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Deep Learning · Generative Models and Autoencoders

Qingsong Wang, Zhengchao Wan, Misha Belkin, Yusu Wang

Diffusion models transform random noise into images of remarkable fidelity, yet the structure of this noise-to-image map remains largely unexplored. We investigate this relationship using patch-wise Principal Component Analysis (PCA) and empirically demonstrate that low-frequency components of the initial noise predominantly influence the compositional structure of generated images. Our analyses reveal that noise seeds inherently contain universal compositional cues, evident when identical seeds produce images with similar structural attributes across different datasets and model architectures. Leveraging these insights, we develop and theoretically justify a simple yet effective Patch PCA denoiser that extracts underlying structure from noise using only generic natural image statistics. The robustness of these structural cues is observed to persist across both pixel-space models and latent diffusion models, highlighting their fundamental nature. Finally, we introduce a zero-shot editing method that enables injecting compositional control over generated images, providing an intuitive approach to guided generation without requiring model fine-tuning or additional training.

Theory · Learning Theory

Artin Tajdini, Jonathan Scarlett, Kevin Jamieson

We study stochastic linear bandits with heavy-tailed rewards, where the rewards have a finite $(1+\epsilon)$-absolute central moment bounded by $\upsilon$ for some $\epsilon \in (0,1]$. We improve both upper and lower bounds on the minimax regret compared to prior work. When $\upsilon = \mathcal{O}(1)$, the best prior known regret upper bound is $\tilde{O}(d T^{\frac{1}{1+\epsilon}})$. While a lower with the same scaling has been given, it relies on a construction using $\upsilon = d$, and adapting the construction to the bounded-moment regime with $\upsilon = \mathcal{O}(1)$ yields only a $\Omega(d^{\frac{\epsilon}{1+\epsilon}} T^{\frac{1}{1+\epsilon}})$ lower bound. This matches the known rate for multi-armed bandits and is generally loose for linear bandits, in particular being $\sqrt{d}$ below the optimal rate in the finite-variance case ($\epsilon = 1$). We propose a new elimination-based algorithm guided by experimental design, which achieves regret $\tilde{\mathcal{O}}(d^{\frac{1+3\epsilon}{2(1+\epsilon)}} T^{\frac{1}{1+\epsilon}})$, thus improving the dependence on $d$ for all $\epsilon \in (0,1)$ and recovering a known optimal result for $\epsilon = 1$. We also establish a lower bound of $\Omega(d^{\frac{2\epsilon}{1+\epsilon}} T^{\frac{1}{1+\epsilon}})$, which strictly improves upon the multi-armed bandit rate and highlights the hardness of heavy-tailed linear bandit problems. For finite action sets of size $n$, we derive upper and lower bounds of $\tilde{\mathcal{O}}(\sqrt d (\log n)^{\frac{\epsilon}{1+\epsilon}}T^{\frac{1}{1+\epsilon}})$ and $\tilde\Omega(d^{\frac{\epsilon}{1+\epsilon}}(\log n)^{\frac{\epsilon}{1+\epsilon}} T^{\frac{1}{1+\epsilon}})$, respectively. Finally, we provide action-set-dependent regret upper bounds and show that for some geometries, such as $l_p$-norm balls for $p \le 1 + \epsilon$, we can further reduce the dependence on $d$.

Deep Learning · Attention Mechanisms

Songlin Yang, Yikang Shen, Kaiyue Wen, Shawn Tan, Mayank Mishra, Liliang Ren, Rameswar Panda, Yoon Kim

The attention mechanism is a core primitive in modern large language models (LLMs) and AI more broadly. Since attention by itself is permutation-invariant, position encoding is essential for modeling structured domains such as language. Rotary position encoding (RoPE) has emerged as the de facto standard approach for position encoding and is part of many modern LLMs. However, in RoPE the key/query transformation between two elements in a sequence is only a function of their relative position and otherwise independent of the actual input. This limits the expressivity of RoPE-based transformers. This paper describes PaTH, a flexible data-dependent position encoding scheme based on accumulated products of Householder(like) transformations, where each transformation is data-dependent, i.e., a function of the input. We derive an efficient parallel algorithm for training through exploiting a compact representation of products of Householder matrices, and implement a FlashAttention-style blockwise algorithm. Across both targeted synthetic benchmarks and moderate-scale real-world language modeling experiments, we find that PaTH improves upon RoPE and other recent baselines. Finally, we show that we can convert pretrained RoPE transformers into PaTH with continued pretraining.

Optimization · Neural Network Optimization

Chris Kolb, Laetitia Frost, Bernd Bischl, David Rügamer

Structured sparsity regularization offers a principled way to compact neural networks, but its non-differentiability breaks compatibility with conventional stochastic gradient descent and requires either specialized optimizers or additional post-hoc pruning without formal guarantees. In this work, we propose $D$-Gating, a fully differentiable structured overparameterization that splits each group of weights into a primary weight vector and multiple scalar gating factors. We prove that any local minimum under $D$-Gating is also a local minimum using non-smooth structured $L_{2,2/D}$ penalization, and further show that the $D$-Gating objective converges at least exponentially fast to the $L_{2,2/D}$–regularized loss in the gradient flow limit. Together, our results show that $D$-Gating is theoretically equivalent to solving the original group sparsity problem, yet induces distinct learning dynamics that evolve from a non-sparse regime into sparse optimization. We validate our theory across vision, language, and tabular tasks, where $D$-Gating consistently delivers strong performance–sparsity tradeoffs and outperforms both direct optimization of structured penalties and conventional pruning baselines.

Applications · Robotics

Wenyao Zhang, Hongsi Liu, Zekun Qi, Yunnan Wang, XinQiang Yu, Jiazhao Zhang, Runpei Dong, Jiawei He, He Wang, Zhizheng Zhang 等

Recent advances in vision-language-action (VLA) models have shown promise in integrating image generation with action prediction to improve generalization and reasoning in robot manipulation. However, existing methods are limited to challenging image-based forecasting, which suffers from redundant information and lacks comprehensive and critical world knowledge, including geometry, semantics and spatial information. To address these limitations, we propose DreamVLA, a novel VLA framework that integrates comprehensive world knowledge forecasting to enable inverse dynamics modeling, thereby establishing an action-forecasting loop for manipulation tasks. Specifically, DreamVLA introduces a dynamic-region-guided world knowledge prediction mechanism, which anticipates visual, depth, geometric, semantic, and segmentation cues to provide compact yet comprehensive representations for action planning. This design aligns with how humans interact with the world by first forming abstract multimodal reasoning chains before acting. Moreover, to model the conditional distribution over future actions, we employ a diffusion-based transformer that disentangles action representations from shared latent features and better captures multimodal uncertainty. Extensive experiments on both real-world and simulation environments demonstrate that DreamVLA achieves 76.7% success rate on real robot tasks and 4.45 average length on the CALVIN ABC-D benchmarks.

Reinforcement Learning · Deep RL

Chunyu Wei, Wenji Hu, Xingjia Hao, Xin Wang, Yifan Yang, Yunhai Wang, Yang Tian, Yueguo Chen

Large Language Models (LLMs) face significant limitations when applied to large-scale graphs, struggling with context constraints and inflexible reasoning. We introduce GraphChain, a novel framework enabling LLMs to analyze large graphs by orchestrating dynamic sequences of specialized tools, mimicking human exploratory processes. GraphChain incorporates two core technical contributions: (1) Progressive Graph Distillation, a reinforcement learning approach that learns to generate tool sequences balancing task relevance and intermediate state compression, thereby overcoming LLM context limitations. (2) Structure-aware Test-Time Adaptation (STTA), a mechanism using a lightweight, self-supervised adapter conditioned on graph spectral properties to efficiently adapt a frozen LLM policy to diverse graph structures via soft prompts without retraining. Experiments show GraphChain significantly outperforms prior methods, enabling scalable and adaptive LLM-driven graph analysis.

Computer Vision · Everything Else

Ori Lifschitz, Tali Treibitz, Dan Rosenbaum

We address the problem of looking into the water from the air, where we seek to remove image distortions caused by refractions at the water surface. Our approach is based on modeling the different water surface structures at various points in time, assuming the underlying image is constant. To this end, we propose a model that consists of two neural-field networks. The first network predicts the height of the water surface at each spatial position and time, and the second network predicts the image color at each position. Using both networks, we reconstruct the observed sequence of images and can therefore use unsupervised training. We show that using implicit neural representations with periodic activation functions (SIREN) leads to effective modeling of the surface height spatio-temporal signal and its derivative, as required for image reconstruction. Using both simulated and real data we show that our method outperforms the latest unsupervised image restoration approach. In addition, it provides an estimate of the water surface.

Deep Learning · Generative Models and Autoencoders

Yichao Fu, Junda Chen, Siqi Zhu, Fu, Zhongdongming Dai, Yonghao Zhuang, Yian Ma, Aurick Qiao, Tajana S Rosing, Ion Stoica 等

Test-time reasoning algorithms such as chain-of-thought, self-consistency, and MCTS enhance LLM problem-solving but can wastefully generate many tokens without improving accuracy. At the same time, we observe that these algorithms exhibit answer stabilization: their intermediate solutions often cease to change after a certain point, and further investment of compute does not change their final answer. To quantify this phenomenon, we introduce Certaindex, an algorithm-agnostic metric measuring this evolving stability, signaling when further computation is unlikely to alter the final result. Certaindex is lightweight, can accelerate reasoning program inference via early exit, and further enables dynamic token allocation, gang scheduling, and many opportunities when integrated with real-world LLM serving systems. To quantify real-world benefits, we built Certaindex as a scheduler into Dynasor, our reasoning-aware LLM serving system, and demonstrate up to 50\% compute savings and 3.3$\times$ higher throughput in real workloads with no accuracy drop. Our code is available at https://github.com/hao-ai-lab/Dynasor.git

Social Aspects · Accountability, Transparency and Interpretability

Xiaoyan Bai, Ike Peng, Aditya Singh, Chenhao Tan

Consider this prompt "Draw a unicorn with two horns". Should large language models (LLMs) recognize that a unicorn has only one horn by definition and ask users for clarifications, or proceed to generate something anyway? We introduce *concept incongruence* to capture such phenomena where concept boundaries clash with each other, either in user prompts or in model representations, often leading to under-specified or mis-specified behaviors. In this work, we take the first step towards defining and analyzing model behavior under concept incongruence. Focusing on temporal boundaries in the Role-Play setting, we propose three behavioral metrics---abstention rate, conditional accuracy, and answer rate---to quantify model behavior under incongruence due to the role's death. We show that models fail to abstain after death and suffer from an accuracy drop compared to the Non-Role-Play setting. Through probing experiments, we identify two main causes: (i) unreliable encoding of the "death" state across different years, leading to unsatisfactory abstention behavior, and (ii) role playing causes shifts in the model’s temporal representations, resulting in accuracy drops. We leverage these insights to improve consistency in the model's abstention and answer behaviors. Our findings suggest that concept incongruence leads to unexpected model behaviors and point to future directions on improving model behavior under concept incongruence.

Reinforcement Learning · Deep RL

Jian-Ting Guo, Yu-Cheng Chen, Ping-Chun Hsieh, Kuo-Hao Ho, Po-Wei Huang, Ti-Rong Wu, I-Chen Wu

Human-like agents have long been one of the goals in pursuing artificial intelligence. Although reinforcement learning (RL) has achieved superhuman performance in many domains, relatively little attention has been focused on designing human-like RL agents. As a result, many reward-driven RL agents often exhibit unnatural behaviors compared to humans, raising concerns for both interpretability and trustworthiness. To achieve human-like behavior in RL, this paper first formulates human-likeness as trajectory optimization, where the objective is to find an action sequence that closely aligns with human behavior while also maximizing rewards, and adapts the classic receding-horizon control to human-like learning as a tractable and efficient implementation. To achieve this, we introduce Macro Action Quantization (MAQ), a human-like RL framework that distills human demonstrations into macro actions via Vector-Quantized VAE. Experiments on D4RL Adroit benchmarks show that MAQ significantly improves human-likeness, increasing trajectory similarity scores, and achieving the highest human-likeness rankings among all RL agents in the human evaluation study. Our results also demonstrate that MAQ can be easily integrated into various off-the-shelf RL algorithms, opening a promising direction for learning human-like RL agents. Our code is available at https://rlg.iis.sinica.edu.tw/papers/MAQ.

Theory · Reinforcement Learning and Planning

Feng Zhu, David Simchi-Levi

Thompson Sampling (TS) has emerged as a powerful algorithm for sequential decision-making, with strong empirical success and theoretical guarantees. However, it has been shown that its behavior under stringent safety and robustness criteria --- such as safety of cumulative regret distribution and robustness to model mis-specification --- can sometimes perform poorly. In this work, we try to address these aspects through the lens of adaptive variance inflation for Gaussian Thompson Sampling. Our one-line change introduces a time- and arm-dependent inflation factor into the sampling variance, and yields several compelling benefits. The resulting policy achieves provably worst-case optimal expected regret and worst-case optimal fast-decaying regret tail bounds, even in the presence of heavy-tailed (sub-exponential) noise or mis-specified environments. The policy is also robust to mis-specified noise variances. Beyond cumulative regret, we further demonstrate that our method ensures strong post-experiment guarantees: simple regret and estimation error per arm exhibit fast-decaying tail probabilities, contributing to more reliable and robust downstream decisions. Finally, we extend our policy to incorporate settings with unknown arm-specific variances and empirically validate the consistent performance of our approach across a range of environments.

Computer Vision · Everything Else

Xingjian Ran, Yixuan Li, Linning Xu, Mulin Yu, Bo Dai

Realistic 3D indoor scene synthesis is vital for embodied AI and digital content creation. It can be naturally divided into two subtasks: object generation and layout generation. While recent generative models have significantly advanced object-level quality and controllability, layout generation remains challenging due to limited datasets. Existing methods either overfit to these datasets or rely on predefined constraints to optimize numerical layout that sacrifice flexibility. As a result, they fail to generate scenes that are both open-vocabulary and aligned with fine-grained user instructions. We introduce DirectLayout, a framework that directly generates numerical 3D layouts from text descriptions using generalizable spatial reasoning of large language models (LLMs). DirectLayout decomposes the generation into three stages: producing a Bird's-Eye View (BEV) layout, lifting it into 3D space, and refining object placements. To enable explicit spatial reasoning and help the model grasp basic principles of object placement, we employ Chain-of-Thought (CoT) Activation based on the 3D-Front dataset. Additionally, we design CoT-Grounded Generative Layout Reward to enhance generalization and spatial planning. During inference, DirectLayout addresses asset-layout mismatches via Iterative Asset-Layout Alignment through in-context learning. Extensive experiments demonstrate that DirectLayout achieves impressive semantic consistency, generalization and physical plausibility.

Deep Learning · Generative Models and Autoencoders

Herbert Woisetschläger, Ryan Zhang, Shiqiang Wang, Hans Arno Jacobsen

Open-weight large language model (LLM) zoos provide access to numerous high-quality models, but selecting the appropriate model for specific tasks remains challenging and requires technical expertise. Most users simply want factually correct, safe, and satisfying responses without concerning themselves with model technicalities, while inference service providers prioritize minimizing operating costs. These competing interests are typically mediated through service level agreements (SLAs) that guarantee minimum service quality. We introduce MESS+, a stochastic optimization algorithm for cost-optimal LLM request routing while providing rigorous SLA compliance guarantees. MESS+ learns request satisfaction probabilities of LLMs in real-time as users interact with the system, based on which model selection decisions are made by solving a per-request optimization problem. Our algorithm includes a novel combination of virtual queues and request satisfaction prediction, along with a theoretical analysis of cost optimality and constraint satisfaction. Across a wide range of state-of-the-art LLM benchmarks, MESS+ achieves an average of $2\times$ cost savings compared to existing LLM routing techniques.

Data-centric AI · Everything Else

Amaya Dharmasiri, William Yang, Polina Kirichenko, Lydia Liu, Olga Russakovsky

Coreset selection methods have shown promise in reducing the training data size while maintaining model performance for data-efficient machine learning. However, many large real-world datasets suffer from unknown spurious correlations and hidden biases. Therefore, it is crucial to understand how such biases would affect downstream tasks via the selected coresets. In this work, we conduct the first comprehensive analysis of the implications of data selection on the bias levels of the selected coresets and the robustness of downstream models trained on them. We use an extensive experimental setting spanning ten different spurious correlations benchmarks, five score metrics to characterize sample importance/ difficulty, and five data selection policies across a broad range of coreset sizes to identify important patterns and derive insights. Thereby, we unravel a series of nontrivial nuances in well-known interactions between sample difficulty and bias alignment, as well as dataset bias and resultant model robustness. For example, we show that embedding-based sample characterizations run a comparatively lower risk of inadvertently exacerbating bias when used for selecting coresets compared to characterizations based on learning dynamics. Our analysis also reveals that lower bias levels achieved by coresets of difficult samples do not reliably guarantee downstream robustness. Most importantly, we show that special considerations need to be made when the coreset size is very small, since there is a unique risk of highly prototypical coresets reaching high average performance while obscuring their low group-robustness.

Theory · Learning Theory

Arnab Bhattacharyya, Sutanu Gayen, Philips George John, Sayantan Sen, N. V. Vinodchandran

This work establishes a novel link between the problem of PAC-learning high-dimensional graphical models and the task of (efficient) counting and sampling of graph structures, using an online learning framework. The problem of efficiently counting and sampling graphical structures, such as spanning trees and acyclic orientations, has been a vibrant area of research in algorithms. We show that this rich algorithmic foundation can be leveraged to develop new algorithms for learning high-dimensional graphical models. We present the first efficient algorithm for (both realizable and agnostic) learning of Bayes nets with a chordal skeleton. In particular, we present an algorithm that, given integers $k,d > 0$, error parameter $\varepsilon > 0$, an undirected chordal graph $G$ on $n$ vertices, and sample access to a distribution $P^\ast$ on $[k]^n$; (1) returns a Bayes net $\widehat{P}$ with skeleton $G$ and indegree $d$, whose KL-divergence from $P^\ast$ is at most $\varepsilon$ more than the optimal KL-divergence between $P^\ast$ and any Bayes net with skeleton $G$ and indegree $d$, (2) uses $\widetilde{O}(n^3k^{d+1}/\varepsilon^2)$ samples from $P^\ast$ and runs in time $\mathrm{poly}(n,k,\varepsilon^{-1})$ for constant $d$. Prior results in this spirit were for only for trees ($d=1$, tree skeleton) via Chow-Liu, and in the realizable setting for polytrees (arbitrary $d$ but tree skeleton). Thus, our result significantly extends the state-of-the-art in learning Bayes net distributions. We also establish new results for learning tree and polytree distributions.

General Machine Learning · Causality

Zirui Yan, Emre Acartürk, Ali Tajer

Causal representation learning (CRL) is the process of disentangling the *latent* low-dimensional causally-related generating factors underlying high-dimensional observable data. Extensive recent studies have characterized CRL identifiability and *perfect* recovery of the latent variables and their attendant causal graph. This paper introduces the notion of *reward-oriented* CRL, the purpose of which is to move away from perfectly learning the latent representation and instead learning it to the extent needed for optimizing a desired downstream task (reward). In reward-oriented CRL, perfectly learning the latent representation can be excessive; instead, it must be learned at the *coarsest* level sufficient for optimizing the desired task. Reward-oriented CRL is formalized as the optimization of a desired function of the observable data over the space of all possible interventions and focuses on linear causal and transformation models. To sequentially identify the optimal subset of interventions, an adaptive exploration algorithm is designed that learns the latent causal graph and the variables needed to identify the best intervention. It is shown that for an $n$-dimensional latent space and a $d$-dimensional observation space, over a horizon $T$ the algorithm's regret scales as $\tilde O(d^{\frac{1}{3}}n^{\frac{1}{3}}u^{\frac{2}{3}}T^{\frac{2}{3}} + u\sqrt{T})$, where $u$ measures total uncertainty in the graph estimates. Furthermore, an almost-matching lower bound is shown to scale as $\Omega(d^{\frac{1}{3}}n^{\frac{1}{3}}p^{\frac{2}{3}}T^{\frac{2}{3}} + p\sqrt{T})$, in which $u$ is replaced by $p$ that counts the number of causal paths in the graph.

General Machine Learning · Representation Learning

Sean Lamont, Christian Walder, Amir Dezfouli, Paul Montague, Michael Norrish

A key challenge in automated formal reasoning is the intractable search space, which grows exponentially with the depth of the proof. This branching is caused by the large number of candidate proof tactics which can be applied to a given goal. Nonetheless, many of these tactics are semantically similar or lead to an execution error, wasting valuable resources in both cases. We address the problem of effectively pruning this search, using only synthetic data generated from previous proof attempts. We first demonstrate that it is possible to generate semantically aware tactic representations which capture the effect on the proving environment, likelihood of success, and execution time. We then propose a novel filtering mechanism which leverages these representations to select semantically diverse and high quality tactics, using Determinantal Point Processes. Our approach, 3D-Prover, is designed to be general, and to augment any underlying tactic generator. We demonstrate the effectiveness of 3D-Prover on the miniF2F and LeanDojo benchmarks by augmenting popular open source proving LLMs. We show that our approach leads to an increase in the overall proof rate, as well as a significant improvement in the tactic success rate, execution time and diversity. We make our code available at https://github.com/sean-lamont/3D-Prover.

Reinforcement Learning · Deep RL

Gunshi Gupta, Karmesh Yadav, Zsolt Kira, Yarin Gal, Rahaf Aljundi

To enable embodied agents to operate effectively over extended timeframes, it is crucial to develop models that form and access memories to stay contextualized in their environment. In the current paradigm of training transformer-based policies for embodied sequential decision-making tasks, visual inputs often overwhelm the context limits of transformers, while humans can maintain and utilize a lifetime of experience compressed as memories. Significant compression is possible in principle, as much of the input is irrelevant and can be abstracted. However, existing approaches predominantly focus on either recurrent models with fixed-size memory or transformers with full-context reliance. In this work, we propose Memo, a transformer-based architecture and training recipe for reinforcement learning (RL) on memory-intensive, long-horizon tasks. Memo incorporates the creation and retrieval of memory by interleaving periodic summarization tokens with the inputs of a model during training. We demonstrate Memo’s effectiveness on a grid-world meta-RL benchmark and a multi-object navigation task in photo-realistic indoor settings. Memo outperforms naive long-context transformer baselines while being more compute and storage efficient. Additionally, Memo generalizes better to longer contexts at inference time and remains robust in streaming settings, where historical context must be truncated to fit inference constraints.

Ning Zhang, Henry Kenlay, Li Zhang, Mihai Cucuringu, Xiaowen Dong

Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these models, i.e., their sensitivity to small changes in the graph structure, remains in rather limited settings, hampering the development and deployment of robust and trustworthy models in practice. To fill this gap, we study how small perturbations in the graph topology affect GCNN outputs and propose a novel formulation for analyzing model stability. Unlike prior studies that focus only on worst-case perturbations, our distribution-aware formulation characterizes output perturbations across a broad range of input data. This way, our framework enables, for the first time, a probabilistic perspective on the interplay between the statistical properties of the node data and perturbations in the graph topology. We conduct extensive experiments to validate our theoretical findings and demonstrate their benefits over existing baselines, in terms of both representation stability and adversarial attacks on downstream tasks. Our results demonstrate the practical significance of the proposed formulation and highlight the importance of incorporating data distribution into stability analysis.

Computer Vision · Vision Models & Multimodal

Xiaoyu Zhan, Wenxuan Huang, Hao Sun, Xinyu Fu, Changfeng Ma, Shaosheng Cao, Bohan Jia, Shaohui Lin, Zhenfei Yin, LEI BAI 等

Recent advances in Multimodal Large Language Models (MLLMs) have significantly improved 2D visual understanding, prompting interest in their application to complex 3D reasoning tasks. However, it remains unclear whether these models can effectively capture the detailed spatial information required for robust real-world performance, especially cross-view consistency, a key requirement for accurate 3D reasoning. Considering this issue, we introduce Viewpoint Learning, a task designed to evaluate and improve the spatial reasoning capabilities of MLLMs. We present the Viewpoint-100K dataset, consisting of 100K object-centric image pairs with diverse viewpoints and corresponding question-answer pairs. Our approach employs a two-stage fine-tuning strategy: first, foundational knowledge is injected to the baseline MLLM via Supervised Fine-Tuning (SFT) on Viewpoint-100K, resulting in significant improvements across multiple tasks; second, generalization is enhanced through Reinforcement Learning using the Group Relative Policy Optimization (GRPO) algorithm on a broader set of questions. Additionally, we introduce a hybrid cold-start initialization method designed to simultaneously learn viewpoint representations and maintain coherent reasoning thinking. Experimental results show that our approach significantly activates the spatial reasoning ability of MLLM, improving performance on both in-domain and out-of-domain reasoning tasks. Our findings highlight the value of developing foundational spatial skills in MLLMs, supporting future progress in robotics, autonomous systems, and 3D scene understanding.