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Category: Tutorials

  • Infinitesimal Operator World Models: Finite-Sample Guarantees for Offline Reinforcement Learning

    Infinitesimal Operator World Models: Finite-Sample Guarantees for Offline Reinforcement Learning

    [Submitted on 13 Nov 2025 (v1), last revised 9 Oct 2026 (this version, v2)]

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    Abstract:Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline reinforcement learning from historical data. However, there is limited statistical understanding of the approximation errors inherent in learning policies from offline datasets. We address this by linking reinforcement learning to the Hamilton-Jacobi-Bellman equation and proposing an operator-theoretic algorithm based on a simple dynamic programming recursion. Specifically, we represent our world model in terms of the infinitesimal generator of controlled diffusion processes learned in a reproducing kernel Hilbert space. By integrating statistical learning methods and operator theory, we establish global convergence of the value function under sufficiently small generator-approximation error and derive explicit finite-sample guarantees with bounds tied directly to system properties such as smoothness and stability. Our theoretical and proof-of-concept results indicate that operator-based approaches may hold promise for solving offline reinforcement learning using continuous-time optimal control.

    Submission history

    From: Nicolas Hoischen [view email]
    [v1] Thu, 13 Nov 2025 14:58:30 UTC (1,427 KB)
    [v2] Fri, 9 Oct 2026 13:08:08 UTC (2,717 KB)

  • Market Impact Estimation via Causal Foundation Models

    Market Impact Estimation via Causal Foundation Models

    [Submitted on 8 Oct 2026]

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    Abstract:When a trader executes a large order, the relevant question is not emph{what will the price be?} but emph{what would the price have been had I not traded?} Market impact is thus a causal quantity, yet classical models (Almgren–Chriss, propagators) regress price on flow, which is biased whenever informed flow moves prices through information as well as trading. We present a proof-of-concept emph{Causal Market Simulator}: a continuous-time causal prior-data fitted network (PFN) trained on a synthetic market prior in which a hidden informational flow confounds the flow–price relation by construction, with confounding strength an exact per-episode knob. On this prior, the naive estimator’s bias follows a closed form we confirm empirically (up to 68% overestimation), while the PFN tracks the unbiased true-parameter oracle at high confounding. Its emph{do-ablated twin}, the same model with the intervention inputs removed, collapses onto the pre-window mean. Zero-shot, the model responds at the ground-truth scale to metaorders in an ABIDES limit-order book ($+0.38$ pre-onset standard deviations against seed-replay counterfactuals), and its intervention response replicates on about 2,300 detected flow bursts in BTC/ETH/SOL perpetuals and 3,800 on Nasdaq equities, evidence consistent with, though not proof of, causal transfer. Off-prior the response degrades gracefully, and split-conformal recalibration repairs interval calibration. Transfer hinges on encoding the metaorder as added flow rather than a clamped price level, not on more training. A recurrent state-space variant closes the remaining shape gap: its impact accrues over execution duration where the transformer’s stays flat, raising the correlation with measured metaorder impact from $+0.68$ to between $+0.92$ and $+0.96$, at the cost of weaker on-prior deconfounding that traces to the training recipe rather than to recurrence.

    Submission history

    From: Dennis Thumm [view email]
    [v1] Thu, 8 Oct 2026 13:29:39 UTC (182 KB)

  • On the Rate of Convergence of GD in Non-linear Neural Networks: An Adversarial Robustness Perspective

    On the Rate of Convergence of GD in Non-linear Neural Networks: An Adversarial Robustness Perspective

    [Submitted on 2 Mar 2026 (v1), last revised 8 Oct 2026 (this version, v2)]

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    Abstract:We study the convergence dynamics of Gradient Descent (GD) in a minimal binary classification setting, consisting of a two-neuron ReLU network and two training instances. We prove that even under these strong simplifying assumptions, while GD successfully converges to an optimal robustness margin, effectively maximizing the distance between the decision boundary and the training points, this convergence occurs at a prohibitively slow rate, scaling strictly as $Theta(1/ln(t))$. To the best of our knowledge, this establishes the first explicit lower bound on the convergence rate of the robustness margin in a non-linear model. Through empirical simulations, we further demonstrate that this inherent failure mode is pervasive, exhibiting the exact same tight convergence rate across multiple natural network initializations. Our theoretical guarantees are derived via a rigorous analysis of the GD trajectories across the distinct activation patterns of the model. Specifically, we develop tight control over the system’s dynamics to bound the trajectory of the decision boundary, overcoming the primary technical challenge introduced by the non-linear nature of the architecture.

    Submission history

    From: Guy Smorodinsky [view email]
    [v1] Mon, 2 Mar 2026 17:13:33 UTC (38 KB)
    [v2] Thu, 8 Oct 2026 18:50:56 UTC (38 KB)

  • GlucoPRISM: Protocol-Supervised Pretraining for Cross-Cohort Glucose Transfer

    GlucoPRISM: Protocol-Supervised Pretraining for Cross-Cohort Glucose Transfer

    [Submitted on 8 Oct 2026]

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    Abstract:Continuous glucose monitoring (CGM) foundation models encode each day as one vector that mixes who the person is, what happened that day and how the sensor measured it, so measurement differences travel with the representation into new cohorts. We ask whether pretraining can place the measurement component that harms transfer in known coordinates, so that deployment drops them with a fixed projection and no target data. GlucoPRISM supervises a GlucoFM backbone with response contracts, rules for how each part of the representation should change when only the day or only the sensor changes: a 64-dimensional Trait band should change with neither, a 48-dimensional State band only across days, and a 16-dimensional Sensor band should track the device. Synthetic sensor views calibrated on paired Dexcom and Libre recordings, different-day pairs and glucose-summary targets supply this supervision without clinical labels. Across twelve cross-cohort directions, dropping the Sensor band from the same frozen encoder raises mean transfer AUROC from 68.75 to 73.57, against 69.3 for GlucoFM. The gain has two parts. Into CGMacros, the one target cohort recorded with two sensor types, filtering adds 11 to 19 points, and this holds when the generator is recalibrated on half of the participants and scored on the other half. On the other eight directions filtering is neutral and the encoder itself exceeds GlucoFM by 3.5 points. The device remains linearly decodable after filtering, so the filter removes a device-related component that harms transfer rather than all measurement information. The retained bands improve window AUROC on thirteen of fourteen public task–cohort cells (Holm-adjusted p=0.031) and correlation on fourteen of fifteen clinical endpoints in an external cohort of 9,303 participants.

    Submission history

    From: Imran Razzak [view email]
    [v1] Thu, 8 Oct 2026 09:14:26 UTC (2,902 KB)

  • CacheScope: Exact-Compute Allocation for Training-Free Diffusion Acceleration

    CacheScope: Exact-Compute Allocation for Training-Free Diffusion Acceleration

    [Submitted on 8 Oct 2026]

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    Abstract:Training-free feature reuse accelerates diffusion transformer inference by replacing full denoising computation at selected steps with cached approximations. Existing methods mainly improve the reconstruction of skipped features, but we find that once a stable first-order reconstructor is used, increasing reconstruction complexity brings limited gains, whereas the placement of exact-computation steps has a much larger effect on fidelity. More importantly, absolute shallow-probe variation is jointly affected by input-trajectory displacement and network response strength, and therefore does not directly reflect cache risk. We address this confounding by normalizing probe-output variation with the corresponding input displacement, yielding a directional gain per unit trajectory movement. Based on this signal, we propose CacheScope, which identifies high-risk reuse steps online and selectively falls back to full denoising computation while leaving the underlying cache reconstructor unchanged. CacheScope requires no additional training, gradients, auxiliary networks, or prompt-specific offline schedule optimization. Across FLUX.1-dev, Wan2.1-T2V-1.3B, and Open-Sora 1.2, CacheScope achieves up to 3.57x acceleration and reduces median LPIPS by up to 70.1% over the strongest probe-based baseline.

    Submission history

    From: Qinhan Lyu [view email]
    [v1] Thu, 8 Oct 2026 10:19:34 UTC (2,655 KB)

  • ABLEIST: Intersectional Disability Bias in LLM-Generated Hiring Scenarios

    ABLEIST: Intersectional Disability Bias in LLM-Generated Hiring Scenarios

    [Submitted on 13 Oct 2025 (v1), last revised 8 Oct 2026 (this version, v2)]

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    Abstract:Large language models (LLMs) are increasingly under scrutiny for perpetuating identity-based discrimination in high-stakes domains such as hiring, particularly against people with disabilities (PwD). However, existing research remains largely Western-centric, overlooking how intersecting forms of marginalization–such as gender and caste–shape experiences of PwD in the Global South. We conduct a comprehensive audit of six LLMs across 2,820 hiring scenarios spanning diverse disability, gender, nationality, and caste profiles. To capture subtle intersectional harms and biases, we introduce ABLEIST (Ableism, Inspiration, Superhumanization, and Tokenism), a set of five ableism-specific and three intersectional harm metrics grounded in disability studies literature. Our results reveal significant increases in ABLEIST harms towards disabled candidates–harms that many state-of-the-art models failed to detect. These harms were further amplified by sharp increases in intersectional harms (e.g., Tokenism) for gender and caste-marginalized disabled candidates, highlighting critical blind spots in current safety tools and the need for intersectional safety evaluations of frontier models in high-stakes domains like hiring.

    Submission history

    From: Hayoung Jung [view email]
    [v1] Mon, 13 Oct 2025 04:18:23 UTC (1,493 KB)
    [v2] Thu, 8 Oct 2026 22:37:37 UTC (1,389 KB)

  • S-Space: Exploring Spatial Workspace in Multimodal Language Models

    S-Space: Exploring Spatial Workspace in Multimodal Language Models

    [Submitted on 9 Oct 2026]

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    Abstract:Multimodal language models (MLLMs) exhibit promising spatial reasoning capabilities, yet the internal mechanisms supporting them remain poorly understood. We uncover S-Space, a linear representation subspace in which object-token representations encode continuous coordinates along horizontal, vertical, and distance axes. Although we identify these axes by differentiating spatial-answer scores with respect to object-token activations, S-Space is intrinsic rather than induced by specific data or prompts, remaining readable under non-spatial questions. We show that S-Space functions as an internal spatial workspace of MLLMs. Perception encodes object locations into it, forming spatial representations that can be directly read out to support accurate spatial judgments. Internal reasoning transforms it for changing viewpoints. Verbal responses selectively access it, evidenced by causal interventions that alter spatial judgments while largely preserving non-spatial responses. Case studies further show that S-Space assigns locations to unseen entities and the observer, and connects physical directions with abstract linguistic meanings, suggesting both the capabilities and limitations of large-scale language training. Finally, we use S-Space as a diagnostic tool for spatial reasoning failures. Direction-word readouts reveal systematic coupling between cardinal and image-relative reference frames. More importantly, a perception-computation decomposition exposes a key bottleneck: MLLMs can form capable spatial representations, yet fall short in the spatial transformations required to reason reliably across viewpoint changes.

    Submission history

    From: Jialong Wu [view email]
    [v1] Fri, 9 Oct 2026 12:48:41 UTC (13,229 KB)

  • Tracing and Taming Hallucinated Terms via Subsequence-Association Filtering and Breadth-Aware Selection for LLM Query Expansion

    Tracing and Taming Hallucinated Terms via Subsequence-Association Filtering and Breadth-Aware Selection for LLM Query Expansion

    [Submitted on 9 Oct 2026]

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    Abstract:Large language models (LLMs) are now a standard source of query expansion terms but they hallucinate. They inject non existent entities and off-topic terms that add ranking noise and can hurt strong retrievers. Existing remedies such as corpus grounding, mutual verification and preference alignment treat hallucinated terms as an undifferentiated nuisance to be filtered by agreement heuristics, without a mechanistic account of why a given term appears or a principled criterion for how many terms to keep. We propose Subsequence-Association Filtered, breadth-aware query expansion (SAFE-QE), a training-free, retriever agnostic method that draws on the subsequence-association account of hallucination. We score each candidate expansion term by its corpus conditioned cross-context reproducibility, terms that reappear under randomised query contexts yet lack support in the pseudo-relevant set are flagged as products of dominant hallucinatory associations and down-weighted. Drawing on the characterisation of language generation as a trade-off between consistency (no hallucination) and breadth (coverage), we cast term selection as constrained coverage maximisation over the pseudo-relevant set, keeping a set that is approximately broad but consistent and stable across resampling. We also introduce the Hallucinated Expansion Term Rate, a query side faithfulness metric that counts injected expansion terms no relevant document supports. We evaluate our approach on benchmarked TREC and BEIR collections. Our SAFE-QE is statistically indistinguishable from generative and corpus-steered expansion on nDCG@10 while injecting fewer unsupported terms 4.3 per query against 27.8 for Query2doc and 57.5 for HyDE and on a strong learned sparse retriever, where every expansion method regresses. Faithfulness is therefore available at no measurable cost in ranking quality.

    Submission history

    From: Sagar Uprety [view email]
    [v1] Fri, 9 Oct 2026 16:22:16 UTC (1,365 KB)

  • Locate, Judge, Read: Role-Specialized Tool Agents over a Knowledge-Point Index for Open-Domain Multimodal Document QA

    Locate, Judge, Read: Role-Specialized Tool Agents over a Knowledge-Point Index for Open-Domain Multimodal Document QA

    [Submitted on 9 Oct 2026]

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    Abstract:Question answering over large heterogeneous document collections requires first finding the right passages and then reading them, yet current retrieval-augmented agents give one model both kinds of tools and let it schedule itself. We present KnowForge, a pipeline separated by job: a hybrid-retrieval knowledge-point index; a Locator agent that can only search; a code-scheduled bridge judge that forces the missing second hop; a typed, size-bounded evidence pool that merges every search’s ranking; a Deep Reader agent that can only read text, images and tables; and a synthesizer with a format checker. With a self-hosted Qwen3.6-35B-A3B (3B active), KnowForge reaches F1 47.5 on the full open-domain M3DocVQA (2,441 questions, 3,368 PDFs), +11.0 over the published M3DocRAG system and +7.1 over one-shot retrieve-and-answer on the same index and model, and 53.5 with DeepSeek-V4-Flash. On MultiHop-RAG it reaches 73.5 accuracy, above the strongest published RAG and GraphRAG results (71.2); on the single-document MMLongBench-Doc it lifts the same model from 34.8 to 47.0, level with GPT-4o reading page images (46.3). Per-job ablations on the full benchmarks attribute the gain: the Deep Reader is worth 3.8, 9.8 and 0 points on the three corpora, tracking how visual each is; merging both agents into one with all tools and twice the rounds loses 1.9 F1 because it keeps searching instead of reading; a round-budget sweep shows a step at four Locator rounds and a plateau beyond; query latency scales with model calls rather than corpus size. We serve the three indexed benchmarks as read-only knowledge bases (free registration) and release all prompts and the runner code: this https URL

    Submission history

    From: Wenlin Lin [view email]
    [v1] Fri, 9 Oct 2026 07:21:36 UTC (47 KB)

  • BoundaryEvo: Data-Model Co-Evolution at the Capability Boundary for Long-Chain Reasoning Distillation

    BoundaryEvo: Data-Model Co-Evolution at the Capability Boundary for Long-Chain Reasoning Distillation

    [Submitted on 9 Oct 2026]

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    Abstract:Distilling long-chain reasoning trajectories from large teacher models provides an effective way to improve the reasoning ability of small language models. However, existing methods typically select a fixed training set before distillation, overlooking that the usefulness of a reasoning example changes as the student evolves. This mismatch becomes especially costly when only a small number of teacher trajectories can be used for training. Besides, examples already mastered provide little new supervision, while examples far beyond the capability of student may be difficult to learn from. Training data should therefore adapt as model capability evolves, yet reliable data selection is difficult when the student is initially weak. To address these challenges, our key idea is to first establish the basic reasoning capability and then adapt the training data to the evolving capability boundary of the student. We propose BoundaryEvo, a two-stage data–model co-evolution framework. In Capability Priming, we directly distill a small set of teacher-generated long reasoning trajectories without using a separate model to judge and filter them, allowing the student to acquire an initial reasoning capability before capability-aware data selection. In Capability-Boundary Co-Evolution, we repeatedly select questions that the current student has not mastered but the expert can reliably solve, and update the training data as the student evolves. With only 1,000 training examples, BoundaryEvo consistently outperforms static and dynamic data selection baselines across 11 reasoning benchmarks, raising the original Qwen3.5-4B accuracy from 62.9 to 75.3 on IMO-AnswerBench and from 26.8 to 46.0 on AMO-Bench. The code and data will be made publicly available.

    Submission history

    From: Jiaming Su [view email]
    [v1] Fri, 9 Oct 2026 09:37:33 UTC (3,035 KB)