Most existing equivariant architectures for Hamiltonian prediction propagate features in direct-sum spaces of irreducible spherical tensors, whereas the target Hamiltonian is naturally an operator block in a direct-product representation over local orbital and spin bases. This representation mismatch fragments contiguous Hamiltonian blocks, obscures direct manipulation of orbital couplings, and organizes features into irregular angular-momentum components that require numerous transformations and are poorly aligned with efficient hardware execution and memory management. To address both the representation mismatch and computational bottleneck, we propose DP-Learner, an equivariant learning framework that performs message passing directly on Hamiltonian-like operator blocks in the direct-product space. Theoretically, we propose Lie-generator-based directional embedding and invariantly weighted left--right products and contractions that preserve equivariance to SO(3), SU(2), and spatial inversions, without explicit Clebsch--Gordan decomposition or inverse reconstruction. Methodologically, we instantiate this principle as a Transformer architecture, in which Hamiltonian-like feature matrices or tensors evolve through equivariant operators in the direct-product space, while non-linear invariant scalar routing controls structured gating over matrix units, directional propagation, attention, and environment-embedded context interactions. We further construct MP-HAM-110K, a large-scale Hamiltonian dataset comprising more than 110,000 material structures covering 68 elements with both Hamiltonian and wavefunction data. Experiments on MP-HAM-110K and Materials-HAM-SOC demonstrate that DP-Learner dramatically improves Hamiltonian prediction accuracy and inference efficiency over the state-of-the-art method.
Durable execution engines replay a recorded history and do not compare activity payloads. When a model repairs a workflow that failed partway through, it must either pay again for calls that succeeded or accept a recorded result whose payload changed. We define a revision contract for workflows whose orchestration code is written by a model. Each capability call carries a structural identity built from its callsite, its fanout position, and its occurrence count, and the identity stays stable under rewrites that leave the call in place, so committed identities form a frozen prefix. The frozen unit is the call expression, and the surrounding code stays writable. A static gate rejects a rewrite that would change a committed call before a container starts. A runtime digest stops a changed payload at a committed identity, and an occurrence ledger names a repeated paid payload. Under three assumptions, a candidate the gate accepts replays every committed call it invokes, executes only new work, and reports the identities it skips. No local identity is both relocation-invariant and free of wrong reuse, so callsite identity turns a relocation into a pre-spend stop. On media workflows, 22 gate-passed repairs replay 258 committed identities with no duplicate, and a live six-way fanout makes seven paid calls instead of twelve. A 12-task customer-support study applies the same identity, replay, and boundary checks on two models.
LLM agents learn by interacting with environments, yet existing environments are designed for specific tasks and fail to generalize to new ones. Recent methods automate environment construction with LLMs. However, they generate each environment from scratch, neither reusing parts shared across environments nor carrying a fix from one environment to the rest. To address this, we propose a new paradigm of evolving environment atoms, which composes environments from reusable atoms (intent, rule, data and server) and evolves the atoms when an environment fails to give reliable feedback (e.g., an application lacks a tool the task requires). To instantiate this paradigm, we introduce LegoEnv, which builds 5,465 verified environments over 223 applications, and one round of evolution raises the share of solvable environments from 71.6% to 88.3%. On AutomationBench, SFT on these environments lifts Qwen3.6-27B from 16.0% to 32.0%, and RL with their verifiers lifts Qwen3.8-27B from 37.6% to 40.3%. Further analyses show steady gains with corpus size, transfer to unseen applications, and failures concentrated in a few shared root causes.
Yueyang Pan, Qianchao Zhu, Yuliang Liu, Teng Ma, Sanidhya Kashyap
Position-independent caching reuses chunk KV caches across positions and requests. Independent encoding, however, omits cross-chunk interactions and can degrade accuracy. In our study, neither PIC training nor rule-based recomputation, alone or combined, consistently recovers full-prefill accuracy. Oracle-guided recomputation on PIC-trained models improves accuracy at the same budget, motivating better selection. We present CacheWeave, which adapts the full backbone to PIC, then freezes it and trains a model-native block selector on the adapted model's oracles. The selector uses compact cached chunk features and question hidden states without extracting backbone attention scores. It selects contiguous token blocks aligned with KV blocks to support efficient recomputation and limit copy-on-write amplification. Its runtime, CacheWeave-Serve, supports private and shared KV caches, keeps selection and recomputation on the GPU, and stages sliding-window KV for hybrid attention models. Across three models and four tasks, CacheWeave outperforms CacheBlend and ProphetKV by 7.2 and 3.5 percentage points on average at a 5% recomputation budget, with a mean relative accuracy loss of 1.6% to full prefill. With 32-token blocks, CacheWeave-Serve cuts single-request TTFT by up to 16.1x over full prefill and 1.7x over ProphetKV, and raises SLO goodput under load by up to 7.8x.
Kailai Feng, Haoxiang Rao, Yuxiang Wei, Bo Chen, Junsong Li, Yang Pan, Chengkun Cai, Jagmohan Chauhan
Developing on-device image models requires considering practical user needs, task types and device resource constraints. However, existing benchmarks provide limited guidance on identifying capability gaps between on-device models and server-side models. We introduce MoI-Bench, a benchmark grounded in mobile user needs, comprising 64 subtasks and 1150 samples. It defines 16 operations, such as removal and replacement, and eight visual target categories covering content such as portraits and text. These form two orthogonal axes whose applicable combinations define specific tasks, such as removing facial makeup. To better guide model improvement, we further propose MoI-Eval, which introduces task-specific criteria covering instruction following, visual quality and detail preservation. We further construct sample-level evaluation questions and aggregate their scores into overall quality and capability profiles along the operation, target and criteria axes. We evaluate representative on-device and server-side models and measure mobile deployment costs. Results show that this decoupled Operation x Target design provides finer-grained guidance for improving compact models. For example, it highlights the need to prioritize specific capability gaps (e.g., text-replacement) over broad application-level goals (e.g., improving text editing). Unlike conventional benchmarks that rank models using a single score, we introduce a two-dimensional Quality-Deployability capability map to assess models for practical mobile use. The map shows that current on-device models can achieve efficient generation or editing but expanding their task coverage deserves greater attention than further improving deployment efficiency. Further progress requires improving editing quality, particularly identity preservation and text rendering, while broadening task coverage.