#01Nov 4, 2026
cs.LG
Template Gap Reconstruction for Shell Output Simulation with Small Language Models
Jarrod Ragsdale, Rajendra Boppana
Small language models offer a compact basis for shell simulation without executing submitted commands, but full-output decoding requires them to predict recurring utility structure alongside content that varies across executions. We introduce template gap reconstruction (TGR), which supplies reusable output literals interspersed with sentinels to be interleaved with autoregressively generated gaps. A template selector chooses which template to be reconstructed, with the empty template retaining full-output decoding. We construct a template bank from 18.7 million outputs collected across heterogeneous execution environments and train a template selector and five reconstruction models initialized from various small language model checkpoints on a target environment excluded from bank construction. Evaluation demonstrates that TGR improves output edit similarity (O-ES) over full-output decoding (FOD) when the optimal template covers more than 25\% of the template, while performing similarly for lower-coverage outputs. Additionally, TGR outperforms FOD for shorter gap sequences, with O-ES values of 0.964 and 0.812, respectively, while maintaining similar performance for longer sequences. TGR reduces the number of tokens generated by 26.3--38.3\% across used tokenizer families. These results support using a reusable output structure as a practical design choice for small shell simulators, improving response fidelity and shortening generation targets while keeping template selection and residual prediction central to response quality.
#02Nov 4, 2026
cs.RO
Perceptive Humanoid Motion from Simulation
Siyuan Hu, Abulikemu Abuduweili, Yue Meng and 5 more
Humanoid robots have the potential to automate a wide range of physical tasks. Progress toward generalist humanoid autonomy, however, remains constrained by a data bottleneck: mapping pixels and free-form language to low-level joint commands requires paired supervision, and no corpus of such data exists at sufficiently large scale. Some approaches rely on human teleoperation and wearable capture devices, which require at least an hour of human time to produce an hour of data. We present HALO, a humanoid autonomy system powered by a pipeline that synthesizes vision-language-motion data across a thousand procedurally generated homes. The corpus scales with compute rather than human labor. HALO acquires a repertoire of physical skills, including sitting on chairs, navigating to named objects, stepping sideways through half-open doors, crouching and crawling beneath tables, and pushing boxes. It orchestrates these skills to solve composite, long-horizon tasks. Without ever seeing a real home during training, HALO transfers zero-shot to the physical world, achieving a 91% success rate across 360 trials in six unmapped real-world environments. See https://apple-aiml-research.github.io/ml-halo/ for code and videos.
#03Nov 4, 2026
math.ST
Regularization vs. Convolution in Kernel-Based Hypothesis Testing
Omar Hagrass, Bharath K. Sriperumbudur
The maximum mean discrepancy (MMD) test is a popular nonparametric test on general domains. Two lines of work have studied its optimality through structurally different approaches. The first, a convolution approach on $\mathbb{R}^d$, uses translation-invariant kernels with a shrinking bandwidth and is minimax optimal over Sobolev balls under $L^2$-separation; the second, a regularization approach on general measurable spaces, uses spectral regularization of the kernel covariance operator and is minimax optimal over Hellinger- and $χ^2$-separated alternatives. In this paper, we study the regularization approach over Sobolev balls under $L^2$-separation, which reveals the connection between the two approaches. We show that, with a translation-invariant kernel on $\mathbb{R}^d$, both are ways of meeting a single condition on the kernel's spectral density: the spectral regularized discrepancy captures the $L^2$-separation $Δ$ of a Sobolev alternative of smoothness $s$ as soon as the regularization parameter $λ$ is below the spectral density on frequencies up to $Δ^{-1/(2s)}$. A kernel with a shrinking bandwidth $h$ meets this condition with $λ\asymp h^d$, and under this coupling the constant regularizer, which gives the MMD test itself, attains the Sobolev minimax rate. This explains, from a spectral perspective, the need for a shrinking bandwidth in the convolution approach. With a non-constant spectral regularizer, our analysis requires the bandwidth to shrink only when the spectral density decays faster than any polynomial, as for the Gaussian kernel. Thus, for Matérn and Laplace kernels, a fixed bandwidth with $λ\to 0$ attains the Sobolev minimax rate. Finally, an adaptive test over a grid of bandwidths and regularization parameters is minimax optimal, up to a $\log\log$ factor, over both classes without prior knowledge of the smoothness.
#04Nov 4, 2026
cs.LG
Message-passing graph persistence
Jorge Luiz Franco, Arthur Queiroz Moura, Moacir Ponti and 1 more
Message-passing graph neural networks (GNNs) are limited in expressive power by the one-dimensional Weisfeiler-Leman test. Persistent homology (PH) provides topological descriptors that can complement GNN representations, but existing approaches typically compute persistence separately from the representation learning process. In this paper, we introduce Message-Passing Graph Persistence (MGP), a family of topological descriptors that incorporates message passing into graph filtrations. At each filtration step, node embeddings are updated using the current subgraph and associated with persistence events. These embeddings also determine the representatives of connected components during persistence computation. We prove that MGP is invariant under graph isomorphism and that it is strictly more expressive than the PH-based descriptors it extends. We evaluate MGP on an expressivity benchmark and on several graph classification and regression datasets. Experiments show that MGP outperforms other PH-based descriptors on most of these datasets.
#05Nov 4, 2026
cs.LG
Context--Answer Metamodels: Forecasting LLM Activations Before the First Answer Token
Tommy He, Thomas Jiralerspong
Under stochastic decoding, a single context can elicit many different answers from a language model. Characterizing this variation typically requires many expensive autoregressive rollouts, each revealing only one realization. We ask whether the activations produced while reading the context can directly forecast the model's rollout activations. We train context--answer metamodels that map a context activation sequence to point or distribution forecasts of mean-pooled answer activations. We find that (i) the four metamodel families we study forecast mean-pooled answer activations with high fidelity, and the distribution metamodels also capture rollout variability; (ii) performance improves as the training set grows to 500,000 prompts, and the metamodels generalize zero-shot to out-of-domain datasets; (iii) their forecasts retain behavior-predictive signal; and (iv) context activations from Qwen2.5 predict mean-pooled answer activations from Qwen3.5 and Gemma 4, suggesting that activation forecasts can transfer across models. Together, these results suggest that context activation traces can support scalable forecasts of behaviors in LLM answers before the first answer token is generated.