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.

Prior work has shown that text-conditioned diffusion models can learn to identify and manipulate primitive concepts underlying a compositional data-generating process, enabling generalization to entirely novel, out-of-distribution compositions. Beyond performance evaluations, these studies develop a rich empirical phenomenology of learning dynamics, showing that models generalize sequentially, respecting the compositional hierarchy of the data-generating process. Moreover, concept-centric structures within the data significantly influence a model's speed of learning the ability to manipulate a concept. In this paper, we aim to better characterize these empirical results from a theoretical standpoint. Specifically, we propose an abstraction of prior work's compositional generalization problem by introducing a structured identity mapping (SIM) task, where a model is trained to learn the identity mapping on a Gaussian mixture with structurally organized centroids. We mathematically analyze the learning dynamics of neural networks trained on this SIM task and show that, despite its simplicity, SIM's learning dynamics capture and help explain key empirical observations on compositional generalization with diffusion models identified in prior work. Our theory also offers several new insights---e.g., we find a novel mechanism for non-monotonic learning dynamics of test loss in early phases of training. We validate our new predictions by training a text-conditioned diffusion model, bridging our simplified framework and complex generative models. Overall, this work establishes the SIM task as a meaningful theoretical abstraction of concept learning dynamics in modern generative models.

Knowledge Editing (KE) algorithms alter models’ weights to perform targeted updates to incorrect, outdated, or otherwise unwanted factual associations. However, recent work has shown that applying KE can adversely affect models’ broader factual recall accuracy and diminish their reasoning abilities. Although these studies give insights into the potential harms of KE algorithms, e.g., performance evaluations on benchmarks, little is understood about why such destructive failures occur. Motivated by this, we define a novel synthetic task in which a Transformer is trained from scratch to internalize a "structured" knowledge graph. The structure enforces relationships between entities of the graph, such that editing a factual association has "trickling effects" on other entities (e.g., altering X’s parent is Y to Z affects who X’s siblings’ parent is). Through evaluations of edited models on this task, we show that KE inadvertently affects representations of entities beyond the targeted one, distorting relevant structures that allow a model to infer unseen knowledge about an entity. We call this phenomenon representation shattering and demonstrate that it degrades models’ factual recall and reasoning performance. We further corroborate our findings in naturalistic settings with pre-trained Llama and Mamba models as well. Overall, our work yields a precise mechanistic hypothesis to explain why KE has adverse effects on model abilities.

Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. To unravel the underlying mechanisms of stepwise inference we propose to study autoregressive Transformer models on a synthetic task that embodies the multi-step nature of problems where stepwise inference is generally most useful. Specifically, we define a graph navigation problem wherein a model is tasked with traversing a path from a start to a goal node on the graph. We find we can empirically reproduce and analyze several phenomena observed at scale: (i) the stepwise inference reasoning gap, the cause of which we find in the structure of the training data; (ii) a diversity-accuracy trade-off in model generations as sampling temperature varies; (iii) a simplicity bias in the model’s output; and (iv) compositional generalization and a primacy bias with in-context exemplars. Overall, our work introduces a grounded, synthetic framework for studying stepwise inference and offers mechanistic hypotheses that can lay the foundation for a deeper understanding of this phenomenon.

Modern generative models demonstrate impressive capabilities, likely stemming from an ability to identify and manipulate abstract concepts underlying their training data. However, fundamental questions remain: what determines the concepts a model learns, the order in which it learns them, and its ability to manipulate those concepts? To address these questions, we propose analyzing a model’s learning dynamics via a framework we call the concept space, where each axis represents an independent concept underlying the data generating process. By characterizing learning dynamics in this space, we identify how the speed at which a concept is learned, and hence the order of concept learning, is controlled by properties of the data we term concept signal. Further, we observe moments of sudden turns in the direction of a model’s learning dynamics in concept space. Surprisingly, these points precisely correspond to the emergence of hidden capabilities, i.e., where latent interventions show the model possesses the capability to manipulate a concept, but these capabilities cannot yet be elicited via naive input prompting. While our results focus on synthetically defined toy datasets, we hypothesize a general claim on emergence of hidden capabilities may hold: generative models possess latent capabilities that emerge suddenly and consistently during training, though a model might not exhibit these capabilities under naive input prompting.

Modern generative models exhibit unprecedented capabilities to generate extremely realistic data. However, given the inherent compositionality of the real world, reliable use of these models in practical applications requires that they exhibit the capability to compose a novel set of concepts to generate outputs not seen in the training data set. Prior work demonstrates that recent diffusion models do exhibit intriguing compositional generalization abilities, but also fail unpredictably. Motivated by this, we perform a controlled study for understanding compositional generalization in conditional diffusion models in a synthetic setting, varying different attributes of the training data and measuring the model's ability to generate samples out-of-distribution. Our results show: (i) the order in which the ability to generate samples from a concept and compose them emerges is governed by the structure of the underlying data-generating process; (ii) performance on compositional tasks exhibits a sudden "emergence" due to multiplicative reliance on the performance of constituent tasks, partially explaining emergent phenomena seen in generative models; and (iii) composing concepts with lower frequency in the training data to generate out-of-distribution samples requires considerably more optimization steps compared to generating in-distribution samples. Overall, our study lays a foundation for understanding emergent capabilities and compositionality in generative models from a data-centric perspective.

Opinion formation and propagation are crucial phenomena in social networks and have been extensively studied across several disciplines. Traditionally, theoretical models of opinion dynamics have been proposed to describe the interactions between individuals (i.e., social interaction) and their impact on the evolution of collective opinions. Although these models can incorporate sociological and psychological knowledge on the mechanisms of social interaction, they demand extensive calibration with real data to make reliable predictions, requiring much time and effort. Recently, the widespread use of social media platforms provides new paradigms to learn deep learning models from a large volume of social media data. However, these methods ignore any scientific knowledge about the mechanism of social interaction. In this work, we present the first hybrid method called Sociologically-Informed Neural Network (SINN), which integrates theoretical models and social media data by transporting the concepts of physics-informed neural networks (PINNs) from natural science (i.e., physics) into social science (i.e., sociology and social psychology). In particular, we recast theoretical models as ordinary differential equations (ODEs). Then we train a neural network that simultaneously approximates the data and conforms to the ODEs that represent the social scientific knowledge. In addition, we extend PINNs by integrating matrix factorization and a language model to incorporate rich side information (e.g., user profiles) and structural knowledge (e.g., cluster structure of the social interaction network). Moreover, we develop an end-to-end training procedure for SINN, which involves Gumbel-Softmax approximation to include stochastic mechanisms of social interaction. Extensive experiments on real-world and synthetic datasets show SINN outperforms six baseline methods in predicting opinion dynamics.

Massive spatio-temporal event data sets are now available that cover events such as disease outbreaks, armed conflicts and crimes. Predicting such events and revealing the underlying triggering patterns are a crucial task for many applications, ranging from disease control to global politics. Traditional event prediction models based on Hawkes processes capture the spatio-temporal relationships between events, but cannot incorporate complex and heterogeneous external features, including population distribution, weather and terrain. This paper proposes an event prediction method that effectively utilizes the rich external information present in sets of unstructured data (e.g., map images, satellite images and weather map). Specifically, we extend a convolutional neural network (CNN) by combining it with continuous kernel convolution; and design the conditional intensity of Hawkes process based on the extended neural network model that accepts images as its input. Our approach of using the continuous convolution kernel provides a flexible way to discover the complex effect of external factors on the triggering process, as well as yielding tractable optimization algorithms. We use real-world event data from different domains (i.e., disease outbreaks, armed conflicts and protests) to demonstrate that the proposed method has better prediction performance than existing methods.

Sequences of events including infectious disease outbreaks, social network activities, and crimes are ubiquitous and the data on such events carry essential information about the underlying diffusion processes between communities (e.g., regions, online user groups). Modeling diffusion processes and predicting future events are crucial in many applications including epidemic control, viral marketing, and predictive policing. Hawkes processes offer a central tool for modeling the diffusion processes, in which the influence from the past events is described by the triggering kernel. However, the triggering kernel parameters, which govern how each community is influenced by the past events, are assumed to be static over time. In the real world, the diffusion processes depend not only on the influences from the past, but also the current (time-evolving) states of the communities, e.g., people's awareness of the disease and people's current interests. In this paper, we propose a novel Hawkes process model that is able to capture the underlying dynamics of community states behind the diffusion processes and predict the occurrences of events based on the dynamics. Specifically, we model the latent dynamic function that encodes these hidden dynamics by a mixture of neural networks. Then we design the triggering kernel using the latent dynamic function and its integral. The proposed method, termed DHP (Dynamic Hawkes Processes), offers a flexible way to learn complex representations of the time-evolving communities' states, while at the same time it allows to computing the exact likelihood, which makes parameter learning tractable. Extensive experiments on four real-world event datasets show that DHP outperforms five widely adopted methods for event prediction.

We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data sets with various granularities by hierarchically incorporating Gaussian processes. With the proposed model, a distribution for each auxiliary data set on the continuous space is modeled using a Gaussian process, where the representation of uncertainty considers the levels of granularity. The finegrained target data are modeled by another Gaussian process that considers both the spatial correlation and the auxiliary data sets with their uncertainty. We integrate the Gaussian process with a spatial aggregation process that transforms the fine-grained target data into the coarse-grained target data, by which we can infer the fine-grained target Gaussian process from the coarse-grained data. Our model is designed such that the inference of model parameters based on the exact marginal likelihood is possible, in which the variables of finegrained target and auxiliary data are analytically integrated out. Our experiments on real-world spatial data sets demonstrate the effectiveness of the proposed model.

Predicting when and where events will occur in cities, like taxi pick-ups, crimes, and vehicle collisions, is a challenging and important problem with many applications in fields such as urban planning, transportation optimization and location-based marketing. Though many point processes have been proposed to model events in a continuous spatio-temporal space, none of them allow for the consideration of the rich contextual factors that affect event occurrence, such as weather, social activities, geographical characteristics, and traffic. In this paper, we propose DMPP (Deep Mixture Point Processes), a point process model for predicting spatio-temporal events with the use of rich contextual information; a key advance is its incorporation of the heterogeneous and high-dimensional context available in image and text data. Specifically, we design the intensity of our point process model as a mixture of kernels, where the mixture weights are modeled by a deep neural network. This formulation allows us to automatically learn the complex nonlinear effects of the contextual factors on event occurrence. At the same time, this formulation makes analytical integration over the intensity, which is required for point process estimation, tractable. We use real-world data sets from different domains to demonstrate that DMPP has better predictive performance than existing methods.

We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can only utilize the sufficiently fine-grained auxiliary data sets on the same domain (e.g., a city). With the proposed model, the functions for respective areal data sets are assumed to be a multivariate dependent Gaussian process (GP) that is modeled as a linear mixing of independent latent GPs. Sharing of latent GPs across multiple areal data sets allows us to effectively estimate the spatial correlation for each areal data set; moreover it can easily be extended to transfer learning across multiple domains. To handle the multivariate areal data, we design an observation model with a spatial aggregation process for each areal data set, which is an integral of the mixed GP over the corresponding region. By deriving the posterior GP, we can predict the data value at any location point by considering the spatial correlations and the dependences between areal data sets, simultaneously. Our experiments on real-world data sets demonstrate that our model can 1) accurately refine coarse-grained areal data, and 2) offer performance improvements by using the areal data sets from multiple domains.

Predicting traffic flows on multiple inter-city roads play a critical role in traffic management. Temporal patterns of traffic flow can dynamically change over time as a result of traffic management measures such as the construction of new roads. Given this possibility, it is sensible to use only recent data, instead of all past data. In this study, by incorporating the latent factor model into a conventional approach, we construct a novel traffic prediction method for multiple inter-city roads based on the most recent training data. This formulation leads to a reduction in the number of model parameters, since it assumes that there is a set of patterns underlying the data (in our case, the periodic patterns shared across roads in traffic flow data), which inherently offers robustness against sparse observations. In addition, we adopt stochastic variational Bayes method to solve the optimization problem, which allows us to update model parameters online. By continually updating the model based on the most recent training data, we can instantly provide accurate predictions of inter-city traffic flow that have intermittently changing patterns. Using a real-world traffic flow dataset collected in the Greater Tokyo Area via GPS-equipped mobile phones, we evaluate the predictive performance of the proposed method, and confirm that it performs better than existing methods in the sparse domain.