#01Oct 30, 2026
cs.CL
Subquadratic Attention with a Hierarchical Tree-Structured Indexer
Leon Lufkin, Cutter Dawes, Alexander Speicher and 3 more
The quadratic scaling of attention is a fundamental bottleneck limiting the long-context capabilities of large language models (LLMs). A variety of approaches have attempted to circumvent this, but they either fail to match attention's expressiveness (e.g., sliding-window or linear attention variants with fixed-size state) or only achieve constant-factor speedups (e.g., sparse attention methods whose indexers themselves scale quadratically). In this paper, we derive an asymptotically subquadratic sparse attention method based on a hierarchical, tree-structured indexer, which we call Zyphra Hierarchical Attention (ZHA). ZHA constructs a tree of recursively compressed key summaries over the KV cache, which future queries traverse from the top down to retrieve a sparse subset of keys. Crucially, by iteratively growing the tree's depth, the total cost including routing and final attention grows sublinearly in sequence length, resulting in overall subquadratic (but superlinear) scaling for attention. We demonstrate that ZHA can be cheaply applied to existing pretrained models with only a short KL distillation training stage over a few billion tokens, and maintains performance on long-context retrieval and challenging reasoning, mathematical, and agentic coding evaluation tasks. Moreover, we show that our method is highly robust to tree geometry including very deep trees of up to 6 levels. Finally, we develop a detailed performance model and show that our approach scales subquadratically, dramatically outperforms competing methods beyond 1 million context, and ultimately has the potential to extend effective context windows to the hundreds of millions or billions of tokens.
#02Oct 30, 2026
cs.LG
Gradient Descent on Two ReLU Neurons: Global Landscape and Bifurcation Dynamics
Binghua Li, Mengzhe Li, Denny Wu and 1 more
Understanding how gradient descent learns features remains a central challenge in neural network theory. We study this question in a minimal multi-index setting that already exhibits rich multi-phase gradient dynamics: a well-specified two-neuron ReLU teacher-student model under isotropic Gaussian inputs, trained by population gradient flow from small initialization. We show that the dynamics are organized by two directions: the "easy" bisector direction, which carries the leading signal, and the "hard" splitting direction, which governs specialization. To characterize the loss structure and learning behavior, we analyze the population squared-loss landscape and show that every critical point with both student weights nonzero is either a global minimum or a saddle. We then track the gradient-flow trajectory, showing that student neurons first collapse toward a bisector saddle before escaping and specializing to teacher neurons. Our results provide both a landscape and dynamics account of the multi-phase symmetry-breaking behavior that arises in a simple multi-index model and under standard algorithmic and architectural choices.
#03Oct 30, 2026
cs.LG
Towards Understanding the Impact of Plasticity Loss on Reinforcement Learning in Stochastic Environments
Philipp Bordne, André Biedenkapp
Deep reinforcement learning (RL) is a powerful framework for sequential decision-making. Despite many high-profile successes in recent years, deep RL is known to be brittle. An emerging line of research attributes this brittleness to a loss of plasticity in neural networks. However, plasticity loss has so far been understudied in stochastic environments. We study this interplay systematically, training SAC agents on three DeepMind Control tasks augmented with controlled levels of observation and action noise. We find that plasticity-preserving methods increase learning robustness on the two harder tasks, with their advantage growing as observation noise increases, while combining resets with layer normalization underperforms resets alone at every observation noise level tested. Further, stochasticity can accelerate the loss of plasticity in harder environments, whereas in easier settings noise can act as a regularizer that sustains plasticity. Lastly, plasticity loss is most pronounced in the early stages of training. In the most challenging stochastic settings, TD instability rather than gradual plasticity loss becomes the dominant failure mode.
#04Oct 30, 2026
cs.LG
Hyperbolic Inverse Reinforcement Learning
Iulia Rusu, Anoop Praturu, Sergei Gepshtein and 1 more
Inverse reinforcement learning (IRL) seeks to infer the reward function underlying observed behavior, but its predictive accuracy and interpretability depend on how that reward is computed from the underlying features. While prior IRL reward functions have been implemented through a variety of techniques including linear weights, neural networks, or other function approximators, none make assumptions about the geometry of the underlying feature space. Inspired by geometric organization observed in neural circuits, we introduce Hyperbolic inverse reinforcement learning (Hyperbolic IRL), which parameterizes reward as a function of Hyperbolic distance between the feature vector and a learned parameter vector, as well as its Euclidean distance variant. We tested our methods against a range of linear and nonlinear IRL baselines under both deterministic and stochastic policies. Our Hyperbolic approach achieved comparable performance to state-of-the-art models on established benchmarks and excelled in the low data limit and across dense environments. Applied to human navigation among multiple exhibits in a museum room, Hyperbolic IRL reveals reward structure that depends not only on individual exhibit-distance features, but also on non-separable conjunctions between them. Together, these results demonstrate that a Hyperbolic reward parameterization can improve both the predictive accuracy and interpretability of IRL, providing a framework for studying how non-separable, conjunctive structure can begin to explain behavior.
#05Oct 30, 2026
cs.CV
A Better Critic Matters for Distribution Matching Distillation
Zongze Wu, Xianbang Wang, Zhengyang Geng and 5 more
Distribution Matching Distillation (DMD) trains a few-step student using the difference between a teacher's score and an online critic's estimate of the student distribution's score. We investigate what the critic needs, in capacity and in information, to provide a reliable training signal. On the capacity side, controlled experiments across seven SiT model sizes on ImageNet show that increasing teacher size while keeping a small critic fixed can degrade student quality and cause training collapse. Scaling the critic alongside the teacher, a strategy we call joint scaling, prevents collapse in our experiments and allows the student to benefit from larger teachers. On the information side, rather than forcing the critic to model a step-agnostic mixture of student outputs, we introduce a step-aware critic (STAC) that conditions on the student's generation step to estimate step-specific scores. Together, joint scaling and STAC consistently improve few-step distillation across class-conditional ImageNet generation, text-to-image generation with SDXL and FLUX.2, and text-to-video generation with Wan2.1.