We study the optimal memorization capacity of modern Hopfield models and Kernelized Hopfield Models (KHMs), a transformer-compatible class of Dense Associative Memories. We present a tight analysis by establishing a connection between the memory configuration of KHMs and spherical codes from information theory. Specifically, we treat the stored memory set as a specialized spherical code. This enables us to cast the memorization problem in KHMs into a point arrangement problem on a hypersphere. We show that the optimal capacity of KHMs occurs when the feature space allows memories to form an optimal spherical code. This unique perspective leads to: (i) An analysis of how KHMs achieve optimal memory capacity, and identify corresponding necessary conditions. Importantly, we establish an upper capacity bound that matches the well-known exponential lower bound in the literature. This provides the first tight and optimal asymptotic memory capacity for modern Hopfield models. (ii) A sub-linear time algorithm $\mathtt{U}\text{-}\mathtt{Hop}$+ to reach KHMs' optimal capacity. (iii) An analysis of the scaling behavior of the required feature dimension relative to the number of stored memories. These efforts improve both the retrieval capability of KHMs and the representation learning of corresponding transformers. Experimentally, we provide thorough numerical results to back up theoretical findings.

Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require storing each pattern in a separate set of synaptic weights, which leads to the increase of the number of synaptic weights when new patterns are introduced. In this work we propose an alternative formulation of this class of models using random features, commonly used in kernel methods. In this formulation the number of network's parameters remains fixed. At the same time, new memories can be added to the network by modifying existing weights. We show that this novel network closely approximates the energy function and dynamics of conventional Dense Associative Memories and shares their desirable computational properties.

Existing benchmarks often highlight the remarkable performance achieved by state-of-the-art Multimodal Foundation Models (MFMs) in leveraging temporal context for video understanding. However, how well do the models truly perform visual temporal reasoning? Our study of existing benchmarks shows that this capability of MFMs is likely overestimated as many questions can be solved by using a single, few, or out-of-order frames. To systematically examine current visual temporal reasoning tasks, we propose three principles with corresponding metrics: (1) Multi-Frame Gain, (2) Frame Order Sensitivity, and (3) Frame Information Disparity. Following these principles, we introduce TOMATO, Temporal Reasoning Multimodal Evaluation, a novel benchmark crafted to rigorously assess MFMs' temporal reasoning capabilities in video understanding. TOMATO comprises 1,484 carefully curated, human-annotated questions spanning six tasks (i.e., action count, direction, rotation, shape & trend, velocity & frequency, and visual cues), applied to 1,417 videos, including 805 self-recorded and -generated videos, that encompass human-centric, real-world, and simulated scenarios. Our comprehensive evaluation reveals a human-model performance gap of 57.3% with the best-performing model. Moreover, our in-depth analysis uncovers more fundamental limitations beyond this gap in current MFMs. While they can accurately recognize events in isolated frames, they fail to interpret these frames as a continuous sequence. We believe TOMATO will serve as a crucial testbed for evaluating the next-generation MFMs and as a call to the community to develop AI systems capable of comprehending human world dynamics through the video modality.

Broadly intelligent agents should form task-specific abstractions that selectively expose the essential elements of a task, while abstracting away the complexity of the raw sensorimotor space. In this work, we present Neuro-Symbolic Predicates, a first-order abstraction language that combines the strengths of symbolic and neural knowledge representations. We outline an online algorithm for inventing such predicates and learning abstract world models. We compare our approach to hierarchical reinforcement learning, vision-language model planning, and symbolic predicate invention approaches, on both in- and out-of-distribution tasks across five simulated robotic domains. Results show that our approach offers better sample complexity, stronger out-of-distribution generalization, and improved interpretability.

Sequential recommender systems (SRSs) aim to predict the subsequent items which may interest users via comprehensively modeling users' complex preference embedded in the sequence of user-item interactions. However, most of existing SRSs often model users' single low-level preference based on item ID information while ignoring the high-level preference revealed by item attribute information, such as item category. Furthermore, they often utilize limited sequence context information to predict the next item while overlooking richer inter-item semantic relations. To this end, in this paper, we proposed a novel hierarchical preference modeling framework to substantially model the complex low- and high-level preference dynamics for accurate sequential recommendation. Specifically, in the framework, a novel dual-transformer module and a novel dual contrastive learning scheme have been designed to discriminatively learn users' low- and high-level preference and to effectively enhance both low- and high-level preference learning respectively. In addition, a novel semantics-enhanced context embedding module has been devised to generate more informative context embedding for further improving the recommendation performance. Extensive experiments on six real-world datasets have demonstrated both the superiority of our proposed method over the state-of-the-art ones and the rationality of our design.

Recent advancements in large-scale multi-task robot learning offer the potential for deploying robot fleets in household and industrial settings, enabling them to perform diverse tasks across various environments. However, AI-enabled robots often face challenges with generalization and robustness when exposed to real-world variability and uncertainty. We introduce Sirius-Fleet, a multi-task interactive robot fleet learning framework to address these challenges. Sirius-Fleet monitors robot performance during deployment and involves humans to correct the robot's actions when necessary. We employ a visual world model to predict the outcomes of future actions and build anomaly predictors to predict whether they will likely result in anomalies. As the robot autonomy improves, the anomaly predictors automatically adapt their prediction criteria, leading to fewer requests for human intervention and gradually reducing human workload over time. Evaluations on large-scale benchmarks demonstrate Sirius-Fleet's effectiveness in improving multi-task policy performance and monitoring accuracy. We demonstrate Sirius-Fleet's performance in both RoboCasa in simulation and Mutex in the real world, two diverse, large-scale multi-task benchmarks. More information is available on the project website: https://ut-austin-rpl.github.io/sirius-fleet

Visual imitation learning (VIL) provides an efficient and intuitive strategy for robotic systems to acquire novel skills. Recent advancements in Vision Language Models (VLMs) have demonstrated remarkable performance in vision and language reasoning capabilities for VIL tasks. Despite the progress, current VIL methods naively employ VLMs to learn high-level plans from human videos, relying on pre-defined motion primitives for executing physical interactions, which remains a major bottleneck. In this work, we present VLMimic, a novel paradigm that harnesses VLMs to directly learn even fine-grained action levels, only given a limited number of human videos. Specifically, VLMimic first grounds object-centric movements from human videos, and learns skills using hierarchical constraint representations, facilitating the derivation of skills with fine-grained action levels from limited human videos. These skills are refined and updated through an iterative comparison strategy, enabling efficient adaptation to unseen environments. Our extensive experiments exhibit that our VLMimic, using only 5 human videos, yields significant improvements of over 27% and 21% in RLBench and real-world manipulation tasks, and surpasses baselines by over 37% in long-horizon tasks. Code and videos are available at our home page.

The rapid advancements in Vision-Language Models (VLMs) have shown great potential in tackling mathematical reasoning tasks that involve visual context. Unlike humans who can reliably apply solution steps to similar problems with minor modifications, we found that SOTA VLMs like GPT-4o can consistently fail in these scenarios, revealing limitations in their mathematical reasoning capabilities. In this paper, we investigate the mathematical reasoning robustness in VLMs and evaluate how well these models perform under different variants of the same question, such as changes in visual numerical values or function graphs. While several vision-based math benchmarks have been developed to assess VLMs' problem-solving capabilities, these benchmarks contain only static sets of problems and cannot easily evaluate mathematical reasoning robustness. To fill this gap, we introduce DynaMath, a dynamic visual math benchmark designed for in-depth assessment of VLMs. DynaMath includes 501 high-quality, multi-topic seed questions, each represented as a Python program. Those programs are carefully designed and annotated to enable the automatic generation of a much larger set of concrete questions, including many different types of visual and textual variations. DynaMath allows us to evaluate the generalization ability of VLMs, by assessing their performance under varying input conditions of a seed question. We evaluated 14 SOTA VLMs with 5,010 generated concrete questions. Our results show that the worst-case model accuracy, defined as the percentage of correctly answered seed questions in all 10 variants, is significantly lower than the average-case accuracy. Our analysis emphasizes the need to study the robustness of VLMs' reasoning abilities, and DynaMath provides valuable insights to guide the development of more reliable models for mathematical reasoning.

In recent years, machine learning models have made strides towards human-like reasoning capabilities from several directions. In this work, we review the current state of the literature and describe the remaining steps to achieve a neural model which can perform System 2 reasoning analogous to a human. We argue that if current models are insufficient to be classed as performing reasoning, there remains very little additional progress needed to attain that goal.

As language models (LMs) become integral to fields like healthcare, law, and journalism, their ability to differentiate between fact, belief, and knowledge is essential for reliable decision-making. Failure to grasp these distinctions can lead to significant consequences in areas such as medical diagnosis, legal judgments, and dissemination of fake news. Despite this, current literature has largely focused on more complex issues such as theory of mind, overlooking more fundamental epistemic challenges. This study systematically evaluates the epistemic reasoning capabilities of modern LMs, including GPT-4, Claude-3, and Llama-3, using a new dataset, KaBLE, consisting of 13,000 questions across 13 tasks. Our results reveal key limitations. First, while LMs achieve 86% accuracy on factual scenarios, their performance drops significantly with false scenarios, particularly in belief-related tasks. Second, LMs struggle with recognizing and affirming personal beliefs, especially when those beliefs contradict factual data, which raises concerns for applications in healthcare and counseling, where engaging with a person's beliefs is critical. Third, we identify a salient bias in how LMs process first-person versus third-person beliefs, performing better on third-person tasks (80.7%) compared to first-person tasks (54.4%). Fourth, LMs lack a robust understanding of the factive nature of knowledge, namely, that knowledge inherently requires truth. Fifth, LMs rely on linguistic cues for fact-checking and sometimes bypass the deeper reasoning. These findings highlight significant concerns about current LMs' ability to reason about truth, belief, and knowledge while emphasizing the need for advancements in these areas before broad deployment in critical sectors.