#01Nov 6, 2026
cs.LG
From PAC bounds on the generalization error to PAC bounds on the parameter estimation error
Mihaly Petreczky, John Leth, Emma Lukacs and 1 more
Probably Approximately Correct (PAC) bounds on the generalization error (the difference between the empirical prediction error computed on the training data and its expectation) are an established tool in statistical machine learning, and there have been several extensions of these bounds to dynamical systems. In parallel, in recent years, there has been growing interest in finite-sample bounds for parameter estimation error in system identification. The latter bounds tend to be algorithm-specific, relying on reformulating the identification algorithm as a least-squares regression problem. This is in contrast to classical PAC bounds, which are algorithm-agnostic and can be applied to any identification algorithm based on minimizing a cost function involving the empirical loss. In this paper, we show how oracle bounds derived from PAC bounds can be used to derive finite-sample bounds for dynamical systems. As an illustration of this approach, we present finite-sample parameter-estimation bounds for linear and bilinear systems with bounded inputs and noise. These bounds apply to identification algorithms based on minimizing a regularized empirical loss function. The key ingredient is to establish an oracle inequality, i.e., an inequality between the true prediction error of the learned model and the minimum achievable true prediction error, and then use either the convexity of the true loss or system-theoretic properties of the loss function to derive bounds on the parameter estimation error. We also analyze the rates of the obtained bounds and compare them with those of classical asymptotic results.
#02Nov 6, 2026
cs.LG
On the (non-)closedness of the set of ReLU networks
Eloi Martinet, Leon Bungert
We prove that the set $\mathcal{N}_N$ of ReLU networks with one hidden layer and at most $N\in\mathbb N$ neurons is weakly closed in $W^{1,p}(Ω)$, for a bounded connected open set $Ω\subset\mathbb R^d$. Consequently, every coercive, weakly lower semicontinuous energy on this space attains its minimum over $\mathcal{N}_N$. This covers the Deep Ritz method with convex integrands, Sobolev training and Lipschitz learning. Moreover, as the weight decay parameter tends to zero, minimizers of the regularized problem converge, up to subsequences, to minimizers with minimal parameter norm. We also prove that the set of ReLU networks with two hidden layers of bounded widths is not closed in $W^{1,p}(Ω)$ or in $C(\overlineΩ)$. This disproves a conjecture of Petersen, Raslan and Voigtlaender.
#03Nov 6, 2026
cs.CL
ROSE: Risk-Aware Orthogonal Subspace Navigation for Lifelong Knowledge Editing in Multimodal Large Language Models
Lingyun Song, Ziyao Chen, Kang Pan and 5 more
Multimodal Large Language Models (MLLMs) require continuous factual updates to stay current, yet lifelong knowledge editing remains a daunting challenge. The primary obstacle is the severe Locality Erosion and Catastrophic Forgetting, where sequential edits inevitably interfere with pre-trained capabilities and prior updates. In this paper, we propose \textbf{ROSE}, a \textbf{R}isk-aware \textbf{O}rthogonal \textbf{S}ubspace navigation framework for lifelong knowledge \textbf{E}diting. ROSE addresses forgetting by aiming to restrict parameter updates to the orthogonal complement of previously edited subspaces. Crucially, it introduces a risk-guided mechanism that utilizes a dynamically computed risk mask to safeguard specific factual parameter subspaces essential for model stability. During inference, ROSE employs a multi-granularity knowledge integration strategy, featuring prototype-anchored semantic gating and perturbation-driven subspace fusion to precisely activate edited knowledge for relevant queries while limiting interference on unrelated inputs. Comprehensive experiments on two prominent multimodal benchmarks show that ROSE is competitive with state-of-the-art approaches across five key metrics, while maintaining outstanding stability over $1,000$ sequential updates. Our code is available at https://github.com/sunlitsong/ROSE.
#04Nov 6, 2026
cs.AI
Test-Time Compute Scales Better with Parallel Agent Teams
Junlin Wang, Haozhe Chen, Ang Li and 2 more
Test-time scaling improves the performance of a fixed model by spending more computation at inference. There are two common ways to spend it on agents when a verifier can score every attempt. Best-of-N sampling runs many independent agents and keeps the best result but saturates quickly. One large team of collaborating agents can score higher but stops improving as it grows. Can we get the best of both? Our method, parallel agent teams, does so by sampling many small teams in parallel and keeping the best team's result. We test it on 12 long-horizon tasks from GPU kernels and formal proofs to exploit development. With a 27B model and a budget of 100 agents, parallel teams of ten beat parallel agents on 10 of 12 tasks and beat one team of 100 on all four tasks where we ran such large teams. At equal dollar cost the same parallel teams beat a frontier model on half the tasks. A simple statistical model shows that individual agents lose because their many samples have a low mean and that one large team loses because a single sample gets no gain from variance. Sampling many small teams in parallel balances a high mean with the gain from variance. Parallel agent teams thus offer a more effective way to scale test-time compute.
#05Nov 6, 2026
cs.CL
Language as Trait, Politeness as Strategy: Controlled Tests of Linguistic Effects in LLM Social-Deduction Agents
Yuchen Li, Lisa Liu, Runqi Zou and 3 more
Large language model (LLM) agents coordinate through conversation, and the same message can be phrased in simpler or more complex language, bluntly or politely. We test whether such differences change how other agents judge and act, using the LURK Werewolf framework, which separates each utterance's speech-act predicate from its natural-language realization. We rewrite only the realization, check that the game content is preserved, and replay each game day from saved checkpoints against a re-sampled control. We vary linguistic range consistently across a speaker's messages and politeness strategy per utterance. Across 30 games and 4,335 replays, neither manipulation changes the trust other agents place in the speaker, and no effect on votes or night actions survives correction for multiple comparisons; the largest uncorrected effect is that shifting range away from a neutral paraphrase changes about 4 percentage points more of the other players' votes. In natural play, 88% of face-threatening speech is bald on-record regardless of role.