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Applications · Chemistry and Drug Discovery

Ishan Amin, Sanjeev Raja, Aditi Krishnapriyan

The foundation model (FM) paradigm is transforming Machine Learning Force Fields (MLFFs), leveraging general-purpose representations and scalable training to perform a variety of computational chemistry tasks. Although MLFF FMs have begun to close the accuracy gap relative to first-principles methods, there is still a strong need for faster inference speed. Additionally, while research is increasingly focused on general-purpose models which transfer across chemical space, practitioners typically only study a small subset of systems at a given time. At test time, MLFFs must also obey physical constraints unique to the downstream use case, such as energy conservation for molecular dynamics simulations. This underscores the need for fast, specialized MLFFs relevant to specific downstream applications, which preserve test-time physical soundness while maintaining train-time scalability. In this work, we introduce a method for transferring general-purpose representations from MLFF foundation models to smaller, faster MLFFs specialized to specific regions of chemical space. We formulate our approach as an architecture-agnostic knowledge distillation procedure, where the smaller "student" MLFF is trained to match the Hessians of the energy predictions of the "teacher" foundation model. We demonstrate our approach across multiple recent foundation models, large-scale datasets, chemical subsets, and downstream tasks. Our specialized MLFFs can be up to 20 times faster than the original foundation model, while retaining, and in some cases exceeding, its performance and that of undistilled models. We also show that distilling from a teacher model with a direct force parameterization into a student model trained with conservative forces (i.e., computed as derivatives of the potential energy) successfully leverages the representations from the large-scale teacher for improved accuracy, while maintaining energy conservation during test-time molecular dynamics simulations. More broadly, our work suggests a new paradigm for MLFF development, in which foundation models are released along with smaller, specialized simulation ``engines" for common chemical subsets. The implementation of our method is available at https://github.com/ASK-Berkeley/MLFF-distill.

Deep Learning · Generative Models and Autoencoders

Sumeet Singh, Vikas Sindhwani, Stephen Tu

A crucial design decision for any robot learning pipeline is the choice of policy representation: what type of model should be used to generate the next set of robot actions? Owing to the inherent multi-modal nature of many robotic tasks, combined with the recent successes in generative modeling, researchers have turned to state-of-the-art probabilistic models such as diffusion models for policy representation. In this work, we revisit the choice of energy-based models (EBM) as a policy class. We show that the prevailing folklore---that energy models in high dimensional continuous spaces are impractical to train---is false. We develop a practical training objective and algorithm for energy models which combines several key ingredients: (i) ranking noise contrastive estimation (R-NCE), (ii) learnable negative samplers, and (iii) non-adversarial joint training. We prove that our proposed objective function is asymptotically consistent and quantify its limiting variance. On the other hand, we show that the Implicit Behavior Cloning (IBC) objective is actually biased even at the population level, providing a mathematical explanation for the poor performance of IBC trained energy policies in several independent follow-up works. We further extend our algorithm to learn a continuous stochastic process that bridges noise and data, modeling this process with a family of EBMs indexed by scale variable. In doing so, we demonstrate that the core idea behind recent progress in generative modeling is actually compatible with EBMs. Altogether, our proposed training algorithms enable us to train energy-based models as policies which compete with---and even outperform---diffusion models and other state-of-the-art approaches in several challenging multi-modal benchmarks: obstacle avoidance path planning and contact-rich block pushing.

Applications · Computer Vision

Jaeyeon Kim, Heeseung Yun, Gunhee Kim

Spatial audio is essential for enhancing the immersiveness of audio-visual experiences, yet its production typically demands complex recording systems and specialized expertise. In this work, we address a novel problem of generating first-order ambisonics, a widely used spatial audio format, directly from silent videos. To support this task, we introduce YT-Ambigen, a dataset comprising 102K 5-second YouTube video clips paired with corresponding first-order ambisonics. We also propose new evaluation metrics to assess the spatial aspect of generated audio based on audio energy maps and saliency metrics. Furthermore, we present Video-to-Spatial Audio Generation (ViSAGe), an end-to-end framework that generates first-order ambisonics from silent video frames by leveraging CLIP visual features, autoregressive neural audio codec modeling with both directional and visual guidance. Experimental results demonstrate that ViSAGe produces plausible and coherent first-order ambisonics, outperforming two-stage approaches consisting of video-to-audio generation and audio spatialization. Qualitative examples further illustrate that ViSAGe generates temporally aligned high-quality spatial audio that adapts to viewpoint changes.

Applications · Chemistry and Drug Discovery

Yurou Liu, Jiahao Chen, Rui Jiao, Jiangmeng Li, Wenbing Huang, Bing Su

Denoising learning of 3D molecules learns molecular representations by imposing noises into the equilibrium conformation and predicting the added noises to recover the equilibrium conformation, which essentially captures the information of molecular force fields. Due to the specificity of Potential Energy Surfaces, the probabilities of physically reasonable noises for each atom in different molecules are different. However, existing methods apply the shared heuristic hand-crafted noise sampling strategy to all molecules, resulting in inaccurate force field learning. In this paper, we propose a novel 3D molecular pre-training method, namely DenoiseVAE, which employs a Noise Generator to acquire atom-specific noise distributions for different molecules. It utilizes the stochastic reparameterization technique to sample noisy conformations from the generated distributions, which are inputted into a Denoising Module for denoising. The Noise Generator and the Denoising Module are jointly learned in a manner conforming with the paradigm of Variational Auto Encoder. Consequently, the sampled noisy conformations can be more diverse, adaptive, and informative, and thus DenoiseVAE can learn representations that better reveal the molecular force fields. Extensive experiments show that DenoiseVAE outperforms the current state-of-the-art methods on various molecular property prediction tasks, demonstrating the effectiveness of it.

Theory · Online Learning and Bandits

Jack Sandberg, Niklas Åkerblom, Morteza Haghir Chehreghani

We consider the combinatorial volatile Gaussian process (GP) semi-bandit problem. Each round, an agent is provided a set of available base arms and must select a subset of them to maximize the long-term cumulative reward. We study the Bayesian setting and provide novel Bayesian cumulative regret bounds for three GP-based algorithms: GP-UCB, GP-BayesUCB and GP-TS. Our bounds extend previous results for GP-UCB and GP-TS to the \emph{infinite}, \emph{volatile} and \emph{combinatorial} setting, and to the best of our knowledge, we provide the first regret bound for GP-BayesUCB. Volatile arms encompass other widely considered bandit problems such as contextual bandits.Furthermore, we employ our framework to address the challenging real-world problem of online energy-efficient navigation, where we demonstrate its effectiveness compared to the alternatives.

Probabilistic Methods · Variational Inference

Hoang Phuc Hau Luu, Hanlin Yu, Bernardo Williams, Marcelo Hartmann, Arto Klami

Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function of Kullback–Leibler divergence can be written as the sum of the negative entropy and the potential energy, making forward-backward Euler the method of choice. Notably, the backward step admits a closed-form solution in this case, facilitating the practicality of the scheme. However, the forward step is not exact since the Bures-Wasserstein gradient of the potential energy involves "intractable" expectations. Recent approaches propose using the Monte Carlo method -- in practice a single-sample estimator -- to approximate these terms, resulting in high variance and poor performance. We propose a novel variance-reduced estimator based on the principle of control variates. We theoretically show that this estimator has a smaller variance than the Monte-Carlo estimator in scenarios of interest. We also prove that variance reduction helps improve the optimization bounds of the current analysis. We demonstrate that the proposed estimator gains order-of-magnitude improvements over the previous Bures-Wasserstein methods.

Reinforcement Learning · Deep RL

Hoang Khoi Nguyen Do, Truc Nguyen, Malik Hassanaly, Raed Alharbi, Jung Seo, My Thai

Despite a plethora of anomaly detection models developed over the years, their ability to generalize to unseen anomalies remains an issue, particularly in critical systems. This paper aims to address this challenge by introducing Swift Hydra, a new framework for training an anomaly detection method based on generative AI and reinforcement learning (RL). Through featuring an RL policy that operates on the latent variables of a generative model, the framework synthesizes novel and diverse anomaly samples that are capable of bypassing a detection model. These generated synthetic samples are, in turn, used to augment the detection model, further improving its ability to handle challenging anomalies. Swift Hydra also incorporates Mamba models structured as a Mixture of Experts (MoE) to enable scalable adaptation of the number of Mamba experts based on data complexity, effectively capturing diverse feature distributions without increasing the model’s inference time. Empirical evaluations on ADBench benchmark demonstrate that Swift Hydra outperforms other state-of-the-art anomaly detection models while maintaining a relatively short inference time. From these results, our research highlights a new and auspicious paradigm of integrating RL and generative AI for advancing anomaly detection.

Deep Learning · Graph Neural Networks

Daeho Um, Jongin Lim, Sunoh Kim, Yuneil Yeo, Yoonho Jung

Node-level out-of-distribution (OOD) detection on graphs has received significant attention from the machine learning community. However, previous approaches are evaluated using unrealistic benchmarks that consider only randomly selected OOD nodes, failing to reflect the interactions among nodes. In this paper, we introduce a new challenging task to model the interactions of OOD nodes in a graph, termed spreading OOD detection, where a newly emerged OOD node spreads its property to neighboring nodes. We curate realistic benchmarks by employing the epidemic spreading models that simulate the spreading of OOD nodes on the graph. We also showcase a ``Spreading COVID-19" dataset to demonstrate the applicability of spreading OOD detection in real-world scenarios. Furthermore, to effectively detect spreading OOD samples under the proposed benchmark setup, we present a new approach called energy distribution-based detector (EDBD), which includes a novel energy-aggregation scheme. EDBD is designed to mitigate undesired mixing of OOD scores between in-distribution (ID) and OOD nodes. Our extensive experimental results demonstrate the superiority of our approach over state-of-the-art methods in both spreading OOD detection and conventional node-level OOD detection tasks across seven benchmark datasets. The source code is available at https://github.com/daehoum1/edbd.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Sagi Shaier, Francisco Pereira, Katharina Kann, Lawrence E Hunter, Matt Jones

The evolution of biological neural systems has led to both modularity and sparse coding, which enables energy efficiency and robustness across the diversity of tasks in the lifespan. In contrast, standard neural networks rely on dense, non-specialized architectures, where all model parameters are simultaneously updated to learn multiple tasks, leading to interference. Current sparse neural network approaches aim to alleviate this issue but are hindered by limitations such as 1) trainable gating functions that cause representation collapse, 2) disjoint experts that result in redundant computation and slow learning, and 3) reliance on explicit input or task IDs that limit flexibility and scalability.In this paper we propose Conditionally Overlapping Mixture of ExperTs (COMET), a general deep learning method that addresses these challenges by inducing a modular, sparse architecture with an exponential number of overlapping experts. COMET replaces the trainable gating function used in Sparse Mixture of Experts with a fixed, biologically inspired random projection applied to individual input representations. This design causes the degree of expert overlap to depend on input similarity, so that similar inputs tend to share more parameters. This results in faster learning per update step and improved out-of-sample generalization. We demonstrate the effectiveness of COMET on a range of tasks, including image classification, language modeling, and regression, using several popular deep learning architectures.

Deep Learning · Generative Models and Autoencoders

João Bravo

Despite the rise to dominance of deep learning in unstructured data domains, tree-based methods such as Random Forests (RF) and Gradient Boosted Decision Trees (GBDT) are still the workhorses for handling discriminative tasks on tabular data. We explore generative extensions of these popular algorithms with a focus on explicitly modeling the data density (up to a normalization constant), thus enabling other applications besides sampling. As our main contribution we propose an energy-based generative boosting algorithm that is analogous to the second-order boosting implemented in popular libraries like XGBoost. We show that, despite producing a generative model capable of handling inference tasks over any input variable, our proposed algorithm can achieve similar discriminative performance to GBDT on a number of real world tabular datasets, outperforming alternative generative approaches. At the same time, we show that it is also competitive with neural-network-based models for sampling.Code is available at https://github.com/ajoo/nrgboost.

Deep Learning · Large Language Models

Patrick Pynadath, Ruqi Zhang

Controlled text generation allows for enforcing user-defined constraints on large language model outputs, an increasingly important field as LLMs become more prevalent in everyday life. One common approach uses energy-based decoding, which defines a target distribution through an energy function that combines multiple constraints into a weighted average. However, these methods often struggle to balance fluency with constraint satisfaction, even with extensive tuning of the energy function's coefficients. In this paper, we identify that this suboptimal balance arises from sampling in continuous space rather than the natural discrete space of text tokens. To address this, we propose \emph{Discrete Auto-regressive Biasing}, a controlled decoding algorithm that leverages gradients while operating entirely in the discrete text domain.Specifically, we introduce a new formulation for controlled text generation by defining a joint distribution over the generated sequence and an auxiliary bias sequence. To efficiently sample from this joint distribution, we propose a Langevin-within-Gibbs sampling algorithm using gradient-based discrete MCMC. Our method significantly improves constraint satisfaction while maintaining comparable or better fluency, all with lower computational costs. We demonstrate the advantages of our controlled decoding method on sentiment control, language detoxification, and keyword-guided generation.

Optimization · Non-Convex

Timothee Leleu, Sam Reifenstein

We propose a general framework for a hybrid continuous-discrete algorithm that integrates continuous-time deterministic dynamics with Metropolis-Hastings (MH) steps to combine search dynamics that either preserve or break detailed balance. Our purpose is to study the non-equilibrium dynamics that leads to the ground state of rugged energy landscapes in this general setting. Our results show that MH-driven dynamics reach ``easy'' ground states more quickly, indicating a stronger bias toward these solutions in algorithms using reversible transition probabilities. To validate this, we construct a set of Ising problem instances with a controllable bias in the energy landscape that makes certain degenerate solutions more accessible than others. The constructed hybrid algorithm demonstrates significant improvements in convergence and ground-state sampling accuracy, achieving a 100x speedup on GPU compared to simulated annealing, making it well-suited for large-scale applications.

Yuhan Chen, Yihong Luo, Yifan Song, Pengwen Dai, Jing Tang, Xiaochun Cao

Despite extensive research efforts focused on Out-of-Distribution (OOD) detection on images, OOD detection on nodes in graph learning remains underexplored. The dependence among graph nodes hinders the trivial adaptation of existing approaches on images that assume inputs to be i.i.d. sampled, since many unique features and challenges specific to graphs are not considered, such as the heterophily issue. Recently, GNNSafe, which considers node dependence, adapted energy-based detection to the graph domain with state-of-the-art performance, however, it has two serious issues: 1) it derives node energy from classification logits without specifically tailored training for modeling data distribution, making it less effective at recognizing OOD data; 2) it highly relies on energy propagation, which is based on homophily assumption and will cause significant performance degradation on heterophilic graphs, where the node tends to have dissimilar distribution with its neighbors. To address the above issues, we suggest training Energy-based Models (EBMs) by Maximum Likelihood Estimation (MLE) to enhance data distribution modeling and removing energy propagation to overcome the heterophily issues. However, training EBMs via MLE requires performing Markov Chain Monte Carlo (MCMC) sampling on both node feature and node neighbors, which is challenging due to the node interdependence and discrete graph topology. To tackle the sampling challenge, we introduce Decoupled Graph Energy-based Model (DeGEM), which decomposes the learning process into two parts—a graph encoder that leverages topology information for node representations and an energy head that operates in latent space. Additionally, we propose a Multi-Hop Graph encoder (MH) and Energy Readout (ERo) to enhance node representation learning, Conditional Energy (CE) for improved EBM training, and Recurrent Update for the graph encoder and energy head to promote each other. This approach avoids sampling adjacency matrices and removes the need for energy propagation to extract graph topology information. Extensive experiments validate that DeGEM, without OOD exposure during training, surpasses previous state-of-the-art methods, achieving an average AUROC improvement of 6.71% on *homophilic* graphs and 20.29% on *heterophilic* graphs, and even outperform methods trained with OOD exposure. Our code is available at: [https://github.com/draym28/DeGEM](https://github.com/draym28/DeGEM).

Huiang He, Minghui HU, Chuanxia Zheng, Chaoyue Wang, Tat-Jen Cham

Recent advances in style and appearance transfer are impressive, but most methods isolate global style and local appearance transfer, neglecting semantic correspondence. Additionally, image and video tasks are typically handled in isolation, with little focus on integrating them for video transfer. To address these limitations, we introduce a novel task, *Semantic Style Transfer*, which involves transferring style and appearance features from a reference image to a target visual content based on semantic correspondence. We subsequently propose a training-free method, *Semantix*, an energy-guided sampler designed for Semantic Style Transfer that simultaneously guides both style and appearance transfer based on semantic understanding capacity of pre-trained diffusion models. Additionally, as a sampler, *Semantix* can be seamlessly applied to both image and video models, enabling semantic style transfer to be generic across various visual media. Specifically, once inverting both reference and context images or videos to noise space by SDEs, *Semantix* utilizes a meticulously crafted energy function to guide the sampling process, including three key components: *Style Feature Guidance*, *Spatial Feature Guidance* and *Semantic Distance* as a regularisation term. Experimental results demonstrate that *Semantix* not only effectively accomplishes the task of semantic style transfer across images and videos, but also surpasses existing state-of-the-art solutions in both fields.

Yongqi Ding, Lin Zuo, Mengmeng Jing, Pei He, Hanpu Deng

Spiking neural networks (SNNs) exhibit superior energy efficiency but suffer from limited performance. In this paper, we consider SNNs as ensembles of temporal subnetworks that share architectures and weights, and highlight a crucial issue that affects their performance: excessive differences in initial states (neuronal membrane potentials) across timesteps lead to unstable subnetwork outputs, resulting in degraded performance. To mitigate this, we promote the consistency of the initial membrane potential distribution and output through membrane potential smoothing and temporally adjacent subnetwork guidance, respectively, to improve overall stability and performance. Moreover, membrane potential smoothing facilitates forward propagation of information and backward propagation of gradients, mitigating the notorious temporal gradient vanishing problem. Our method requires only minimal modification of the spiking neurons without adapting the network structure, making our method generalizable and showing consistent performance gains in 1D speech, 2D object, and 3D point cloud recognition tasks. In particular, on the challenging CIFAR10-DVS dataset, we achieved 83.20\% accuracy with only four timesteps. This provides valuable insights into unleashing the potential of SNNs.

Deep Learning · Generative Models and Autoencoders

Jiachen Li, Qian Long, Jian (Skyler) Zheng, Xiaofeng Gao, Robinson Piramuthu, Wenhu Chen, William Wang

In this paper, we focus on enhancing a diffusion-based text-to-video (T2V) model during the post-training phase by distilling a highly capable consistency model from a pretrained T2V model. Our proposed method, T2V-Turbo-v2, introduces a significant advancement by integrating various supervision signals, including high-quality training data, reward model feedback, and conditional guidance, into the consistency distillation process. Through comprehensive ablation studies, we highlight the crucial importance of tailoring datasets to specific learning objectives and the effectiveness of learning from diverse reward models for enhancing both the visual quality and text-video alignment. Additionally, we highlight the vast design space of conditional guidance strategies, which centers on designing an effective energy function to augment the teacher ODE solver. We demonstrate the potential of this approach by extracting motion guidance from the training datasets and incorporating it into the ODE solver, showcasing its effectiveness in improving the motion quality of the generated videos with the improved motion-related metrics from VBench and T2V-CompBench. Empirically, our T2V-Turbo-v2 establishes a new state-of-the-art result on VBench, **with a Total score of 85.13**, surpassing proprietary systems such as Gen-3 and Kling.

Optimization · Learning for Optimization

Vincenzo Di Vito Francesco, Mostafa Mohammadian, Kyri Baker, Ferdinando Fioretto

Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control strategies must be determined for systems governed by ordinary or stochastic differential equations. Despite its significance, the computational challenges associated with these problems have limited their practical use. To address these limitations, this paper introduces a learning-based approach to DE-constrained optimization that combines techniques from proxy optimization \citep{kotary2021end} and neural differential equations \citep{chen2019neural}. The proposed approach uses a dual-network architecture, with one approximating the control strategies, focusing on steady-state constraints, and another solving the associated DEs. This combination enables the approximation of optimal strategies while accounting for dynamic constraints in near real-time.Experiments across problems in energy optimization and finance modeling show that this method provides full compliance with dynamic constraints and it produces results up to 25 times more precise than other methods which do not explicitly model the system's dynamic equations.

Applications · Neuroscience, Cognitive Science

Will Dorrell, Kyle Hsu, Luke Hollingsworth, Jin Hwa Lee, Jiajun Wu, Chelsea Finn, Peter Latham, Timothy Behrens, James Whittington

Why do biological and artificial neurons sometimes modularise, each encoding a single meaningful variable, and sometimes entangle their representation of many variables? In this work, we develop a theory of when biologically inspired networks---those that are nonnegative and energy efficient---modularise their representation of source variables (sources). We derive necessary and sufficient conditions on a sample of sources that determine whether the neurons in an optimal biologically-inspired linear autoencoder modularise. Our theory applies to any dataset, extending far beyond the case of statistical independence studied in previous work. Rather we show that sources modularise if their support is ``sufficiently spread''. From this theory, we extract and validate predictions in a variety of empirical studies on how data distribution affects modularisation in nonlinear feedforward and recurrent neural networks trained on supervised and unsupervised tasks. Furthermore, we apply these ideas to neuroscience data, showing that range independence can be used to understand the mixing or modularising of spatial and reward information in entorhinal recordings in seemingly conflicting experiments. Further, we use these results to suggest alternate origins of mixed-selectivity, beyond the predominant theory of flexible nonlinear classification. In sum, our theory prescribes precise conditions on when neural activities modularise, providing tools for inducing and elucidating modular representations in brains and machines.

Deep Learning · Large Language Models

Zongyue Qin, Ziniu Hu, Zifan He, Neha Prakriya, Jason Cong, Yizhou Sun

Large language models (LLMs) have achieved remarkable success across diverse tasks, yet their inference processes are hindered by substantial time and energy demands due to single-token generation at each decoding step. While previous methods such as speculative decoding mitigate these inefficiencies by producing multiple tokens per step, each token is still generated by its single-token distribution,thereby enhancing speed without improving effectiveness. In contrast, our work simultaneously enhances inference speed and improves the output effectiveness. We consider multi-token joint decoding (MTJD), which generates multiple tokens from their joint distribution at each iteration, theoretically reducing perplexity and enhancing task performance. However, MTJD suffers from the high cost of sampling from the joint distribution of multiple tokens. Inspired by speculative decoding, we introduce multi-token assisted decoding (MTAD), a novel framework designed to accelerate MTJD. MTAD leverages a smaller auxiliary model to approximate the joint distribution of a larger model, incorporating a verification mechanism that not only ensures the accuracy of this approximation, but also improves thedecoding efficiency over conventional speculative decoding. Theoretically, we demonstrate that MTAD closely approximates exact MTJD with bounded error. Empirical evaluations using Llama-2 and OPT models ranging from 13B to 70B parameters across various tasks reveal that MTAD reduces perplexity by 21.2% and improves downstream performance compared to standard single-token sampling.Furthermore, MTAD achieves a 1.42× speed-up and consumes 1.54× less energy than conventional speculative decoding methods. These results highlight MTAD’s ability to make multi-token joint decoding both effective and efficient, promoting more sustainable and high-performance deployment of LLMs.

Deep Learning · Other Representation Learning

Core Francisco Park, Andrew Lee, Ekdeep Singh Lubana, Yongyi Yang, Maya Okawa, Kento Nishi, Martin Wattenberg, Hidenori Tanaka

Recent work demonstrates that structured patterns in pretraining data influence how representations of different concepts are organized in a large language model’s (LLM) internals, with such representations then driving downstream abilities. Given the open-ended nature of LLMs, e.g., their ability to in-context learn novel tasks, we ask whether models can flexibly alter their semantically grounded organization of concepts. Specifically, if we provide in-context exemplars wherein a concept plays a different role than what the pretraining data suggests, can models infer these novel semantics and reorganize representations in accordance with them? To answer this question, we define a toy “graph tracing” task wherein the nodes of the graph are referenced via concepts seen during training (e.g., apple, bird, etc.), and the connectivity of the graph is defined via some predefined structure (e.g., a square grid). Given exemplars that indicate traces of random walks on the graph, we analyze intermediate representations of the model and find that as the amount of context is scaled, there is a sudden re-organization of representations according to the graph’s structure. Further, we find that when reference concepts have correlations in their semantics (e.g., Monday, Tuesday, etc.), the context-specified graph structure is still present in the representations, but is unable to dominate the pretrained structure. To explain these results, we analogize our task to energy minimization for a predefined graph topology, which shows getting non-trivial performance on the task requires for the model to infer a connected component. Overall, our findings indicate context-size may be an underappreciated scaling axis that can flexibly re-organize model representations, unlocking novel capabilities.