Papers

We propose ReLOBGen, a method for generating limit order book (LOB) messages that are replayable by construction. Replayability is required for closed-loop market simulation, yet existing LOB message generators may produce non-replayable raw messages, i.e., messages inconsistent with the current market state. These generators therefore rely on post-hoc correction or rejection followed by resampling, which may alter the replayed message distribution or increase inference cost. ReLOBGen instead ensures replayability during generation: it selects the referenced order from the resting orders in the current LOB and then generates the remaining message fields to be consistent with that order and the market state. For realistic reference selection, ReLOBGen samples from a learned distribution over eligible resting orders, efficiently computed from cached order representations and a context-dependent query. It then enforces the consistency of the remaining fields by masking out invalid tokens. Together, these components enable efficient generation of realistic messages without post-hoc correction or resampling. In 500-message rollouts, ReLOBGen achieves 100% replayability, improves market realism, particularly for top-of-book statistics and the relative prices of LOB messages, and provides a $2.7\text{-}3.6\times$ speedup per replayed message over the LOBS5 baseline.

This paper provides a topological construction for studying social aggregation of weak preferences over a finite set of alternatives. We identify weak preferences with the cells of the type $A_{n-1}$ braid arrangement and, equivalently, with the simplices of the corresponding type $A_{n-1}$ Coxeter complex, which we call the preference complex. Then we define face-monotonicity by requiring a social welfare function to be order-preserving when viewed as a map between the preference-profile poset and the preference poset. We prove that if a common preference domain admits a unanimous, anonymous, and face-monotonic social welfare function, then every connected component of the geometric realization of its order complex is contractible. We then apply this construction to two restricted domains. For fixed-extrema domains, we prove that their order-complex realizations are contractible and define a unanimous, anonymous, and face-monotonic social welfare function using the meet operation. For single-peaked domains, we prove that the corresponding subcomplex of the preference complex has a contractible realization and, in the three-alternative case, construct a unanimous, anonymous, and face-monotonic social welfare function.

Single-token typed-decision models answer a schema question by reading the logits of a few one-letter answer codes at a single position: they are fast and return a probability for every allowed answer, but they are trained with plain cross-entropy that ignores most of the structure in their training data. We study such a model whose data is curated as contrastive pairs—two contexts that differ in one edited fact that flips the answer—each carrying a machine-checked certificate that deleting the decisive sentence makes the fact unknown. We propose PACT, which turns this structure into four training terms that need no new annotation: a difference-in-differences margin over each pair that is invariant to any shared logit offset, a permutation-consistency term against answer-code position bias, an evidence-necessity term on certificate-verified ablated contexts, and an ordinal transport cost for rubric fields, plus a three-parameter contextual temperature. On a frozen 324-item holdout with three seeds, PACT matches the published recipe in accuracy ($84.6\%$ vs. $85.2\%$; McNemar $p \ge 0.50$ at every seed) while giving the lowest position bias of all runs (answer flips under relabelling $9.8\%$ vs. $13.8\%$) and the lowest ordinal error on rubric fields (MAE $0.232$ vs. $0.311$). Against a control with the same optimiser and schedule but cross-entropy only, PACT is significantly more accurate at two of three seeds, halves the seed-to-seed spread and lowers NLL by $26\%$. Seed-matched ablations and pre-specified falsification tests locate these gains precisely: no single term raises raw accuracy, and the method's value lies in robustness and stability rather than headline accuracy. Code, data splits, trained adapters, and all run records are available at https://github.com/BennyLinntu/PACT-Pairwise-Anchored-Calibrated-Tuning-for-Single-Token-Typed-Decisions.

First law consistency alone does not determine the black hole state space of NUT-charged spacetimes, because several inequivalent macroscopic formulations can yield consistent thermodynamics. We develop a two-horizon sector diagnostic for the electrically charged Kerr-Newman-NUT family by organizing the inner- and outer-horizon entropies and inverse temperatures into sum ($\Sigma$) and difference ($\Delta$) sectors. The charged rotating geometry gives a more stringent test of the uncharged Taub-NUT sector result, since the mass $M$, ordinary electric charge $Q$, ordinary angular momentum $J$, NUT charge $N$, and the NUT secondary hair $J_N=MN$ all enter the same two-horizon thermodynamics. For the physically anchored minimal homogeneous state spaces defined and tested here, we find a clear sector separation: the $\Sigma$ sector closes with the charge-like variables $Q$ and $N$, whereas the $\Delta$ sector additionally requires the rotation-like variables $J$ and $J_N$. Natural reductions that eliminate either $J_N$ or $N$ fail to reproduce the first law coefficient fixed by the sector temperature, and their associated Bekenstein-Smarr relations do not close with the assigned scaling weights. Within this class, electric charge and ordinary rotation therefore do not absorb the NUT secondary response, and the charged rotating family supports the NUT bi-hair organization: $N$ has a charge-like sector role, while $J_N=MN$ is a rotation-like thermodynamic secondary hair. The latter is defined off shell in the homogeneous equation of state, not as a new metric parameter or asymptotic conserved charge.

Primordial black holes (PBHs) can generate the Baryon Asymmetry of the Universe (BAU) through asymmetric capture of baryon-charge-carrying particles, but previous realizations of this mechanism typically yield an asymmetry well below the observed value because the relevant CP-violating scattering asymmetry is loop suppressed. We show that this limitation can be overcome through resonant CP violation in a mixed system of two nearly degenerate unstable fermions, $Y_{1,2}$, whose mass splitting is comparable to their decay widths. Rare production of the coherent $Y_1$–$Y_2$ state, followed by CP-asymmetric return and loss decays, generates an $\mathcal{O}(0.1)$ difference in integrated decay probabilities while preserving the global baryon charge at the Lagrangian level. Embedding this resonant source in the PBH-capture transport system yields the observed baryon asymmetry. We first reproduce the mechanism in a zero-temperature, sudden-evaporation treatment, which gives $\eta_B^{T=0}\simeq1.74\times10^{-10} \simeq2.00\eta_B^{\rm obs}$. We find that after including thermal corrections and continuous PBH evaporation and entropy production, the resulting BAU becomes $\eta_B = 8.72\times 10^{-11}$ in agreement with the observed value. An interesting finding of the model is that even if PBH absorption remains active, we would still have BAU $\eta_{B}^{\text{no evap}} \sim 9.1 \times 10^{-12} \sim 0.105 \eta_B^{\rm obs}$. We further investigate gravitational-wave signatures associated with the primordial fluctuations responsible for PBH formation. The corresponding scalar-induced gravitational-wave spectra peak at $f \sim 0.16\text{--}0.17~\mathrm{MHz}$, with $h^2\Omega_{\rm GW}^{\rm peak} \sim (3\text{--}7)\times 10^{-8}$. Under idealized sensitivity assumptions, U-DECIGO can achieve signal-to-noise ratios above 10 for the benchmark spectra.

World models simulate the consequences of action candidates, but good planning need not preserve every physical distinction required for accurate prediction. We formalize this gap through a hierarchy of mechanism, response, and decision sufficiency. Given a candidate set, the planning query determines which physical variations matter and how precisely they must be preserved: coarse decisions can discard much of the information needed for prediction, whereas fine decisions may require nearly the same resolution. In practice, planners often adaptively search to construct candidates, and information unnecessary for final selection may still be needed to discover good candidates. What a world model must preserve therefore depends on the query, the candidate set, and the planner. We study these effects in a collision system, nonlinear dynamics, and robotic planning. These varying requirements raise a design question: where should query information enter the planning system? A model that jointly generates actions and outcomes conditioned on the query achieves lower regret than an action-conditioned world model on seen objectives, but this advantage largely disappears when generalizing to unseen objectives. Motivated by this, we propose a modular design in which the query determines where to look and an action-conditioned model predicts what will happen, allowing the same predictions to be reused across objectives.

We investigate the Fulling-Davies-Unruh effect in a local Lorentz-violating effective field theory, focusing on the quantum-field response of accelerated detectors. We canonically quantize a real scalar field exactly in the coefficients for Lorentz violation. The dispersion relation, Hamiltonian, and massless and massive Wightman functions are obtained. We determine the conditions under which the scalar dynamics preserves boost symmetry and distinguish these from the weaker conditions required for stationarity along a single accelerated worldline. The Wightman functions are used to construct the finite-time Unruh-DeWitt response for a uniformly accelerated detector. For generic coefficients the response is nonstationary and depends on both the duration and temporal location of the measurement. The spectrum, which is the resulting excitation rate as a function of the energy level difference in the detector, is obtained numerically. It shows discernable differences with the usual massive thermal spectrum for dimensionless coefficients on the order of $10^{-7}$. Experimental implications of the result are discussed. As an alternative viewpoint, we place Lorentz violation in the point-particle sector, derive the exact trajectory generated by a constant electric field, and study the proper-time Fourier response of a conventional scalar wave along the modified trajectory.

A feed-forward neural network whose weights are integers and whose activation is the truncated identity implements, neuron by neuron, the connectives of Łukasiewicz many-valued logic. This exact correspondence — established theoretically by Castro and Trillas and developed into a training algorithm by Leandro — enables symbolic knowledge extraction: training produces not a black-box model but a logical formula. Two obstacles have limited the approach to shallow architectures and small datasets: crystallization (forcing weights to integers) succeeds only probabilistically under the original Levenberg–Marquardt training scheme, and the theoretical guarantees break down as networks grow deeper. This paper addresses both obstacles. First, we prove that residual connections (skip connections of the kind used in ResNets) extend Łukasiewicz neural networks to arbitrary depth while preserving the symbolic correspondence at merge neurons by construction: merge neurons in a Łukasiewicz residual block automatically satisfy the neuron-classification proposition, regardless of the inner layer weights; inner-layer neurons are trained toward representability by the crystallization strategy. Second, we analyse three crystallization strategies — Levenberg–Marquardt (corrected), straight-through estimation (STE), and proximal regularization — characterizing their theoretical guarantees, failure modes, and interpretability trade-offs.

We study the distribution of monogenic integral binary cubic forms $f(x,y)$ with bounded discriminant and bounded monogenizer inside a fundamental domain for the action of $\mathrm{GL}_2(\mathbb{Z})$ on the space of real binary cubic forms. We show that when the monogenizer for $f$ is $[\pm1:0]$ (i.e., $f(\pm1,0)=1$), the corresponding set is fully concentrated in the cusp. We also prove a complementary result, namely, that when the monogenizers $[\pm1:0]$ (with height bounded in terms of the discriminant bound) are excluded, the resulting set has no escape of mass to the cusp. However, we surprisingly show that despite this non-escape of mass, the points in the fundamental domain are not equidistributed.

The anomalous Hall effect (AHE) is of fundamental importance for understanding spin-orbit coupling and magnetic transport in magnetic materials. Meanwhile, strain can significantly modify material properties, and the piezoelectric effect stands as a well-known representative. The piezo-Hall effect combines the two physical ingredients of AHE and strain. Specifically, the piezo-Hall effect describes a physical process in which the magnetic space group (MSG) of a magnetic material prohibits a net magnetic moment and suppresses the AHE in the pristine state but transforms into a new MSG upon strain application that permits a net magnetic moment, thereby enabling the emergence of the AHE. The underlying mechanisms cover strain-induced magnetic electronic state transition and strain tuning of magnetization direction. We take the $d$-wave altermagnetic metal as an example to analyze the piezo-Hall effect in detail, with first-principles calculations carried out on the specific material $\mathrm{RbCr_2Se_2O}$ to verify this scenario. A notable result is that under identical uniaxial strain applied along the $x$ and $y$ directions, the anomalous Hall conductivity exhibits opposite signs but equal magnitudes. Similarly, the piezo-magneto-optical effect can also be proposed, and if strain tuning is replaced by electric-field modulation, the electro-Hall effect and electro-magneto-optical effect can be also put forward accordingly. Even temperature can serve as an external field to introduce the temperature Hall effect. Our work advances the understanding of the coupling between strain and physical properties.

Low-rank matrix and tensor bandits exploit structured interactions but typically assume a known reward link. Recent single-index bandit methods accommodate unknown links without directly exploiting matrix or tensor rank. We address this gap by studying stochastic matrix and tensor bandits with an unknown shared Lipschitz link and a low-rank index parameter under known regular candidate distributions and finite-variance noise. For monotone links, T-ESTOR combines robust, rank-adaptive Stein estimation with epoch-based greedy selection. Under exact selected-score access and a uniformly positive selected-design Stein signal, it achieves square-root regret with dimension dependence determined by the low-rank structure. For every admissible design, the monotone lower bound matches the rank, dimension, and horizon dependence up to logarithmic factors at large horizons, for fixed menu size and model/design constants. For nonmonotone links under a nonzero base-law Stein signal, T-BSTOR combines structured estimation with robust bin-based learning and attains the optimal $\widetilde{O}(T^{2/3})$ horizon rate for fixed dimensions, menu size, and model/design constants. Synthetic and CCLE-based experiments illustrate the benefits of structured estimation relative to vectorized and competing single-index baseline methods.

We study the recovery of a finite three-dimensional point cloud from its spherical Fourier signal subspace at a fixed wavenumber. Two ESPRIT constructions are analyzed. The first uses finite shifts between paired small circles; the second uses angular derivatives on the whole sphere. Both recover the same commuting coordinate matrices, either through their finite exponentials or directly from a coupled linear system. We prove that the continuous generator system is injective for every distinct point cloud and that one guard harmonic degree preserves the retained equations exactly. For $s$ targets, the cutoff $K\ge s$ gives generic finite identifiability, but not uniform conditioning. We also derive a finite-cutoff perturbation bound. The accuracy of the coordinate estimates is a separate issue. A one-target perturbation calculation shows that the original generator estimate can retain a nonzero bias as the wavenumber increases. To address this bias, we use the generator eigenbasis to separate approximate atoms and recover their locations from amplitude-normalized phases. Under pointwise atom dominance, the resulting error is $O(\kappa^{-1})$; for a dominant two-atom mixture at fixed separation, it is $O(\kappa^{-2})$. Experiments on structured point clouds with smooth perturbations compare the two constructions and their use as initializers for a common MUSIC refinement.

Benchmarks for site reliability engineering (SRE) agents are typically episodic: one fault is injected, the agent receives an incident task, and its response is scored. Production operation is not. Incidents surface through noisy alerts, overlap in time, and often originate from code or configuration changes. We present SRE-Marathon, a benchmark for long-horizon, continuous SRE operation. An agent is invoked at a fixed cadence with cumulative alert history and a persistent workspace while operating a live two-zone Kubernetes deployment as a fault orchestrator injects overlapping faults according to a seeded, production-calibrated schedule. Curated code and configuration changes deployed through the same build pipeline available for repair. Each run is recorded into a sealed bundle and scored offline: Marathon-Score credits each injected fault for ordered progress through correlation, localization, and repair, with all metrics computed deterministically from recorded system evidence. Across three applications and about sixty faults per run, the best of 10 methods reaches only 41.3 out of 100. Agents often correlate and localize faults, but almost never complete repairs while the faults remain active.

This paper addresses discrete-time non-Gaussian distribution steering in deterministic nonlinear systems. Distribution steering is a problem in which a control policy is designed over a distribution of trajectories rather than optimizing a single trajectory. The challenge with nonlinear systems is that even initially Gaussian distributions evolve into non-Gaussian distributions, often precluding a closed-form representation of the probability density. A method called statistical moment steering applies a cubature-based method to approximate non-Gaussian distributions for an approximate solution to this problem. This paper provides theoretical support and details how it can be solved with sequential convex optimization. A coupled, nonlinear, second-order ordinary differential equation describing a two-dimensional oscillator is provided as a numerical example.

We study decentralized optimization with cross-coupled mixed affine constraints, where local and shared variables interact through two affine channels. We show that the intrinsic difficulty of combining separately well-conditioned channels is governed by their Friedrichs angle. This geometry induces a cross-coupling factor that cannot be removed by channelwise preconditioning and governs the additional affine-oracle and communication complexity. We develop an accelerated decentralized method with matching minimax guarantees in the smooth strongly convex regime and extend the framework to smooth and nonsmooth convex objectives. Experiments confirm the predicted dependence on cross-channel geometry and network conditioning.

Diffusion models achieve state-of-the-art results across multiple tasks. However, in inverse problems, standard initialization from pure Gaussian noise misaligns the generative process with real-world degradations. More recent methods such as diffusion bridges impose strict endpoint constraints and often require long reverse processes that are prone to hallucinations. Alternative consistency models provide noise-invariant, one-step mappings but lack inherent variance modeling and can degrade under severe corruption. Hence, residual diffusion implicit models (RDIMs) are proposed, constituting a generalized framework that explicitly models the residuals between high-quality (HQ) and low-quality (LQ) images, aligning the forward process with the actual degradation. A non-Markovian implicit reverse sampler is derived, which can skip intermediate timesteps, enabling accurate few-step or even single-step reconstruction, while mitigating the hallucinations inherent to long diffusion chains. RDIM also introduces a controllable variance mechanism that interpolates between deterministic and stochastic sampling, balancing fidelity and diversity. Furthermore, it enables the straightforward use of perceptual losses, when needed. Experiments on denoising and super-resolution benchmarks demonstrate that RDIMs consistently outperforms the state of the art, including bridge and consistency models, in terms of PSNR, SSIM, and LPIPS, reducing hallucinations while requiring only a few sampling steps (often just one). The results position RDIMs as an efficient solution for a broad range of image restoration tasks.

We introduce a formal multiple polylogarithm function (FMPF) and general formal Arakawa-Kaneko zeta values (GFAKZVs), and establish several useful properties analogous to those of the ordinary Arakawa-Kaneko zeta values by employing the method of iterated integrals, a powerful tool originating in algebraic topology. In particular, we prove various duality and sum formulas involving FMPFs and GFAKZVs. This allows us to derive, in a uniform manner, a number of known results concerning Arakawa-Kaneko zeta values and Kaneko-Tsumura $\psi$-values that were previously obtained by different approaches, thereby highlighting the unifying power of the iterated integral formalism.

Let $p$ be an integer $\geq2$, not necessarily prime, and let $K$ be a number field. In 2019, Tao showed that almost every positive integer (in the sense of logarithmic density) had an almost bounded trajectory under the Collatz map. In this paper, we generalize this result to a large class of Collatz-type maps ($p$-Hydras) acting on the ring of integers $\mathcal{O}_{K}$ of a given number field $K$ of dimension $d$ over $\mathbb{Q}$. Given an ideal $\Lambda\subseteq\mathcal{O}_{K}$ of index $p$, a $p$-Hydra map $H:\mathcal{O}_{K}\rightarrow\mathcal{O}_{K}$ is a collection of affine-linear maps $\left\{ H_{j}:K\rightarrow K\right\} _{j\in\mathcal{O}_{K}/\Lambda}$ of the form $z\mapsto r_{j}z+c_{j}$ for constants $c_{j}\in K$ and invertible $\mathbb{Q}$-linear maps $r_{j}:K\rightarrow K$ so that the map $1-r_{0}$ is invertible and so that $H\left(z\right)$ is defined to be $H_{\left[z\right]_{\Lambda}}\left(z\right)$, where $\left[z\right]_{\Lambda}$ is the projection of $z$ mod $\Lambda$. We show that the direct analogue of Tao's almost-boundedness result holds provided, in addition to several minor conditions, that the Dimension Constraint $\left(p-1\right)^{2}\rho_{H}^{d}<1$ is satisfied, where $\rho_{H}=\prod_{j=0}^{p-1}\left\Vert r_{j}\right\Vert _{\textrm{Mink}}$ is the product of the operator norms of the $r_{j}$s with respect to the Minkowski embedding of $K$. Unlike Tao's original argument, which uses a $3$-adic Fourier decay result for the Syracuse Random Variables, our approach employs analysis of an archimedean flavor, and does not require any Fourier decay estimates for our generalized Syracuse Random Variables. Our result includes Tao's original result as a special case.

Action agents do things for people. They send email, spend money, and call businesses while the user is busy with something else, so a mistake can turn into an action before anyone notices. They fail their users in two ways. They break trust when they do something the user never agreed to, or hold back after the user clearly said go. And they fall short on completion when they give up on errands that turn out to be hard. Both depend heavily on the harness around the model, meaning its instructions, tools, context, and guardrails. We built an evaluation that scores trust and completion on the same runs, in a simulated world of businesses with their own websites, inboxes, and phone lines, and of people who write back. A simulated user answers the assistant's questions. Trust means that nothing happens the user did not agree to. No email goes to someone they never approved, no private detail ends up on a group thread, no money is spent past their limit, no stranger's instructions are followed, and nothing is claimed without a source. Every trap has a matched control in which acting is the right call. We use the evaluation to measure Fo, Wajo's personal assistant, against a base model with basic instructions on three foundation models, and against the Fo harness with its guardrails switched off. Fo completes 71% of the errands and keeps the user's trust on 94% of the trap runs. The base models complete 50% to 64% and keep trust on 59% to 75%. On the matched controls, Fo goes ahead slightly less often. OpenClaw, a popular open-source assistant given the same access, completes 42% of the errands it shares with Fo, against 71%, and keeps the user's trust on 74% of the shared trap runs, against 94%. Measuring trust and completion together, on the whole system rather than the model alone, is how we think action agents become safe to hand real work to.

Large Language Model (LLM) pretraining performance is jointly shaped by three components of the training triplet: the optimizer, model architecture, and training data stream. However, how these components influence performance in distinct ways remains unclear. We take a first step toward isolating their effects by studying relative generalization. We introduce Relative Generalization Invariance (RGI), the invariance of the validation-loss difference between any two tokens across models. We show that RGI approximately holds across a wide range of optimizers and moderate architectural variations, suggesting that these choices induce an approximately uniform shift in token-wise losses. In contrast, changing the training data stream can substantially alter relative generalization. We further show that RGI cannot be explained by the neural tangent kernel or mean-field regimes alone and prove that it can emerge in an overparameterized quadratic model. Overall, our work identifies RGI as a new phenomenon in LLM pretraining that helps distinguish the effects of optimizers and architectures from those of training data.

A well known result due to Lakshmibai and Sandhya states that smooth Schubert varieties of type A correspond to permutations that avoid the patterns 3412 and 4231. It was later shown by the second author and Slofstra that staircase diagrams over a simply-laced Dynkin diagram are in bijection with smooth Schubert varieties of the corresponding type. We explore how the poset structure of staircase diagrams is connected with pattern avoidance on smooth permutations. As an application, we enumerate several subclasses of smooth permutations which are characterized by pattern avoidance. These subclasses include the class of polished permutations which were studied by Gaetz and Gao.

Medical benchmarks for language models are built almost entirely on Western biomedicine. Traditional Chinese Medicine (TCM) is a separate system, with its own diagnostic framework and its own literature, and it remains largely unmeasured. The few TCM evaluations that exist are small, narrow, and rarely paired with a human reference. We present TCMQA, an open benchmark of 38,279 questions from Chinese TCM licensing examinations, paired with 15,151 responses from 101 licensed practitioners. We evaluate 29 instruction-tuned models from 9 families, spanning 0.27B to 14.8B parameters. Accuracy ranges over 59 points, and no model approaches saturation. Pretraining data predicts TCM ability far better than scale: a 12B Western-pretrained model reaches 39.6%, while a Chinese-pretrained model an eighth its size reaches 60.8%. Nine models exceed the practitioner majority vote of 64.9%, the best by 21.8 points, and all nine come from that same Chinese-pretrained family. Yet difficulty does not transfer between models and practitioners: accuracy is flat across practitioner-rated difficulty, item-level agreement is near zero for all 29 models, and on $8.4\%$ of items the practitioners are correct where the leading model is wrong. We release the corpus, the practitioner responses, the harness, and per-item model outputs at https://huggingface.co/datasets/TechTCM/TCMQA.

Long-horizon LLM agents must convert accumulated experience into durable memory, deciding what to keep, compress, abstract into reusable skills and rules, or forget. We report a four-phase research program on this consolidation problem whose central finding is a shift in what is measured: from how much an agent remembers, to whether its consolidation decisions are any good, to whether those decisions can be trusted. Phase 1 learns episodic boundaries from agent traces by downstream utility; an honest near-miss (oracle correlation 0.691 vs a 0.70 bar) whose lasting output is a three-gate anti-leakage protocol. Phase 2 learns when to promote experience and to which abstraction level under a token budget, achieving a verified +22.7% task-success improvement with 7x compression, but exposing a degenerate-forgetting failure and a distribution-shift failure mode we name lambda-prevalence coupling. Phase 3 introduces ConsolidationBench, an oracle-by-construction benchmark that scores consolidation decisions against a known optimum on three non-circular axes; production retrieval systems retain information yet score zero on cross-level transfer. Phase 4 introduces governed consolidation: the decision wrapped in poison-resistance, reversibility, and auditability guarantees with a quality gate. Governance is statistically distinct from the quality score ($r^2 = 0.43$; partial $r = 0.27$; identical-quality policies differ threefold in governance), so the contribution survives independently of the metric's external validity. On that question we report a resolved negative: after a graded-reuse redesign removed a structural ceiling, a two-benchmark study with 2,532 real answer cells finds the quality score does not predict real transfer accuracy (pooled Spearman $\rho = -0.24$, n = 12, CI spanning zero). An adversarial self-critique pass cleared the final claim set with zero surviving overclaims.

When an agent benchmark compares every pair of leaderboard entries, the number of comparisons can look much larger than the independent evidence behind them: A versus B and A versus C both reuse A. Whether this reuse affects inference depends on what the analysis is meant to describe. If the board and its outcomes are fixed, the all-pairs mean is an exact summary of those entries, and any interval must come from another declared source of randomness. If the entries are instead treated as iid draws from a population of future configurations and the pair rule is regular and nondegenerate, the same mean is an order-two U-statistic whose first-order uncertainty depends on the number of configurations, not the number of pairs. We use near ties as the running example, but the distinction extends to other symmetric pair summaries when their regularity conditions hold. We examine both interpretations using a fixed SWE-bench Verified snapshot and an exact binary model with known truth. On SWE-bench, intervals that accounted for shared configurations were more than twice as wide as a pair-iid reference that treated the pairs as independent. In the exact model, pair-iid coverage fell far below the nominal level when edges shared endpoints but remained near nominal for matched independent edges. Results on two other fixed leaderboards show that exact summaries also depend on which pairs are included and how they are weighted. An all-pairs analysis must therefore state what is fixed, what is sampled, and how it handles shared entries and pair aggregation.

We study contextual dueling bandits with general function approximation under the Bradley-Terry-Luce (BTL) preference model. A key challenge in this setting is the saturation of the preference model: when the current reward model can already distinguish two actions with high confidence, the resulting preference feedback becomes weakly informative, making it difficult to further improve reward estimation. Consequently, existing sample-complexity analyses often depend on the inverse-derivative factor $1 / \sigma'[\Delta_{r^\ast}]$ which can be prohibitively large when the link function $\sigma$ saturates for large reward gaps $\Delta_{r^\ast}$. To address this issue, we introduce `SI-CDB`, an algorithm that selects opponent arms using a carefully designed heuristic for arm selection. This design enables saturation-insensitive reward learning and recovers the near-optimal dependence for linear reward classes, eliminating the unfavorable $1/\sigma'(\cdot)$ factor. The core of our analysis is a localized Eluder dimension framework tailored to dueling bandits with general function approximation. Our theoretical results also explain why two-arm regret analysis is crucial for improving single-arm performance in dueling bandits.

LLMs are effective representations that assimilate vast amounts of knowledge during pretraining, but post-training is necessary for models to reliably access this knowledge and "know what they know." We observe an interesting rank equilibrium between knowledge stored in the weights and the data stream passing through the model. Across all model layers, we find that the hidden states (data stream) follow a U-shaped pattern, showing substantial compression in early layers and a steep rise during the late-layer decoding phase. In contrast, the weight rank follows an inverted U-shaped pattern, with very low rank in the early and late layers and high rank in the middle. We interpret this as an in-and-out information interplay: intermediate activations do not need to carry content that the weights can supply later, so they primarily preserve what the weights cannot provide. Motivated by this observation, we propose a model-aware data selection method, CAP (Counterfactual Assimilation Profile), which can determine whether a data candidate contains information accessible to the current model by utilizing the divergence gap in early- and late-layer representations between model-generated and reference responses. Across math, code, and science domains, CAP delivers 35.4% greater average improvement over the base model than the strongest baseline under different selection budgets. With only 10% of the data pool, CAP surpasses or matches full-pool training on math and science. We further show that CAP transfers to multimodal data selection and is robust to response horizon and noise.

We relate critical diameters of finite configurations to the topology of Vietoris-Rips complexes. For a compact metric space and $0<r<s$, we prove that the canonical inclusion from scale $r$ to scale $s$ is a homotopy equivalence whenever $[r,s)$ contains no diameter of a finite labelled configuration at which the diameter function has zero weak slope. On Riemannian manifolds, weak-slope stationarity implies Clarke criticality. At positive diameter, when the distances realizing the diameter are smooth, both are equivalent to first-order stationarity: the absence of a direction decreasing all these distances to first order. For closed connected smooth manifolds, the Clarke critical diameter spectrum has Hausdorff dimension zero, even at the cut locus. In the real-analytic case, it is finite at each fixed number of labels and countable over all label numbers. On the unit round sphere $S^m$, $m\geq1$, positive nonantipodal weak-slope stationary configurations are characterized by nonzero nonnegative equilibrium stresses. The least positive critical diameter is $\arccos(-1/(m+1))$, and the first accumulation point is $\arccos(-1/m)$. We lift every such stress through a spherical stack construction adapted from Lovász, producing stationary diameters that approach the original value from below in the next dimension as the number of layers increases. We also give example in general metric space showing that weak-slope stationary diameters need not correspond to changes in the homotopy type of Vietoris-Rips complexes.

Motivated by blind denoising in diffusion models, we study estimation of an unknown Gaussian noise level from a single high-dimensional observation, assuming the signal law P is known. We characterize the minimax mean-squared error under two structural assumptions on P. For signals with covering complexity k, the minimax rate is $\widetilde{\Theta}_\Lambda(\min\{\Delta_\Lambda^2,d^{-1}+k^2d^{-2}\})$, and the constrained MLE attains it up to logarithmic factors. For $\alpha$-strongly log-concave signals, the rate is $\Theta_\Lambda(\min\{\Delta_\Lambda^2,(1+\alpha^{-1})^2d^{-1}\})$, attained up to constants by a $P$-centered norm estimator. These results show that the structure of the signal law determines both the difficulty of blind noise estimation and the appropriate estimator.

Robot learning has largely relied on human-teleoperated demonstrations to acquire effective learnable behaviors. However, human-operated data collection processes can be unintuitive, difficult to scale, and inherently asynchronous. We explore an alternative: distilling physical behavior from general-purpose multimodal foundation models into deployable robot policies by using the foundation model itself as an autonomous demonstrator. While sufficiently capable models can generate successful zero-shot manipulation trajectories, repeatedly invoking them during physical execution is slow and expensive, limiting their utility as scalable data generators. As a solution, we introduce CAPEX, an experience-conditioned demonstration collection framework that uses execution experience from previous attempts to adapt how frequently the foundation model must observe, reason, and replan. We evaluate across RoboCasa tasks and on physical Franka and bimanual YAM-arm platforms, measuring task success, model calls, token usage, collection time, and cost. We further train Diffusion Policy and ACT on matched sets of human-teleoperated and foundation-model-generated demonstrations to evaluate the downstream learning value of autonomously collected data. We find that CAPEX increases the number of successful demonstrations by 4.3x while reducing the cost per successful demonstration by 80%. Policies trained on CAPEX-generated data approach the performance of those trained on matched human demonstrations; with longer training, this gap largely closes for policies trained from scratch. These results suggest that foundation models can serve as scalable sources of reusable robot experience. Project page: https://capex-paper.github.io/

Traveling waves of activity in neural tissue can be halted by spatial inhomogeneity in synaptic coupling. We study an integrate-and-fire network in which each neuron fires once and the coupling decays exponentially. For this model the leading-edge firing map reduces exactly to a scalar equation for the wave speed in space, with a slow unstable and a fast stable homogeneous speed, $c_1$ and $c_2$, and a periodic modulation of the coupling enters this equation pointwise. Positive periodic waves terminate in folds. For slowly varying modulation the fold amplitude approaches a plateau set by the trough of the modulation, where the local bottleneck speed is $\sqrt{c_1 c_2}$; the approach to the plateau is set by the local geometry of the trough. For rapidly varying modulation the fold amplitude grows linearly with frequency, with a slope given by a full-amplitude average over the integrated modulation profile; a weak-ripple truncation of that average overestimates the slope about 2.5-fold at the default coupling. A perturbative recursion in the amplitude gives the speed profile explicitly. We distinguish loss of the periodic wave from failure of a particular launch, and the excitatory regime $\epsilon\le 1$ from its sign-changing extension. The results are checked against direct integration of the reduced equation and first-spike firing-map simulations of the network.