Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving

Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly possess some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.

Can AI Be as Creative as Humans?

Creativity serves as a cornerstone for societal progress and innovation. With the rise of advanced generative AI models capable of tasks once reserved for human creativity, the study of AI's creative potential becomes imperative for its responsible development and application. In this paper, we provide a theoretical answer to the question of whether AI can be creative. We prove in theory that AI can be as creative as humans under the condition that AI can fit the existing data generated by human creators. Therefore, the debate on AI's creativity is reduced into the question of its ability of fitting a massive amount of data. To arrive at this conclusion, this paper first addresses the complexities in defining creativity by introducing a new concept called Relative Creativity. Instead of trying to define creativity universally, we shift the focus to whether AI can match the creative abilities of a hypothetical human. This perspective draws inspiration from the Turing Test, expanding upon it to address the challenges and subjectivities inherent in assessing creativity. This methodological shift leads to a statistically quantifiable assessment of AI's creativity, which we term Statistical Creativity. This concept allows for comparisons of AI's creative abilities with those of specific human groups, and facilitates the theoretical findings of AI's creative potential. Building on this foundation, we discuss the application of statistical creativity in prompt-conditioned autoregressive models, providing a practical means for evaluating creative abilities of contemporary AI models, such as Large Language Models (LLMs). In addition to defining and analyzing creativity, we introduce an actionable training guideline, effectively bridging the gap between theoretical quantification of creativity and practical model training.

Unlearning via Sparse Representations

Machine \emph{unlearning}, which involves erasing knowledge about a \emph{forget set} from a trained model, can prove to be costly and infeasible by existing techniques. We propose a nearly compute-free zero-shot unlearning technique based on a discrete representational bottleneck. We show that the proposed technique efficiently unlearns the forget set and incurs negligible damage to the model's performance on the rest of the data set. We evaluate the proposed technique on the problem of \textit{class unlearning} using three datasets: CIFAR-10, CIFAR-100, and LACUNA-100. We compare the proposed technique to SCRUB, a state-of-the-art approach which uses knowledge distillation for unlearning. Across all three datasets, the proposed technique performs as well as, if not better than SCRUB while incurring almost no computational cost.

Leveraging the Third Dimension in Contrastive Learning

Self-Supervised Learning (SSL) methods operate on unlabeled data to learn robust representations useful for downstream tasks. Most SSL methods rely on augmentations obtained by transforming the 2D image pixel map. These augmentations ignore the fact that biological vision takes place in an immersive three-dimensional, temporally contiguous environment, and that low-level biological vision relies heavily on depth cues. Using a signal provided by a pretrained state-of-the-art monocular RGB-to-depth model (the \emph{Depth Prediction Transformer}, Ranftl et al., 2021), we explore two distinct approaches to incorporating depth signals into the SSL framework. First, we evaluate contrastive learning using an RGB+depth input representation. Second, we use the depth signal to generate novel views from slightly different camera positions, thereby producing a 3D augmentation for contrastive learning. We evaluate these two approaches on three different SSL methods -- BYOL, SimSiam, and SwAV -- using ImageNette (10 class subset of ImageNet), ImageNet-100 and ImageNet-1k datasets. We find that both approaches to incorporating depth signals improve the robustness and generalization of the baseline SSL methods, though the first approach (with depth-channel concatenation) is superior. For instance, BYOL with the additional depth channel leads to an increase in downstream classification accuracy from 85.3\% to 88.0\% on ImageNette and 84.1\% to 87.0\% on ImageNet-C.

Stateful active facilitator: Coordination and Environmental Heterogeneity in Cooperative Multi-Agent Reinforcement Learning

In cooperative multi-agent reinforcement learning, a team of agents works together to achieve a common goal. Different environments or tasks may require varying degrees of coordination among agents in order to achieve the goal in an optimal way. The nature of coordination will depend on properties of the environment -- its spatial layout, distribution of obstacles, dynamics, etc. We term this variation of properties within an environment as heterogeneity. Existing literature has not sufficiently addressed the fact that different environments may have different levels of heterogeneity. We formalize the notions of coordination level and heterogeneity level of an environment and present HECOGrid, a suite of multi-agent RL environments that facilitates empirical evaluation of different MARL approaches across different levels of coordination and environmental heterogeneity by providing a quantitative control over coordination and heterogeneity levels of the environment. Further, we propose a Centralized Training Decentralized Execution learning approach called Stateful Active Facilitator (SAF) that enables agents to work efficiently in high-coordination and high-heterogeneity environments through a differentiable and shared knowledge source used during training and dynamic selection from a shared pool of policies. We evaluate SAF and compare its performance against baselines IPPO and MAPPO on HECOGrid. Our results show that SAF consistently outperforms the baselines across different tasks and different heterogeneity and coordination levels.

Discrete Key-Value Bottleneck

Deep neural networks perform well on prediction and classification tasks in the canonical setting where data streams are i.i.d., labeled data is abundant, and class labels are balanced. Challenges emerge with distribution shifts, including non-stationary or imbalanced data streams. One powerful approach that has addressed this challenge involves self-supervised pretraining of large encoders on volumes of unlabeled data, followed by task-specific tuning. Given a new task, updating the weights of these encoders is challenging as a large number of weights needs to be fine-tuned, and as a result, they forget information about the previous tasks. In the present work, we propose a model architecture to address this issue, building upon a discrete bottleneck containing pairs of separate and learnable (key, value) codes. In this setup, we follow the encode; process the representation via a discrete bottleneck; and decode paradigm, where the input is fed to the pretrained encoder, the output of the encoder is used to select the nearest keys, and the corresponding values are fed to the decoder to solve the current task. The model can only fetch and re-use a limited number of these (key, value) pairs during inference, enabling localized and context-dependent model updates. We theoretically investigate the ability of the proposed model to minimize the effect of the distribution shifts and show that such a discrete bottleneck with (key, value) pairs reduces the complexity of the hypothesis class. We empirically verified the proposed methods' benefits under challenging distribution shift scenarios across various benchmark datasets and show that the proposed model reduces the common vulnerability to non-i.i.d. and non-stationary training distributions compared to various other baselines.

Coordinating Policies Among Multiple Agents via an Intelligent Communication Channel

In Multi-Agent Reinforcement Learning (MARL), specialized channels are often introduced that allow agents to communicate directly with one another. In this paper, we propose an alternative approach whereby agents communicate through an intelligent facilitator that learns to sift through and interpret signals provided by all agents to improve the agents' collective performance. To ensure that this facilitator does not become a centralized controller, agents are incentivized to reduce their dependence on the messages it conveys, and the messages can only influence the selection of a policy from a fixed set, not instantaneous actions given the policy. We demonstrate the strength of this architecture over existing baselines on several cooperative MARL environments.

Learning to Induce Causal Structure

The fundamental challenge in causal induction is to infer the underlying graph structure given observational and/or interventional data. Most existing causal induction algorithms operate by generating candidate graphs and then evaluating them using either score-based methods (including continuous optimization) or independence tests. In this work, instead of proposing scoring function or independence tests, we treat the inference process as a black box and design a neural network architecture that learns the mapping from both observational and interventional data to graph structures via supervised training on synthetic graphs. We show that the proposed model generalizes not only to new synthetic graphs but also to naturalistic graphs.

Systematic Evaluation of Causal Discovery in Visual Model Based Reinforcement Learning

Inducing causal relationships from observations is a classic problem in machine learning. Most work in causality starts from the premise that the causal variables themselves are observed. However, for AI agents such as robots trying to make sense of their environment, the only observables are low-level variables like pixels in images. To generalize well, an agent must induce high-level variables, particularly those which are causal or are affected by causal variables. A central goal for AI and causality is thus the joint discovery of abstract representations and causal structure. However, we note that existing environments for studying causal induction are poorly suited for this objective because they have complicated task-specific causal graphs which are impossible to manipulate parametrically (e.g., number of nodes, sparsity, causal chain length, etc.). In this work, our goal is to facilitate research in learning representations of high-level variables as well as causal structures among them. In order to systematically probe the ability of methods to identify these variables and structures, we design a suite of benchmarking RL environments. We evaluate various representation learning algorithms from the literature and find that explicitly incorporating structure and modularity in models can help causal induction in model-based reinforcement learning.

Neural Production Systems

Visual environments are structured, consisting of distinct objects or entities. These entities have properties -- both visible and latent -- that determine the manner in which they interact with one another. To partition images into entities, deep-learning researchers have proposed structural inductive biases such as slot-based architectures. To model interactions among entities, equivariant graph neural nets (GNNs) are used, but these are not particularly well suited to the task for two reasons. First, GNNs do not predispose interactions to be sparse, as relationships among independent entities are likely to be. Second, GNNs do not factorize knowledge about interactions in an entity-conditional manner. As an alternative, we take inspiration from cognitive science and resurrect a classic approach, production systems, which consist of a set of rule templates that are applied by binding placeholder variables in the rules to specific entities. Rules are scored on their match to entities, and the best fitting rules are applied to update entity properties. In a series of experiments, we demonstrate that this architecture achieves a flexible, dynamic flow of control and serves to factorize entity-specific and rule-based information. This disentangling of knowledge achieves robust future-state prediction in rich visual environments, outperforming state-of-the-art methods using GNNs, and allows for the extrapolation from simple (few object) environments to more complex environments.