arXiv:2512.16082v2 Announce Type: replace
Abstract: Ben-Sasson, Goldreich and Sudan showed that a binary error correcting code admitting a $2$-query tester cannot be good, i.e., it cannot have both linear distance and constant rate. They also showed that there are no good codes if the alphabet is a finite field $\mathbb{F}$, the code is $\mathbb{F}$-linear, and the $2$-query tester is $\mathbb{F}$-linear. We show that those are essentially the only limitations on the existence of good locally testable codes (LTCs). That is, there are good $2$-query LTCs on any alphabet with more than $2$ letters, and good $3$-query LTCs with a binary alphabet. Similarly, there are good $3$-query $\mathbb{F}$-linear LTCs, and for every $\mathbb{F}$-vector space $V$ of dimension greater than $1$, there are good $2$-query LTCs with alphabet $V$ whose tester is $\mathbb{F}$-linear. This completely solves, for every $q\geq 2$ and alphabet (resp. $\mathbb{F}$-vector space) $\Sigma$, the question of whether there is a good $q$-query LTC (resp. $\mathbb{F}$-LTC) with alphabet $\Sigma$. Our proof builds on the recent good $2$-query $\mathbb{F}$-LTCs of the first author and Kaufman, by establishing a general method for reducing the alphabet size of a good low-query LTC.
Science Journals
arXiv:2601.15995v2 Announce Type: replace
Abstract: Parkour tasks for quadrupeds have emerged as a promising benchmark for agile locomotion. While human athletes can effectively perceive environmental characteristics to select appropriate footholds for obstacle traversal, endowing legged robots with similar perceptual reasoning remains a significant challenge. Existing methods often rely on hierarchical controllers that follow pre-computed footholds, thereby constraining the robot's real-time adaptability and the exploratory potential of reinforcement learning. To overcome these challenges, we present PUMA, an end-to-end learning framework that integrates visual perception and foothold priors into a single-stage training process. This approach leverages terrain features to estimate egocentric polar foothold priors, composed of relative distance and heading, guiding the robot in active posture adaptation for parkour tasks. Extensive experiments conducted in simulation and real-world environments across various discrete complex terrains, demonstrate PUMA's exceptional agility and robustness in challenging scenarios.
arXiv:2601.16152v2 Announce Type: replace
Abstract: Data systems increasingly operate under persistent legal, political, and analytic disagreement, where no single interpretive authority can be assumed. A neutral substrate provides stable shared reference without requiring agreement about causal or normative interpretation: it fixes reference structurally and leaves interpretation to extension layers.
This paper derives the identity structure such a substrate requires using a small transformation algebra. Identity is treated as transformation-invariance: a referent is individuated by the admissible operations that preserve it. Once routine record operations are fixed, individuation becomes a structural calculation.
That calculation exposes a mismatch between reference kinds and identity regimes. An accountability substrate must refer to six carrier kinds: obligation-bearers, rules, occurrences, scopes, records, and plain referents. Three kinds have more than one admissible basis. A scope may be fixed by extension or structure; a rule by content or structure; a plain referent by locus or object. Decomposition separates the scope readings, refinement separates the rule readings, and forking separates the plain-referent readings.
Counting reference kinds gives six, while transformation analysis forces at least nine identity regimes. The three additional regimes add no new kind to the inventory. They arise from identity behavior under ordinary operations, and any attempt to collapse them reappears as a hidden regime that persistent disagreement cannot hold fixed.
The result is a conditional lower bound. A richer transformation basis may leave the bound unchanged or force further splits, but it cannot erase a distinction witnessed here. The additional regimes correspond to distinctions often handled by modeling convention, but such conventions cannot substitute for regime-level identity commitments under persistent disagreement.
arXiv:2601.20136v2 Announce Type: replace
Abstract: Fault slip modeling, based on laboratory-derived friction laws, has significantly enhanced our understanding of fault mechanics. Agreement between model predictions and observations supports the hypothesis that observed slip diversity, including fast earthquakes and slow transient slips (Slow Slip Events; SSEs), originates from frictional heterogeneity. However, quantitative assessments of frictional heterogeneity from geodetic observations while fully incorporating fault mechanics are lacking due to the difficulties of high-dimensional optimization. In this study, we aim to address this gap using Physics-Informed Neural Networks (PINNs) to link frictional heterogeneity with geodetic observations. PINNs employ a neural network to represent the spatially variable frictional properties, making their estimation feasible. Targeting the 2010 Bungo SSE in southwest Japan, our estimation reveals heterogeneous friction coinciding with localized SSE nucleation in southwest Shikoku, and subsequent westward propagation. The calculated fault slip of SSE successfully reproduces the spatio-temporal pattern of observed surface displacements. This PINN-based inversion provides a mechanically consistent fault slip model validated through quantitative comparison with observations. Furthermore, we forecast the future fault slip evolution, demonstrating the importance of assimilating observations spanning multiple SSE cycles. Our results demonstrate the potential of PINN for advancing understanding of fault mechanics and enabling physics-based fault slip forecasting.
arXiv:2607.09820v1 Announce Type: new
Abstract: Predict-then-optimize systems usually compress uncertainty into a point forecast and then solve a downstream optimization problem as if the forecast were reliable. Distributionally robust optimization (DRO) offers protection against misspecification, but the ambiguity set is often centered at historical samples and uses a fixed radius. We propose \emph{learned predictive ambiguity sets} (LPAS): a deep contextual model outputs a finite nominal scenario distribution, a state-dependent Wasserstein radius, and optionally an anisotropic ground metric. These outputs define a contextual ambiguity set that feeds a DRO decision layer. The radius is trained by a combination of conditional quantile calibration, size regularization, and downstream decision loss, so that robustness is adaptive rather than globally fixed. We derive the finite dual form used by the decision layer, present a staged training algorithm, and evaluate the method on distributionally robust portfolio optimization with 20 S&P 500 constituents from 2018--2026. The proposed method substantially improves over equal-weight, predict-then-optimize, and historical Wasserstein DRO baselines, achieving 26.28% annualized return, Sharpe ratio 1.30, final wealth 1.61, and lower tail loss than a deep fixed-radius DRO baseline while using a smaller average radius. The results show that learned ambiguity radii can recover most of the performance of strong fixed-radius DRO while reducing unnecessary conservatism and improving regime adaptivity.
arXiv:2607.10062v1 Announce Type: new
Abstract: For an edge-weighted graph $G=(V,E)$ and a stretch parameter $t\geq 1$, a $t$-spanner is a subgraph $H\subseteq G$ such that the shortest path distances in $G$ and $H$ satisfy $\delta_H(u,v)\leq t\, \delta_G(u,v)$ for all $u,v\in V$. In metric spanners, $V$ is a finite metric space, and $G$ is the complete graph with edge weights corresponding to the distances between the endpoints. When $G$ is the complete graph on $n$ points in the plane, $O(n)$-size $t$-spanners are possible for any $t>1$: For every $\varepsilon>0$, there is an $(1+\varepsilon)$-spanner with $O(n/\varepsilon)$ edges (i.e., the stretch can be arbitrarily close to 1).
When $G=K(R,B)$ is the complete bipartite graph on $n$ bichromatic points in the plane, in general, no spanner construction can guarantee stretch $t<3$ with $o(n^2)$ edges. Bose et al.~(SICOMP 2009) constructed a $(3+\varepsilon)$-spanner with $O(n\log n)$ edges for any constant $\varepsilon>0$. Our main result is a new construction for a $(3+\varepsilon)$-spanner with $O(\sqrt{1/\varepsilon}\cdot n)$ edges. Eliminating the $O(\log n)$ factor resolves a problem left open for more than 17 years, and raises a new research problem about optimizing the dependence on $\varepsilon$. We also study spanners for $G=K(R,B)$ on $n$ bichromatic points on the real line: In this case, we show that the MST of $K(R,B)$ is a 7-spanner, and we construct a 3-spanner with at most $2n-3$ edges.
arXiv:2601.22146v2 Announce Type: replace
Abstract: Due to limited supervised training data, large language models (LLMs) are typically pre-trained via a self-supervised "predict the next word" objective on a vast amount of unstructured text data. To make the resulting model useful to users, it is further trained on a far smaller amount of "instruction-tuning" data comprised of supervised training examples of instructions and responses. To overcome the limited amount of supervised data, we propose a procedure that can transform the knowledge in internet-scale pre-training documents into billions of synthetic instruction and answer training pairs. The resulting dataset, called FineInstructions, uses ~18M instruction templates created from real user-written queries and prompts. These instruction templates are matched to and instantiated with human-written source documents from unstructured pre-training corpora. With "supervised" synthetic training data generated at this scale, an LLM can be pre-trained from scratch solely with the instruction-tuning objective, which is far more in-distribution with the expected downstream usage of LLMs (responding to user prompts). We conduct controlled token-for-token training experiments and find pre-training on FineInstructions outperforms standard pre-training and other proposed synthetic pre-training techniques on standard benchmarks measuring free-form response quality. Our resources can be found at https://huggingface.co/fineinstructions .
arXiv:2602.00620v2 Announce Type: replace
Abstract: The zero-shot evaluation of time series foundation models (TSFMs) for classification typically uses a frozen encoder followed by a task-specific classifier. However, this practice violates the training-free premise of zero-shot deployment and introduces evaluation bias due to classifier-dependent training choices. To address this issue, we propose TIC-FM, an in-context learning framework that treats the labeled training set as context and predicts labels for all test instances in a single forward pass, without parameter updates. TIC-FM pairs a time series encoder and a lightweight projection adapter with a split-masked latent memory Transformer. We further provide theoretical justification that in-context inference can subsume trained classifiers and can emulate gradient-based classifier training within a single forward pass. Experiments on 128 UCR datasets show strong accuracy, with consistent gains in the extreme low-label situation, highlighting training-free transfer for time series classification.The source code is publicly available at https://github.com/fangjuntao/TIC-FM.
arXiv:2602.01415v5 Announce Type: replace
Abstract: LLMs offer tremendous opportunities for pedagogical agents to help students construct knowledge and develop problem-solving skills, yet many of these agents operate on a "one-size-fits-all" basis, limiting their ability to personalize support. To address this, we introduce Evidence-Decision-Feedback (EDF), a theoretical framework for adaptive scaffolding with LLM agents. EDF integrates elements of intelligent tutoring systems (ITS) and agentic behavior by organizing interactions around evidentiary inference, pedagogical decision-making, and adaptive feedback. We instantiate EDF through Copa, a Collaborative Peer Agent for STEM+C problem-solving. In an authentic high school classroom study, we show that EDF-guided interactions align feedback with students' demonstrated understanding and task mastery; promote scaffold fading; and support interpretable, evidence-grounded explanations without fostering overreliance.
arXiv:2602.03564v2 Announce Type: replace
Abstract: Time series forecasting can be viewed as a generative problem that requires both semantic understanding over contextual conditions and stochastic modeling of continuous temporal dynamics. Existing approaches typically rely on either autoregressive large language models (LLMs) for semantic context modeling or diffusion-like models for continuous probabilistic generation. However, neither method alone can adequately model both aspects simultaneously. In this work, we propose CoGenCast, a hybrid generative framework that couples pre-trained LLMs with flow-matching mechanism for effective time series forecasting. Specifically, we reconfigure pre-trained decoder-only LLMs into a native forecasting encoder-decoder backbone by modifying only the attention topology, enabling bidirectional context encoding and causal representation generation. Building on this, a flow-matching mechanism is further integrated to model temporal evolution, capturing continuous stochastic dynamics conditioned on the autoregressively generated representation. Notably, CoGenCast naturally supports multimodal forecasting and cross-domain unified training. Extensive experiments on multiple benchmarks show that CoGenCast achieves competitive performance compared to previous baselines. Code is available at https://github.com/liuyaguo/_CoGenCast.
arXiv:2602.04408v3 Announce Type: replace
Abstract: We study the Pareto frontier (optimal trade-off) between utility and separation, a fairness criterion requiring predictive independence from sensitive attributes conditional on the true outcome. Through an information-theoretic lens, we prove a characterization of the utility-separation Pareto frontier, establish its concavity, and thereby prove the increasing marginal cost of separation in terms of utility. In addition, we characterize the conditions under which this trade-off becomes strict, providing a guide for trade-off selection in practice. Based on the theoretical characterization, we develop an empirical regularizer based on conditional mutual information (CMI) between predictions and sensitive attributes given the true outcome. The CMI regularizer is compatible with any deep model trained via gradient-based optimization and serves as a scalar monitor of residual separation violations, offering tractable guarantees during training. Finally, numerical experiments support our theoretical findings: across COMPAS, UCI Adult, UCI Bank, and CelebA, the proposed method substantially reduces separation violations while matching or exceeding the utility of established baseline methods. This study thus offers a provable, stable, and flexible approach to enforcing separation in deep learning.
arXiv:2602.04584v2 Announce Type: replace
Abstract: Saliency estimation has received growing attention in recent years due to its importance in a wide range of applications. In the context of 360-degree video, it has been particularly valuable for tasks such as viewport prediction and immersive content optimization. In this paper, we propose SalFormer360, a novel saliency estimation model for 360-degree videos built on a transformer-based architecture. Our approach is based on the combination of an existing encoder architecture, SegFormer, and a custom decoder. The SegFormer model was originally developed for 2D segmentation tasks, and it has been fine-tuned to adapt it to 360-degree content. To further enhance prediction accuracy in our model, we incorporated Viewing Center Bias to reflect user attention in 360-degree environments. Extensive experiments on the three largest benchmark datasets for saliency estimation demonstrate that SalFormer360 outperforms existing state-of-the-art methods. In terms of Pearson Correlation Coefficient, our model achieves 8.4% higher performance on Sport360, 2.5% on PVS-HM, and 18.6% on VR-EyeTracking compared to previous state-of-the-art.
arXiv:2602.14551v2 Announce Type: replace
Abstract: Human-robot collaborative assembly requires robots to interpret ambiguous corrective instructions while producing physically executable motions. Vision-language models (VLMs) provide semantic reasoning but may select logically inconsistent targets or misjudge execution outcomes. We propose a replanning framework that maps human instructions to Action Target candidates, including grasp poses and tool selections, and combines an Internal Correction Model for pre-execution logical verification with an External Correction Model for post-execution visual verification. The framework integrates VLM reasoning with 6-DoF grasp generation and collision-free trajectory planning. Simulation ablations show configuration-dependent effects: internal correction improves candidate validity, whereas external correction enables recovery for a low-latency VLM but can reduce success when visual verification produces false negatives. Experiments with an upper-body humanoid robot achieved 66.7% success in real-world object fixation, 100% in initial tool selection, and 75.0% in corrective tool selection. These results demonstrate interactive replanning across spatial and semantic collaborative tasks while identifying visual-state verification as a key limitation.
arXiv:2602.14687v2 Announce Type: replace
Abstract: Improving Sparse Autoencoders (SAEs) requires benchmarks that can precisely validate architectural innovations. Current LLM-based SAE benchmarks are too noisy to differentiate architectural improvements, while commonly used synthetic-data experiments are too small-scale, unstandardized, and unrealistic to be meaningful. We introduce SynthSAEBench, a benchmark and toolkit for evaluating SAEs against large-scale synthetic data with realistic feature characteristics including correlation, hierarchy, and superposition, while providing ground-truth features and firings. SynthSAEBench acts as a controlled lower-bound test: SAE architectures that fail when the Linear Representation Hypothesis holds by construction have little hope on real LLMs. The benchmark reproduces known LLM SAE phenomena including the disconnect between reconstruction and latent quality, poor SAE probing, and a precision-recall trade-off mediated by L0, demonstrating that SynthSAEBench findings reproduce results on LLM SAEs. We further identify a novel failure mode: Matching Pursuit SAEs exploit superposition noise to improve reconstruction without learning ground-truth features, suggesting more expressive encoding procedures can easily overfit. SynthSAEBench complements LLM benchmarks with ground-truth features and controlled ablations for diagnosing SAE failure modes, while providing a clear target for SAE architecture work.
arXiv:2602.17686v5 Announce Type: replace
Abstract: Chain-of-Thought (CoT) reasoning has significantly improved LLMs' mathematical problem-solving capabilities, but distilling such capabilities into smaller models remains challenging due to the capacity mismatch between verbose teachers and compact students. Directly copying teachers' lengthy reasoning chains causes capacity overload, resulting in truncated outputs or repetitive failure. Existing remedies each sacrifice a critical property of CoT: implicit reasoning methods (e.g., compressing reasoning into hidden states) trade away interpretability and verifiability, while heuristic compression strategies (e.g., random step pruning) destroy logical integrity. To address this, we propose BRIDGE, a curriculum framework that first establishes structural understanding via masked reconstruction, then uses GRPO-based reinforcement learning to guide students in self-discovering the optimal balance between accuracy and brevity, and finally internalizes complex reasoning through teacher-guided rewriting on failure cases. On GSM8K, BRIDGE enables Qwen2.5-3B to achieve 11.29% accuracy improvement and 27.4% token reduction over the original model, outperforming instruction-tuned variants and distillation baselines. Zero-shot transfer experiments on SVAMP and MATH-500 further confirm the generalization of internalized reasoning. Our code and model checkpoints are publicly available at https://github.com/Applied-Machine-Learning-Lab/SDM2026_BRIDGE and https://huggingface.co/bowen0815/BRIDGE.
arXiv:2607.10202v1 Announce Type: new
Abstract: Cross-model comparisons read divergence in value dispositions as evidence that language models hold individuated values. Under single-draw measurement this conflates two quantities: a difference in central tendency (a genuine value difference) and a difference in response determinism (how sharply a model commits to a forced choice). We introduce a separation protocol -- no-rule value dilemmas with counterbalanced, repeated forced-choice measurement and a determinism index -- and a determinism-corrected decomposition that splits an apparent cross-model distance into a direction-flip component (genuine disagreement) and a same-side-more-extreme component we label determinism. Across nine models, determinism varies substantially (0.66-0.95 among engaging models); whether it is a per-model trait or tracks provider and scale is a question our method makes measurable but our sample leaves open. Correcting for determinism shrinks apparent individuation, while a few cross-family disagreements survive a strict test. We then isolate a second confound: the access harness serving each model. Re-collecting the same models through raw provider APIs, we find the deployment client shifts a model's value profile substantially and client-specifically: one subscription CLI moves a profile by 0.31, flips four of eighteen items, and inflates the flagship's apparent softness (0.34 via CLI vs 0.66 via raw API), whereas another provider's client is clean, confounding provider family with access client. The harness is a value-shaping layer: a base model that refuses one-in-ten forced choices is made compliant by an agent system prompt, established causally in a white-box control. An audit ranking models by single-draw value distance thus ranks a determinism-inflated quantity, confounded further by the client used. We contribute the decomposition and identify the deployment harness as a distinct value confound.
arXiv:2607.10206v1 Announce Type: new
Abstract: Flow-matching policies are promising for imitation learning because they model complex multimodal action distributions. However, their stochasticity is largely passive: repeated sampling may yield diverse behaviors, but users cannot directly choose among valid continuations from the same state. We propose Source-Lifted Flow Matching (SL-FM), a source-intervenable flow-matching policy that exposes such a handle while keeping the velocity field shared and latent-free. The handle selects only the source endpoint of the conditional flow, not a mode-specific field, preserving the standard formulation while avoiding decomposition into separate mode-conditioned dynamics. The core mechanism is \textbf{Orthogonal Source Lifting}, designed to prevent path-crossing ambiguity. Instead of partitioning target actions by mode, SL-FM lifts handle-specific sources into auxiliary orthogonal coordinates and keeps targets in the original action subspace. This preserves the demonstrated action distribution while allowing one shared field to carry different branches without merging at crossings. To keep handles usable across states, we learn a state-dependent source mixture end to end and use a responsibility floor, giving each handle weak supervision and mitigating dead modes. Experiments on crossing-flow diagnostics and robot-control benchmarks show that SL-FM converts passive source randomness into an actionable intervention variable. It removes crossing-induced composite trajectories, changes future routes in 91.1\% of matched-prefix interventions, and achieves strong free-deployment performance, with improvements in several benchmark settings. Overall, source geometry provides actionable multimodal control without conditioning the velocity field on the selected mode.
arXiv:2607.11096v1 Announce Type: new
Abstract: The U-Net style models have been widely used in many applications. A critical step in these models is to reconstruct the lower-level features using a top-down decoder. This reconstruction requires precise fusion of high-level semantics and low-level details. Existing attention-based fusion methods typically derive attention weights from the top-down decoder features (global) alone or the correlation between the top-down decoder features and the bottom-up encoder features (local), then modulate the encoder features using these weights. In this work, we explore a different paradigm: deriving attention weights from the difference between the two feature streams. To this end, we propose two difference-based gating approaches: Feature-difference gating (FDG), which directly uses the absolute difference between global and local features to generate adaptive gating maps, and Entropy-difference gating (EDG), which measures the representational certainty of each stream via information entropy and uses their signed entropy difference to derive the attention weights. Both methods produce coupled gating maps that simultaneously modulate the global and local features. Experiments on different tasks including medical image segmentation, remote sensing image cloud removal and speech separation showed that both methods outperformed existing attention-based fusion methods, and EDG performed better. The results suggested a new paradigm for multi-scale feature fusion in the U-Net style structures.
arXiv:2607.10216v1 Announce Type: new
Abstract: The theory of simplicial complexes is a cornerstone of topology, offering a sophisticated tool for computing invariants. We present a formalization of abstract simplicial complexes and stellar subdivisions in the Lean proof assistant. We adopt a purely combinatorial framework in order to provide a cohesive foundation for studying the theory of stellar subdivisions as seen in many contexts of combinatorial topology. In particular, we provide formalizations of morphisms between abstract simplicial complexes; several crucial constructions and operations on complexes, such as links and joins; and perform a comprehensive study of how stellar subdivisions interact with these operations. We state and prove a number of identities commonly used in the study of triangulated manifolds, such as deriving equivalences between links in an abstract simplicial complex $K$ and in a stellar subdivision $\sigma_s K$, including results with no references in the standard literature. To our knowledge, this is the first formalization of stellar subdivisions in any proof assistant.
arXiv:2607.10583v1 Announce Type: new
Abstract: UAV-based vehicle re-identification (ReID) has emerged as a promising technique for traffic surveillance, urban monitoring, and public-safety applications thanks to the flexible viewpoints and wide-area coverage provided by unmanned aerial vehicles. However, despite recent progress on UAV-based vehicle ReID benchmarks, the robustness of existing methods under adverse weather remains insufficiently studied. This is important because weather degradation can significantly affect the fine-grained appearance cues required for reliable vehicle matching in aerial imagery, especially under small object scale, viewpoint variation, and complex backgrounds. In this paper, we present a controlled comparative study of three representative recent vehicle ReID methods, namely CLIP-ReID, MSINet, and AdaSP, on two UAV-based benchmarks, VRU and UAV-VeID. To ensure consistent robustness evaluation, we generate synthetic foggy and rainy variants of both datasets using an analytical weather-effect pipeline while preserving the original identities and data splits. All methods are then trained and evaluated under matched clean, foggy, and rainy conditions. Experimental results show that adverse weather consistently degrades retrieval performance across both datasets, with rain causing larger drops than fog in nearly all settings. Among the evaluated methods, AdaSP demonstrates the strongest robustness, achieving 93.0% and 88.5% mAP on VRU-Large, and 88.7% and 76.2% mAP on UAV-VeID-Test under foggy and rainy conditions, respectively. Overall, our findings show that simulated adverse weather substantially increases the difficulty of UAV-based vehicle ReID, reveals clear robustness differences among recent methods, and highlights the need for weather-aware model design and evaluation protocols in future aerial ReID research. The code is released at https://github.com/tranminhvu945/Benchmarking-ReID.
arXiv:2602.06938v3 Announce Type: replace
Abstract: The classification performance of deep neural networks relies strongly on access to large, accurately annotated datasets. In medical imaging, however, obtaining such datasets is particularly challenging since annotations must be provided by specialized physicians, which severely limits the pool of annotators. Furthermore, class boundaries can often be ambiguous or difficult to define which further complicates machine learning-based classification. In this paper, we want to address this problem and introduce a framework for mislabel detection in medical datasets. This is validated on the two largest, publicly available datasets for Video Capsule Endoscopy, an important imaging procedure for examining the gastrointestinal tract based on a video stream of lowresolution images. In addition, potentially mislabeled samples identified by our pipeline were reviewed and re-annotated by three experienced gastroenterologists. Our results show that the proposed framework successfully detects incorrectly labeled data and results in an improved anomaly detection performance after cleaning the datasets compared to current baselines.
arXiv:2602.17993v2 Announce Type: replace
Abstract: Complex problems, whether in math, logic, or planning, are solved by humans through a sequence of steps where the result of one step informs the next. In this work, we adopt the perspective that the reasoning power of Transformers is fundamentally limited by a fixed maximum number of steps along any latent path of computation. To address this, we introduce Turbo Connection (TurboConn), a novel architecture that overcomes the fixed-depth constraint by routing multiple residual connections from the higher-layer hidden states of each token $t$ to the lower layers of token $t+1$. Fine-tuning pre-trained LLMs with our method not only yields accuracy gains of 0.9% to over 10% on benchmarks like GSM8K, Parity, and multi-step arithmetic, but also demonstrates that the density of these backward connections is critical; our dense interaction significantly outperforms "sparse" alternatives that only pass a single hidden state or vector. Notably, TurboConn can be integrated into pre-trained LLMs to overcome task-specific plateaus: while a fine-tuned Qwen-3-1.7B achieves only 53.78% on Parity, adding our architectural modification enables the model to reach 100% accuracy, all without the necessity to retrain the full model from scratch or sophisticated curriculum learning. Our results provide strong empirical evidence that the depth of the computational path is a key factor in reasoning ability, also offering a new mechanism to enhance LLMs without significantly affecting generation latency.
arXiv:2607.11628v1 Announce Type: cross
Abstract: In 1992, Billera and Sturmfels introduced coherent monotone paths on polytopes as part of their description of the fiber polytope construction, and later in 1994 showed with Kapranov that these coherent monotone paths capture the topology of the space of all monotone paths, paths from a minimum to a maximum, in the directed graph of a polytope with orientation induced by a linear function. Those results motivate the following analog of the polynomial Hirsch conjecture: Does there always exist a coherent monotone path of polynomial length on a polytope for any choice of orientation induced by a linear function? We show this is not the case by exhibiting a family of polytopes and corresponding linear functions for which every coherent monotone path is exponentially long. As applications, we strengthen longstanding results pertaining to lower bounds for the shadow simplex method, geometric transversals in discrete geometry, and parametric linear optimization.
arXiv:2607.09697v1 Announce Type: new
Abstract: Existing safety mechanisms for multimodal large language models (MLLMs) face a fundamental trade-off between safety and utility. Model fine-tuning achieves robust safety but compromises general utility. Input-side safety guardrails offer a lightweight alternative, yet they suffer from severe over-refusal, indiscriminately blocking benign queries or those the model could have safely answered through refusal or advisory responses. We identify that the root cause of over-refusal lies in the input-aware paradigm: safety guardrails make safety decisions without considering whether the model itself is capable of generating safe responses. Usually, MLLMs already possess intrinsic safety mechanisms that can transform harmful inputs into harmless outputs, but input-side safety guardrails override this capability, degrading user experience. Motivated by this insight, we propose a paradigm shift toward output-aware safety guardrails. Our method operates within the model's hidden state space to predict whether the forthcoming generation will be unsafe before it is fully produced. By training a lightweight classifier via multi-instance contrastive learning on hidden state representations, our approach distinguishes between inputs that will lead to unsafe outputs and those that will not, even when the inputs themselves contain risky elements. This enables precise intervention only when the model's actual response would be harmful. Extensive experiments demonstrate that our output-aware safety guardrail matches the safety performance of existing methods while drastically reducing over-refusal, preserving the model's utility and built-in safety capabilities. Code is available at: https://github.com/kunzhan/OutGuard
arXiv:2607.11104v1 Announce Type: new
Abstract: Low-count Positron Emission Tomography (PET) reconstruction is severely hindered by the dissipative nature of prevailing generative models, where the inherent phase-space contraction leads to the numerical extinction (``wash-out'') of weak but diagnostically critical lesion signals. To overcome this geometric limitation, we propose \textbf{FlowPET}, a physics-informed framework that reformulates reconstruction as volume-preserving transport in a symplectic phase space. By parameterizing the posterior dynamics via a Separable Hamiltonian System, our approach guarantees a divergence-free vector field by construction, theoretically immunizing weak signals against probability mass collapse. To steer this conservative flow, we introduce conjugate boundary conditions based on the Range-Null space decomposition of the PET operator; this strictly enforces data consistency in the range space while confining stochastic uncertainty injection to the unobserved null space. We train the model via symplectic flow matching and perform inference using a symplectic leapfrog integrator. Extensive experiments on BrainWeb, clinical pediatric, and UDPET datasets demonstrate that \textbf{FlowPET} not only surpasses state-of-the-art deterministic and stochastic baselines in SSIM and PSNR but, more crucially, exhibits superior recovery of low-contrast lesions. The results confirm that imposing Hamiltonian structural constraints offers a robust geometric safeguard for medical inverse problems in high-noise regimes.