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Foundation models exhibit significant capabilities in decision-making and logical deductions. Nonetheless, a continuing discourse persists regarding their genuine understanding of the world as opposed to mere stochastic mimicry. This paper meticulously examines a simple transformer trained for Othello, extending prior research to enhance comprehension of the emergent world model of Othello-GPT. The investigation reveals that Othello-GPT encapsulates a linear representation of opposing pieces, a factor that causally steers its decision-making process. This paper further elucidates the interplay between the linear world representation and causal decision-making, and their dependence on layer depth and model complexity. We have made the code public.

Systems for making determinations on socially-constructed and complex concepts at scale are increasingly being deployed. To make such fuzzy concepts tractable for training and evaluating AI, aligning model outputs, or human-in-the-loop workflows, the prevailing strategy involves developing `constitutions' in the form of rules, policies, or principles. However, high-level rules often fail to capture situational nuances or have differing interpretations, resulting in inconsistent decisions. In this work, we introduce case law grounding (CLG), a hybrid workflow inspired by case law in the legal realm where past judgments on specific cases inform new decisions. Evaluating on two task domains, we find that CLG can improve alignment of decisions (+9.6% and +10.9% accuracy) and consistency ($\Delta\bar{\kappa}$ of +0.263 and +0.433) of human decision-makers, while also providing auditable rationales. We also find similarly substantial alignment improvements for an LLM decision-maker (+25% and +23% accuracy).

The Central Pattern Generator (CPG) is adept at generating rhythmic gait patterns characterized by consistent timing and adequate foot clearance. Yet, its open-loop configuration often compromises the system's control performance in response to environmental variations. On the other hand, Reinforcement Learning (RL), celebrated for its model-free properties, has gained significant traction in robotics due to its inherent adaptability and robustness. However, initiating traditional RL approaches from the ground up presents computational challenges and a heightened risk of converging to suboptimal local minima. In this paper, we propose an innovative quadruped locomotion framework, SYNLOCO, by synthesizing CPG and RL that can ingeniously integrate the strengths of both methods, enabling the development of a locomotion controller that is both stable and natural. Furthermore, we introduce a set of performance-driven reward metrics that augment the learning of locomotion control. To optimize the learning trajectory of SYNLOCO, a two-phased training strategy is presented. Our empirical evaluation, conducted on a Unitree GO1 robot under varied conditions--including distinct velocities, terrains, and payload capacities--showcases SYNLOCO's ability to produce consistent and clear-footed gaits across diverse scenarios. The developed controller exhibits resilience against substantial parameter variations, underscoring its potential for robust real-world applications.

Significant advancements have occurred in the application of Large Language Models (LLMs) for various tasks and social simulations. Despite this, their capacities to coordinate within task-oriented social contexts are under-explored. Such capabilities are crucial if LLMs are to effectively mimic human-like social behavior and produce meaningful results. To bridge this gap, we introduce collaborative generative agents, endowing LLM-based Agents with consistent behavior patterns and task-solving abilities. We situate these agents in a simulated job fair environment as a case study to scrutinize their coordination skills. We propose a novel framework that equips collaborative generative agents with human-like reasoning abilities and specialized skills. Our evaluation demonstrates that these agents show promising performance. However, we also uncover limitations that hinder their effectiveness in more complex coordination tasks. Our work provides valuable insights into the role and evolution of LLMs in task-oriented social simulations.

We revisit the problem of learning a single neuron with ReLU activation under Gaussian input with square loss. We particularly focus on the over-parameterization setting where the student network has $n\ge 2$ neurons. We prove the global convergence of randomly initialized gradient descent with a $O\left(T^{-3}\right)$ rate. This is the first global convergence result for this problem beyond the exact-parameterization setting ($n=1$) in which the gradient descent enjoys an $\exp(-\Omega(T))$ rate. Perhaps surprisingly, we further present an $\Omega\left(T^{-3}\right)$ lower bound for randomly initialized gradient flow in the over-parameterization setting. These two bounds jointly give an exact characterization of the convergence rate and imply, for the first time, that over-parameterization can exponentially slow down the convergence rate. To prove the global convergence, we need to tackle the interactions among student neurons in the gradient descent dynamics, which are not present in the exact-parameterization case. We use a three-phase structure to analyze GD's dynamics. Along the way, we prove gradient descent automatically balances student neurons, and use this property to deal with the non-smoothness of the objective function. To prove the convergence rate lower bound, we construct a novel potential function that characterizes the pairwise distances between the student neurons (which cannot be done in the exact-parameterization case). We show this potential function converges slowly, which implies the slow convergence rate of the loss function.

SUPERB was proposed to evaluate the generalizability of self-supervised learning (SSL) speech models across various tasks. However, it incurs high computational costs due to the large datasets and diverse tasks. In this paper, we introduce MiniSUPERB, a lightweight benchmark that efficiently evaluates SSL speech models with comparable results to SUPERB but lower computational costs significantly. We carefully select representative tasks, sample datasets, and extract model representations offline. Our approach achieves a Spearman's rank correlation of 0.954 and 0.982 with SUPERB Paper and SUPERB Challenge, respectively. Additionally, we reduce the computational cost by 97% in terms of Multiply-ACcumulate operations (MACs). Furthermore, we evaluate SSL speech models in few-shot scenarios and observe significant variations in their performance. To our knowledge, this is the first study to examine both the computational cost of the model itself and the cost of evaluating it on a benchmark.

We study the optimal order (or sequence) of contracting a tensor network with a minimal computational cost. We conclude 2 different versions of this optimal sequence: that minimize the operation number (OMS) and that minimize the time complexity (CMS). Existing results only shows that OMS is NP-hard, but no conclusion on CMS problem. In this work, we firstly reduce CMS to CMS-0, which is a sub-problem of CMS with no free indices. Then we prove that CMS is easier than OMS, both in general and in tree cases. Last but not least, we prove that CMS is still NP-hard. Based on our results, we have built up relationships of hardness of different tensor network contraction problems.

Many natural language processing tasks solely rely on sparse dependencies between a few tokens in a sentence. Soft attention mechanisms show promising performance in modeling local/global dependencies by soft probabilities between every two tokens, but they are not effective and efficient when applied to long sentences. By contrast, hard attention mechanisms directly select a subset of tokens but are difficult and inefficient to train due to their combinatorial nature. In this paper, we integrate both soft and hard attention into one context fusion model, "reinforced self-attention (ReSA)", for the mutual benefit of each other. In ReSA, a hard attention trims a sequence for a soft self-attention to process, while the soft attention feeds reward signals back to facilitate the training of the hard one. For this purpose, we develop a novel hard attention called "reinforced sequence sampling (RSS)", selecting tokens in parallel and trained via policy gradient. Using two RSS modules, ReSA efficiently extracts the sparse dependencies between each pair of selected tokens. We finally propose an RNN/CNN-free sentence-encoding model, "reinforced self-attention network (ReSAN)", solely based on ReSA. It achieves state-of-the-art performance on both Stanford Natural Language Inference (SNLI) and Sentences Involving Compositional Knowledge (SICK) datasets.

State-of-the-art Convolutional Neural Network (CNN) benefits a lot from multi-task learning (MTL), which learns multiple related tasks simultaneously to obtain shared or mutually related representations for different tasks. The most widely-used MTL CNN structure is based on an empirical or heuristic split on a specific layer (e.g., the last convolutional layer) to minimize different task-specific losses. However, this heuristic sharing/splitting strategy may be harmful to the final performance of one or multiple tasks. In this paper, we propose a novel CNN structure for MTL, which enables automatic feature fusing at every layer. Specifically, we first concatenate features from different tasks according to their channel dimension, and then formulate the feature fusing problem as discriminative dimensionality reduction. We show that this discriminative dimensionality reduction can be done by 1x1 Convolution, Batch Normalization, and Weight Decay in one CNN, which we refer to as Neural Discriminative Dimensionality Reduction (NDDR). We perform ablation analysis in details for different configurations in training the network. The experiments carried out on different network structures and different task sets demonstrate the promising performance and desirable generalizability of our proposed method.