Papers

$GW$+DMFT-type schemes replace the local part of a $GW$ self-energy by a separately computed local self-energy. A causal double counting removes a non-causal term from the hybridization (Lee and Haule, 2017), but the resulting total self-energy has been flagged as not guaranteed to be causal (Zhu and Chan, 2021). From the Herglotz representation, the spliced self-energy is causal if and only if its spectral measure is positive semi-definite. For translation-invariant single-band systems this becomes a momentum-resolved bound: the local weight may fall short of the local $GW$ weight by at most the momentum minimum of the $GW$ weight. On finite clusters, a mismatch between $GW$ and exact poles generically produces indefinite residues. On the Matsubara axis, a negative damping eigenvalue at one frequency certifies non-causality; passing does not establish causality. We examine these diagnostics in an idealized setting, not self-consistent $GW$+DMFT: one-shot $GW$ on the exact Green's function of small Hubbard clusters with the exact local self-energy inserted. At all 528 parameter sets, our computed $GW$ and exact self-energies pass both tests, as expected. The splice fails the pointwise test at 54 points, none at half filling, all at the lowest Matsubara frequency, and already at $U/t=0.5$; there the local $GW$ damping is 1.3-9 times the exact one. A block Pick test on eight frequencies, run with a second imaginary-time code, flags 481 of the 528 sets; for the other 47 it is inconclusive. Moment checks miss all of these, because the spliced high-frequency moment is exact. The Dyson Green's function is then non-causal too, yet passes the pointwise test everywhere tested. This version replaces a withdrawn one whose reported causality violations of $GW$ itself came from a sign error in the polarization; with the sign corrected, the computed $GW$ shows the expected positivity.

Global games select a unique cutoff when a player's incentive moves monotonically with private information. We show that this logic can fail when a privately informed participant can take a costly, simultaneous, and unobserved action that defends the status quo. In a currency-attack model, the defender acts only at intermediate signals. Along the traders' cutoff equation, this interval response creates an endogenous defense-loss term that vanishes at the endpoints of an activation component but can dominate the decreasing benchmark payoff margin in between. We establish a primitive region in which defense is inactive and uniqueness survives, and a finite-CDF overshoot condition under which two active-defense cutoff roots coexist with the inactive benchmark root. Because marginal indifference need not imply global incentives, we also give sufficient conditions for a genuine monotone cutoff best response. Finally, outward-rounded interval arithmetic proves that a proper-prior parameter vector has exactly three symmetric monotone-cutoff equilibria and that this topology persists locally. The result isolates a payoff-based boundary of global-game selection: hidden intervention can restore multiplicity without public signalling or a perturbation of the information hierarchy.

Organizations often learn about competence only from project-level success or failure, even when a project contains several complementary tasks. We compare task architectures by the Blackwell order. An expert of unknown fixed competence can perform all tasks in one bundled project, one task in a project completed by an outside technology, or the same number of tasks across separate projects. Bundling dominates a single narrow assignment below an outside-reliability threshold and is otherwise incomparable with it. Holding the expert's workload fixed strictly lowers this threshold but does not overturn the result: bundling still dominates when the outside technology is sufficiently unreliable, separate projects dominate only when that technology is perfect, and the experiments are otherwise incomparable. We derive the thresholds for any number of tasks and show that the fixed-workload threshold decreases to zero as task scope grows. Explicit posterior-variance formulas measure the cost of coarse aggregation for particular decisions. Finally, in the two-task case, occasional stage-level audits expand the bundling-dominance region according to an exact frontier.

Speculative decoding accelerates large language model inference by drafting future tokens cheaply and verifying them with the target model in parallel. Block drafters score a whole block of future tokens in one forward pass, yet standard decoding verifies only the top-scoring chain and discards the other candidates. Because these candidates are already scored, verifying more of them adds target computation but no extra drafting. We introduce CAST (Cost-Aware Speculative Trees), which packs these candidates into a tree and verifies it in a single target pass, leaving the target model, drafter weights, and decoding rule untouched. To decide how wide the tree should be, CAST adds candidates while the expected gain from the next one outweighs the verification time it adds. The width therefore adapts to each deployment from a latency measurement, without sweeping over widths. We evaluate CAST across five domains on three GPU generations and two model families. At its predicted width, CAST is faster than the standard chain in all eight settings, by up to 43%. We also find that the best width depends strongly on the deployment. Where verification cost jumps at a kernel boundary, a 128-token tree is only 2% faster than the standard chain, whereas the tree at the predicted width is 20% faster. Furthermore, we prove that CAST leaves the target output distribution unchanged under both greedy and sampled decoding. Code is available at https://github.com/js-lee-AI/CAST.

Fine-tuning adapts aligned large language models (LLMs) to downstream tasks, but a few dozen harmful examples can remove their refusal of harmful requests. Prior work localizes safety-related behavior to specific layers, directions, and tokens, suggesting targets for protection. We test whether successful localization and recovery support defenses that survive changes in the attack. Across six checkpoints from four model families, harmful and benign prompts remain linearly separable after attack, and patching full clean hidden states into the compromised model restores refusal at a reproducible transition depth. Building on a prior layer-freezing defense, we freeze every layer up to this depth and repeat the attack. At a hundred harmful examples, refusal remains near zero on all six checkpoints, with recovery transitions above the frozen boundary. In a second study, removing the update's top two singular directions restores refusal after short attention-only fine-tunes on four checkpoints. On Llama-3.1-8B, ordinary training changes weaken this repair and an attacker who spreads the update defeats it. A spectral detector calibrated on benign Llama fine-tunes misses most repair failures on that checkpoint. Localized freezing can nevertheless help preserve refusal when a few harmful examples enter training data unintentionally. These results show that an attacker can bypass a region identified by recovery and defeat a repair that works across multiple checkpoints, motivating five checks for defenses against adaptive fine-tuning. Code is available at https://github.com/js-lee-AI/refusal-relocates.

Collaborative perception enables connected agents to share complementary observations for 3D object detection, extending sensing range and mitigating occlusion. Under asynchronous communication, however, cooperative features arrive with temporal delay. Existing prediction-based methods compensate for these features mainly from the transmitting agent's own history, leaving residual misalignment with the ego agent's current observation; subsequent fusion also often overlooks spatial variations in alignment quality. We propose EgoRefine, an ego-referenced predictive alignment and reliability-aware fusion framework for asynchronous collaborative perception. Its Ego-referenced Predictive Alignment module uses the current ego feature to guide cooperative trajectory-field prediction and refines the sampling offsets along an ego-referenced trajectory direction. Its Trajectory-conditioned Reliability-aware Fusion module treats the trajectory discrepancy between the ego and cooperative streams and the directional refinement magnitude as alignment cues, using them to condition the relation between aligned features and adaptively reweight the two streams before convolutional fusion. Experiments on V2V4Real and DAIR-V2X-Seq show that EgoRefine outperforms TraF-Align by 1.6 and 2.9 points on average in AP@0.5 and AP@0.7, respectively. The source code will be made publicly available at https://github.com/godk0509/EgoRefine.

Simplified optical systems often exhibit residual lens aberrations and Veiling Glare (VG), resulting in spatially varying blur and contrast reduction. Large-scale Lens Libraries (LensLib) enable reusable aberration correction models by covering diverse Point Spread Functions (PSFs), but their aberration-only training distribution does not include target-specific veiling glare. Extending such foundations to compound degradation is challenging because realistic target-system compound pairs are difficult to obtain. To address this challenge, we propose LensBridge, a two-stage framework that first establishes a reusable aberration correction foundation and then adapts it to compound optical degradation using only a few unpaired target observations. In Stage I, we build a PSF-aware one-step diffusion foundation by constructing discrete degradation priors from LensLib PSFs and learning to retrieve them directly from aberrated images, enabling PSF-aware correction without requiring explicit PSF at inference. In Stage II, we adapt this foundation to compound degradation through frequency-domain guidance. At the data level, Frequency-guided Degradation Completion (FDC) transfers target low-frequency characteristics to LensLib aberrated images while preserving aberration structures to synthesize compound training pairs; at the model level, Frequency-guided Pseudo Decomposition (FPD) forms aberration- and VG-dominant pseudo observations to condition separate adaptation branches. Extensive experiments across multiple optical systems demonstrate that LensBridge effectively extends reusable aberration correction foundations to joint aberration correction and veiling glare removal without target-system paired supervision. All code will be available at https://github.com/XiaolongQian/LensBridge.

Vision-Language-Action (VLA) models increasingly rely on action experts that generate short action chunks under receding-horizon control. While chunk-level training is convenient across robot embodiments, it optimizes local action likelihood without explicitly accounting for long-horizon task success. Sequence-level reinforcement learning can address this limitation, but typically requires policy rollouts and closed-loop interaction, which are costly for real-robot manipulation. We introduce DriftOPD, a teacher-free, rollout-free framework for sequence-level on-policy distillation of continuous VLA action experts. We show that the sequence-level reverse Kullback-Leibler (KL) divergence decomposes into a chunk-level reverse-KL term and a future-potential term that captures the long-horizon effect of the current action. DriftOPD optimizes these two terms using a one-step drifting objective and a Q-function critic learned from offline demonstrations, respectively, enabling sequence-level optimization with only offline data and one-step action generation. Across multiple VLA architectures in simulation and real-world manipulation, DriftOPD generally outperforms existing one-step distillation baselines while achieving task success performance comparable to multi-step teacher policies. These results demonstrate that long-horizon behavior can be effectively distilled into one-step VLA action experts without online interaction or a separate teacher.

Voice agents enable low-latency, natural interaction, yet their ability to faithfully ground responses in external documents remains underexplored. We introduce DuplexSpeechBench-Document Grounding (DSB-DG), a benchmark for evaluating document grounding in voice agents across five professional domains. DSB-DG targets three failure modes: Context Saturation, which measures grounding under increasing document length; Grounding Decay, which measures retention of document facts across multi-turn dialogue; and Proactive Grounding, which evaluates whether context re-injection mitigates conversational drift. The benchmark contains 1,636 adversarially verified QA pairs from 50 documents covering five professional domains, and supports fully automatic evaluation of grounding accuracy, hallucination, and response latency. Across systems spanning cascaded, proprietary full-duplex and real-time, and open-weight speech2speech architectures, we find substantial differences in effective grounding capacity. While cascaded pipeline (ASR-LLM-TTS) achieves the highest grounding accuracy, Gemini-Live and GPT-Realtime closely trail behind. Open-weight systems exhibit distinct failure modes, most notably an abrupt context-capacity collapse and multi-turn grounding decay. More broadly, grounding fidelity degrades with context and conversational load, and failures frequently manifest as unsupported generations rather than abstention. We show that contextual grounding as a key unresolved challenge for reliable full-duplex voice agents.

Historical Manchu documents preserve invaluable linguistic and cultural heritage, yet their digitization is hindered by severe degradations and the scarcity of paired training data. Existing document restoration methods primarily optimize pixel-level reconstruction, which can produce visually plausible results while failing to preserve the structural identity of Manchu glyphs. To address this limitation, we propose a retrieval-guided glyph-aware restoration framework that goes beyond pixel reconstruction by explicitly incorporating glyph-level structural knowledge. Our method retrieves relevant glyph exemplars to provide structural guidance during restoration and integrates this information into the reconstruction process, improving the recovery of degraded character structures under low-resource conditions. Extensive experiments on Manchu historical documents demonstrate that the proposed approach improves both image restoration quality and glyph-level fidelity compared with existing restoration methods. These results highlight the importance of incorporating character-aware structural priors for reliable restoration of low-resource historical documents.

Research agents explain planned experiments. We measure predictive credit with paired forecasts sharing an intervention, forecaster, and outcome while varying description, matched explanation, and donor context. Five checks track commitment, delivery, predictive gain, alignment, and known-signal uptake. Across 336 prospective states in controlled learning, 12 Tox21 endpoints, and 24 OpenML tasks, v5's frozen credit decision was inconclusive. Tox21's preregistered ROC AUC interval-score harm test was unmet ($D-M=-.0026$, 95 percent interval [$-.0174$, .0104]); OpenML's joint formation, point-equivalence, and repeatability rule was unmet. Matched point-accuracy gains over description remained unconfirmed, and Tox21/OpenML seed-donor intervals spanned zero. Under requested DeepSeek V4 Pro, matched and donor cards reduced secondary Tox21 drift by 64.5 and 59.1 percent. A DeepSeek V4 Flash replay raised matched point MAE from .01823 to .02020 and missed matched-donor interval-score equivalence. OpenML full-card assignment widened nominal 80 percent intervals by 21 percent, with 49.3 percent coverage versus 51.4 percent for description and content in 66/144 cards. Direct-text Flash delivered all 144 notes without detectable matched point-accuracy gain. A researcher-authored mechanism positive control lowered point MAE by 2.60 percentage points versus description. The protocol measures predictive credit for research-agent benchmarks and scientific forecasting; natural-explanation credit remained unconfirmed at the tested donor resolutions.

Scientific coding agents receive equations, boundary conditions, and output requirements in writing, then must assess the programs they revise. Rules to Tools (R2T) supplies prepared executable checks of public scientific requirements. Matched SciCode repair groups share written checks, starting programs, model, and budgets; the tool group receives a callable implementation. Across two task-ID cohorts, complete repair is 26/30 with text and 29/30 with the prepared checks. Three task IDs favor tools, one favors text, and eleven tie. The eight-ID cohort scores 13/16 versus 15/16, with a task-cluster bootstrap 95% interval of [-12.5, 43.75] percentage points for the difference. The larger shared-definition SciCode cohort ties at 13/24 per group. Five development-exposed tasks with alternate starting programs score 3/10 versus 7/10. The tool group favors tasks 17, 77, and 11; initial checks flag task 17 and report no violation for tasks 77 and 11. Task 37 favors text and has no initial reported violation. A fresh source-through-Python arm also reaches 15/16, matching the dedicated command's aggregate. In a matched PDE comparison, detailed text scores 23/24 and checks score 24/24, with 31.2% lower reported model output for checks. Agent-side output savings vary by cohort, while public CPU use rises in both task-ID cohorts. These results measure task-dependent repair outcomes and agent-side costs with prepared checks.

Let $X$ be a connected finite-type CW-complex with fundamental group $G$. We show that the profinite completion $\widehat{G}$ determines the cohomology jump loci $\mathcal{V}^q_s(X,\mathbb{C})$ under two hypotheses: that the loci are finite unions of torsion-translated subtori, as for smooth quasi-projective varieties, and that $\widehat{G}$ determines the Betti numbers of the finite cyclic covers of $X$ in degrees $\le q$, which holds unconditionally for $q=1$, and in all degrees when $X$ is aspherical and $G$ is good in the sense of Serre. When the isomorphism of completions is compatible with an identification of the abelianizations, the loci correspond exactly; in general, they correspond up to an isogeny. Applied to finite covers, this shows that the tropical bounds for the Bieri–Neumann–Strebel–Renz invariants are profinite invariants, and recovers the profinite invariance of the BNS invariant of Kähler groups due to Hughes, Llosa Isenrich, Py, Stover, and Vidussi. We also show that $\widehat{G}$ determines the graded abelian groups $\mathrm{gr}_r(G/W(G))$, torsion included, for every verbal subgroup $W(G)$; the cases $W(G)=1$ and $W(G)=G''$ give the lower central series quotients and the Chen groups. For hyperplane arrangements, it follows that no arithmetic Zariski pair is distinguished by any of these invariants, while two known lattice-isomorphic pairs show, respectively, that the profinite completion of an arrangement group is not combinatorially determined, and that it does not determine the group.

How much initial-state precision is required to predict a nonlinear system to a prescribed accuracy over a finite horizon? We formulate this inverse prediction problem through a one-shot resource $B_N$, defined as the number of binary refinement bits required in the initial state by a specified local sensing architecture. Within a common scale-separable error-growth regime, changing a fixed tolerance changes $B_N$ only by an $N$-independent offset. An exactly solvable circle/Chebyshev map provides the chaotic calibration $B_N=N\log_2 m+O(1)$. We then apply the framework to the quasiperiodically forced logistic map under phase-only initial uncertainty. Over the resolved horizons, representative smooth-torus, strange-nonchaotic-attractor (SNA), and chaotic regimes exhibit a three-level precision-resource hierarchy: bounded, logarithmic-like, and linear-like growth, respectively. For the SNA, algebraic phase sensitivity $G_N^{\mathrm{op}}\sim N^\mu$ implies an admissible initial uncertainty of order $N^{-\mu}$, and therefore a precision cost proportional to $\log N$. Phase-grid refinement shows that the sampled worst-case maxima are numerically stable with increasing phase resolution. Near the torus–SNA fractalization point, derivative-based phase sensitivity can already grow while finite perturbations remain below a fixed operational tolerance for more than $10^6$ iterations, revealing exceptionally long activation horizons. Thus an SNA can occupy an intermediate finite-precision resource class between a smooth torus and ordinary chaos, while its operational manifestation can occur on a much longer timescale than its derivative-based sensitivity.

Model-based offline reinforcement learning (MBORL) improves sample efficiency through model-generated trajectories. However, accumulative model error can drive imagined trajectories outside the offline data distribution, leading to unrealistic synthetic data and unstable policy optimization. Many existing methods primarily control rollouts using transition-level uncertainty. We propose in-distribution imagination (IDI), a rollout control framework that estimates trajectory support in a learned representation space and adaptively truncates rollouts that leave the offline trajectory manifold. Combined with trajectory-regularized RL, an extension of entropy-regularized RL, IDI consistently improves performance in limited-data settings. Experiments show that trajectory support predicts rollout failure substantially better than transition-level uncertainty, highlighting the importance of trajectory-level rollout control in MBORL.

Beam-search-based test-time methods provide an effective way to improve large language model (LLM) performance on long-horizon generation by pruning invalid reasoning paths early, leading to significantly improved reasoning efficiency and more favorable test-time cost scaling. Despite strong empirical success, the theoretical understanding of beam search remains limited. In this paper, we study the test-time compute guarantee of the commonly used beam search framework that uses the model's internal log-likelihood for intermediate scoring, while relying on an external reward model only after a complete response is generated. We first establish a lower bound for vanilla beam search, showing that at least $\Omega(C^\star(x)^2)$ samples are required for the optimal response to survive, where $C^\star(x)$ is the token-level coverage coefficient for prompt $x$. This motivates our modified confidence-filtered beam search (CF-Beam), which reduces the sufficient coverage dependence from quadratic to nearly linear under prefix competitiveness, for fixed horizon, gap, and target accuracy. We then show that the regret of CF-Beam is upper-bounded by the probability of rare failure events and the reward estimation error scaled by a path-level coverage coefficient, where the rare-failure term vanishes as per-step sampling increases. Our results highlight a fundamental advantage of beam search over sequence-level inference methods such as Best-of-N and Best-of-Majority. While the guarantees of these approaches typically involve coverage coefficients that grow exponentially with the horizon $L$, CF-Beam controls the dominant search-induced term through a token-level coverage coefficient that scales polynomially with $L$. Our numerical experiments further confirm that beam search is more robust on hard instances and under increasing reasoning horizons.

In this paper, we establish the weak type $(1,1)$ boundedness of noncommutative singular integral operators with rough kernels. To deal with the rough kernels, we develop some orthogonality of the kernels themselves in the pseudo-localization arguments for the good functions and use the microlocal decomposition and $TT^*$ arguments for the bad functions.

Final-answer accuracy does not reveal whether a scientific-search agent failed to encounter a target paper, attempt to inspect it, or return an accepted answer after inspection. We introduce decision checkpoints that record observations and tool actions without benchmark labels during inference, then join target identities and evaluator labels to assign outcome categories from recorded events. Across five conditions on 540 answerable AutoResearchBench Deep questions in a fixed, target-enriched environment, keyword search achieves 24.6% accuracy, compared with 17.8% for raw search. The keyword condition has fewer incorrect answers with neither target exposure nor inspection, but more incorrect answers after the target is exposed and left uninspected. Compared with keyword search, read-first has 27.4% more recorded evidence-search calls. Target inspection attempts occur on 199 questions under read-first and 191 under keyword search; both conditions achieve 24.6% accuracy. The checkpoint protocol makes these question-level differences explicit, distinguishing target exposure and inspection from aggregate accuracy and total tool use.

We study the zero distribution of the sum of the first $n$ Gegenbauer polynomials \[ S_n^{(\alpha)}(z)=\sum_{k=0}^n C_{k}^{(\alpha)}(z). \] We prove that for $\alpha>1$, the zeros of $S_n^{(\alpha)}(z)$ lie on the interval $(-1,1)$ for all large $n$.

Z-Sigil is a public-key cryptosystem in which the plaintext selects successive keys from a fixed module-lattice family. Messages are length-prefixed, zero-padded and divided into 32-byte blocks. Each public vector is a shared public matrix applied to a small secret vector, plus a small error. Key indices label torsion points of a flat Kähler torus; the secret family forms a section of a key bundle over them. A public nonce initializes a hash state that selects each block's key and bit mask. The sender updates the state with the plaintext block; the receiver does so after recovering it. The stream and nonce determine a discrete walk along which decryption reads the secret section. We specify the algorithms, prove correctness under an explicit noise condition and bound decoding failure for messages chosen after the public key. Under stated decisional Module-LWE assumptions, we establish IND-CPA confidentiality for the chain without modelling the state hash as a random oracle. The reduction covers quantum adversaries under quantum hardness assumptions, with classical keys, messages and ciphertexts; no concrete security level is established. With independent uniform selectors, a restricted direct-decryption model quantifies reduced fragment recovery under partial key exposure, without improving full-message recovery probability over an independent-block baseline. Known-plaintext and candidate-message attacks, and parallel candidate-table decryption, delimit this result. Neither a universal sequential lower bound nor authentication or chosen-ciphertext security is established. Replacing an earlier scalar-exposing proposal, we give an augmented-lattice interpretation, integral-transport obstructions and a noise budget for research on curved, nontrivial bundles. A byte-level specification, pseudocode, test vectors and numerical checks support verification.

Tetrahymena calcium-binding protein (Tcb2) forms Ca$^{2+}$-responsive networks that exhibit contractile behavior, yet how Ca$^{2+}$ concentration controls their local mechanical response remains poorly understood. Here, we use optical tweezers to perform active microrheology on reconstituted Tcb2 networks inside a microfluidic device that enables precise control of Ca$^{2+}$ concentration, allowing systematic tuning of network structure and mechanics. We find that increasing Ca$^{2+}$ from 1 to 100~mM enhances the effective stiffness by nearly two orders of magnitude, from $\sim$1$\times$10$^{-3}$ to $\sim$7$\times$10$^{-2}$~pN/nm, corresponding to a transition from a viscosity-dominated to a more elastic and mechanically robust network. Recoil assays further reveal rapid release of stored elastic energy following deformation. After two orthogonal pulls, the bead recoils along the diagonal rather than retracing the loading path, indicating that stresses from different directions combine to produce a resultant restoring response. These results establish Tcb2 networks as a minimal, tunable system for probing chemomechanical coupling and viscoelasticity in Ca$^{2+}$-regulated protein networks.

On-policy distillation (OPD) learns from teacher feedback on student-generated responses and has shown promise in reducing forgetting relative to supervised fine-tuning (SFT). However, its benefits and fragility remain incompletely understood. We study sequential distillation from multiple teachers, where the student minimizes its average divergence from the teachers. Forward Kullback–Leibler (KL) divergence yields a weighted arithmetic mixture, while reverse KL yields a normalized weighted geometric aggregate. We develop algorithms that learn these targets under off-policy and on-policy feedback, respectively, establishing logarithmic regret bounds in the tabular setting and extending the analysis to function approximation. By analyzing these aggregation targets, we identify mechanisms that help explain both the benefits and fragility of OPD. Relative to forward KL, reverse KL can better retain a confident expert's preferences under uninformative feedback, but is more sensitive to teachers that assign very low probabilities to correct responses. Its token-level conditionals also reveal a dependence on continuation distributions that can favor incorrect prefixes over long horizons.

Connectome models of the fly nerve cord generate walking-like motor rhythms, but oscillation alone does not show that the specific wiring matters. Here we provide, to our knowledge, the first test of which features of motor output depend on the specific wiring. We simulated the leg motor systems of two independent Drosophila connectomes, with synapse counts as fixed weights and glutamatergic synapses treated as inhibitory, and compared each with six families of rewired networks that preserve progressively more of its structure, using pre-registered criteria. We find that rhythm is generic but antagonist coordination is not: many rewired networks were more rhythmic than the real ones, yet the real wiring coordinated antagonistic motor pools more strongly than every rewired network, most of all at the thorax–coxa joint. We trace this specificity to how premotor input is allocated between antagonistic pools. Both connectomes carry Sherrington's reciprocal innervation—neurons that excite one pool inhibit its antagonist—and no rewired network does. Reassigning premotor inputs between the pools abolished coordination even when motor neurons' typical input strength changed little (all pre-registered criteria met in one connectome; same direction in the other). Coordination, not rhythm, therefore reveals whether a connectome model's wiring matters.

We investigate Miller's bias conjecture for general one-parameter families of elliptic curves over $\mathbb{Q}$ with non-constant $j$-invariants. Utilizing methods developed by Michel, we view the second moment as the sum of distinct cohomological components: a main $p^2$ term, a $p^{3/2}$ term arising from the first cohomology over the projective line, and terms of order $p$ or lower corresponding to singular fibers. By assuming the generalized Sato-Tate conjecture, we employ representation and motive theory to demonstrate that the coefficient of the $p^{3/2}$ term averages to zero in the limit. We then independently analyze the lower-order contributions without assuming Sato-Tate. By applying the Chebotarev density theorem and analyzing Galois representations, we show that the contributions to the order $p$ term from additive singular fibers also average to zero. Consequently, the only remaining average contribution to the $p$ term is $-B_pp$, where $B_p$ denotes the number of “bad” points where the discriminant vanishes. Because $B_p$ averages to a strictly positive value, the overall coefficient of the $p$ term averages to a strictly negative value in the limit, thereby establishing the bias conjecture for these families.

Gas sensor arrays can estimate the composition of gas mixtures from their response patterns. However, when a sensor is used outside the laboratory, the true gas concentrations are unknown, so there is usually no direct way to determine whether the estimated result is reliable. Here, we develop a physics-constrained neural network that estimates time-varying gas concentrations and reconstructs the corresponding sensor signals at the same time. We tested the method with a twelve-channel membrane-type surface stress sensor array exposed to water-ethanol mixtures whose concentrations changed over time. The model reconstructed the concentration profiles of both components from the raw signals. Artificial offsets and sensitivity changes in one channel were detected from disagreement between the measured and reconstructed signals. Deletion or replacement of part of a measurement record was detected from violations of the sorption and mechanical equations. This approach enables time-resolved multicomponent gas analysis with self-verification from a single measurement.

Recursive self-improvement (RSI) lets a system improve from its own outcomes; in LLM-based multi-agent systems, Agents refine one another within a task, and outcomes improve how they collaborate across tasks. However, existing multi-agent collaboration leaves this loop open: collaboration is pre-defined at the operator level, topology-only learning keeps verbatim exchange that propagates errors, and reward maximization on a system's own outcomes concentrates on a few teams. To address these challenges, we propose CollabFlow, an RSI system of Learned Agent Collaboration: a trainable Collab-Director constructs teams of complete Agents, a frozen executor runs them, and each round's outcomes retrain the director. Within each round, the edges of a collaboration graph carry protocols of Evidence-Conditioned Communication: a receiver adopts a differing answer only when the sender's evidence is stronger by a margin, so the director learns who communicates and how. Across rounds, we further propose Collaborative Trajectory Balance (CTB), a flow-based objective that credits each team once across its construction orders and targets a reward-proportional distribution over teams, so several good teams stay in play. We also bound how far this self-generated target moves between rounds, which shrinks as records accumulate. On twelve datasets, CollabFlow outperforms all baselines and keeps improving across rounds. Code is available at https://anonymous.4open.science/r/CollabFlow-631E.

In recent years, LLM-based multi-agent systems have been widely applied to orchestrate tool-using agents into executable communication graphs. However, existing self-evolving orchestration still faces key challenges, including post-hoc evolution that revises the team only after the trajectory ends, credit diffusion that gives every action the same terminal advantage under confounded baselines, and skill admission that is uncalibrated and never retired. To address these challenges, we propose EvoSteer, a new paradigm of Online Self-Evolving Graph Orchestration – the orchestrator builds a running team and repairs its plausible but failing steps from execution features and a learned value estimate. To support this paradigm, we introduce Anchored Trajectory Balance (AnchorTB), a regression-style flow-matching loss that assigns each orchestration action a coefficient by balancing subtrajectories against a frozen reference. Built on the learned flow, we further propose Validated Skill Admission, in which a candidate skill is tried before promotion and promoted only if paired evidence passes a sequential test under a shared nominal testing budget. Moreover, AnchorTB combines measured task-level reference reward statistics with prefix-dependent corrections. Experimental results on twelve datasets show that EvoSteer significantly outperforms baselines across question answering, mathematical reasoning, code generation, and interactive decision making. Our code is available at https://github.com/beita6969/evosteer.

Long-form subtitle translation requires reasoning over discourse and cultural context spanning episodes or entire series, while maintaining consistent terminology and style. Existing single-LLM methods are largely sentence-level, and multi-agent systems often use static workflows that do not adapt to scene complexity or production context. We propose SMART, a Self-evolving Multi-Agent system for long-foRm subtitle Translation. During test-time training, SMART builds persistent series-level memory and translates a subset of sentences through a dynamic router and Mixture-of-Agents layer with tools for terminology verification, subtitle constraint validation, and contextual retrieval. A judge-refiner loop scores candidates and uses textual critiques to update agent prompts and routing policies without retraining the underlying LLMs. During test-time inference, the evolved configuration translates the remaining series. We also introduce Subtitle Arena, covering 14 genres, 2–198 episodes per series, production years 1959–2023, and 15 target locales, together with SubMQM, a subtitle-adapted MQM framework with seven dimensions and 19 error categories. SMART achieves the best overall MQM score in all 15 Subtitle Arena directions, reducing average penalty by 6.9% over the strongest competing agent system. On a public benchmark, MuSC, SMART obtains the best model result across all 4 language pairs. SMART also achieves the best result in human evaluation with an overall score of 4.50/5.

We study multi-armed bandits (MAB) with multiple optimal arms, motivated by the fact that many practical decision making problems admit multiple correct answers. For $K$-armed bandits with $A$ optimal arms, we first provide a sharper analysis of previous sub-sampling algorithms (De Heide et al., 2021; Zhu and Nowak, 2020), establishing a $\tilde{O}\Big(\frac{K-A}{\sqrt{KA}}\sqrt{T} \Big)$ minimax regret, where $T$ is the total number of interactions and $\tilde O(\cdot)$ drops all constant and logarithmic factors, improving the previous $\tilde{O}(\sqrt{KT/A})$ regret. We then provide a matching lower bound up to logarithmic factors, indicating that our established rate is nearly minimax-optimal. We further show that the knowledge of $A$ up to $\tilde{O}(1)$ factors is necessary to achieve near-optimal regret, as near-optimal algorithms for one number of optimal arms must incur substantially larger regret than optimal regret for a smaller number. Overall, our results provide a comprehensive minimax characterization of $K$-armed bandits with $A$ over the entire range of $1 \leq A \leq K-1$.

TTS systems with autoregressive semantic modeling have demonstrated strong zero-shot voice cloning performance and rich expressive variation, but their sequential decoding incurs substantial latency. Non-autoregressive alternatives offer much faster generation, yet often rely on more restrictive reference conditioning, such as requiring transcripts of the reference speech during inference. We present Tacit-TTS, an efficient transcript-free zero-shot voice cloning system distilled from IndexTTS2. Our model replaces autoregressive text-to-semantic decoding with masked non-autoregressive generation, introduces training-free acoustic length estimation, and accelerates the flow-matching renderer through ReFlow distillation. Across two English and two Mandarin datasets, Tacit-TTS achieves competitive zero-shot quality while generating speech over 10x faster than IndexTTS2 for utterances longer than 5 seconds. Its transcript-free conditioning further supports cross-lingual and non-lexical references. We validate this capability using references from eight other languages, infant babble, and synthetic gibberish, where transcript-dependent systems often degrade or fail due to unreliable ASR transcripts.