Symbolic regression (SR) aims to discover interpretable analytical expressions that accurately describe observed data. Amortized SR promises to be much more efficient than the predominant genetic programming SR methods, but currently struggles to scale to realistic scientific complexity. We find that a key obstacle is the lack of a fast reduction of equivalent expressions to a concise normalized form. Amortized SR has addressed this with general-purpose Computer Algebra Systems (CAS) like SymPy, but the high computational cost severely limits training and inference speed. We propose SimpliPy, a rule-based simplification engine achieving a 100-fold speed-up over SymPy at comparable quality. This enables substantial improvements in amortized SR, including scalability to much larger training sets, more efficient use of the per-expression token budget, and systematic training set decontamination with respect to equivalent test expressions. We demonstrate these advantages in our Flash-ANSR framework, which achieves much better accuracy than amortized baselines (NeSymReS, E2E) on the FastSRB benchmark. Moreover, it performs on par with state-of-the-art direct optimization (PySR) while recovering more concise rather than more complex expressions with increasing inference budget.

Diffusion-based language models offer a compelling alternative to autoregressive (AR) models by enabling parallel and controllable generation. Within this family, Masked Diffusion Models (MDMs) currently perform best but still underperform AR models in perplexity and lack key inference-time efficiency features, most notably KV caching. We introduce Eso-LMs, a new family of models that fuses AR and MDM paradigms, smoothly interpolating between their perplexities while overcoming their respective limitations. Unlike prior work, which uses transformers with bidirectional attention as MDM denoisers, we exploit the connection between MDMs and Any-Order autoregressive models and adopt causal attention. This design lets us compute the exact likelihood of MDMs for the first time and, crucially, enables us to introduce KV caching for MDMs while preserving parallel generation for the first time, significantly improving inference efficiency. Combined with an optimized sampling schedule, Eso-LMs establish a new state of the art on the speed-quality Pareto frontier for unconditional generation. We provide the code, model checkpoints, and the video tutorial on the project page: https://s-sahoo.com/Eso-LMs.

Despite the remarkable practical success of transformer-based language models, recent work has raised concerns about their ability to perform state tracking. In particular, a growing body of literature has shown this limitation primarily through failures in out-of-distribution (OOD) generalization, such as length extrapolation. In this work, we shift attention to the in-distribution implications of these limitations. We conduct a large-scale experimental study of the data efficiency of transformers and recurrent neural networks (RNNs) across multiple supervision regimes. We find that the amount of training data required by transformers grows much more rapidly with state-space size and sequence length than for RNNs. Furthermore, we analyze the extent to which learned state-tracking mechanisms are shared across different sequence lengths. We show that transformers exhibit negligible or even detrimental weight sharing across lengths, indicating that they learn length-specific solutions in isolation. In contrast, recurrent models exhibit effective amortized learning by sharing weights across lengths, allowing data from one sequence length to improve performance on others. Together, these results demonstrate that state tracking remains a fundamental challenge for transformers, even when training and evaluation distributions match.

This position paper argues that current benchmarking practice in 12-lead ECG representation learning must be fixed to ensure progress is reliable and aligned with clinically meaningful objectives. The field has largely converged on three public multi-label benchmarks (PTB-XL, CPSC2018, CSN) dominated by arrhythmia and waveform-morphology labels, even though the ECG is known to encode substantially broader clinical information. We argue that downstream evaluation should expand to include an assessment of structural heart disease and patient-level forecasting, in addition to other evolving ECG-related endpoints, as relevant clinical targets. Next, we outline evaluation best practices for multi-label, imbalanced settings, and show that when they are applied, the literature's current conclusion about which representations perform best is altered. Furthermore, we demonstrate the surprising result that a randomly initialized encoder with linear evaluation matches state-of-the-art pre-training on many tasks. This motivates the use of a random encoder as a reasonable baseline model. We substantiate our observations with an empirical evaluation of five representative ECG pre-training approaches across six evaluation settings: the three standard benchmarks, a structural disease dataset, hemodynamic inference, and patient forecasting.

Large language models (LLMs) are increasingly used as scalable judges in pairwise evaluation, but they remain prone to miscalibration and biases. We propose SCOPE (Selective Conformal Optimized Pairwise Evaluation), a framework that calibrates an acceptance threshold so that, under exchangeability, the error rate among non-abstained judgments is at most a user-specified level $α$. To supply SCOPE with a bias-neutral uncertainty signal, we introduce Bidirectional Preference Entropy (BPE), which queries the judge under both response positions and converts the order-averaged preference probability into an entropy-based score. Across various pairwise judging benchmarks, BPE outperforms standard confidence proxies in calibration and discrimination, while SCOPE consistently satisfies the target risk bound (empirical FDR $\approx 0.097$ to $0.099$ at $α= 0.10$) and retains substantial coverage. Compared to vanilla baselines, SCOPE accepts up to $2.4\times$ more judgments under the same risk constraint, demonstrating that BPE enables reliable and high-coverage LLM-based evaluation.

A core aspect of human perception is situated awareness, the ability to relate ourselves to the surrounding physical environment and reason over possible actions in context. However, most existing benchmarks for multimodal foundation models (MFMs) emphasize environment-centric spatial relations (relations among objects in a scene), while largely overlooking observer-centric relationships that require reasoning relative to agent's viewpoint, pose, and motion. To bridge this gap, we introduce SAW-Bench (Situated Awareness in the Real World), a novel benchmark for evaluating egocentric situated awareness using real-world videos. SAW-Bench comprises 786 self-recorded videos captured with Ray-Ban Meta (Gen 2) smart glasses spanning diverse indoor and outdoor environments, and over 2,071 human-annotated question-answer pairs. It probes a model's observer-centric understanding with six different awareness tasks. Our comprehensive evaluation reveals a human-model performance gap of 37.66%, even with the best-performing MFM, Gemini 3 Flash. Beyond this gap, our in-depth analysis uncovers several notable findings; for example, while models can exploit partial geometric cues in egocentric videos, they often fail to infer a coherent camera geometry, leading to systematic spatial reasoning errors. We position SAW-Bench as a benchmark for situated spatial intelligence, moving beyond passive observation to understanding physically grounded, observer-centric dynamics.

Probing is widely adopted in computer vision to faithfully evaluate self-supervised learning (SSL) embeddings, as finetuning may misrepresent their inherent quality. In contrast, audio SSL models still rely on finetuning because simple probing fails to unlock their full potential and alters their rankings when competing on AudioSet. Hence, a robust and efficient probing mechanism is required to guide the trajectory of audio SSL towards reliable and reproducible methods. We introduce Convex Gated Probing (CGP), a prototype-based method that significantly closes the gap between finetuning and probing in audio. CGP efficiently utilizes all frozen layers via a gating mechanism and exposes the location of latent task-relevant information. Guided by CGP as a reliable post-hoc evaluation probe, we rework the entire SSL pipeline of current best performing audio models that use legacy implementations of prior SSL methods. By refining data preprocessing, model architecture, and pretraining recipe, we introduce Better Audio Transformer (BAT), and establish new SOTA on audio benchmarks.

Evaluating the quality of automatically generated text often relies on LLM-as-a-judge (LLM-judge) methods. While effective, these approaches are computationally expensive and require post-processing. To address these limitations, we build upon ParaPLUIE, a perplexity-based LLM-judge metric that estimates confidence over ``Yes/No'' answers without generating text. We introduce *-PLUIE, task specific prompting variants of ParaPLUIE and evaluate their alignment with human judgement. Our experiments show that personalised *-PLUIE achieves stronger correlations with human ratings while maintaining low computational cost.

Graph Neural Networks (GNNs) learn node representations through iterative network-based message-passing. While powerful, deep GNNs suffer from oversmoothing, where node features converge to a homogeneous, non-informative state. We re-frame this problem of representational collapse from a \emph{bifurcation theory} perspective, characterizing oversmoothing as convergence to a stable ``homogeneous fixed point.'' Our central contribution is the theoretical discovery that this undesired stability can be broken by replacing standard monotone activations (e.g., ReLU) with a class of functions. Using Lyapunov-Schmidt reduction, we analytically prove that this substitution induces a bifurcation that destabilizes the homogeneous state and creates a new pair of stable, non-homogeneous \emph{patterns} that provably resist oversmoothing. Our theory predicts a precise, nontrivial scaling law for the amplitude of these emergent patterns, which we quantitatively validate in experiments. Finally, we demonstrate the practical utility of our theory by deriving a closed-form, bifurcation-aware initialization and showing its utility in real benchmark experiments.

This paper concerns the question of how AI systems encode semantic structure into the geometric structure of their representation spaces. The motivating observation is that the natural geometry of these representation spaces should reflect the way models use representations to produce behavior. We focus on the important special case of representations that define softmax distributions. In this case, we argue that the natural geometry is information geometry. Our focus is on the role of information geometry on semantic encoding and the linear representation hypothesis. As an illustrative application, we develop "dual steering", a method for robustly steering representations to exhibit a particular concept using linear probes. We prove that dual steering optimally modifies the target concept while minimizing changes to off-target concepts. Empirically, we find that dual steering enhances the controllability and stability of concept manipulation.

Neurosim is a fast, real-time, high-performance library for simulating sensors such as dynamic vision sensors, RGB cameras, depth sensors, and inertial sensors. It can also simulate agile dynamics of multi-rotor vehicles in complex and dynamic environments. Neurosim can achieve frame rates as high as ~2700 FPS on a desktop GPU. Neurosim integrates with a ZeroMQ-based communication library called Cortex to facilitate seamless integration with machine learning and robotics workflows. Cortex provides a high-throughput, low-latency message-passing system for Python and C++ applications, with native support for NumPy arrays and PyTorch tensors. This paper discusses the design philosophy behind Neurosim and Cortex. It demonstrates how they can be used to (i) train neuromorphic perception and control algorithms, e.g., using self-supervised learning on time-synchronized multi-modal data, and (ii) test real-time implementations of these algorithms in closed-loop. Neurosim and Cortex are available at https://github.com/grasp-lyrl/neurosim .

Multimodal misinformation increasingly mixes realistic im-age edits with fluent but misleading text, producing persuasive posts that are difficult to verify. Existing systems usually rely on a single evidence source. Content-based detectors identify local inconsistencies within an image and its caption but cannot determine global factual truth. Retrieval-based fact-checkers reason over external evidence but treat inputs as coarse claims and often miss subtle visual or textual manipulations. This separation creates failure cases where internally consistent fabrications bypass manipulation detectors and fact-checkers verify claims that contain pixel-level or token-level corruption. We present D-SECURE, a framework that combines internal manipulation detection with external evidence-based reasoning for news-style posts. D-SECURE integrates the HAMMER manipulation detector with the DEFAME retrieval pipeline. DEFAME performs broad verification, and HAMMER analyses residual or uncertain cases that may contain fine-grained edits. Experiments on DGM4 and ClaimReview samples highlight the complementary strengths of both systems and motivate their fusion. We provide a unified, explainable report that incorporates manipulation cues and external evidence.

On-device fine-tuning enables privacy-preserving personalization of large language models, but mobile devices impose severe memory constraints, typically 6--12GB shared across all workloads. Existing approaches force a trade-off between exact gradients with high memory (MeBP) and low memory with noisy estimates (MeZO). We propose Memory-efficient Structured Backpropagation (MeSP), which bridges this gap by manually deriving backward passes that exploit LoRA's low-rank structure. Our key insight is that the intermediate projection $h = xA$ can be recomputed during backward at minimal cost since rank $r \ll d_{in}$, eliminating the need to store it. MeSP achieves 49\% average memory reduction compared to MeBP on Qwen2.5 models (0.5B--3B) while computing mathematically identical gradients. Our analysis also reveals that MeZO's gradient estimates show near-zero correlation with true gradients (cosine similarity $\approx$0.001), explaining its slow convergence. MeSP reduces peak memory from 361MB to 136MB for Qwen2.5-0.5B, enabling fine-tuning scenarios previously infeasible on memory-constrained devices.

Navigational signs enable humans to navigate unfamiliar environments without maps. This work studies how robots can similarly exploit signs for mapless navigation in the open world. A central challenge lies in interpreting signs: real-world signs are diverse and complex, and their abstract semantic contents need to be grounded in the local 3D scene. We formalize this as sign grounding, the problem of mapping semantic instructions on signs to corresponding scene elements and navigational actions. Recent Vision-Language Models (VLMs) offer the semantic common-sense and reasoning capabilities required for this task, but are sensitive to how spatial information is represented. We propose SignScene, a sign-centric spatial-semantic representation that captures navigation-relevant scene elements and sign information, and presents them to VLMs in a form conducive to effective reasoning. We evaluate our grounding approach on a dataset of 114 queries collected across nine diverse environment types, achieving 88% grounding accuracy and significantly outperforming baselines. Finally, we demonstrate that it enables real-world mapless navigation on a Spot robot using only signs.

Graph link prediction (LP) plays a critical role in socially impactful applications such as job recommendation and friendship formation, making fairness a critical concern in this task. While many fairness-aware methods manipulate graph structures to mitigate prediction disparities, the topological biases inherent to social graphs remain poorly understood and are consistently conflated with homophily alone. In this work, we study the relationship between structural biases and fairness outcomes in LP. To this end, we formalize a taxonomy of topological bias measures and introduce a graph generation method producing a diverse corpus of synthetic graphs with controlled structural properties. Using this corpus, we show empirically that fairness outcomes are strongly correlated with graph topology, and that current fairness-aware methods remain sensitive to structural biases beyond homophily. These findings highlight the need for structurally grounded evaluations in fair graph learning.

Molecular dynamics (MD) is a central computational tool in physics, chemistry, and biology, enabling quantitative prediction of experimental observables as expectations over high-dimensional molecular distributions such as Boltzmann distributions and transition densities. However, conventional MD is fundamentally limited by the high computational cost required to generate independent samples. Generative molecular dynamics (GenMD) has recently emerged as an alternative, learning surrogates of molecular distributions either from data or through interaction with energy models. While these methods enable efficient sampling, their transferability across molecular systems is often limited. In this work, we show that incorporating auxiliary sources of information can improve the data efficiency and generalization of transferable implicit transfer operators (TITO) for molecular dynamics. We find that coarse-grained TITO models are substantially more data-efficient than Boltzmann Emulators, and that incorporating protein language model (pLM) embeddings further improves out-of-distribution generalization. Our approach, PLaTITO, achieves state-of-the-art performance on equilibrium sampling benchmarks for out-of-distribution protein systems, including fast-folding proteins. We further study the impact of additional conditioning signals such as structural embeddings, temperature, and large-language-model-derived embeddings on model performance.

The Earth's subsurface is a cornerstone of modern society, providing essential energy resources like hydrocarbons, geothermal, and minerals while serving as the primary reservoir for $CO_2$ sequestration. However, full physics numerical simulations of these systems are notoriously computationally expensive due to geological heterogeneity, high resolution requirements, and the tight coupling of physical processes with distinct propagation time scales. Here we propose the $\textbf{Adaptive Physics Transformer}$ (APT), a geometry-, mesh-, and physics-agnostic neural operator that explicitly addresses these challenges. APT fuses a graph-based encoder to extract high-resolution local heterogeneous features with a global attention mechanism to resolve long-range physical impacts. Our results demonstrate that APT outperforms state-of-the-art architectures in subsurface tasks across both regular and irregular grids with robust super-resolution capabilities. Notably, APT is the first architecture that learns directly from HR-adaptive mesh refinement simulations. We also demonstrate APT's favorable scaling behavior and cross-dataset learning capability, positioning it as a robust and scalable backbone for large-scale subsurface foundation model development.

Large language models are typically trained in two broad phases: pretraining to produce a base model, followed by further training to improve downstream performance. However, hyperparameter optimization and scaling laws are studied primarily from the perspective of the base model's validation loss, overlooking a crucial model property: downstream adaptability. In this work, we study pretraining from the perspective of model plasticity, that is, the ability of the base model to successfully adapt to downstream tasks upon additional training. We focus on the role of weight decay, a key regularization parameter during pretraining, and show through systematic experiments that larger weight decay increases the plasticity of the pretrained model, resulting in greater performance gains downstream after fine-tuning. This effect can lead to counterintuitive trade-offs where base models that perform worse after pretraining can perform better after further training. Further investigation of weight decay's mechanistic effects on model behavior reveals that it encourages linearly separable representations, regularizes attention matrices, and reduces overfitting on the training data. Together, these findings highlight the importance of pretrained model plasticity, the limits of using cross-entropy loss as the sole metric for hyperparameter optimization, and the multifaceted role that a single optimization hyperparameter plays in shaping model behavior.

Remote change detection in LLMs is a difficult problem. Existing methods are either too expensive for deployment at scale, or require initial white-box access to model weights or grey-box access to log probabilities. We aim to achieve both low cost and strict black-box operation, observing only output tokens. Our approach hinges on specific inputs we call Border Inputs, for which there exists more than one output top token. From a statistical perspective, optimal change detection depends on the model's Jacobian and the Fisher information of the output distribution. Analyzing these quantities in low-temperature regimes shows that border inputs enable powerful change detection tests. Building on this insight, we propose the Black-Box Border Input Tracking (B3IT) scheme. Extensive in-vivo and in-vitro experiments show that border inputs are easily found for non-reasoning tested endpoints, and achieve performance on par with the best available grey-box approaches. B3IT reduces costs by $30\times$ compared to existing methods, while operating in a strict black-box setting.

Existing multimodal retrieval systems excel at semantic matching but implicitly assume that query-image relevance can be measured in isolation. This paradigm overlooks the rich dependencies inherent in realistic visual streams, where information is distributed across temporal sequences rather than confined to single snapshots. To bridge this gap, we introduce DeepImageSearch, a novel agentic paradigm that reformulates image retrieval as an autonomous exploration task. Models must plan and perform multi-step reasoning over raw visual histories to locate targets based on implicit contextual cues. We construct DISBench, a challenging benchmark built on interconnected visual data. To address the scalability challenge of creating context-dependent queries, we propose a human-model collaborative pipeline that employs vision-language models to mine latent spatiotemporal associations, effectively offloading intensive context discovery before human verification. Furthermore, we build a robust baseline using a modular agent framework equipped with fine-grained tools and a dual-memory system for long-horizon navigation. Extensive experiments demonstrate that DISBench poses significant challenges to state-of-the-art models, highlighting the necessity of incorporating agentic reasoning into next-generation retrieval systems.

As Large Language Models (LLMs) are increasingly deployed in social and strategic scenarios, it becomes critical to understand where and why their behavior diverges from that of humans. While behavioral game theory (BGT) provides a framework for analyzing behavior, existing models do not fully capture the idiosyncratic behavior of humans or black-box, non-human agents like LLMs. We employ AlphaEvolve, a cutting-edge program discovery tool, to directly discover interpretable models of human and LLM behavior from data, thereby enabling open-ended discovery of structural factors driving human and LLM behavior. Our analysis on iterated rock-paper-scissors reveals that frontier LLMs can be capable of deeper strategic behavior than humans. These results provide a foundation for understanding structural differences driving differences in human and LLM behavior in strategic interactions.

Pairwise preference learning is central to machine learning, with recent applications in aligning language models with human preferences. A typical dataset consists of triplets $(x, y^+, y^-)$, where response $y^+$ is preferred over response $y^-$ for context $x$. The Bradley--Terry (BT) model is the predominant approach, modeling preference probabilities as a function of latent score differences. Standard practice assumes data follows this model and learns the latent scores accordingly. However, real data may violate this assumption, and it remains unclear what BT learning recovers in such cases. Starting from triplet comparison data, we formalize the preference information it encodes through the conditional preference distribution (CPRD). We give precise conditions for when BT is appropriate for modeling the CPRD, and identify factors governing sample efficiency -- namely, margin and connectivity. Together, these results offer a data-centric foundation for understanding what preference learning actually recovers.

KV-cache retrieval is essential for long-context LLM inference, yet existing methods struggle with distribution drift and high latency at scale. We introduce ParisKV, a drift-robust, GPU-native KV-cache retrieval framework based on collision-based candidate selection, followed by a quantized inner-product reranking estimator. For million-token contexts, ParisKV supports CPU-offloaded KV caches via Unified Virtual Addressing (UVA), enabling on-demand top-$k$ fetching with minimal overhead. ParisKV matches or outperforms full attention quality on long-input and long-generation benchmarks. It achieves state-of-the-art long-context decoding efficiency: it matches or exceeds full attention speed even at batch size 1 for long contexts, delivers up to 2.8$\times$ higher throughput within full attention's runnable range, and scales to million-token contexts where full attention runs out of memory. At million-token scale, ParisKV reduces decode latency by 17$\times$ and 44$\times$ compared to MagicPIG and PQCache, respectively, two state-of-the-art KV-cache Top-$k$ retrieval baselines, code is available at https://github.com/amy-77/ParisKV/tree/main.

Chain-of-thought (CoT) reasoning and its variants have substantially improved the performance of language models on complex reasoning tasks, yet the precise mechanisms by which different strategies facilitate generalization remain poorly understood. While current explanations often point to increased test-time computation or structural guidance, establishing a consistent, quantifiable link between these factors and generalization remains challenging. In this work, we identify intrinsic dimensionality as a quantitative measure for characterizing the effectiveness of reasoning chains. Intrinsic dimensionality quantifies the minimum number of model dimensions needed to reach a given accuracy threshold on a given task. By keeping the model architecture fixed and varying the task formulation through different reasoning strategies, we demonstrate that effective reasoning strategies consistently reduce the intrinsic dimensionality of the task. Validating this on GSM8K with Gemma-3 1B and 4B, we observe a strong inverse correlation between the intrinsic dimensionality of a reasoning strategy and its generalization performance on both in-distribution and out-of-distribution data. Our findings suggest that effective reasoning chains facilitate learning by better compressing the task using fewer parameters, offering a new quantitative metric for analyzing reasoning processes.

Understanding an agent's goals helps explain and predict its behaviour, yet there is no established methodology for reliably attributing goals to agentic systems. We propose a framework for evaluating goal-directedness that integrates behavioural evaluation with interpretability-based analyses of models' internal representations. As a case study, we examine an LLM agent navigating a 2D grid world towards a goal state. Behaviourally, we evaluate the agent against optimal policies across varying grid sizes, obstacle densities, and goal structures, finding that performance scales with task difficulty while remaining robust to difficulty-preserving transformations and multi-goal structures. We then use probing methods to decode internal representations of the environment and multi-step action plans. We find that the LLM agent non-linearly encodes a coarse spatial map, preserving approximate task-relevant cues about its position and the goal location; that its actions are broadly consistent with these internal representations; and that reasoning reorganises them, shifting from spatial cues towards immediate action selection. Our findings support the view that introspective examination is required beyond behavioural evaluations to characterise how agents represent and pursue their objectives.

We study the problem of transformation inversion on general Lie groups: a datum is transformed by an unknown group element, and the goal is to recover an inverse transformation that maps it back to the original data distribution. Such unknown transformations arise widely in machine learning and scientific modeling, where they can significantly distort observations. We take a probabilistic view and model the posterior over transformations as a Boltzmann distribution defined by an energy function on the data space. To sample from this posterior, we introduce a diffusion process on Lie groups that keeps all updates on-manifold and only requires computations in the associated Lie algebra. Our method, Transformation-Inverting Energy Diffusion (TIED), relies on a new trivialized target-score identity that enables efficient score-based sampling of the transformation posterior. As a key application, we focus on test-time equivariance, where the objective is to improve the robustness of pretrained neural networks to input transformations. Experiments on image homographies and PDE symmetries demonstrate that TIED can restore transformed inputs to the training distribution at test time, showing improved performance over strong canonicalization and sampling baselines. Code is available at https://github.com/jw9730/tied.

Modern AI systems are typically developed through multiple stages-pretraining, fine-tuning rounds, and subsequent adaptation or alignment, where each stage builds on the previous ones and updates the model in distinct ways. This raises a critical question of accountability: when a deployed model succeeds or fails, which stage is responsible, and to what extent? We pose the accountability attribution problem for tracing model behavior back to specific stages of the model development process. To address this challenge, we propose a general framework that answers counterfactual questions about stage effects: how would the model's behavior have changed if the updates from a particular stage had not occurred? Within this framework, we introduce estimators that efficiently quantify stage effects without retraining the model, accounting for both the data and key aspects of model optimization dynamics, including learning rate schedules, momentum, and weight decay. We demonstrate that our approach successfully quantifies the accountability of each stage to the model's behavior. Based on the attribution results, our method can identify and remove spurious correlations learned during image classification and text toxicity detection tasks that were developed across multiple stages. Our approach provides a practical tool for model analysis and represents a significant step toward more accountable AI development.

Flow-based generative models can be viewed through a physics lens: sampling transports a particle from noise to data by integrating a learned velocity field, and each sample corresponds to a trajectory with its own dynamical effort. Motivated by classical mechanics, we introduce Kinetic Path Energy (KPE), an action-like, per-sample diagnostic that measures the accumulated kinetic effort along an ordinary differential equation (ODE) trajectory. Empirically, KPE exhibits two robust correspondences: {i} higher KPE predicts stronger semantic fidelity; {ii} high-KPE trajectories land in sparse representation regions. We further provide theoretical guarantees linking trajectory energy to data sparsity. Paradoxically, this correlation is non-monotonic. At sufficiently high energy, generation can degenerate into memorization. Leveraging the closed-form formula of empirical flow matching, we show that extreme energies drive trajectories toward near-copies of training examples. This yields a Goldilocks principle and motivates Kinetic Trajectory Shaping (KTS), a training-free two-phase inference strategy that boosts early motion and enforces a late-time soft landing, reducing memorization and improving generation quality across benchmark tasks.

Large Language Models (LLMs) have shown strong potential in complex medical reasoning yet face diminishing gains under inference scaling laws. While existing studies augment LLMs with various knowledge types, it remains unclear how effectively the additional costs translate into accuracy. In this paper, we explore how meta-cognition of LLMs, i.e., their self-assessment of their own cognitive states, can regulate the reasoning process. Specifically, we propose MedCoG, a Medical Meta-Cognition Agent with Knowledge Graph, where the meta-cognitive assessments of task complexity, familiarity, and knowledge density dynamically regulate utilization of procedural, episodic, and factual knowledge. The LLM-centric on-demand reasoning aims to mitigate the diminishing returns under scaling law by (1) reducing costs via avoiding indiscriminate scaling, (2) improving accuracy via filtering out distractive knowledge. To validate this, we empirically characterize the scaling curve and introduce inference density to quantify inference efficiency. Experiments demonstrate the effectiveness and efficiency of MedCoG on five hard sets of medical benchmarks, yielding 6.2x inference density. Furthermore, the Oracle study highlights the significant potential of meta-cognitive regulation.

Spatial intelligence is crucial for vision--language models (VLMs), yet many scene-centric benchmarks evaluate unconstrained environments where a single image may admit multiple plausible 3D interpretations. We introduce SSI-Bench, a VQA benchmark for Structure-Centric Spatial Reasoning (SCSR) in constraint-governed spaces. Built from complex real-world 3D structures, it uses structural constraints from geometry, topology, and physical feasibility to make component relations more determinate from visual evidence. The benchmark contains 1,000 ranking questions spanning geometric and topological reasoning, where correct ordering requires resolving all candidate-wise 3D relations, imposing stronger demands on spatial understanding. It is created through a fully human-centered pipeline with over 400 researcher-hours of image curation, component annotation, and question design. Evaluating 31 VLMs reveals a large gap to humans: the best open-source model achieves 22.2% accuracy and the strongest closed-source model reaches 33.6%, while humans score 91.6%. Further results show that chain-of-thought reasoning brings only marginal gains, and error analysis reveals fundamental limitations in current models' spatial understanding within constraint-governed spaces. Project page: https://ssi-bench.github.io.