#01Nov 5, 2026
math.OC
From What Is Used to What Is Missing: Rethinking Dynamic Rank in LoRA
Peng Xue, Guodong Fan, Guang-Yong Chen and 1 more
Parameter-efficient fine-tuning with LoRA is governed by rank, which controls parameter budget and locally accessible task updates. Existing dynamic-rank methods mainly focus on capacity allocation, leaving unresolved whether the current adaptation space is sufficient for the task. We characterize the first-order information boundary of standard factor gradients, showing that their unobservable subspace coincides with the normal space of the low-rank manifold. Thus, factor gradients alone cannot distinguish under-optimization within the current space from task-relevant directions beyond its first-order reach. This motivates a geometric view of rank evolution, where tangent information optimizes existing degrees of freedom and the normal spectrum quantifies the value of new ones. Under a local quadratic model, we show that leading normal singular directions yield the locally optimal rank expansion, with spectral energy determining its gain. Building on this characterization, we propose GEAR, which turns the tangent--normal decomposition into rank evolution through tangent-space optimization, matrix-free normal-spectrum estimation for rank expansion, and task-induced geometric initialization. Across language and vision benchmarks, GEAR achieves the best average performance in all evaluated settings with substantially fewer trainable parameters. On LLaMA3-8B, it raises the average commonsense score from 86.61 to 88.45 while reducing trainable parameters from 42.0M to 14.4M.
#02Nov 5, 2026
cs.LG
Adversarial Multiplicity: Cherry-Picked Models and the Limits of Disclosure
Cassandra C. Chou, Benjamin Q. Huynh, Allison Koenecke and 1 more
Predictive multiplicity -- where similarly accurate models disagree on individual predictions -- can be leveraged to optimize secondary metrics (e.g., fairness) without loss in predictive performance. However, exploiting multiplicity opens the opportunity for motivated parties (or coding agents gaming their objectives) to steer predictions toward their own ends, such as in litigation or consumer disputes with automated decision-making tools. In these adversarial multiplicity settings, we distinguish soft manipulation, where parties optimize over innocuous model choices (e.g., hyperparameter tuning, feature engineering), from hard manipulation, where parties directly perturb model parameters. We find a sufficiently flexible model can be manipulated to reverse any individual prediction with minimal change in predictive performance while passing black-box audits, making hard manipulation viable in most regulatory settings. Soft manipulation has smaller effects but can pass white-box audits requiring full access to code and data. Even aggregate estimates can be manipulated: a model's estimated effect of climate change on wildfires can be fully reversed by hard edits and soft search. We find the Reconcile algorithm typically resolves most disagreements between models, but more often in favor of the manipulator when the opposing model is chosen adversarially compared to at random. We map which manipulations can plausibly pass existing regulations and disclosure policies, and recommend mitigations such as pre-registration, proof of model training, sensitivity analyses, multi-metric evaluations, and committing to versioned public models.
#03Nov 5, 2026
cs.LG
Provably Efficient Representation Learning for Low-Rank CMDPs
Kaixuan Liu, Guojun Xiong, Shengpu Tang and 2 more
We study representation learning in low-rank Constrained Markov Decision Processes (CMDPs), where both value and reward functions are approximated by a set of unknown representation vectors, and the transition dynamics admit a low-rank factorization. The objective is to maximize expected cumulative rewards while complying with constraints on the expected cumulative utility. To achieve this, we propose \texttt{MFRLC} (Model-Free Representation Learning for Low-Rank CMDP), a model-free algorithm that uses a primal-dual scheme to effectively balance reward regret and constraint violations. To the best of our knowledge, \texttt{MFRLC} is the first representation-learning method for low-rank CMDPs that combines the Least-Squares Value Iteration with Upper Confidence Bound (LSVI-UCB) and primal-dual techniques. \texttt{MFRLC} further enhances value function estimation with bonuses for function approximation and learns the mapping from representations to value functions directly, avoiding explicit estimation of the transition kernel. We prove that, with high probability, \texttt{MFRLC} achieves $\widetilde O(K^{3/4})$ reward regret and cumulative constraint violation over $K$ deployment rounds, independent of the size of the state space. To our knowledge, these are the first sublinear regret and violation guarantees for CMDPs with unknown features.
#04Nov 5, 2026
math.OC
Last-Iterate Convergence of Stochastic Gradient Methods for Unbounded Problems
Kevin Kurian Thomas Vaidyan, Ahmet Alacaoglu, Michael P. Friedlander
Last-iterate convergence guarantees for stochastic gradient methods have attracted significant attention as practical implementations typically return the last iterate instead of an average of the iterates. In this paper, we study two approaches for analyzing the last-iterate convergence of proximal and projected stochastic gradient methods without bounded domain or bounded variance assumptions, where black-box variational inference serves as a running example. Under two related assumptions relaxing the bounded variance, we show near-optimal anytime rate $\widetilde{\mathcal{O}}(1/\sqrt{T})$ for the last iterate. Moreover, when the horizon $T$ is known, we remove the logarithmic factor and obtain the optimal order $\mathcal{O}(1/\sqrt{T})$, matching the order known under bounded variance or bounded domain assumptions.
#05Nov 5, 2026
cs.LG
IMUDINO: Self-distilled Foundation Model for Inertial Sensing
Zhoutong Ye, Chengwen Zhang, Zixuan Wang and 9 more
We present IMUDINO, the first foundation model (FM) for inertial sensing to achieve competitive performance across diverse sensing tasks including human activity recognition (HAR), health, motion capture, and odometry. Prior inertial FMs often focus on one subfield of inertial sensing and sometimes underperform state-of-the-art supervised methods (e.g., in HAR), making their scope considerably narrower than FMs for vision and natural language. Moreover, they often require fixed input length and sampling rate, and generalize poorly to unseen sensor locations. To build a general-purpose foundation model for inertial sensing, we adapt the DINO self-supervised learning (SSL) paradigm to inertial data through a set of semantics-preserving motion transformations that simulate variations in motion pattern and sensor setup. For model architecture, we use a plain transformer encoder with frequency-aware positional encoding that natively supports varying input length and sampling rate. This simple setup proved remarkably effective for learning global and dense features generalizable across users, sensor setups, tasks, and, in the case of robot odometry, embodiments. We hope IMUDINO can serve as a backbone for inertial sensing and kickstart the development of general-purpose inertial FMs.