Deep State Space Models (SSMs) reignite physics-grounded compute paradigms, as RNNs could natively be embodied into dynamical systems. This calls for dedicated learning algorithms obeying to core physical principles, with efficient techniques to simulate these systems and guide their design. We propose Recurrent Hamiltonian Echo Learning (RHEL), an algorithm which provably computes loss gradients as finite differences of physical trajectories of non-dissipative, Hamiltonian systems. In ML terms, RHEL only requires three "forward passes" irrespective of model size, without explicit Jacobian computation, nor incurring any variance in the gradient estimation. Motivated by the potential to implement our algorithm in non-digital physical systems, we first introduce RHEL in continuous time and demonstrate its formal equivalence with the continuous adjoint state method.

Dataset distillation seeks to condense datasets into smaller but highly representative synthetic samples. While diffusion models now lead all generative benchmarks, current distillation methods avoid them and rely instead on GANs or autoencoders, or, at best, sampling from a fixed diffusion prior. This trend arises because naive backpropagation through the long denoising chain leads to vanishing gradients, which prevents effective synthetic sample optimization. To address this limitation, we introduce Latent Dataset Distillation with Diffusion Models (LD3M), the first method to learn gradient-based distilled latents and class embeddings endto-end through a pre-trained latent diffusion model. A linearly decaying skip connection, injected from the initial noisy state into every reverse step, preserves the gradient signal across dozens of timesteps without requiring diffusion weight fine-tuning. Across multiple ImageNet subsets at 128 128and 256 256, LD3M improves downstream accuracy by up to 4.8 percentage points (1 IPC) and 4.2 points (10 IPC) over the prior state-of-the-art.

Cluster DAGs (C-DAGs) provide an abstraction of causal graphs in which nodes represent clusters of variables, and edges encode both cluster-level causal relationships and dependencies arisen from unobserved confounding. C-DAGs define an equivalence class of acyclic causal graphs that agree on cluster-level relationships, enabling causal reasoning at a higher level of abstraction. However, when the chosen clustering induces cycles in the resulting C-DAG, the partition is deemed inadmissible under conventional C-DAG semantics. In this work, we extend the C-DAG framework to support arbitrary variable clusterings by relaxing the partition admissibility constraint, thereby allowing cyclic C-DAG representations. We extend the notions of d-separation and causal calculus to this setting, significantly broadening the scope of causal reasoning across clusters and enabling the application of C-DAGs in previously intractable scenarios.

In contrast to the classic formulation of partial monitoring, linear partial monitoring can model infinite outcome spaces, while imposing a linear structure on both the losses and the observations. This setting can be viewed as a generalization of linear bandits where loss and feedback are decoupled in a flexible manner. In this work, we address a nonstochastic (adversarial), finite-actions version of the problem through a simple instance of the exploration-by-optimization method that is amenable to efficient implementation. We derive regret bounds that depend on the game structure in a more transparent manner than previous theoretical guarantees for this paradigm. Our bounds feature instance-specific quantities that reflect the degree of alignment between observations and losses, and resemble known guarantees in the stochastic setting. Notably, they achieve the standard T rate in easy (locally observable) games and T2/3 in hard (globally observable) games, where T is the time horizon. We instantiate these bounds in a selection of old and new partial information settings subsumed by this model, and illustrate that the achieved dependence on the game structure can be tight in interesting cases.

The loss landscapes of neural networks contain minima and saddle points that may be connected in flat regions or appear in isolation. We identify and characterize a special structure in the loss landscape: channels along which the loss decreases extremely slowly, while the output weights of at least two neurons, ai and aj, diverge to infinity, and their input weight vectors, wi and wj, become equal to each other. At convergence, the two neurons implement a gated linear unit: aiσ(wi x) + ajσ(wj x) cσ(w x) + (v x)σ (w x). Geometrically, these channels to infinity are asymptotically parallel to symmetry-induced lines of critical points. Gradient flow solvers, and related optimization methods like SGD or ADAM, reach the channels with high probability in diverse regression settings, but without careful inspection they look like flat local minima with finite parameter values. Our characterization provides a comprehensive picture of these quasi-flat regions in terms of gradient dynamics, geometry, and functional interpretation. The emergence of gated linear units at the end of the channels highlights a surprising aspect of the computational capabilities of fully connected layers.

Large Language Models (LLMs) have demonstrated impressive performance across various tasks, yet they remain vulnerable to generating toxic content, necessitating detoxification strategies to ensure safe and responsible deployment. Test-time detoxification methods, which typically introduce static or dynamic interventions into LLM representations, offer a promising solution due to their flexibility and minimal invasiveness. However, current approaches often suffer from imprecise interventions, primarily due to their insufficient exploration of the transition space between toxic and non-toxic outputs. To address this challenge, we propose Autoregressive Reward Guided Representation Editing (ARGRE), a novel testtime detoxification framework that explicitly models toxicity transitions within the latent representation space, enabling stable and precise reward-guided editing. ARGRE identifies non-toxic semantic directions and interpolates between toxic and non-toxic representations to reveal fine-grained transition trajectories. These trajectories transform sparse toxicity annotations into dense training signals, enabling the construction of an autoregressive reward model that delivers stable and precise editing guidance. At inference, the reward model guides an adaptive two-step editing process to obtain detoxified representations: it first performs directional steering based on expected reward gaps to shift representations toward non-toxic regions, followed by lightweight gradient-based refinements. Extensive experiments across 8 widely used LLMs show that ARGRE significantly outperforms leading baselines in effectiveness (-62.21%

A common approach for accelerating optimization algorithms is to minimize the loss achieved in a fixed time, which enables a differentiable framework with respect to the algorithm's hyperparameters. In contrast, the complementary objective of minimizing the time to reach a target loss is traditionally considered non-differentiable. To address this limitation, we propose a differentiable discrete stopping time and theoretically justify it based on its connection to continuous differential equations. We design an efficient algorithm to compute its sensitivities, thereby enabling a new differentiable formulation for directly accelerating algorithms. We demonstrate its effectiveness in applications such as online hyperparameter tuning and learning to optimize. Our proposed methods show superior performance in comprehensive experiments across various problems, which confirms their effectiveness.

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Pretraining language models with extended context windows enhances their ability to leverage rich information during generation. Existing methods split input sequences into chunks, broadcast them across multiple devices, and compute attention block by block which incurs significant communication overhead. While feasible in high-speed clusters, these methods are impractical for decentralized training over low-bandwidth connections. We propose a compression method for communication-efficient context parallelism in decentralized settings, achieving a remarkable compression rate of over 95%with negligible overhead and no loss in convergence. Our key insight is to exploit the intrinsic low-rank structure of activation outputs by dynamically constraining them to learned mixtures of subspaces via efficient reparameterizations. We demonstrate scaling billion-parameter decentralized models to context lengths exceeding 100Ktokens on networks as slow as 300Mbps, matching the wall-clock convergence speed of centralized models on 100Gbps interconnects.

Tensorized Incomplete Multi-View Clustering (TIMVC) algorithms have attracted growing attention for their ability to capture high-order correlations across multiple views. However, most existing TIMVC methods rely on simplistic noise assumptions using specific norms (e.g., ℓ1 or ℓ2,1), which fail to reflect the complex noise patterns encountered in real-world scenarios. Moreover, they primarily focus on modeling the global Euclidean structure of the tensor representation, while overlooking the preservation of local manifold structures. To address these limitations, we propose a novel approach, GaUssian regressIon-driven TIMVC with dual mAnifold Regularization (GUITAR). Specifically, we employ a Gaussian regression model to characterize complex noise distributions in a more realistic and flexible manner. Meanwhile, a dual manifold regularization is introduced in tensor representation learning, simultaneously modeling manifold information at both the view-specific and cross-view consensus levels, thereby promoting intra-view and inter-view consistency in the tensor representation. Furthermore, to better capture the intrinsic low-rank structure, we propose the high-preservation ℓδ-norm tensor rank constraint, which applies differentiated penalties to the singular values, thereby enhancing the robustness of the tensor representation. In addition, an efficient optimization algorithm is developed to solve the resulting non-convex problem with provable convergence. Extensive experiments on six datasets demonstrate that our method outperforms SOTA approaches.