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.

Vision Transformers (ViTs) demonstrate remarkable performance in image classification through visual-token interaction learning, particularly when equipped with local information via region attention or convolutions. Although such architectures improve the feature aggregation from different granularities, they often fail to contribute to the robustness of the networks. Neural Cellular Automata (NCA) enables the modeling of global visual-token representations through local interactions, as its training strategies and architecture design confer strong generalization ability and robustness against noisy input. In this paper, we propose Adaptor Neural Cellular Automata (AdaNCA) for Vision Transformers that uses NCA as plug-and-play adaptors between ViT layers, thus enhancing ViT's performance and robustness against adversarial samples as well as out-of-distribution inputs. To overcome the large computational overhead of standard NCAs, we propose Dynamic Interaction for more efficient interaction learning. Using our analysis of AdaNCA placement and robustness improvement, we also develop an algorithm for identifying the most effective insertion points for AdaNCA. With less than a 3% increase in parameters, AdaNCA contributes to more than 10% of absolute improvement in accuracy under adversarial attacks on the ImageNet1K benchmark. Moreover, we demonstrate with extensive evaluations across eight robustness benchmarks and four ViT architectures that AdaNCA, as a plug-and-play module, consistently improves the robustness of ViTs.

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.

Uncertainty Quantification (UQ) is vital for decision makers as it offers insights into the potential reliability of data and model, enabling more informed and risk-aware decision-making. Graphical models, capable of representing data with complex dependencies, are widely used across domains. Existing sampling-based UQ methods are unbiased but cannot guarantee convergence and are time-consuming on largescale graphs. There are fast UQ methods for graphical models with closed-form solutions and convergence guarantee but with uncertainty underestimation. We propose LinUProp, a UQ method that utilizes a novel linear propagation of uncertainty to model uncertainty among related nodes additively instead of multiplicatively, to offer linear scalability, guaranteed convergence, and closed-form solutions without underestimating uncertainty. Theoretically, we decompose the expected prediction error of the graphical model and prove that the uncertainty computed by LinUProp is the generalized variance component of the decomposition. Experimentally, we demonstrate that LinUProp is consistent with the sampling-based method but with linear scalability and fast convergence. Moreover, LinUProp outperforms competitors in uncertainty-based active learning on four real-world graph datasets, achieving higher accuracy with a lower labeling budget.

Undirected graphical models are compact representations of joint probability distributions over random variables. To solve inference tasks of interest, graphical models of arbitrary topology can be trained using empirical risk minimization. However, to solve inference tasks that were not seen during training, these models (EGMs) often need to be re-trained. Instead, we propose an inference-agnostic adversarial training framework which produces an infinitely-large ensemble of graphical models (AGMs). The ensemble is optimized to generate data within the GAN framework, and inference is performed using a finite subset of these models.

Graph data are inherently complex and heterogeneous, leading to a high natural diversity of distributional shifts. However, it remains unclear how to build machine learning architectures that generalize to the complex distributional shifts naturally occurring in the real world. Here, we develop GraphMETRO, a Graph Neural Network architecture that models natural diversity and captures complex distributional shifts. GraphMETRO employs a Mixture-of-Experts (MoE) architecture with a gating model and multiple expert models, where each expert model targets a specific distributional shift to produce a referential representation w.r.t. a reference model, and the gating model identifies shift components. Additionally, we design a novel objective that aligns the representations from different expert models to ensure reliable optimization. GraphMETRO achieves state-of-the-art results on four datasets from the GOOD benchmark, which is comprised of complex and natural real-world distribution shifts, improving by 67% and 4.2% on the WebKB and Twitch datasets.

Cambridge, United Kingdom – The fate of Ukraine and the future of European security hangs in the balance as United States and Russian diplomats prepared to discuss an accelerated peace plan this week. The uncertainty and dreadful possibilities of this historical moment, with Russia occupying a fifth of Ukrainian soil, dominated the atmosphere of Firewalling the Future, a conference on the future of Ukraine held at Cambridge University on Monday. Organised by programme leader Victoria Vdovychenko and professor of Ukrainian studies Rory Finnin under the auspices of the Centre for Geopolitics, it brought together Ukrainian, European and British diplomats, soldiers and academics. Dominant among the Ukrainians and Eastern Europeans present was the sentiment that with Trump's re-election, the international order is irrecoverably lost and needs to be rebuilt. Some spoke openly of a post-NATO reality in which Europe must form new structures and alliances to fend for itself.

Tiny machine learning (TinyML) promises to revolutionize fields such as healthcare, environmental monitoring, and industrial maintenance by running machine learning models on low-power embedded systems. However, the complex optimizations required for successful TinyML deployment continue to impede its widespread adoption. A promising route to simplifying TinyML is through automatic machine learning (AutoML), which can distill elaborate optimization workflows into accessible key decisions. Notably, Hardware Aware Neural Architecture Searches - where a computer searches for an optimal TinyML model based on predictive performance and hardware metrics - have gained significant traction, producing some of today's most widely used TinyML models. Nevertheless, limiting optimization solely to neural network architectures can prove insufficient. Because TinyML systems must operate under extremely tight resource constraints, the choice of input data configuration, such as resolution or sampling rate, also profoundly impacts overall system efficiency. Achieving truly optimal TinyML systems thus requires jointly tuning both input data and model architecture. Despite its importance, this "Data Aware Neural Architecture Search" remains underexplored. To address this gap, we propose a new state-of-the-art Data Aware Neural Architecture Search technique and demonstrate its effectiveness on the novel TinyML ``Wake Vision'' dataset. Our experiments show that across varying time and hardware constraints, Data Aware Neural Architecture Search consistently discovers superior TinyML systems compared to purely architecture-focused methods, underscoring the critical role of data-aware optimization in advancing TinyML.

Memorization is a fundamental ability of Transformer-based Large Language Models, achieved through learning. In this paper, we propose a paradigm shift by designing an architecture to memorize text directly, bearing in mind the principle that memorization precedes learning. We introduce MeMo, a novel architecture for language modeling that explicitly memorizes sequences of tokens in layered associative memories. By design, MeMo offers transparency and the possibility of model editing, including forgetting texts. We experimented with the MeMo architecture, showing the memorization power of the one-layer and the multi-layer configurations.

Commonsense temporal reasoning at scale is a core problem for cognitive systems. The correct inference of the duration for which fluents hold is required by many tasks, including natural language understanding and planning. Many AI systems have limited deductive closure because they cannot extrapolate information correctly regarding existing fluents and events. In this study, we discuss the knowledge representation and reasoning schemes required for robust temporal projection in the Cyc Knowledge Base. We discuss how events can start and end risk periods for fluents. We then use discrete survival functions, which represent knowledge of the persistence of facts, to extrapolate a given fluent. The extrapolated intervals can be truncated by temporal constraints and other types of commonsense knowledge. Finally, we present the results of experiments to demonstrate that these methods obtain significant improvements in terms of Q/A performance.