Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.23009

"Deep lifts": Neural networks can generalize even with the dumbest optimizer

Sunil Madhow·Yu-Xiang Wang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Given a labeled dataset $\{(x_i, y_i)\}_{i = 1}^n$, consider drawing a parameter vector $\hatθ$ uniformly at random from those that interpolate the data within a width-$W$ depth-$D$ ReLU architecture with continuous weights bounded within $[-M, M]$. We study the generalization properties of $\hatθ$ in the case where the dataset can, in fact, be explained by a smaller $w$-by-$d$ ReLU network. Despite the obliviousness of the selection rule for $\hatθ$, it adaptively generalizes at the rate $\tilde O\left(\frac{wdWD}{n}\right)$, rather than being governed by the VC dimension of the full $W$-by-$D$ hypothesis class. The reason is due to a particular inductive bias in ReLU networks: the $w$-by-$d$ parameter *witnesses* an exponential volume of $W$-by-$D$ interpolating parameters, which dwarfs the volume of poorly generalizing parameters (conditioned on interpolation). We explicitly construct this set of near-equivalent $W$-by-$D$ parameters by a proof technique called *deep lifting*, and then tie the achievable volume to stability properties of the $w$-by-$d$ witness. Examples show that these techniques allow us to convert approximation-theoretic results into generalization guarantees for nonparametric classes. We further show that generalization of uniform-random interpolators can survive label corruptions.

Explore related subjects

cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sunil Madhow, Yu-Xiang Wang. 2026-10-16. "Deep lifts": Neural networks can generalize even with the dumbest optimizer. https://arxiv.org/abs/2610.23009

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Is the Policy Gradient a Gradient?

The policy gradient theorem describes the gradient of the expected discounted return with respect to an agent's policy parameters. However, many policy gradient methods omit the outer discount factor, yielding an update that need not equal the gradient of the discounted objective. Is the resulting update the gradient of another objective? This has been an open question for several years, and this lack of theoretical clarity has led to an abundance of misstatements in the literature. We answer this question for the resulting episode-summed, on-policy update by proving that it need not equal the gradient of any function. Further, we construct a counterexample in which exact expected updates drive the policy toward a deterministic limit that is globally pessimal with respect to both the discounted and undiscounted objectives, while the parameter diverges. We motivate this work by surveying the literature and showing that there remains a widespread misunderstanding regarding discounted policy gradient methods, with errors present even in highly-cited papers published at top conferences.

cs.LG↗
arXiv2026

Harnessing Trust in Directed Graphs: Redefining Robustness of Graph Learning

Existing research on robust Graph Neural Networks (GNNs) focuses predominantly on undirected graphs, overlooking the trustworthiness inherent in the link directions of directed graphs. In this work, we analyze the limitations of current approaches from both the attack and defense perspectives and redefine the robustness of GNNs in directed graphs. From the attack side, we introduce a more realistic directed graph attack setting that addresses the shortcomings of existing attacks. From the defense side, we propose a simple yet effective message-passing framework that serves as a plug-in layer to strengthen GNN robustness while avoiding a false sense of robustness. Our findings show that the trust signals encoded in directed graphs can be harnessed to substantially improve the robustness of GNNs. When combined with existing defense strategies, the framework achieves state-of-the-art robust performance alongside strong clean accuracy against both transfer and adaptive attacks. These results point to a novel and promising direction for strengthening the robustness of graph deep learning.

cs.LG↗
arXiv2026

Learning Agentic Time Series Forecasting via Trajectory Distillation and Memory-Based Reinforcement Learning

Recent agentic time series forecasting (TSF) approaches use large language models (LLMs) to autonomously orchestrate analytical and forecasting tools and reason about temporal patterns using the resulting evidence. However, many such approaches rely on powerful LLMs in training-free, prompt-driven workflows, leaving open whether smaller models can learn these interaction and reasoning capabilities. In this paper, we introduce Cast-R1, an 8Bparameter agentic forecasting model trained through trajectory distillation and multi-turn reinforcement learning with structured memory. First, we develop a forecasting agent harness with specialized analysis and prediction tools to generate multi-turn interaction trajectories using a teacher LLM, which are subsequently evaluated and selected for supervised fine-tuning. Second, we apply group relative policy optimization (GRPO) across multi-turn forecasting episodes, with structured memory preserving diagnostic evidence and intermediate forecasts for state construction. Rewards based on prediction accuracy and temporal structure guide tool selection, model routing, and forecast refinement. A difficulty-aware curriculum combines sample filtering and progressive sample ordering during training. Extensive experiments on multiple datasets demonstrate the effectiveness of Cast-R1. These findings highlight the potential of forecasting-specific post-training to equip smaller LLMs with multi-turn, tool-augmented forecasting capabilities within structured workflows.

cs.LG↗