roles do the dynamics prediction modules play during the physical reasoning process? Most studies focus on designing dynamics prediction networks and treating physical reasoning as a downstream task without investigating the questions above, taking for granted that the designed dynamics prediction would undoubtedly help the reasoning process. In this work, we take a closer look at this assumption, exploring this fundamental hypothesis by comparing two learning mechanisms: Learning from Dynamics (LfD) and Learning from Intuition (LfI). In the first experiment, we directly examine and compare these two mechanisms. Results show a surprising finding: Simple LfI is better than or on par with state-of-the-art LfD.