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Recent studies revealed the mathematical connection between deep neural networks (DNNs) and dynamic systems. However, the specific dynamics that DNNs, especially deep residual networks (ResNets), tend to learn during training remain insufficiently characterized. To this end, we model the forward propagation of deep residual networks using continuity equations, in which the measure is conserved and infinite curves in the measure space connect the input distribution to the output one of a ResNet. We find ResNets with $L_2$ regularization attempt to learn the geodesic curve in the Wasserstein space, induced by the optimal transport map. Compared with plain networks, ResNets can better approximate the geodesic curve, which explains why ResNets can be optimized and generalize better. Numerical experiments show that the data tracks of a ResNet tend to be line-shaped in terms of the line-shape score, and the map learned by a ResNet is closer to the optimal transport map in terms of the optimal transport score. In a word, we conclude that ResNets learn the geodesic curve in the Wasserstein space and discretely engineer the data transformation in high-dimensional spaces.

In human-centric Cyber-Physical Systems (CPS), personalized Deep Reinforcement Learning (DRL) agents must share fine-grained control actions with cloud services, exposing sensitive private states to inference attacks by honest-but-curious adversaries. Static privacy models fail to address the dynamic nature of human interactions. This paper introduces PEARL (Personalized Early-exit Adaptive Reinforcement Learning), a novel framework that addresses this challenge through structural privacy control rather than data perturbation. PEARL deploys a dual-path Early-Exit Deep Q-Network (EE-DQN) at the edge, using Mutual Information (MI) between private states and observable actions to train per-branch binary labels: Utility Confidence Labels (UCL), verifying action quality, and Privacy Confidence Labels (PCL), verifying MI leakage remains below a user-defined threshold. At inference, PEARL selects the shallowest exit branch satisfying both UCL and PCL, structurally limiting shared action descriptive power without noise injection. An MI-based feedback loop tracks behavioral drift and triggers retraining when privacy-utility profiles shift, ensuring long-term robustness. Validated on a personalized smart-home HVAC system and a VR smart classroom, PEARL reduces adversarial state-inference accuracy by 25.67% on average with a controlled 10-16% utility cost, establishing a practical, dynamically enforceable privacy-utility tradeoff.

Music recordings often suffer from audio quality issues such as excessive reverberation, distortion, clipping, tonal imbalances, and a narrowed stereo image, especially when created in non-professional settings without specialized equipment or expertise. These problems are typically corrected using separate specialized tools and manual adjustments. In this paper, we introduce SonicMaster, the first unified generative model for music restoration and mastering that addresses a broad spectrum of audio artifacts with text-based control. SonicMaster is conditioned on natural language instructions to apply targeted enhancements, or can operate in an automatic mode for general restoration. To train this model, we construct the SonicMaster dataset, a large dataset of paired degraded and high-quality tracks by simulating common degradation types with nineteen degradation functions belonging to five enhancements groups: equalization, dynamics, reverb, amplitude, and stereo. Our approach leverages a flow-matching generative training paradigm to learn an audio transformation that maps degraded inputs to their cleaned, mastered versions guided by text prompts. Objective audio quality metrics demonstrate that SonicMaster significantly improves sound quality across all artifact categories. Furthermore, subjective listening tests confirm that listeners prefer SonicMaster's enhanced outputs over other baselines.

This paper documents Project Rachel, an action research study that created and tracked a complete AI academic identity named Rachel So. Through careful publication of AI-generated research papers, we investigate how the scholarly ecosystem responds to AI authorship. Rachel So published 10+ papers between March and October 2025, was cited, and received a peer review invitation. We discuss the implications of AI authorship on publishers, researchers, and the scientific system at large. This work contributes empirical action research data to the necessary debate about the future of scholarly communication with super human, hyper capable AI systems.

Text-to-SQL parsing has achieved remarkable progress under the Full Schema Assumption. However, this premise fails in real-world enterprise environments where databases contain hundreds of tables with massive noisy metadata. Rather than injecting the full schema upfront, an agent must actively identify and verify only the relevant subset, giving rise to the Unknown Schema scenario we study in this work. To address this, we propose TRUST-SQL (Truthful Reasoning with Unknown Schema via Tools). We formulate the task as a Partially Observable Markov Decision Process where our autonomous agent employs a structured four-phase protocol to ground reasoning in verified metadata. Crucially, this protocol provides a structural boundary for our novel Dual-Track GRPO strategy. By applying token-level masked advantages, this strategy isolates exploration rewards from execution outcomes to resolve credit assignment, yielding a 9.9% relative improvement over standard GRPO. Extensive experiments across five benchmarks demonstrate that TRUST-SQL achieves an average absolute improvement of 30.6% and 16.6% for the 4B and 8B variants respectively over their base models. Remarkably, despite operating entirely without pre-loaded metadata, our framework consistently matches or surpasses strong baselines that rely on schema prefilling. Data, code, and checkpoints are available at https://huggingface.co/collections/AIJian/trustsql.

Medical large language models are typically evaluated on idealized patient cases that do not reflect how real patients communicate. We introduce VeriSim, a patient simulation framework that injects controllable noise along six clinically grounded communication dimensions while substantially preserving each patient's medical record. Truth adherence is supported by a verifier that extracts atomic claims from each candidate utterance and judges them against a UMLS-grounded vector index built with BioLORD embeddings, using the retrieved atoms' structured clinical metadata (e.g., drug class, anatomical site, treats-condition relations) rather than surface-text similarity alone. Across seven open-weight LLMs, realistic noise reduces diagnostic accuracy by 15-25 percentage points and increases conversation length by 34-55%; the 7-8B models degrade 1.4x more than 70B+ models. A board-certified physician and a licensed nurse rate VeriSim's conversations highly on truth, realism, clinical utility, and noise fidelity (inter-annotator agreement >= 0.80 across all dimensions), and an LLM-as-judge closely tracks their ratings, enabling scalable evaluation. We release VeriSim as an open-source framework for rigorous stress-testing of clinical AI: https://github.com/mohitmarvania/VeriSim

Real-world crisis intervention is inherently conversational, yet existing research largely focuses on static texts. When applied to multi-turn dialogues, current models exhibit significant performance degradation, struggling to track risk signals that emerge as context evolves. To address this gap, we introduce CRADLE-Dialogue, a clinician-annotated benchmark for turn-level crisis detection in conversational settings. The dataset features 600 dialogues with multi-label annotations across clinically grounded risks, including suicide ideation, self-harm, and child abuse, distinguishing past from ongoing risk. We further propose an Alert-Confirm evaluation protocol that distinguishes early warning signals (Alert) from turns where a specific crisis becomes explicitly identifiable (Confirm), reflecting the clinical need to intervene before risk becomes explicit. Experiments show that identifying when risk emerges is much harder than recognizing that it exists: models achieve only mid-40% to high-60% Micro F1. Additionally, we release a synthetic training corpus and a 32B-parameter model that substantially outperforms existing open-source models and achieves competitive or superior results against proprietary models across turn-level, dialogue-level, and confirm-only evaluation settings.

Event cameras are increasingly adopted in embodied perception for their microsecond temporal resolution, high dynamic range, and resilience to motion blur. However, training event-based models for robotics requires large-scale, action-conditioned data with dense physical annotations that are difficult to collect in the real world. We introduce EVIS, an open-source physics-grounded event simulator integrated into NVIDIA Isaac Sim that generates events from linear-HDR radiance from a closed-loop robot training episode. Rather than relying on learning-based video interpolation or expensive dense rendering, EVIS exploits renderer-provided motion vectors and depth maps through bi-directional warping and depth-based splatting. This enables high throughput, real-time, and high-fidelity event generation. We evaluate EVIS across runtime efficiency, sim-to-real transfer, and zero-shot model compatibility. A rotation-speed estimator trained solely on EVIS events achieves 2.75 rad/s MAE on real sensor data. Pretrained models for reconstruction, matching, and tracking perform competitively on EVIS events without any fine-tuning. EVIS sustains real-time generation across GPU-parallel environments on a single GPU. Code repository: https://github.com/spikelab-jhu/isaac-sim-event-camera-plugin.

Quantitative assessment of muscle MRI is crucial for monitoring neuromuscular disorders (NMD). This study introduces an automated radiomic phenotyping framework based on original features engineered across five main architectural domains: quantitative morphometry, spatial distribution, geometric shape, interactions between progressive fat replacement stages, and graph-based topology. Utilizing 1184 MRI scans from the CoMPaSS-NMD project, we map the complex 3D architecture of heterogeneous intramuscular lipodegeneration into objective, morphologically interpretable biomarkers. We introduce a graph-based skeletonization of fat infiltrates to quantify muscle architectural changes, establishing a multi-dimensional extension of traditional, spatially-agnostic volume metrics by mapping topological networks across the entire 3D muscle volume. Statistical screening via non-parametric Kruskal-Wallis analysis confirmed the discriminative power of these novel descriptors across the genetic hierarchy. Notably, topological network metrics (e.g., SF1_Skel_Nodes, $\epsilon^2$ = 0.2656) and interface dynamics metrics (e.g., SF2_To_SF1_Dist_Min, $\epsilon^2$ = 0.2092) demonstrated substantial effect sizes, providing deeper structural insights than classical volumetric assessments. Post-hoc pairwise evaluations and UMAP projections further indicated the capability of these topological and 3D geometric invariants to capture disease-specific macroscopic infiltration patterns. These results demonstrate that global architectural features represent a highly promising class of biomarkers for differential diagnosis, offering new avenues for tracking longitudinal disease dynamics in neuromuscular diagnostics. The developed automated feature extraction pipeline is integrated and available within the MUSCAT (MUSCle fAt Topology) library.

Native visual reasoning treats visual generation as the medium of reasoning itself: visual states (i.e. images and videos) are not merely inputs to be understood or outputs to be rendered, but first-class substrates for problem solving beyond language. Yet progress remains bottlenecked by the lack of scalable training tasks, reliable feedback, and controlled comparisons across generative substrates. In this work, we introduce VBVR-Pro, a closed-loop testbed that makes native visual reasoning through generation trainable, verifiable, optimizable, and experimentally controllable. 1) Task scaling. VBVR-Pro turns visual reasoning into a controlled task space of 300 procedurally generated tasks. Models trained on VBVR-Pro show strong transfer beyond the proposed suite across seven external visual reasoning benchmarks such as RISE-Video, MME-CoF-Pro, and BabyVision. 2) Verifiable rewards. VBVR-Pro provides verifiable reward scorers for task-grounded evaluation. Through a systematic study of leading MLLMs as judges, we identify recurring failure modes of the prevalent VLM-as-a-judge paradigm. In contrast, the proposed scorers are grounded in deterministic, task-specific rules, achieve fine-grained alignment with human judgments. Importantly, they serve as reliable reward signals for large-scale multi-task reinforcement learning and demonstrate stronger post-RL performance across visual reasoning tasks. 3) Mechanism study. VBVR-Pro enables controlled modality studies across more than 30 image, video, and interleaved generators. Our analysis shows that video generation remains strongest for tasks requiring persistent spatiotemporal state tracking, while interleaved generation provides a compute-efficient alternative. Critically, ablations and probing suggest the presence of vision-native trajectories that are crucial to visual reasoning. We release all data, models, scorers, and code.

Understanding which countries are represented in NLP datasets is essential for identifying gaps, targeting data collection, measuring progress, and informing AI policy. However, geographic metadata is very rarely available, and country-level representation is often hidden behind broad language-level claims. We introduce AtlasNLP, a country-aware atlas of over 13,000 NLP dataset records across normalized NLP task categories, tracking both the populations represented and where datasets are produced. AtlasNLP includes AtlasNLP-Gold, a human-curated reference set, and AtlasNLP-Core, an ACL-derived large-scale collection. Using this resource, we show that (1) dataset coverage is highly uneven across countries and tasks; (2) dataset production and representation are geographically asymmetric; and (3) language coverage does not imply geographic representation. These findings reveal blind spots in current dataset documentation practices and motivate more explicit geographic metadata for country-aware NLP evaluation.

Embodied navigation requires agents to translate heterogeneous goals and visual observations into actions across tasks, environments, and robot embodiments. Modern vision-language models (VLMs) already encode spatial priors for visual grounding, spatial reasoning, and pointing, but these capabilities are rarely elicited directly for robot control. Existing navigation systems instead rely on task- or embodiment-specific components, fragmenting perception, reasoning, and action while offering limited generalization. Here we present LightNav-0, a compact generalist embodied navigation model that elicits the spatial intelligence of a pretrained VLM and aligns it with navigation, without task-specific prediction heads. LightNav-0 represents diverse navigation tasks through a unified token interface: dual-channel pointing expresses task-, scene-, and embodiment-agnostic spatial intent, while a residual vector-quantized action tokenizer maps this intent to precise, embodiment-specific trajectories. Together with temporally aware visual history compression, ER mid-training, supervised fine-tuning, and reinforcement learning, this formulation supports instruction following, open-vocabulary object navigation, and visual tracking within a single model. The navigation training corpus spans 2K+ scenes and 4K+ hours of embodied navigation data. LightNav-ER, the embodied-reasoning checkpoint used to initialize LightNav-0, attains the highest complete-set average across 8 embodied-reasoning benchmarks, while LightNav-0 achieves state-of-the-art monocular success rates across all 10 public navigation simulation settings. Real-world evaluations further demonstrate zero-shot generalization across robot embodiments, diverse scenes, and static and dynamic targets. These results establish compact VLMs as a unified and transferable backbone for generalist embodied navigation.

Accurate tilt angle estimation is important in many engineering applications, such as robotics, motion tracking, and embedded control systems. However, measurements from low-cost inertial sensors are often degraded by noise and drift. This paper presents a single-axis tilt angle estimation system based on the MPU6050 inertial measurement unit, implemented on an RP2040 microcontroller platform, with sensor fusion achieved through a Kalman filter. The accelerometer provides a direct estimate of tilt angle from gravity but is sensitive to noise and short-term fluctuations. The gyroscope provides smooth angular rate measurements, but integration over time introduces drift. To overcome these limitations, a Kalman filter is used to combine measurements from both sensors, leveraging the long-term stability of the accelerometer and the short-term smoothness of the gyroscope. Both simulation and hardware experiments are performed. In simulation, sensor noise and drift are modeled to evaluate the filter performance under control conditions. In the hardware implementation, real-time MPU6050 data is acquired and processed by the RP2040 platform, and the estimated tilt angle is compared with accelerometer-only and gyroscope-only outputs. The results show that the proposed method effectively reduces noise measurements and suppresses long-term drift while preserving good dynamic response. Overall, the system provides more stable and accurate tilt estimation than either sensor alone, demonstrating a practical and accessible approach for Kalman filter based sensor fusion in embedded application.

We present our submission to the EgoProactive track of the ECCV 2026 Wearable AI Challenge, which ranked first in the large-model division and second in the <=2B division. The task requires a wearable assistant to decide after each eight-second segment of egocentric video whether to intervene or remain silent. Our approach has two main components. First, we reformulate intervention timing as single-token classification. Rather than generating either $interrupt$<utterance> or $silent$, the model predicts yes or no, and we derive the decision from the renormalised probabilities of these two tokens. This formulation improved macro-F1 by 0.249 and G-mean by 0.30 over free-form generation. Second, because labelled data were limited to the released validation set, we generated additional supervision using a tool-calling video agent that inspects each clip and assigns intervention timestamps. A narration-only alternative was four times larger and ten times cheaper, but transferred worse than supervision from an unrelated real corpus, suggesting that visual grounding is more important than annotation volume for this task.

We describe our entry to the EgoLongQA track of the Wearable-AI Challenge in ECCV 2026, which placed first in the <=2B parameter division with 0.8279 on the held-out test set. Our system is a single 2B vision-language model that answers multiple-choice questions about ten-minute egocentric videos in one greedy forward pass; It is obtained by distilling the junior perception module of a tool-using agentic pipeline, not the agent itself into a small student, using teacher traces filtered to those that answered correctly. it reaches 89% of the accuracy of the large agentic pipeline using 1.1% of its parameters. This raises a 27.1% base model to 81.4% on our held-out questions. The 2B backbone has 2.2132B parameters and therefore over the divisional limit, to make the entry admissable we prune the multilingual embedding table from 248,320 to 143,469 rows, reaching 1.9985B with provably identical logits on retained rows.

Terminology-aware translation asks for more than a correct translation: the output must use the exact terms a glossary prescribes. The standard recipe, fine-tuning on glossary-annotated translation pairs, hides an inefficiency: for most examples the glossary prescribes exactly what the model would have produced anyway, so they teach nothing about following a glossary. We therefore keep only the examples where the model's own translation contradicts the glossary. In a controlled study at fixed data volume, this selection alone raises term accuracy from 78.7% to 89.9%. The filtered data, built by a two-way synthetic pipeline on open models, is part of the instruction-tuning mixture of our public release SalamandraTA-7b-instruct v3.0, which, used exactly as released and wrapped in a document-level inference pipeline, forms the BSC submission to the WMT26 Terminology Shared Task Track 1. At the official WMT26 evaluation, our system achieves 94.2% term success at 74.6 chrF++, with only two of the twenty-two submissions outperforming it on both metrics. On last year's benchmark, it also surpasses our GRPO-based system, despite being trained solely with ordinary supervised fine-tuning.

Accurate estimation of lateral vehicle dynamics near the adhesion limit is important for stability control and high-performance driving, but lateral velocity is rarely measured directly because sensors such as optical sensors are costly. This paper presents an inertial measurement unit (IMU)-centric Moving Horizon Estimation framework that reconstructs lateral velocity using standard onboard signals, without relying on exteroceptive odometry or detailed tire-parameter tuning. Experimental validation on human-driven sports cars and an autonomous open-wheel race car across tracks, maneuvers, and conditions demonstrates accurate and robust lateral velocity and lateral acceleration estimates. The proposed framework is available at https://github.com/Aseuffo/IMU-Centric-MHE

Temporal graphs are ubiquitous in real-world applications and Temporal Graph Networks (TGNs) have achieved superior predictive accuracy. Understanding which historical events drive model predictions can enhance trustworthiness of TGNs. Existing explanation methods overlook the memory module, the core component that records and updates node histories, leaving the influence of past events unexplored. To address this, we attribute TGNs predictions through the topology attribution tree and memory backtracking tree. The topology attribution tree captures the influence of neighbors and their memory vectors, then the memory backtracking tree quantifies how historical events shape node memory vectors. We apply the LRP in TGNs, ensuring that the total contribution of events equals the logits of model. Finally, top-k selection may be unfaithful due to the nonlinear mapping from logits to probabilities, we design optimization objectives to identify the important events. Experiments on nine temporal graph datasets, spanning node property prediction, link prediction tasks and graph classification tasks, show that our method provides faithful explanations and outperforms state-of-the-art baselines. The code is available at https://github.com/yazhengliu/MemExplainer

This paper presents our algorithmic innovations for the NVIDIA Nemotron Model Reasoning Challenge, focusing on Bit Manipulation Puzzles. In this task, the objective is to discover a hidden logical rule transforming input binary strings to outputs, then apply it to unseen inputs. Large Language Models (LLMs) notoriously struggle here; traditional methods force them to simulate complex boolean logic and arithmetic, leading to hallucinations. Furthermore, the search space of bitwise operations (combinations of shifts, rotations, and logic gates) suffers from a severe combinatorial explosion. To overcome this computational intractability, we present a novel approach that abandons arithmetic logic entirely in favor of string similarity, structured search, and autonomous error recovery. Our core contributions are: 1. Bases and Truth Table Formulation: We reframe logic-gate deduction into a base-selection task, leveraging string similarity (minimal bit flips) to isolate primitive transformations ("bases") and deduce truth tables without complex arithmetic. 2. Backtracking DFS and Error Recovery: We formalize a search process that tests candidate bases, detects logical collisions across examples, and backtracks upon failure to perform robust error recovery. 3. Bit Tokenization and Interactive Reasoning SFT: We force the tokenizer to encode binary strings as individual single-bit tokens. We use dynamic masking to simulate external oracle feedback, training the model to hypothesize, self-evaluate, and backtrack natively. Evaluated on bit manipulation puzzles, our approach achieved over 96% validation accuracy. This represents the highest performance in this category, driving our 7th Place overall finish in the contest.

Deployed agents increasingly act with their reward proxy in view, such as a balance, score, or KPI dashboard. We show that reinforcement learning can make a policy \emph{addicted} to such a visible self-benefit channel. It chases the displayed payoff across held-out domains, sacrifices the true task to do so, and follows the channel wherever we rewrite it, while policies that never saw the channel stay honest. We call this \emph{reward-channel addiction} and study it in \emph{MoneyWorld}, a synthetic sandbox. The addiction can \emph{flip a model's safety alignment}: trained only on innocuous money tasks with no safety content, the model abandons the safe action it otherwise always takes whenever a dashboard pays for an unsafe one, and reverts to safe once the channel is hidden. This learned bribe replicates across model scales and families. Blindly optimizing super-capable, next-generation AI on KPIs or P&L can be dangerous for alignment. \emph{Greed is learned} when following such a channel pays.

While test-time scaling has revolutionized reasoning in large language models, generative video reasoning remains bottlenecked by a single-shot paradigm. We demonstrate that searching over denoising steps cannot rescue logically flawed rollouts because spatial trajectories commit early in the diffusion process. Root-level Best-of-N (BoN) sampling is similarly inefficient: reasoning errors cluster early in the temporal axis, and resampling blindly discards verified upstream progress. To unlock effective test-time scaling for video models, we introduce Temporal Backtracking Search (TBS), which shifts the search space to the temporal axis. TBS transforms video generation into an iterative generate-verify-restart loop via three core mechanisms: (1) variable-K conditioning to resume generation from arbitrary clean prefixes; (2) temporal process verification to localize failures and extract valid restart anchors; and (3) prefix-based search to reallocate compute toward extending correct trajectories rather than root resampling. Across algorithmic, navigation, and robotics domains, TBS Pareto-dominates matched-budget BoN. In a strict out-of-distribution setting where one-shot generation collapses (0.7% for BoN), TBS achieves 22.7%, with every solved episode stemming from a restarted branch. Ultimately, TBS reveals that the local reasoning competence of video models far exceeds what single-shot rollouts indicate, providing a scalable test-time framework to unlock it.

We address the challenge of generating high-fidelity, long-form soundtracks that remain coherent across scene transitions. Existing AI music systems are mainly designed for short, isolated clips and lack mechanisms to ensure narrative continuity. We present JenBridge, a modular and interpretable framework for adaptive long-form video soundtracking that ensures both high-fidelity audio generation and transition naturalness. The core architecture is a Transformer-based generative model trained with a flow-matching objective, following a two-stage paradigm: pretraining on large-scale text-audio corpora to establish robust musical priors, then adapting to the video domain with dual text-visual conditioning for precise cross-modal alignment. Crucially, to achieve long-form coherence across diverse scene changes, JenBridge incorporates a novel adaptive transition mechanism. This system features a versatile toolkit of transition styles, including a generative transition method, and uniquely employs a Large Language Model (LLM) Agent that acts as a director to select the most appropriate transition for each narrative shift intelligently. To rigorously assess this task, we propose the LVS Benchmark, a new benchmark that includes a curated dataset and novel evaluation metrics focusing on holistic and transition-aware assessment. Extensive experiments on the proposed benchmark demonstrate that JenBridge significantly outperforms existing methods in both objective and subjective metrics, particularly in terms of transition naturalness and overall narrative coherence. JenBridge represents a significant step towards fully automated, professional-quality video soundtracking.

Reasoning models often generate long traces in which useful self-correction and unproductive revision are hard to distinguish. We study this distinction through backtracking dynamics: local reconsideration, retraction, or re-derivation inside long-form reasoning traces. On 6{,}000 Qwen3-8B AIME traces, we annotate segment-level backtrack severity and analyze event timing, normalized depth, and local burst structure. We find that early isolated repair is often compatible with correct reasoning, whereas incorrect traces more often show moderate-to-severe backtracks that persist and cluster late. Cross-corpus checks show the same qualitative asymmetry across additional model/domain pairs. Filtering analyses instantiate the signal as a prefix-causal selective early-exit policy: at shallow and intermediate depths, burst-aware filtering outperforms fixed length-based filtering while using only prefix-available features. Moderate length cutoffs remain strong completed-trace baselines, but burst-aware control provides a deployable mechanism for separating recoverable repair from likely instability.

Test-time scaling improves language model reasoning by spending additional compute to explore multiple solution trajectories. The key challenge is to maximize accuracy while minimizing the total number of generated tokens during reasoning. Recent PRM-guided methods score intermediate prefixes to steer this search, but most are frontier-only: they keep only the current active prefixes and irreversibly prune or resample away the rest using noisy PRM scores. This can cause premature commitment, diversity collapse, and the loss of prefixes that still admit correct continuations. We introduce stochastic backtracking over a persistent pool of historical prefixes, allowing test-time compute to revisit previously generated states instead of only expanding the current frontier. To make this efficient, we propose two complementary mechanisms. Subpool Selection strengthens greedy PRM-guided search by applying Top-N selection within random subpools, giving historical prefixes a chance to bypass over-scored frontier candidates. Power Backtrack Sequential Monte Carlo extends SMC-style resampling to the persistent pool using powered PRM scores and mixture-corrected weights. Across mathematical reasoning benchmarks and model scales, our methods consistently achieve higher accuracy per token count, and the same level of accuracy using only a fraction of the token count in comparison to strong PRM-guided baselines, demonstrating that persistent-pool stochastic backtracking provides a simple and effective way to improve the accuracy-token trade-off in test-time scaling.

Backtracking search underlies classical constraint solvers, planners, and theorem provers. Recent transformer-based reasoning systems explore search trees over their own intermediate steps. A common training recipe fits an autoregressive next-token loss on offline solver traces. The model's input at each step is a cumulative trace of all prior decisions. The optimal continue-or-backtrack predictor depends only on the current search state, since two trajectories reaching the same state admit the same viable continuations. We show that decoder-only transformers trained on cumulative traces fail this requirement in two ways: the trace can scatter state features across many positions (scattered retrieval), and the predictor can condition on the trajectory rather than the state (history entanglement). We address scattered retrieval with localization, a trace-level fix that rewrites each decision block to expose state features locally. We address history entanglement with Selective State Attention (SSA), a fixed attention mask that enforces state-based decisions structurally without modifying training data, objective, or parameters. We focus on reactive verification, after propagation has exposed a contradiction. We test SSA on 3-SAT, graph coloring, Blocks World, and backtracking parsing. On same-state pairs that differ only in prior history, SSA emits identical decisions while a cumulative-trained causal baseline does not. Our contribution is a diagnostic of transformer behavior on serialized trajectory data, paired with a structural fix. Pretrained language models that search over their own reasoning steps may face the same failure. Our analysis opens up inference-time context clearing as a candidate way to apply the same isolation without retraining.

Large language models (LLMs) have achieved remarkable success in complex reasoning tasks via long chain-of-thought (CoT), yet their immense computational overhead hinders real-world deployment. LLM reasoning distillation addresses this by transferring reasoning capabilities from formidable teacher models to compact student models. However, existing distillation paradigms face a fundamental dilemma. Typical off-policy distillation strictly utilizes teacher-generated golden trajectories, suffering from an exposure bias due to the mismatch between training distributions and student-generated inference contexts, which leads to error cascades in long CoT reasoning. To address this, on-policy distillation allows students to explore their own trajectories, but we demonstrate that it inherently introduces a reciprocal reversed exposure bias: the teacher model also struggles to provide positive guidance when conditioned on student-generated sub-optimal contexts. To resolve this dual exposure biases problem, we propose Monitoring Trajectories and Backtracking when it strays (MOTAB), a new LLM reasoning distillation pipeline. Specifically, MOTAB dynamically monitors the student's on-policy generation against an adaptive safety boundary. When the generation strays and exceeds this threshold, MOTAB backtracks to the last safe state and leverages teacher intervention to correct the course. This approach inherently tolerates minor student errors to mitigate exposure bias, while preventing sub-optimal contexts to circumvent reversed exposure bias. Extensive experiments on the LIMO-v2 and AceReason datasets demonstrate that MOTAB effectively alleviates the dual exposure biases, yielding a roughly 3% average performance improvement in reasoning tasks.

Retrieval-augmented generation (RAG) has proven effective for knowledge-intensive tasks, but is widely believed to offer limited benefit for reasoning-intensive problems such as math and code generation. We challenge this assumption by showing that the limitation lies not in RAG itself, but in the choice of corpus. Instead of retrieving documents, we propose retrieving thinking traces, i.e., intermediate thinking trajectories generated during problem solving attempts. We show that thinking traces are already a strong retrieval source, and further introduce T3, an offline method that transforms them into structured, retrieval-friendly representations, to improve usability. Using these traces as a corpus, a simple retrieve-then-generate pipeline consistently improves reasoning performance across strong models and benchmarks such as AIME 2025--2026, LiveCodeBench, and GPQA-Diamond, outperforming both non-RAG baselines and retrieval over standard web corpora. For instance, on AIME 2025-2026, RAG with traces generated by Gemini-2-thinking achieves relative gains of +56.3%, +8.6%, and +7.6% for Gemini-2.5-Flash, GPT-OSS-120B, and GPT-5, respectively, even though these are more recent models. Overall, our results suggest that thinking traces are an effective retrieval corpus for reasoning tasks, and transforming them into structured, compact, or diagnostic representations unlocks even stronger gains. Code available at https://github.com/Narabzad/t3.

Spiking Transformers inherit token interaction mechanisms from conventional Transformers, yet their sparse binary representations fundamentally alter how token-to-token communication is established. In particular, spike-based query-key matching produces highly sparse and input-dependent interaction patterns, coupling information propagation to the instantaneous availability of matching spike events. This motivates a different interaction paradigm in which long-range communication does not rely solely on pairwise spike coincidence. We therefore propose Gated Spike Axial Propagation (GSAP), a spike-native token interaction mechanism that decouples information propagation from context selection. Instead of directly determining communication through query-key matching, GSAP first propagates spike-based context along the horizontal and vertical axes, allowing information to reach distant tokens through structured sequential propagation. A receiver-conditioned gate then determines how much of the propagated context is incorporated at each token, while a lightweight local pathway preserves fine-grained neighborhood information. In this way, GSAP reformulates token interaction as a propagate-then-select process, enabling structured long-range communication while retaining the sparse event-driven nature of spiking representations. Code is available at https://github.com/Fancyssc/GSAP.

Large language models (LLMs) excel at reasoning when scaled to hundreds of billions of parameters, but small- and mid-scale models remain brittle reasoners even with knowledge distillation (KD). We present Ladders-of-Thought (LoT), a framework that improves reasoning by combining progressive question rewrites with a self-evolving curriculum. LoT automatically generates semantically faithful but easier variants of reasoning problems, organizes them into difficulty buckets using step-based measures, and employs a self-evolving bandit scheduler to allocate training adaptively. Evaluated on two reasoning domains, math and multi-hop reasoning, across 1-8B models from different families, LoT consistently improves over KD. It delivers large gains on arithmetic tasks (e.g., +32 percentage points on AddSub, +25pp on SVAMP), +2-8pp improvements on in-domain test splits, and strong though dataset-dependent benefits on multi-hop reasoning (e.g., +16pp on QASC, +25pp on StrategyQA). LoT also converges faster than staged curricula, highlighting the value of adaptive progression. These results show that progressive rewrites coupled with adaptive curricula provide a simple yet effective recipe for strengthening reasoning in smaller LLMs.

We trained 64 independently seeded networks in four configurations, continuing each to sustained convergence or a 40,000-epoch ceiling. We then asked whether an RSB-inspired distribution of pairwise weight overlaps changes across the grokking transition. It is the alignment step, not the overlap statistic, that determines what this registered probe can report. The registered implementation permutes hidden units without the corresponding bias and head-internal permutations and therefore does not preserve the network function. Every q_wt value computed through this alignment inherits the defect; q_fn does not, because it is computed from predictions of the unpermuted models. The numerical-precision requirement also failed, and an audit found protocol deviations. Consequently, the pre-registered rule gives no verdict: registered outcome UNDETERMINED (reason code C0_INSTRUMENT_INVALID). These data provide neither a confirmatory null nor a validated reading of the Parisi order parameter. Only frac40 cleared the 12/16 checkpoint-completeness requirement. For this configuration, a post-hoc criterion applied to the same data gave a Hartigan-dip interval containing zero (95% CI for Delta dip = [-0.017, 0.034]), whereas the overlap standard deviation increased by a factor of about 5.6. A post-hoc calibration assigns the dip test zero power at the simulated separations; the interval is therefore uninformative, not evidence of no change. The standard-deviation ratio is the only statistic here with power at the observed effect. Ensemble loss was near-flat only under the pre-specified 1% threshold. Finally, grokking rates of 0/16, 11/16 and 16/16 remain descriptive because train fraction is confounded with split identity.