Agents are minimally entities that are influenced by their past observations and act to influence future observations. This latter capacity is captured by empowerment, which has served as a vital framing concept across artificial intelligence and cognitive science. This former capacity, however, is equally foundational: In what ways, and to what extent, can an agent be influenced by what it observes? In this paper, we ground this concept in a universal agent-centric measure that we refer to as plasticity, and reveal a fundamental connection to empowerment. Following a set of desiderata on a suitable definition, we define plasticity using a new informationtheoretic quantity we call the generalized directed information. We show that this new quantity strictly generalizes the directed information introduced by Massey (1990) while preserving all of its desirable properties. Under this definition, we find that plasticity is well thought of as the mirror of empowerment: The two concepts are defined using the same measure, with only the direction of influence reversed. Our main result establishes a tension between the plasticity and empowerment of an agent, suggesting that agent design needs to be mindful of both characteristics. We explore the implications of these findings, and suggest that plasticity, empowerment, and their relationship are essential to understanding agency.

Lithography orchestrates a symphony of light, mask and photochemicals to transfer the integrated circuit patterns onto the wafer. Lithography simulation serves as the critical nexus between circuit design and manufacturing, where its speed and accuracy fundamentally govern the optimization quality of downstream resolution enhancement techniques (RETs). While machine learning promises to circumvent computational limitations of lithography process through data-driven or physics-informed approximations of computational lithography, existing simulators suffer from inadequate lithographic awareness due to insufficient training data capturing essential process variations and mask correction rules.

Aligning large language models with human feedback at inference time has received increasing attention due to its flexibility. Existing methods rely on generating multiple responses from the base policy for search using a reward model, which can be considered as searching in a discrete response space. However, these methods struggle to explore informative candidates when the base policy is weak or the candidate set is small, resulting in limited effectiveness. In this paper, to address this problem, we propose Simple Energy Adaptation (SEA), a simple yet effective algorithm for inference-time alignment.

We study the dynamics of gradient flow with small weight decay on general training losses F: Rd R. Under mild regularity assumptions and assuming convergence of the unregularised gradient flow, we show that the trajectory with weight decay λ exhibits a two-phase behaviour as λ 0. During the initial fast phase, the trajectory follows the unregularised gradient flow and converges to a manifold of critical points of F. Then, at time of order 1/λ, the trajectory enters a slow drift phase and follows a Riemannian gradient flow minimising the ℓ2-norm of the parameters. This purely optimisation-based phenomenon offers a natural explanation for the grokking effect observed in deep learning, where the training loss rapidly reaches zero while the test loss plateaus for an extended period before suddenly improving. We argue that this generalisation jump can be attributed to the slow norm reduction induced by weight decay, as explained by our analysis.

Diffusion models have made significant advancements in recent years. However, their performance often deteriorates when trained or fine-tuned on imbalanced datasets. This degradation is largely due to the disproportionate representation of majority and minority data in image-text pairs. In this paper, we propose a general fine-tuning approach, dubbed PoGDiff, to address this challenge. Rather than directly minimizing the KL divergence between the predicted and ground-truth distributions, PoGDiff replaces the ground-truth distribution with a Product of Gaussians (PoG), which is constructed by combining the original ground-truth targets with the predicted distribution conditioned on a neighboring text embedding. Experiments on real-world datasets demonstrate that our method effectively addresses the imbalance problem in diffusion models, improving both generation accuracy and quality.

Neurosymbolic (NeSy) predictors combine neural perception with symbolic reasoning to solve tasks like visual reasoning. However, standard NeSy predictors assume conditional independence between the symbols they extract, thus limiting their ability to model interactions and uncertainty -- often leading to overconfident predictions and poor out-of-distribution generalisation. To overcome the limitations of the independence assumption, we introduce neurosymbolic diffusion models (NESYDMS), a new class of NeSy predictors that use discrete diffusion to model dependencies between symbols.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training language models (LMs) on reasoning tasks that elicit emergent long chains of thought (CoTs).

Transformers have demonstrated remarkable capabilities in multi-step reasoning tasks. However, understandings of the underlying mechanisms by which they acquire these abilities through training remain limited, particularly from a theoretical standpoint. This work investigates how transformers learn to solve symbolic multi-step reasoning problems through chain-of-thought processes, focusing on path-finding in trees. We analyze two intertwined tasks: a backward reasoning task, where the model outputs a path from a goal node to the root, and a more complex forward reasoning task, where the model implements two-stage reasoning by first identifying the goal-to-root path and then reversing it to produce the root-to-goal path. Our theoretical analysis, grounded in the dynamics of gradient descent, shows that trained one-layer transformers can provably solve both tasks with generalization guarantees to unseen trees. In particular, our multi-phase training dynamics for forward reasoning elucidate how different attention heads learn to specialize and coordinate autonomously to solve the two subtasks in a single autoregressive path. These results provide a mechanistic explanation of how trained transformers can implement sequential algorithmic procedures. Moreover, they offer insights into the emergence of reasoning abilities, suggesting that when tasks are structured to take intermediate chain-of-thought steps, even shallow multi-head transformers can effectively solve problems that would otherwise require deeper architectures.

Density estimation is essential for generative modeling, particularly with the rise of modern neural networks. While existing methods capture complex data distributions, they often lack interpretability and uncertainty quantification.

Learning dynamics is essential for model-based control and Reinforcement Learning in engineering systems, such as robotics and power systems.