DeltaMomentum: A Key-Value based Anisotropic Momentum Update via Delta Rule

Most modern optimizers form their momentum as an exponential moving average (EMA) of past gradients, forgetting every direction at one fixed rate. However, the inputs a deep network sees during training can be highly anisotropic, with a few directions queried frequently while most are seen rarely. Recent methods address this anisotropy by wrapping extra processing around this buffer, leaving the momentum update itself unchanged. We propose DeltaMomentum, which builds direction-awareness into the momentum update rule. The main observation is that the gradient of a linear layer splits into an input that acts as a key and an output-side error that acts as a value. Exploiting the key-value structure, DeltaMomentum updates the momentum buffer by the canonical delta rule, so each direction is forgotten at a rate set by how often it appears. We prove that it is a valid momentum, that it applies the input-side curvature correction without matrix inversion, and that it clears stale directions faster than EMA under both a fixed and a drifting optimum. It is a drop-in replacement for the momentum buffer of any optimizer, its coefficient transfers across widths under $μ$P, and its extra compute stays between $22.2\%$ and $25.0\%$ of a gated-MLP block's linear cost with no persistent memory. In FineWeb-Edu pretraining, AdamW with DeltaMomentum (DeltaAdamW) reaches AdamW's validation loss in up to $46.39 \pm 4.32\%$ fewer steps at 67M and $22.12 \pm 0.80\%$ at 370M over three seeds, and the gain persists at 1B on a Chinchilla-optimal budget. A Muon baseline tuned under the same protocol sits above DeltaAdamW at both language-model scales, and the gain holds for SGD, ResNet-18, and ViT-Tiny on CIFAR-10. Training-time diagnostics confirm the predicted mechanism, better gradient tracking and healthier input directions.

Hybrid Feedback Sampling for Sample-Efficient Model Predictive Control

Thanks to its parallelizability and flexibility, sampling-based Model Predictive Control (MPC) has become widely popular for controlling real-world robotic systems. However, for high-dimensional and open-loop unstable dynamical systems, the required number of samples to improve the control sequence will grow exponentially with the horizon, leading to poor sample efficiency and numerical instability. This paper investigates the instability of shooting methods in sampling-based MPC and shows that the optimal sampling proposal distribution can be realized by sampling with an optimized feedback policy. We refer to this algorithm as Feedback Sampling MPC (FS-MPC). FS-MPC involves a hybrid sampling design which balances local and global search based on the system stability and the available computation budget. Our theoretical analysis shows that our hybrid sampling approach achieves faster convergence than standard MPPI and better optimality than standard feedback sampling. Empirically, in diverse contact-rich control tasks like humanoid loco-manipulation and dexterous manipulation, we show that FS-MPC successfully tackles dynamically unstable tasks where standard sample-based approaches struggle, and strictly outperforms feedback policies alone. Finally, we validate our method on humanoid robot locomotion and manipulation tasks in the real world.

A Theoretical Framework for Parallel Lifelong MAPF Using Group Decentralized Planning

In the Lifelong Multi-Agent Path Finding (L-MAPF) problem, agents must repeatedly move from one destination to another while avoiding obstacles and inter-agent collisions. Widely regarded as one of the highest-performing solutions to this problem is the Rolling-Horizon Collision Resolution (RHCR) framework. However, commensurate with its quality solutions, it incurs a computational cost that limits its applicability to even modest agent counts. In this paper, leveraging theoretical methods from the Locally Interdependent Multi-Agent MDP literature, we first theoretically prove the near-optimality of RHCR in a discounted MDP formulation of the L-MAPF problem. Then, we leverage these results to naturally motivate an extended framework called Group Decentralized RHCR (GD-RHCR) which incorporates a group decentralized structure that partitions agents based on a transitive communication scheme and plans for each partition of agents in parallel. We show that both RHCR and GD-RHCR achieve similar exponentially close to optimal guarantees, establishing a theoretical duality between the time based restrictions performed by vanilla RHCR and the additional space based partitioning performed by GD-RHCR. Lastly, we show that across varying maps, GD-RHCR is able to attain high throughput that scales into higher agent counts while maintaining a significantly lower per plan cost.

Emergent and Subliminal Misalignment Through the Lens of Data-Mediated Transfer

Fine-tuning LLMs on narrow harmful datasets can induce Emergent Misalignment (EM), where models exhibit misaligned behavior far beyond the fine-tuning distribution. We argue that emergent misalignment can be better understood as a data-mediated transfer phenomenon: harmful fine-tuning examples do not induce uniform behavioral spillover, but interact with the structural properties of the dataset and the difficulty of the tasks relative to the model. Across our experiments, we find that misalignment appears more readily when fine-tuning and evaluation prompts share similar underlying functional structure, when prompts leave more room for coherent harmful completions, and when the target behavior has been more reliably learned by the model. The training pipeline itself also matters: pretraining composition shapes later misalignment. We further study Subliminal Learning (SL), where misalignment is transmitted by fine-tuning on seemingly benign data generated by a harmful teacher. Moving beyond the standard SFT setting, we for the first time compare this transfer under off-policy and on-policy distillation as well, allowing us to separate the roles of the teacher guidance and the training data distribution in transmitting misalignment. Together, these results argue for a data-centric view: Emergent/subliminal misalignment should not be treated as a simple consequence of isolated harmful fine-tuning examples, but as the result of interactions between fine-tuning data structure, pretraining distributions, and training channels.

Revisiting Policy Gradients for Restricted Policy Classes: Escaping Myopic Local Optima with $k$-step Policy Gradients

This work revisits standard policy gradient methods used on restricted policy classes, which are known to get stuck in suboptimal critical points. We identify an important cause for this phenomenon to be that the policy gradient is itself fundamentally myopic, i.e. it only improves the policy based on the one-step $Q$-function. In this work, we propose a generalized $k$-step policy gradient method that couples the randomness within a $k$-step time window and can escape the myopic local optima in MDPs with restricted policy classes. We show this new method is theoretically guaranteed to converge to a solution that is exponentially close in performance to the optimal deterministic policy with respect to $k$. Further, we show projected gradient descent and mirror descent with this $k$-step policy gradient can achieve this exponential guarantee in $O(\frac{1}{T})$ iterations, despite only assuming smoothness and differentiability of the value function. This will provide near optimal solutions to previously elusive applications like state aggregation and partially observable cooperative multi-agent settings. Moreover, our bounds avoid the ubiquitous distribution mismatch factors $||d_μ^{π^*} / d_μ^π||_\infty$ and $||d_μ^{π^*} / μ||_\infty$ enabling the $k$-step policy gradient method to escape suboptimal critical points that emerge from poor exploration in fully observable settings.

Towards Effective Theory of LLMs: A Representation Learning Approach

We propose Representational Effective Theory (RET), a framework for describing large language model computation in terms of learned macrostates rather than microscopic details. RET learns these macrostates from hidden-state trajectories using a BYOL/JEPA-style self-supervised objective, coarse-graining activations into macrovariables that preserve higher-level structure relevant for prediction and interpretation. We evaluate whether these macrovariables are practically relevant for interpretability: RET yields temporally consistent states that reveal "mental-state" trajectories of reasoning, capture high-level semantic structure, support early prediction of behavioral outcomes such as sycophancy, and provide causal handles for steering generations toward interpretable computational phases. Together, these results suggest that LLM computation admits useful effective descriptions via RET: high-level, dynamically meaningful variables that support interpretation, prediction, and intervention.

BLOCK-EM: Preventing Emergent Misalignment by Blocking Causal Features

Emergent misalignment can arise when a language model is fine-tuned on a narrowly scoped supervised objective: the model learns the target behavior, yet also develops undesirable out-of-domain behaviors. We investigate a mechanistic approach to preventing emergent misalignment by identifying a small set of internal features that reliably control the misaligned behavior and then discouraging the model from strengthening these features during fine-tuning. Across six fine-tuning domains, blocking (i.e., constraining) a fixed set of features achieves up to 95\% relative reduction in emergent misalignment with no degradation in model quality or target-task performance. We strengthen validity with disjoint selection/evaluation splits, multiple independent judges, multiple random seeds for key settings, quality metrics, and extensive ablations demonstrating that the reduction in misalignment is specific to the identified mechanism. We also characterize a limiting regime in which misalignment re-emerges under prolonged fine-tuning, present evidence consistent with rerouting through alternative features or layers, and evaluate modifications that partially restore the misalignment-blocking effect. Overall, our results show that targeted training-time constraints on internal mechanisms can mitigate emergent misalignment without degrading target-task performance.

Polynomial Convergence of Riemannian Diffusion Models

Diffusion models have demonstrated remarkable empirical success in the recent years and are considered one of the state-of-the-art generative models in modern AI. These models consist of a forward process, which gradually diffuses the data distribution to a noise distribution spanning the whole space, and a backward process, which inverts this transformation to recover the data distribution from noise. Most of the existing literature assumes that the underlying space is Euclidean. However, in many practical applications, the data are constrained to lie on a submanifold of Euclidean space. Addressing this setting, De Bortoli et al. (2022) introduced Riemannian diffusion models and proved that using an exponentially small step size yields a small sampling error in the Wasserstein distance, provided the data distribution is smooth and strictly positive, and the score estimate is $L_\infty$-accurate. In this paper, we greatly strengthen this theory by establishing that, under $L_2$-accurate score estimate, a {\em polynomially small stepsize} suffices to guarantee small sampling error in the total variation distance, without requiring smoothness or positivity of the data distribution. Our analysis only requires mild and standard curvature assumptions on the underlying manifold. The main ingredients in our analysis are Li-Yau estimate for the log-gradient of heat kernel, and Minakshisundaram-Pleijel parametrix expansion of the perturbed heat equation. Our approach opens the door to a sharper analysis of diffusion models on non-Euclidean spaces.

Transformer-Based Scalable Multi-Agent Reinforcement Learning for Networked Systems with Long-Range Interactions

Multi-agent reinforcement learning (MARL) has shown promise for large-scale network control, yet existing methods face two major limitations. First, they typically rely on assumptions leading to decay properties of local agent interactions, limiting their ability to capture long-range dependencies such as cascading power failures or epidemic outbreaks. Second, most approaches lack generalizability across network topologies, requiring retraining when applied to new graphs. We introduce STACCA (Shared Transformer Actor-Critic with Counterfactual Advantage), a unified transformer-based MARL framework that addresses both challenges. STACCA employs a centralized Graph Transformer Critic to model long-range dependencies and provide system-level feedback, while its shared Graph Transformer Actor learns a generalizable policy capable of adapting across diverse network structures. Further, to improve credit assignment during training, STACCA integrates a novel counterfactual advantage estimator that is compatible with state-value critic estimates. We evaluate STACCA on epidemic containment and rumor-spreading network control tasks, demonstrating improved performance, network generalization, and scalability. These results highlight the potential of transformer-based MARL architectures to achieve scalable and generalizable control in large-scale networked systems.

Comparative Field Deployment of Reinforcement Learning and Model Predictive Control for Residential HVAC

Advanced control strategies like Model Predictive Control (MPC) offer significant energy savings for HVAC systems but often require substantial engineering effort, limiting scalability. Reinforcement Learning (RL) promises greater automation and adaptability, yet its practical application in real-world residential settings remains largely undemonstrated, facing challenges related to safety, interpretability, and sample efficiency. To investigate these practical issues, we performed a direct comparison of an MPC and a model-based RL controller, with each controller deployed for a one-month period in an occupied house with a heat pump system in West Lafayette, Indiana. This investigation aimed to explore scalability of the chosen RL and MPC implementations while ensuring safety and comparability. The advanced controllers were evaluated against each other and against the existing controller. RL achieved substantial energy savings (22\% relative to the existing controller), slightly exceeding MPC's savings (20\%), albeit with modestly higher occupant discomfort. However, when energy savings were normalized for the level of comfort provided, MPC demonstrated superior performance. This study's empirical results show that while RL reduces engineering overhead, it introduces practical trade-offs in model accuracy and operational robustness. The key lessons learned concern the difficulties of safe controller initialization, navigating the mismatch between control actions and their practical implementation, and maintaining the integrity of online learning in a live environment. These insights pinpoint the essential research directions needed to advance RL from a promising concept to a truly scalable HVAC control solution.