Papers

Long-form video understanding requires multimodal agents to iteratively gather evidence over many reasoning steps. However, most existing agentic methods suffer from semantic thrashing: as append-only working memory grows, attention to key evidence collapses, and the agent loses access to what it has already found. First, we provide a structural argument showing that append-only memory can incorporate newly observed target evidence, but cannot remove accumulated noise or prevent ordered context growth without a rewrite operator. Second, motivated by this analysis, we propose VideoLoop, a multimodal agent with two coupled loops. The outer loop reasons over the video and the inner loop, after each step, retrieves artifacts from an unbounded filesystem of past observations and intermediate analysis, and rewrites a bounded working memory. Extensive experiments demonstrate the effectiveness of VideoLoop, which improves four popular LVLM backbones in a plug-and-play manner, with an average gain of 4.2% points over baseline on VideoMME (long). Further analysis of working memory suggests that VideoLoop mitigates semantic thrashing: on the hardest quarter of VideoMME (long) questions, a blind judge that reads only the agent's context answers 81.1% correctly, versus 60.9% for the append-only agent. With Gemini 3.1 Pro, VideoLoop reaches 88.3% on VideoMME (long), 88.8% on VideoMMMU, and 80.9% on LongVideoBench (long).

In this article, we analyze plane-symmetric solutions to the relativistic Euler equations on spatially flat spacetimes with decelerated expansion. We consider a linear equation of state $p(\rho)=K\rho$ and power law inflation $a(t)=t^{\alpha}$, where $0<K<\frac{1}{3}$ and $0\leq\alpha<1$. Previous results imply nonlinear stability of the homogeneous and isotropic solution above an expansion threshold $\alpha_\text{crit}=\frac{2}{3(1-K)}$. We prove that at and below this critical expansion rate there exist arbitrarily small data that exhibit finite-time singularity formation of the shock type, i.e., gradient blowup while the solution stays bounded. For this type of data, we establish lifespan estimates that are polynomial below and exponential at the critical threshold. In addition, we prove a theorem based on energy estimates that provides lower bounds on the lifespan of plane-symmetric solutions generated from small initial data and generalizes to solutions without symmetry in $3+1$-dimensions.

In [OS05] the authors proved an exact triangle for the Heegaard Floer homology of the double branched covers associated to a skein sequence of links, and constructed a spectral sequence from the reduced Khovanov homology to the Heegaard Floer homology of the double branched cover of a link. For $L \subset S^3$ a link and $\Sigma(L)$ its double branched cover, the invariant $HF(\Sigma(L))$ doesn't capture the information of the natural involution on $\Sigma(L)$. In this paper we study the equivariant version of $HF(\Sigma(L))$ and prove that similar exact triangle and spectral sequence hold for this equivariant version.

Long-tailed 3D object detection is treated as a class-frequency problem, but LiDAR supervision quality depends on object observability: similar frequencies can hide different geometric evidence. We introduce Geometry-Augmented Exponentially Weighted Instance-Aware Repeat Factor Sampling (GA-EIRFS), a detector-agnostic method that modulates a frequency-based repeat factor with a fixed geometry score combining point count, surface-normal entropy, and surface coverage. GA-EIRFS changes only frame-sampling probabilities, leaving the detector and inference unchanged. On nuScenes it improves mean average precision (mAP) and the nuScenes detection score (NDS) in four converged experiments with CenterPoint and PointPillars over two seeds; for CenterPoint at seed 666, mAP rises from 0.552 to 0.563 and bicycle AP from 0.306 to 0.359. Per-class gains correlate with the class sampling-weight increase (Spearman rho=0.70, p=0.025) but not with geometry score alone (rho=0.32, p=0.37), so geometry amplifies frequency-driven need. KITTI results vary across seeds, most for the rarest class. Code: https://github.com/Multimodal-Sensing-Lab/GA-EIRFS.

The Brown–Erdős–Sós problem is a fundamental problem in sparse hypergraph Turán theory. For integers $r,k\ge 2$ and $s\ge r$, the problem asks for the maximum number $f^{(r)}(n;s,k)$ of edges in an $n$-vertex $r$-uniform hypergraph containing no $k$ distinct edges spanning at most $s$ vertices. In 1971, Brown, Erdős, and Sós proved that $f^{(r)}\bigl(n;(r-t)k+t,k\bigr)=\Theta(n^t)$ for all $r>t\ge 2$ and $k\ge 2$. However, the existence and the value of the leading coefficient have remained largely open. We determine the coefficient $\pi(r,t,k):=\lim_{n\to\infty}n^{-t}f^{(r)}\bigl(n;(r-t)k+t,k\bigr)$ for every such $r,t,k$, except when $(r,t)=(3,2)$ and $k\ge 4$ is even. In particular, \[ \pi(r,t,k) = \begin{cases} \frac{2}{t!\bigl(2\binom{r}{t}-1\bigr)}, & \text{if $k$ is odd},\\ \frac{1}{t!\binom{r}{t}}, & \text{if $k$ is even and $r\ge4$}. \end{cases} \] Surprisingly, for $r\ge4$, the limit $\pi(r,t,k)$ depends on $k$ only through its parity, not its value. For the remaining case, we prove that $\pi(3,2,k)>1/6$ for all even $k\ge 4$, showing that the natural packing construction is never asymptotically optimal. As an application, we extend a connection of Bennett, Cushman, and Dudek to arbitrary uniformity to resolve several cases of the Erdős–Gyárfás–Shelah generalized Ramsey problem.

Autoregressive video diffusion enables interactive streaming generation, but suffers from error accumulation over long rollouts. Self-rollout training reduces exposure bias, yet finite rollouts leave long-range drift unresolved. We observe that the noise level of the history key-value (K/V) representations trades visual quality against motion, and that restoring gradients through the history aligns causal training far more closely with bidirectional training. Motivated by these observations, we introduce Self-Aligned Forcing (SAF), a training scheme that aligns the history of each block with the noise level of the block being denoised. Specifically, the history is the K/V produced by preceding blocks at the same denoising stage, so all blocks at a stage can be denoised in a single forward pass under a causal mask. This keeps the noisy history differentiable, allowing future losses to optimize how it is encoded. SAF therefore avoids a separate no-gradient rollout and per-block timestep-zero recaching, training up to 1.8x faster than prior methods with lower memory. At inference, SAF achieves the highest single-GPU throughput among existing methods and keeps one history bank per stage for a multi-GPU pipeline, reaching 49.1 FPS on 4 GPUs. Experiments show superior long-horizon generation with a better balance between visual quality and motion. Project page: https://anonymous.4open.science/w/self-aligned-forcing/.

Simulations of archaeological sites can make interpretations of past cultural practices observable and examinable. Generative multi-agent simulations offer a bottom-up approach to modeling how people collectively moved through and used historical spaces. However, current agents designed to simulate everyday life often plan and act independently, limiting their ability to capture how movement depends on others' actions. We introduce IMPACT (Interdependent Movement Planning through Inter-Agent Constraints and Triggers), an architecture that uses culturally specific roles and obligations to define dependencies among agents' activities and guide coordination. IMPACT connects socially gated milestone planning, wait-or-prompt resolution, structured directive issuance, and directive integration. These mechanisms determine whether and when activities can begin or change as social conditions evolve, producing socially constrained and prompted movement as their primary observable outcome. We instantiate IMPACT in a five-hour simulation of a Pompeian dinner involving ten agents across interdependent roles. Analysis of five simulation runs shows how social roles, responsibilities, and status relations shape household activities and spatial practices, as reflected in patterns of co-location, asymmetric waiting, co-movement, and social directives. In a controlled ablation evaluation, thirty-seven participants rated the complete architecture's behavior as more socially coherent and believable than that of two reduced architectures. Interviews with six archaeology experts highlighted historically plausible movement patterns and the simulation's potential to support archaeological interpretation, while identifying areas requiring stronger historical grounding for future work.

Many applications of black-box predictive models require controlling task-relevant error rates, such as missed lesion pixels in segmentation or missed labels in multilabel classification. Conformal risk control (CRC; Angelopoulos et al., arXiv:2208.02814) gives distribution-free guarantees for such losses, but it calibrates a single threshold shared by all inputs. Because conditional risk varies with the input, this marginal guarantee often overprotects easy cases and underprotects hard ones. We propose ReCIRC (Rectified Conformal Risk Control), which inverts each input's estimated local risk curve to reparameterize the calibrated threshold as a risk budget $a$ representing a common target conditional risk, and then applies CRC unchanged to the resulting family. ReCIRC retains CRC's finite-sample marginal guarantee regardless of the accuracy of the estimated curves, while accurate curves yield approximate conditional risk control and, under additional conditions, asymptotically exact conditional risk control; they also support a risk-calibration diagnostic. Across three synthetic and five real-data settings spanning segmentation, multilabel and multiclass classification, and regression, ReCIRC attained the lowest average worst-group risk and mean positive group excess in every setting, while maintaining marginal risk close to the target, whereas changes in prediction size were application-dependent.

Vision-language models (VLMs) may accept false visual premises, answering questions about a target object's color, count, location, or state even when it is absent. We call this reliability-critical behavior a target-absence grounding failure. Existing visual-grounding detectors primarily rely on generated responses, hidden states, or uncertainty measures. We present the first framework to leverage internal routing decisions in Mixture-of-Experts (MoE) VLMs to detect target absence before generation and guide selective correction. We extract target-token routing probabilities from Qwen3-VL-30B-A3B-Instruct and Gemma-4-26B-A4B-it, train a separate L2-regularized linear detector for each model, and use its predictions to selectively invoke a target-aware review prompt. Using routing alone, the Qwen and Gemma detectors achieve ROC-AUCs of 0.9988 and 0.9956 on GQA-Inpaint and retain 0.8095 and 0.7781 on the external OBER dataset, respectively. The resulting routing-gated policy improves end-to-end accuracy on GQA-Inpaint and OBER by +22.25% and +12.17% for Qwen, and by +13.42% and +1.39% for Gemma, without modifying model weights. Further analysis shows that the signal is localized to the target-object token, emerges in early MoE layers, and is distributed across partially substitutable experts. Although cross-dataset threshold shifts require recalibration, false-positive review causes limited harm overall, suggesting that intervention risk can be controlled through joint selection of the detector threshold and review prompt. Overall, we show that routing probabilities alone preserve actionable information about visual perception, allowing computation already produced by an MoE VLM to support low-cost detection and selective visual regrounding.

Gravitational-wave (GW) “dark siren” techniques, namely the statistical association of GW events with a galaxy catalog, have so far been used as a cosmological tool. Yet this association carries distinctive astrophysical information that remains unused—specifically, how compact binaries populate galaxies and the identities of individual hosts. In this work, we turn the dark-siren program into an astrophysical probe by inferring both simultaneously within a single hierarchical framework. The method reduces the many potential hosts to a compact, probabilistically ranked target list, providing a direct follow-up decision tool. Applied blindly to GW170817, it recovers NGC~4993 as the highest-ranked host and constrains the galaxy luminosity weighting, mildly favoring non-uniform host weights. Fixing the galaxy weighting can instead degrade host identification and even favor the wrong host. This framework recasts dark sirens as a potentially unique probe of the astrophysics of electromagnetically dark compact-binary mergers.

The attention operation is naively position invariant. However, positional information is fundamental to natural language, and therefore a variety of explicit position encodings have been developed in transformer-based models, such as rotary position encoding (RoPE). Although explicit position encodings have long been assumed to be required, recent methods that interleave local mixing layers, such as sliding window attention (SWA) and gated linear attention, while not encoding position (NoPE) in global attention layers has recently been shown to be successful at scale. How and why this approach works is not well-understood. In this paper, we develop an explanation of how hybrid models of this sort can implicitly encode position at global NoPE layers. Supported by both theoretical and empirical evidence, our central argument is that SWA and gated linear attention induce a recency bias in the residual stream that propagates to, and is selected by, the global attention logits. Moreover, in contrast to the implicit position encodings found in models with only global NoPE attention, in which positional information arises solely from the causal mask, the recency bias in hybrid models can be maintained across long sequences. In addition to deepening our understanding of how hybrid models encode position, these findings may provide insights for how to encode position in a way that can extrapolate to longer sequence lengths indefinitely.

Large language models (LLMs) enable agents to solve long-horizon tasks by generating a plan and then executing it in an environment. However, successful planning requires two distinct capabilities: selecting an appropriate plan for the task and executing it faithfully. Existing planner–executor systems can fail at either stage, while final task success alone cannot distinguish selection from execution failures. We therefore study the Plan Declaration–Execution Gap and introduce Planning-as-Routing, where an LLM declares one of four planning modes: Predefined, Sequential, Hierarchical, or Search, and a deterministic router dispatches the task to the corresponding pattern-specific executor. Across four benchmarks and three LLMs, we find three consistent patterns. First, generic Plan+ReAct often fails to preserve declared planning structure, especially for longer plans: across three benchmarks, only (22)–(45%) of trajectories preserve it, whereas pattern-specific executors enforce the intended structure. Second, planning-mode effectiveness varies across environments and models: Search performs best on ALFWorld, Hierarchical on SWE-bench, and the strongest pattern can vary across models within the same benchmark. Third, the largest gains come from execution: pattern-specific executors improve task success from (0.48) to (0.92) on ALFWorld and from (0.36) to (0.44) on SWE-bench Verified over Plan+ReAct. Current LLMs, however, do not reliably select the strongest mode for each task, although few-shot examples improve selection in some benchmark–model combinations. Overall, reliable agent planning requires both effective mode selection and faithful execution: routing substantially closes the execution gap, while task-specific mode selection remains open.

Chain-of-thought traces are widely read as records of how models reach their answers, informing debugging, agent auditing, and claims about reasoning. Testing this interpretation is difficult because natural-language thinking traces are rarely mechanically verifiable. We revisit it in iGSM, a synthetic grade-school mathematics benchmark designed to study thinking traces and used to support claims of learned reasoning and planning. Crucially, iGSM exposes the exact quantities and dependencies that a correct solution should use, allowing generated traces to be checked programmatically step by step and enabling us to test whether correct answers are reliably accompanied by valid traces. We first evaluate models trained exclusively on valid, minimal traces. Answer correctness and trace validity nearly coincide in distribution but decouple out of distribution: on the hardest instances, 31.6% of correct answers have invalid traces, over half of which pass all syntactic and arithmetic checks but fail semantic dependency checks. We then intervene on trace supervision. Non-minimal training traces induce non-minimal outputs, while re-asking the same problem with a different query reveals computations inherited from the original query, weakening minimality as evidence of selective planning. Shuffling tokens in 10% of training trace sentences preserves near-clean accuracy even out of distribution despite no trace passing verification. Swapped training traces likewise retain high in-distribution accuracy. We discuss the implications of these findings for chain-of-thought monitoring and interpretation in the context of AI safety.

Speech-LLMs are expensive to run, making compression important for real-world deployment. However, compressed models are usually selected using aggregate word error rate (WER), which can hide how pruning affects different demographic groups. In this work, we systematically study the effect of audio encoder pruning on SLAM-ASR for different demographic groups. Using the Fair-Speech and Common Voice datasets, we found that the pruning does not affect all demographic groups equally; the gap between best- and worst-performing groups increases in fold. These disparities appear across all three encoder scales, but only the largest model initially hides them behind aggregate WER. LoRA adaptation improves WER for every group, but benefits groups already performing well more strongly and widens for certain groups. On Common Voice English, Danish, and Dutch, accent gaps persist but do not clearly widen, showing that the fairness effects of pruning vary across datasets and must be measured directly. Our findings suggest that for pruned models, deployment decisions should include per-group WER, with the worst-performing group's error rate as an explicit criterion.

When interacting with an unfamiliar deformable material, a robot lacks prior knowledge of its physical properties and how it will respond to applied forces and motion. Rapid online identification is therefore essential for reliable manipulation. We present FORM (From Observed Response to Material laws), which identifies material properties from a single robot interaction and reuses the recovered model to plan manipulation under new actions and geometries. We use weak-form momentum balance to convert observed material motion and contact forces into linear equations in the unknown material parameters. These equations are assembled using the same material point method discretization as the forward simulator, so identification reduces to linear least-squares solves whose solutions can be used directly for prediction without refitting or conversion. Across four material classes, FORM reduces identification time from roughly 10–25 minutes for iterative baselines to 2–5 seconds, while maintaining competitive accuracy on new motions, initial conditions, and geometries. We demonstrate our approach in simulation and on hardware across four manipulation tasks: elastic rod insertion, golf putting with an elastic club, elastoplastic shaping, and target-volume pouring. In each task, the model identified from a single interaction is reused to plan new motions or manipulate a different geometry. FORM estimates elastic properties within 3.4% and elastoplastic properties within 2%, achieves 72.4–77.8% IoU in dough shaping, and keeps mean pouring error at 3.8 mL across target volumes of 60–160 mL.

Power-sharpened sampling is an inference-time alternative to reinforcement-learning (RL) post-training for enhancing reasoning in large language models (LLMs). High-probability sequences are amplified under the base model without parameter updates or external rewards, avoiding the costly optimization and jagged generalization of RL. However, this approach faces a fundamental exploration–exploitation trade-off, as % strong sharpening restricts exploration, trapping samplers in plausible but incorrect reasoning trajectories, whereas weak sharpening leaves the answer distribution diffuse. To resolve this trade-off, we introduce Parallel Power Tempering (PPT), instantiating power-sharpened LLM sampling via parallel tempering. Running multiple interacting replicas in parallel at different sharpening levels allows lower-power replicas to explore diverse reasoning trajectories and higher-power chains to further exploit higher-likelihood responses favored by the sharpened target. Specifically, we tailor \method{} to inference-time sampling by mitigating a truncation bias, identified in prior power samplers, and investigate effective swap strategies under finite memory and compute budgets. Extensive experimentation shows that \method{} substantially improves single-chain power-sharpened sampling and outperforms RL-post-trained models, producing higher-quality reasoning traces and even achieving performance comparable to frontier models.

We study local systems on line arrangements for which no admissibility conditions are satisfied. In doing so we demonstrate the existence of these anti-admissible objects in both the finite and infinite setting and discuss their relation to the combinatorial data of arrangements. We also observe the connection between anti-admissibility and smooth branched coverings and how this connection is related to the branch set being minimal in one sense and maximal in another.

Berry curvature and quantum metric of Bloch states govern a wide range of phenomena, yet unified experimental access to both remains limited. Here we show that light spatial-dispersion alters the selection rules of second-order photocurrents and responses forbidden by parity become allowed in centrosymmetric crystals without any external fields, magnetic order, interfaces, strain, or engineered symmetry breaking. The resulting response is intrinsic and its weight is set by the quantum geometry of the Bloch states. Conventional photogalvanic effects are constrained by crystal symmetry and entangle the quantum metric with shift vector contributions. The spatially-dispersive response instead isolates the quantum metric and Berry curvature in distinct polarization channels. Implementing this approach in 1T'-MoTe2 across its temperature-driven transition to Td-Weyl phase, we resolve helicity-even and helicity-odd photocurrents corresponding to quantum metric and Berry curvature contributions, respectively, from the same device. The metric-dominated response persists across both phases and exhibits a robust spectral structure reproduced by first-principles calculations and linked to momentum-resolved quantum metric hotspots. In contrast, the curvature-driven channel emerges only when inversion symmetry is broken and shows strong sensitivity to carrier doping through competing momentum-space contributions. Our results establish photogalvanic effects with spatially varying optical fields as a general route to accessing quantum geometry in materials where photon energy and electronic filling probe different parts of the excitation manifold.

We give a deterministic algorithm that solves a nonsingular linear system $Ax=b$, where $A\in\mathbb{R}^{n\times n}$ has $m$ nonzero entries and condition number $\kappa$, to any relative residual tolerance $0<\epsilon\le1/2$ using $\widetilde{O(}mn\log(\kappa/\epsilon))$ bit operations for inputs with logarithmically many bits per entry. For sparse, polynomially conditioned systems with $m=\widetilde{O}(n)$, this gives an $\widetilde{O}(n^2)$ algorithm for any inverse-polynomial accuracy, improving on the algorithm of Peng and Vempala, as sharpened by Nie, whose running time in this regime is approximately $O(n^{2.2707})$ with the best current matrix multiplication exponent, and largely closing a gap between the idealized performance of the conjugate gradient method in exact arithmetic and the running time achievable with finite-precision computation that has persisted for over 70 years. The algorithm is surprisingly simple. For integer inputs, we apply Dixon's lifting algorithm to the perturbed system $(A+I/R)x=b$ for a suitable integer $R$. After scaling, the matrix of this system is $RA+I\equiv I\pmod R$, so its modular inverse is trivial, and each lifting step needs only a sparse matrix-vector product with $A$ on $O(\log R)$-bit numbers. Fast rational reconstruction then recovers the exact solution of the perturbed system, which is an $\epsilon$-accurate solution of the original one. Normalization and rounding extend the result to fixed-point and floating-point inputs, with floating-point outputs represented using short integer significands and a common encoded exponent. A computable certificate removes the need for prior knowledge of $\kappa$.

The very high-energy ($E > 100$ GeV) afterglow emission in gamma-ray bursts (GRBs) can be explained by synchrotron self-Compton (SSC). Modeling this emission accurately requires fully numerical codes that solve the time-dependent coupled particle–photon kinetic equations while accounting for Klein–Nishina suppression. However, their substantial computational cost makes them impractical for traditional parameter inference techniques such as Markov Chain Monte Carlo (MCMC) sampling. In this work, we present a highly efficient surrogate model based on artificial neural networks (ANNs) that emulates a one-zone kinetic SSC radiation code. To train our ANN, we use a multi-dimensional model parameter grid that constitutes a sample of 100,800 spectra produced by an infinitely thin spherical blast wave propagating inside a constant density interstellar medium (ISM). The ANN reproduces the numerical spectra well, with the median relative error generally below 2 per cent across the full frequency domain. Using this surrogate framework, we perform Bayesian parameter posterior estimation via MCMC and fit the broadband GRB afterglow observations of GRB 190114C from X-rays to TeV $\gamma$-rays at different epochs. We find an energetic jet with isotropic-equivalent kinetic energy of $E_{\rm k,iso}\simeq7.2\times10^{54}$ erg moving with a coasting bulk Lorentz factor of $\Gamma\gtrsim500$ into an ISM with density $n\simeq0.1\,{\rm cm^{-3}}$. The deviation of our model light curve from observations on long timescales suggests that an ISM environment is inconsistent and a radially stratified external medium, as pointed out by \citet{Aguilar-Ruiz+26}, is preferred instead.

Turning decoder-only large language models (LLMs) into strong dense retrievers typically requires some form of retriever training. In this paper, we ask whether LLMs can instead be prompted to produce effective representations for dense retrieval given only a few in-context examples. To answer this, we introduce RICE (Representations from In-Context Examples), a simple "training-free" approach that extracts high-quality dense representations from LLMs. To do so, RICE conditions the LLM on examples that provide a shared context for query and document encoding. Our results demonstrate that RICE embeddings can substantially improve the accuracy of prompt-based LLM embeddings, establishing it as a simple method to build LLM-based dense retrievers that do not require training. We release our code at https://github.com/nourj98/RICE.

Current vision-language models (VLMs) encode visual information in dense hidden states where object identity, spatial layout, and local attributes are implicitly entangled rather than explicitly disentangled, limiting their ability to isolate and modulate the specific visual evidence required by a given language query. Inspired by sparse population coding and top-down modulation in biological vision, we introduce NeuronEye, a plug-in framework that constructs a sparse, concept-level neuron vocabulary from intermediate VLM representations and selectively activates query-relevant visual concepts during inference. NeuronEye decomposes vision-token states into an overcomplete sparse basis organized by concept-level clusters, uses the language query to activate relevant clusters and localize the patches where selected concepts are expressed, and injects the focused evidence back into vision tokens. A complementary suppression mechanism attenuates dominant perceptual directions to preserve weaker but relevant cues. All operations run in a single forward pass over a frozen VLM backbone. On Qwen2.5-VL-7B, NeuronEye raises CV-Bench overall accuracy by +3.1 with gains of +9.5 on Distance, and improves BLINK Multi-view by +8.3, with similar trends on LLaVA-1.6-7B. These results suggest that sparse neuron vocabularies can serve not only as post-hoc interpretability tools but also as active interfaces for concept-level visual reasoning.

We introduce and numerically demonstrate receiver-informed transmitter (RITX) waveform design for 200 Gb/s PAM-4 C-band direct-detection PON. Using 50 GHz optoelectronics, RITX achieves N1/E1 loss classes with FFE-Free ONU, enabling 40 km reach and 48.1%/66.7% network-wide complexity savings at 1:64/1:128 splits

Policies with similar mean returns can differ sharply in rare failures, yet estimating lower-tail conditional value-at-risk (CVaR) accurately can require many costly rollouts. When different conditional components of a stochastic workflow can be queried separately, we ask how to allocate a fixed evaluation budget to estimate a fixed policy's CVaR most accurately. We derive a tail influence for each queryable conditional law that aggregates how its uncertainty affects CVaR across every Bellman reuse. Its variance yields the fixed-design efficiency bound and the oracle Neyman allocation. Tail-Influence Sampling (TIS) estimates these influence scales from a pilot model and reallocates fresh queries toward kernels that matter most for the tail; a visitation-anchored variant protects against pilot underallocation. Under fixed dimension and a positive quantile margin, TIS attains oracle asymptotic variance and first-order MSE including pilot cost, while the anchored variant is within a factor two of the oracle. We also characterize an exact-grid regime in which tail- and mean-optimal allocations coincide. On CliffWalking, TIS reduces MSE by 41% versus learned occupancy and 76% versus complete rollouts at the same charged transition budget. In frozen language-model review workflows, anchored TIS beats an equally regularized mean-influence blend in 23 of 24 MMLU-Pro settings and reaches 2.4-3.4$\times$ lower MSE than rollouts on six-call FinQA reviews.

Backpropagation (BP) dominates deep learning but imposes a massive memory tax. For example, training OPT-30B with Adam requires $\approx$ 600GB of GPU memory (assuming batch size 8 and sequence length 2048). Alternatively, zero-order optimization (ZOO) trains in inference-mode (requiring only $\approx$ 60GB for the same model): no stored activations, no gradients, and no optimizer states. However, ZOO convergence has lagged behind BP. In this work, we evaluate two methods to close this gap. First, we show that reallocating training compute budget from many steps to large effective batch sizes with many perturbations (or probes) but fewer steps, allows 1SPSA (Spall, 1992) to outperform zero order methods like MeZO (Malladi et al., 2023) with less training compute. Next, we introduce 1.5-SPSA, adding a single "clean" forward-pass per step to 1SPSA to calculate a cheap diagonal preconditioner in probe-space, which improves convergence rate and convergence by down-weighting high curvature directions. Benchmarking on 6 post-training datasets on both Qwen3 and OPT model families, we show that 1.5-SPSA achieves State-of-the-Art results over previous ZOO solvers with much less optimization steps. For example, we train OPT-13B (for direct comparison to MeZO) and find 1.5-SPSA achieves +3.1% accuracy on SST-2 over both MeZO and BP in only 70 steps vs. MeZO's 100,000 steps. Finally, we combine an 8-bit-packing random generator, triton fused unpack/apply kernels, and distributed parallelism to achieve fast and stable training of models as large as OPT-30B in-place on commodity GPUs (e.g. A100).

Dimensional homogeneity is a fundamental constraint on physically meaningful models, requiring invariance under changes of units. We present a data-driven method for constructing surrogate models that satisfy this constraint at the level of the hypothesis class. Starting from a dimension matrix of measured variables, the method derives Buckingham $\Pi$-groups, constructs admissible dimensional prefactors, and approximates the remaining dimensionless dependence using truncated harmonic expansions on normalized invariant domains. Once the prefactor and dictionary are fixed, the coefficients are obtained from a regularized linear regression problem. We test the approach on the simple pendulum, Planck's black-body law, the double-pendulum Lyapunov field, and an experimental COBE/FIRAS black-body spectrum dataset. The results show that dimensional constraints improve conditioning, robustness to noise, and sample efficiency relative to unconstrained baselines, while the choice of dictionary becomes important in non-periodic or multi-invariant settings. The learned expressions are explicit and inexpensive to evaluate, which makes them useful as surrogate models for structured physical problems.

Risk aversion in resources could prevent misaligned AI agents from causing catastrophic harm. Misaligned but risk-averse agents would tend to favor safer strategies like making deals with humans over riskier strategies like rebelling. We train agents to be risk averse through character training, finding that persona traits provide a robust mechanism for instilling risk preferences. To do this, we construct a model constitution describing constant absolute risk aversion (CARA) over an agent's resources and instill it through on-policy distillation. Despite never seeing the benchmark's decision format during training, character-trained models are competitive with baselines trained directly on it, and generalise better than them out of distribution on two of our four models. We also modulate different aspects of the constitution, finding that token budget and model choice are the most influential aspect of character training to instill risk aversion. We conclude from these results that character training is a promising and scalable way to instil broad dispositions, which we can use to our advantage in mitigating risk from misaligned AI agents.

We develop a rich theory of dyadic-probabilistic multiresolution methods in the context of flag type singular integrals. We apply these methods to prove a full $T1$ theorem, even a representation theorem, for bi-parameter flag singular integrals. This is the first time a complete $T1$ theorem appears in a multi-parameter setting with an entangled nature; even the related recent advances with Zygmund dilations have been in the cancellative $T1 = 0$ or convolution situations. This theorem comes with a non-trivial necessity argument related to the flag type product $\mathrm{BMO}$ assumption on $T1$. We also present a version of our theorem in the cancellative tri-parameter flag setting showing that our methods are perfectly adaptable to general multi-parameter flag settings. Importantly, our $T1$ representation theorem implies weighted estimates for every flag $A_p$ weight, showing that our dyadic multiresolutions carefully retain the flag invariance of the original singular integrals. Our multiresolution methods also yield flag style paraproduct decompositions of products of functions and lead to a general and efficient method for proving commutator estimates in various flag settings.

Suppose a Hamiltonian $H$ has a unique ground state $|\psi_0\rangle$ with an eigenvalue $E_0$, and we have an estimate $\tilde{E}_0$ such that $|\tilde{E}_0-E_0|\leq\delta$, and there is a gap of at least $3\delta$ between $E_0$ and all other eigenvalues. Suppose we have a unitary $A$ available that can produce a "guiding state'" $A|0\rangle$ that has overlap at least $\gamma$ with $|\psi_0\rangle$. We show how to obtain an $\eta$-approximation of $|\psi_0\rangle$ with probability at least $1-\varepsilon$ using $O(\log(1/\varepsilon)/\gamma\delta + \log(1/\eta)/\delta)$ applications of $U=e^{iH}$ its inverse, and $O(\log(1/\varepsilon)/\gamma)$ applications of $A$ and its inverse. We give two different algorithms, one based on interleaving amplitude amplification and error-reduction in the style of [HMdW03], and one using the composition of transducers. This paper is the state-preparation follow-up to our two recent ground-state-energy estimation papers [JW26,SdW26]. Combined with the optimal energy-estimation of [JW26], our results show the claimed upper bound for ground-state preparation. The bound is optimal up to a constant factor in terms of the number of applications of $U$ and $U^\dagger$ if $\varepsilon=\eta$, as follows from [SdW26]. In one of our approaches to ground state preparation, we construct transducers for amplitude amplification and LCU that might be of independent interest.

Mixture-of-Experts (MoE) models are a compelling architecture for scaling model capacity, making them especially attractive for deployment on resource-constrained, single-GPU systems. However, this benefit is difficult to realize because expert parameters dominate memory, and token-level routing is dynamic, unpredictable, and skewed. Prior work using offloading and caching remains fundamentally reactive, as systems wait for router outputs before moving experts, leading to inefficient cache utilization and an inability to overlap transfers with compute under tight VRAM budgets. To address these challenges, we propose Mira, an algorithm-system co-design that enables high-capacity MoE inference on a single GPU. Mira shifts from a reactive to a proactive stance by coupling predictive expert management with a tailored quantization format. It introduces lightweight per-layer predictors that anticipate expert usage two layers ahead, enabling proactive prefetching. These predictions feed a two-tier HOT+STAGE GPU cache managed by token-level routing telemetry to retain frequently used experts while staging predicted ones. To minimize transfer overhead, Mira implements a custom compression for expert parameters, which reduces metadata and improves packing efficiency, while minimally degrading accuracy. Mira is implemented as a fully integrated runtime that coordinates predictors, caching policies, and quantized transfers to maximize overlap between communication and compute. Our experiments show that Mira reduces expert-induced stalls. Compared against state-of-the-art baselines, Mira achieves a 5.71x speedup in average throughput on a memory-constrained GPU. It accelerates Time-to-First-Token by 11.71x and achieves a 3.84$x average speedup in beam search inference, demonstrating its effectiveness across diverse inference scenarios.