Daily Papers

Machine unlearning, the removal of a training subset's influence from a deployed model, is critical for privacy preservation and model reliability, yet gradient ascent on forget samples often harms retained knowledge. Existing approaches face a persistent tradeoff between effective forgetting and preservation on the retain set. While previous methods provide useful heuristics, they often lack a formal analysis on how exactly forgetting updates harm retained knowledge, and whether the side effects can be removed with theoretical guarantees. To explore a theoretically sound and simple solution, we start from the first principle on how performance on the retain set is actually affected: a first-order analysis of the local change of the retain loss under small parameter updates during model training. We start from a crisp equivalence: the retain loss is unchanged to first order iff the update direction is orthogonal to the subspace spanned by retain gradients ("retain-invariant"). This identifies the entangled component as the tangential part of forget update within the retain-gradient subspace, and characterizes disentanglement as orthogonality. Guided by this, we propose the Geometric-disentanglement Unlearning (GU) that decomposes any candidate forget gradient update into tangential and normal components to retain space and executes only the normal component. Under a standard trust-region budget, the projected direction aligned with the raw forget gradient is optimal among all first-order retain-invariant moves, and we also derive the optimal projected direction for joint forget-retain updating objectives. Our method is plug-and-play and can be attached to existing gradient-based unlearning procedures to mitigate side effects. GU achieves consistent improvement on various methods across three benchmarks TOFU, MUSE, and WMDP.

Large language models are increasingly trained as heterogeneous systems spanning multiple domains, expert partitions, and agentic pipelines, yet prevalent proximal objectives operate at a single scale and lack a principled mechanism for coupling token-level, trajectory-level, and higher-level hierarchical stability control. To bridge this gap, we derive the Aggregational Policy Censoring Objective (APC-Obj), the first exact unconstrained reformulation of sample-based TV-TRPO, establishing that clipping-based surrogate design and trust-region optimization are dual formulations of the same problem. Building on this foundation, we develop Fiber Bundle Gating (FBG), an algebraic framework that organizes sampled RL data as a fiber bundle and decomposes ratio gating into a base-level gate on trajectory aggregates and a fiber-level gate on per-token residuals, with provable first-order agreement with the true RL objective near on-policy. From APC-Obj and FBG we derive Fibration Policy Optimization (or simply, FiberPO), a concrete objective whose Jacobian is block-diagonal over trajectories, reduces to identity at on-policy, and provides better update direction thus improving token efficiency. The compositional nature of the framework extends beyond the trajectory-token case: fibrations compose algebraically into a Fibration Gating Hierarchy (FGH) that scales the same gating mechanism to arbitrary hierarchical depth without new primitives, as demonstrated by FiberPO-Domain, a four-level instantiation with independent trust-region budgets at the domain, prompt group, trajectory, and token levels. Together, these results connect the trust-region theory, a compositional algebraic structure, and practical multi-scale stability control into a unified framework for LLM policy optimization.

Parameter-efficient fine-tuning (PEFT) has become the standard approach for adapting large language models under limited compute and memory budgets. Although previous methods improve efficiency through low-rank updates, quantization, or heuristic budget reallocation, they often decouple the allocation of capacity from the way updates evolve during training. In this work, we introduce CTR-LoRA, a framework guided by curvature trust region that integrates rank scheduling with stability-aware optimization. CTR-LoRA allocates parameters based on marginal utility derived from lightweight second-order proxies and constrains updates using a Fisher/Hessian-metric trust region. Experiments on multiple open-source backbones (7B-13B), evaluated on both in-distribution and out-of-distribution benchmarks, show consistent improvements over strong PEFT baselines. In addition to increased accuracy, CTR-LoRA enhances training stability, reduces memory requirements, and achieves higher throughput, positioning it on the Pareto frontier of performance and efficiency. These results highlight a principled path toward more robust and deployable PEFT.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an important paradigm for unlocking reasoning capabilities in large language models, exemplified by the success of OpenAI o1 and DeepSeek-R1. Currently, Group Relative Policy Optimization (GRPO) stands as the dominant algorithm in this domain due to its stable training and critic-free efficiency. However, we argue that GRPO suffers from a structural limitation: it imposes a uniform, static trust region constraint across all samples. This design implicitly assumes signal homogeneity, a premise misaligned with the heterogeneous nature of outcome-driven learning, where advantage magnitudes and variances fluctuate significantly. Consequently, static constraints fail to fully exploit high-quality signals while insufficiently suppressing noise, often precipitating rapid entropy collapse. To address this, we propose Elastic Trust Regions (ETR), a dynamic mechanism that aligns optimization constraints with signal quality. ETR constructs a signal-aware landscape through dual-level elasticity: at the micro level, it scales clipping boundaries based on advantage magnitude to accelerate learning from high-confidence paths; at the macro level, it leverages group variance to implicitly allocate larger update budgets to tasks in the optimal learning zone. Extensive experiments on AIME and MATH benchmarks demonstrate that ETR consistently outperforms GRPO, achieving superior accuracy while effectively mitigating policy entropy degradation to ensure sustained exploration.

Sharpness-aware minimization (SAM) reports improving domain generalization by reducing the loss surface curvature in the parameter space. However, generalization during fine-tuning is often more dependent on the transferability of representations in the function space. Trust-region methods (TR) target this goal by regularizing representation curvature to reduce catastrophic forgetting of pre-trained task-agnostic information while adopting task-specific skills. We consider unifying these strategies for low curvature in both parameter space and function space to improve out-of-domain (OOD) generalization. We propose Trust Region Aware Minimization (TRAM), a SAM algorithm fine-tuning for low parameter sharpness and smooth, informative representations preserving pre-trained structure. TRAM uses a trust region bound to inform the SAM adversarial neighborhood, introducing an awareness of function curvature within optimization for flatter minima. We empirically validate TRAM in vision (cross-dataset adaptation) and text (OOD language modeling, zero-shot cross-lingual transfer) tasks where robust domain transfer and representation generality are critical. TRAM outperforms SAM- and TR-based optimization across all tasks, notably surpassing competing methods for hard transfer between anticorrelated domains. TRAM establishes a novel standard in fine-tuning for domain-generalizable models with minimal additional computation over previous sharpness-aware methods.