Papers

The Okubo algebra brings together ternary gradings, integral root frames and rank-three geometry. We examine how these structures extend to the complex Exceptional Periodicity algebras. With $N=4(n+1)$, a tetracode character gives eight nonzero homogeneous components of dimension $t_n=8n+3+2^{4n}$. On a tip, a compatible grading has zero component of dimension $8n-5$ and eight nonzero components of dimension $1+2^{4n-3}$. The arithmetic behaves differently: for $n\geq2$, the lattice $D_N^+$ has no full-rank orthogonal frame of unscaled $A_2$ lattices. We exhibit failures of the Jacobi and Jordan identities and determine the derivations and full automorphism group of the ambient algebra above level one. We also give a Clifford-module proof, with the normalization fixed by root products, of the published realization of EP tips as special Vinberg $H$-algebras. This identifies a positive real form and yields explicit formulas for its cone, cubic, Cholesky coordinates and rational dual invariant. The cone is symmetric exactly at $n=1$. Its determinant-one hypersurface belongs to the known $L(8n,1,0)$ series, whose $r$- and $c$-maps give homogeneous scalar manifolds for supergravity theories with eight real supercharges.

The Key-Value (KV) cache constitutes a dominant source of memory consumption during large language model (LLM) inference, particularly in long-context and complex reasoning scenarios. Existing KV cache quantization methods have explored different compression granularities, including layer-wise precision adjustment and token-level information preservation. In practical deployment, however, the key challenge is not merely compression, but how to allocate limited quantization resources among heterogeneous precision preservation strategies under a fixed KV cache memory budget. We propose MultiAlloc, a profiling-guided precision allocation framework for KV cache quantization that adaptively distributes limited quantization resources between layer-wise precision enhancement and token-wise preservation. MultiAlloc employs lightweight offline profiling to characterize layer sensitivity and token importance, enabling adaptive precision allocation under a fixed memory constraint. Guided by the profiled memory–accuracy trade-off, it automatically derives an effective precision allocation strategy without online allocation search, and applies the resulting policy during inference. Extensive experiments on reasoning and long-context benchmarks demonstrate that MultiAlloc consistently improves over layer-wise, token-wise, and recent multi-granularity KV cache quantization methods under matched memory budgets across diverse models, including Mistral, Llama, DeepSeek-Qwen, and QwQ.

Wireless communication remains the most power-consuming operation in embedded systems. Low-power transmitters such as backscatter achieve microwatt-scale operation but produce weak signals susceptible to in-band interference and frequency-selective fading, particularly in non-line-of-sight settings. Multi-band transmission can mitigate these effects through spectral-domain redundancy rather than temporal-domain redundancy, improving reliability without sacrificing bitrate or latency. However, conventional multi-band radio transceivers require duplicated RF chains or power-hungry synthesizers. We introduce HILO, a tunnel diode-based frontend that enables dual-band operation from a single circuit. HILO inverts the conventional paradigm: rather than suppressing the harmonics inherent to tunnel diode nonlinearity, it harnesses them. An external device injection-locks the oscillator to a fundamental frequency, simultaneously stabilizing a higher harmonic and yielding two injection-locked carriers without a second oscillator or frequency multiplier. In transmit mode, HILO exploits self-oscillating mixing to modulate both carriers simultaneously; in receive mode, it uses autodyne downconversion at both frequencies. By turning an inherent nonlinearity into a feature, HILO achieves dual-band links while consuming under 210 $\mu$W.

In Intelligent Transport Systems, protecting vulnerable road users, specifically pedestrians, is a paramount challenge. The present work contributes to this field, putting forth a distributed architecture in which vehicles connected to the cellular infrastructure collect pedestrians' trajectories and fine-tune a foundation model for pedestrian trajectory forecasting via federated training. A server positioned at the edge of the cellular network is responsible for aggregating the local model's parameters from the vehicles and updating the global model's parameters. To reduce radio resource utilization, Low-Rank Adaptation is proposed; to decrease both the number and the size of updates, an increase in the number of training rounds performed by the vehicles per communication round is put forth. A novel figure of merit is then introduced to quantify the use of radio resources dedicated to Vehicle-to-Infrastructure communications as required by the federated solution. The proposed scheme delivers excellent prediction accuracy while significantly reducing the communication cost compared to alternative federated training methods. This shows that combining fine-tuning, Low-Rank Adaptation, and a reduction of the communication periodicity between the vehicles and the edge server is key to enabling a distributed approach to trajectory prediction in vehicular environments.

We show that the guaranties of the Gram-Schmidt Walk Algorithm of Bansal, Dadush, Garg, and Lovett can be achieved by an Ising model. Given vectors $v_1, \ldots, v_n$ of norm less than 1, we give a closed form for a centrally symmetric distribution on a vector $\sigma \in \{\pm 1 \}^n$ so that the signed sum $\sum_j \sigma(j) v_j$ is $1$-subgaussian. We show that the Glauber dynamics for this model mix rapidly provided that the norms of the input vectors are bounded below 1 by an inverse-polynomial. The proofs employ the theory of Lorentzian polynomials, and we use these techniques to show fast mixing bounds for other spin systems.

Combining pretrained models is a common strategy for building AI systems, whether by aligning a vision encoder with a language model or merging fine-tuned checkpoints. However, finding compatible pairs typically requires costly empirical search, as compatibility is known only after alignment or merging. We propose COMPASS (COMPatibility ASsessment Score), a theoretically motivated diagnostic that estimates whether a model pair will be compatible prior to alignment or merging. Building on the observation that representational convergence is most robust at the level of local neighborhoods, COMPASS decomposes model compatibility into two cheap-to-compute axes: a pair-specific ease, defined as the $k$-NN overlap between the two encoders, and a paradigm-level ceiling, capturing the maximum overlap their training paradigms allow. Together, these two axes provide a ranking of candidate model pairs and prescribe how to act on each pair: (i) prioritize pairs that already agree and whose paradigms are compatible, (ii) invest additional compute on pairs with compatible paradigms but low initial agreement, (iii) switch the pretraining paradigm when it cannot support sufficient agreement, or (iv) deprioritize pairs that score poorly on both axes. We apply COMPASS to $72$ cross-modal alignment experiments and $392$ task-arithmetic model merges and show that compatibility estimates by COMPASS strongly correlate with downstream success, achieving average Pearson correlation of $0.91$ on cross-modal alignment tasks and $0.70$ on model merging.

A robot's world model must remember objects that leave the camera's view. FloWM, a learned world model, keeps them in a spatial grid of features that it moves with five built-in velocities. A node memory instead keeps each object's position and velocity as numbers. We compare them in FloWM's own block world, with an oracle-fed Kalman tracker as the node memory. How the grid is read changes its score: a single-cell probe finds 66% of out-of-view blocks, while FloWM's own probe 89%. FloWM also scores 8 points higher in view although no frame is shown, which we attribute to its write-back of its own predictions. Out of view, the tracker reaches FloWM's range in 14KB against 5.6MB, with no probe. On diagonal motion, outside its five velocities, FloWM finds 11% of blocks even after fine-tuning, while the unchanged tracker keeps 93%. Faster blocks defeat both until one more allowed speed takes the tracker to 94%, where FloWM's built-in shifts would need 25 copies of its grid. A learned node memory must still replace the oracles and handle velocity under noise, long gaps, and the bounce.

For a graph G of order n with adjacency eigenvalues lambda_1(G) >= ... >= lambda_n(G), the cospectrality of G within the set G of all graphs of order n is the smallest spectral distance from G to another graph of G. Abdollahi and Zakeri conjectured that for every n >= 4 the cospectrality of the complete tripartite graph K_{n,n,n}, both in the Manhattan and in the Euclidean spectral distance, is attained precisely at K_{n-1,n,n+1}. We show that both conjectures are false for every n >= 4, that is, in the whole range in which they are stated. The counterexample is the graph H_n obtained from K_{n-1,n,n} by adding a vertex adjacent to the part of cardinality n - 1, and it is the natural generalization of the graph which the authors themselves exhibited for n = 3 and considered to be exceptional. We determine the spectrum of H_n in a closed form, and we show that the two spectral distances tend to 1 and to 1/2 respectively, instead of to (2*sqrt(3))/3 and to 2/3 as conjectured. On the other hand, we show that in the Euclidean distance the conjecture becomes asymptotically true when the competing graphs are restricted to complete multipartite graphs, so that it fails because a graph of rank four beats the conjectured minimizer.

The development of a digital twin brings together many stakeholders and technical components. We have previously investigated the reporting of the conceptual architecture for these digital twins as an artifact for discussion. However, we find that the activity of modeling the digital twin for visualization and consensus-building can be quite tedious and time-consuming. In this article, we explore the automation of model generation using large language models, targeting the model required for digital twin reporting. Our approach is designed to ingest digital twin documents and output both the conceptual architecture visualization and a reporting page for that digital twin. We first extract from the input the key details aligning with our twenty-one-characteristic Digital Twin Description Framework described in previous work. Then, we generate a description model in the Ontological Modeling Language, representing the digital twin as a constellation of models, data, enablers, and services. We utilize refinement loops with large language models acting as judges and ontological reasoning to increase artifact quality as measured by our metrics. We investigate how architectural and parameter choices affect artifact quality, such as how refinement loops enable local large language models to produce sufficiently high-quality results comparable to larger models. We also detail insights and lessons learned useful for practitioners, such that they can integrate our techniques to accelerate their digital twin reporting or for other model generation tasks. These insights include the use of medium-sized local models (around 20 billion parameters), the avoidance of large language models as judges and clustering for characteristic extraction, and the recommendation of at least two reasoner loops for Ontological Modeling Language refinement.

Recent studies investigate the weight geometry through its spectral structure, which characterizes how the weights transform different input directions. Within this view, supervised fine-tuning (SFT) is shown to induce dense updates that perturb the spectral geometry of pre-SFT weights along their principal directions, potentially disrupting the model's prior knowledge. These observations motivate using the geometry of pre-SFT weights as a reference for refining learned SFT updates. We study this perspective as Geometric Calibration and develop SPACE Subspace Projection for Adapted Checkpoint Enhancement), a lightweight post-hoc method that selectively reverts SFT update components within the principal subspace of the pre-SFT weights while preserving those in its orthogonal complement. SPACE is a data-free, training-free method that requires only the pre- and post-SFT checkpoints. We evaluate SPACE on Qwen2.5, Qwen3, Qwen3.5, Llama-3.1, and Olmo-3 models ranging from 2B to 14B, across mathematical, coding, and medical SFT, as well as several SFT variants. Overall, SPACE mitigates out-of-domain (OOD) capability regression while further improving in-domain (ID) performance over the uncalibrated SFT checkpoints. For math SFT, SPACE yields average ID/OOD gains of 2.85/2.26 points on Qwen2.5-7B, and 2.41/1.52 points on Qwen3-14B-Base, respectively. These results highlight how the geometric relationship between SFT updates and pre-SFT weights shapes the adapted model's capabilities and, more broadly, motivate geometry-aware parameter updates for continual model improvement.

Transients in galactic nuclei arise from distinct processes, only some of which trace the supermassive black hole (SMBH). These include tidal disruption events (TDEs), changing-look active galactic nuclei, Bowen fluorescence flares (BFFs) and ambiguous nuclear transients, alongside supernovae that appear nuclear but are unrelated to the SMBH. Reliable classification requires spectroscopy, which will not scale to the alert volumes of the Legacy Survey of Space and Time (LSST). We aim to characterise the population of nuclear transients, to identify early observables capable of distinguishing SMBH-related flares, and TDEs in particular, from the dominant supernova background, and to assess the biases this selection introduces. We implemented a real-time filter on the Lasair broker, selecting transients from the Zwicky Transient Facility (ZTF) alert stream by nuclear coincidence with the host galaxy, with no photometric cuts, to retain SMBH-related flares in both quiescent and active hosts. The filter ran over 16 months, with candidates reported for classification through ePESSTO+ and other facilities. The filter returned 476 candidates, of which 202 were spectroscopically classified, yielding predominantly supernovae, 10 confirmed TDEs (5%) and one BFF. The mean g-r colour and the rise time separate TDEs from the supernova background. Our filter recovers 10 of the 25 TDEs classified in the same period and declination range; most misses are technical or observational rather than physical. Simple real-time filtering combined with basic photometric criteria can already isolate TDEs efficiently from nuclear transient alert streams, and high completeness is achievable. In the LSST era, where samples will be predominantly photometric, selection bias will become as important as contamination, and retaining flares in active hosts is necessary if unusual events are not to be excluded.

Solomonoff induction is a general solution for sequence prediction that started the field of algorithmic information theory around 1960. Let $M$ be the universal semimeasure. After observing a string $\omega_1 \cdots \omega_{n-1}$, it predicts the next bit $\omega_n$ to be $b$ with conditional probability proportional to $M(\omega_1 \cdots \omega_{n-1} b)$. Thus the error of this probability is \[ e_\omega(n) = 1 - \frac {M(\omega_1 \cdots \omega_{n-1}\omega_n)} {M(\omega_1 \cdots \omega_{n-1} 0) + M(\omega_{1} \cdots \omega_{n-1} 1)}. \] If $\omega$ a computable infinite sequence with a self-delimiting description of at most $k$ bits, then $\sum_n e_\omega(n) \le k\ln 2+O(1)$. Lattimore, Hutter and Gavane consider the problem of predicting computable patterns in a sequence, for example, the pattern of repeated bits $\omega = 00\,11\,00\,00\,11\,00\cdots$ They show that the error probabilities of the bits fixed by a computable pattern have limit zero, for example, for repeated bits, one has $\lim_n e_\omega(2n) = 0$. We show that for some computable pattern, the sum of $e_{\omega}(n)$ over positions $n$ from the pattern is not bounded. However, the sum of squares $(e_\omega(n))^2$ is bounded exponentially in the program length of the pattern. It is also shown that bits of $\omega$ that are fixed by a computable classification function $f:\{0,1\}^* \rightarrow \{0,1\}$, converges faster: the sum of $(e_\omega(n))^2$ is bounded by a polynomial in the program length for programs whose runtime is bounded by any fixed computable time bound.

We demonstrate how to build a robust phase space electronic Hamiltonian $\hat{H}_\text{PS}(\boldsymbol{R},\boldsymbol{P})$ that depends on nuclear position $\boldsymbol{R}$ and nuclear momentum $\boldsymbol{P}$ in the presence of ionic pseudopotentials. In particular, we show that in order to account for the non-local component of a pseudopotential while also conserving linear and angular momentum, one is forced to introduce a non-local one-electron operator $\hat{\boldsymbol{\Gamma}}^\text{nl}$ that couples electronic and nuclear momenta together. To test the validity of our ansatz, we derive a generalized form of Nafie's exact equality (which relates electronic momentum and electronic position) so as to include the presence of pseudopotentials. We then benchmark our proposed phase space electronic structure theory against this generalized Nafie-like result for a diverse set of diatomic molecules spanning a wide range of elements. We find excellent agreement across this ab initio test set, highlighting the strength of our method in capturing meaningful electronic momentum beyond the Born-Oppenheimer framework.

We consider an infinite-horizon discounted dynamic programming (DP) problem for a countable-innovation belief-state model. The model is a surrogate for a linear-Gaussian dual control problem involving an unknown parameter vector and Gaussian observation noise. The surrogate preserves the first two moments of the Gaussian innovation and the resulting posterior second-moment structure. We allow unbounded belief and control spaces and nonnegative stage costs with quadratic growth in the posterior mean and covariance. Using a posterior-moment weight, we show that the Bellman operator is a contraction in a weighted sup-norm space. We characterize the optimal cost as the unique solution of the Bellman equation in this space, establish the existence of optimal stationary policies. We further prove weighted sup-norm convergence of value iteration, policy iteration, and optimistic policy iteration under vanishing approximation errors. The convergence results under vanishing approximation errors rely on general weighted sup-norm contraction properties and are applicable beyond the particular dual control problem considered here.

We study collective charge excitations in pseudospin-1 triple-point semimetals within the random-phase approximation, considering both the linearised model with a flat-band and its quadratic-corrected counterpart. We analyse their density response, Drude weights, screening, plasmon dispersion and damping, particle-hole continua, and Friedel oscillations from the long-wavelength to the arbitrary-momentum regime. The quadratic correction renders the flat-band dispersive and endows it with a Fermi surface, thereby affecting the overall response. Comparisons with Weyl and Hopf semimetals reveal how bandstructure and quantum geometry jointly govern collective charge dynamics. While the Drude weights are determined by the Fermi surface and band-velocities, interband screening, plasmon dispersion, and Friedel oscillations reflect the quantum geometry of the eigenstates.

We present the design methodology, implementation, and data products of the Energetic Particle Detector (EPD) instrument on-board the Electron Losses and Fields Investigation (ELFIN) dual SmallSat mission. ELFIN was designed to study the time-evolution of energetic particle distributions in Earth's magnetosphere, having operated in polar Low Earth Orbit (LEO) from 2018 to 2022. Each satellite's instrument payload contained a pair of detector heads to sense differential-directional fluxes of 50 keV to $\sim$5 MeV electrons (EPDE), and 50 keV to $\sim$2 MeV atomic ions (EPDI), with an energy resolution better than 50% ($\Delta E/E<0.5$). The satellites were spinning with a nominal period of 2.8 s in a plane containing Earth's background magnetic field, with particle counting intervals subdivided into 16 consecutive spin sectors. Each EPD was paired with a three-axis Fluxgate Magnetometer (FGM) sampled at 80 Hz for local pitch-angle determination. Each detector head operated on the principle of pulse-height analysis (PHA) in solid state media, collimated by a rectangular 22.5$^\circ$ field of view and entrance aperture. The EPDE contained a stack of 6 silicon detectors (0.7 cm total thickness) with 0.15 cm$^2$ str geometric factor, with ion contamination mitigated by an aperture foil and digital coincidence logic. The EPDI contained a stack of 2 silicon detectors (0.1 cm total thickness) with 0.03 cm$^2$ str geometric factor, with electron contamination mitigated by a magnetic broom stage and digital anti-coincidence logic. The total assembled mass, volume, and power required for the EPD detector heads and circuit boards were 939 g, 10$\times$9.8$\times$8.4 cm$^3$, and 2.3 W, respectively. We describe each EPD design element alongside instrument data products and processing.

Interactions happen universally and spontaneously in daily lives. Studying involvement in interactions helps us analyze who can influence who and has a wide potential in applications. Specifically, we consider conversational involvement in free-standing conversations. We study two operationalizations of an FCG: F-formations and conversation floors, and propose that current assumption that F-formations capture single conversations is insufficient. To illustrate how different implementations could impact the detected F-formations, we employ three analyses. First, we propose that speaking status can be used for estimating conversation floors, and leveraged it to analyze floors within F-formations. Second, we analyze spatial characteristics of the detection results by applying different feature sets on chosen baselines, and find that groups resulting from head features are more likely to be subsumed by groups detected using other features. Finally, we do a joint analysis which combines the spatial features and floor patterns in the conversation. We observe that certain pipelines can detect groups with single floors from upper body features, while retaining F-formations with lower body features. We conclude that a more detailed theory and framework is needed to holistically demonstrate conversational involvement within interactions.

The symmetric exclusion process (SEP) is a paradigmatic model of interacting particle transport. Its current–density correlations are governed by an infinite many-body hierarchy of equations. Only recently, this hierarchy was found to collapse at large scales onto a single closed equation. Is this remarkable simplification created by coarse graining, or does it reflect a deeper property already present in the microscopic dynamics? Here we show that the second scenario is realized. At arbitrary time on the lattice, the entire hierarchy collapses onto a single linear equation which is exactly equivalent to a persistence problem for a single auxiliary random walker. Thus an interacting many-body problem reduces exactly to a genuine one-body problem before any scaling limit is taken. This reduction determines the complete finite-time correlation profile, including during nonequilibrium relaxation. More broadly, the microscopic operator uncovered here opens a route to more general correlation functions in the SEP, and may point to a general organizing principle for nonequilibrium interacting particle systems.

Relying on manipulable characteristics to target the allocation of resources is fraught with difficulties. Naively optimal rules lead to falsification and allocative inefficiency. Optimizing the rule for allocative efficiency while accounting for falsification typically induces falsification, at a heavy cost to the agents. Moreover, falsification generates negative externalities. We characterize optimal falsification-proof rules under a broad range of falsification technologies. We also provide an honesty condition under which they solve the unconstrained problem of a planner who maximizes a weighted sum of allocative surplus and agents' welfare.

Pretraining generalist Earth observation foundation models requires data that combine several sensors, varied temporal sampling and, increasingly, text, yet open datasets rarely provide all three in one consistent, easily accessible form. We introduce MajorTOM:Elliot Pretrain, a collection of 279,166 tiles of 10 km drawn from the Major-TOM grid by clustering AlphaEarth embeddings. Each tile stacks Sentinel-2 L1C, Landsat-8/9, Sentinel-1 RTC, Copernicus DEM and ESA WorldCover on a shared 1056x1056-pixel, 10 m grid, complemented by cloud masks, OpenStreetMap entities and ERA5 weather. The tiles are partitioned into three temporal regimes, Monotemporal (250,000 tiles, one acquisition), Monthly (12,500 tiles, twelve acquisitions spread over the annual cycle) and Burst (16,666 tiles, six acquisitions within 30 days), and are released as 6.3 TB of Cloud Optimized GeoTIFFs indexed by TACO v3 Parquet metadata, a standard that allows cloud streaming, efficient data access, and filtering before any pixel is read. A companion library derives sensor-tagged fact sheets, captions and 16 families of vision-language tasks from these layers at load time. We test our design choices in short pretraining runs of OlmoEarth-Base. First, a 25% subset of Major-TOM Core-S2L2A curated with AlphaEarth embeddings matches or exceeds the full corpus on 8 of 9 benchmarks. Second, on Elliot-Pretrain, adding Landsat-8/9 improves or matches Sentinel-2 only pretraining on every benchmark. Third, using DEM and WorldCover as prediction targets during pretraining further improves 8 of 9 benchmarks, while giving the same maps to the encoder as inputs degrades 5 of 9. Fourth, Sentinel-1 helps on 7 of 9 benchmarks, particularly on benchmarks with radar inputs. Fifth, rule-based captions match a small language model at no cost. The dataset is openly available at https://source.coop/major-tom/elliot-pretrain.

We study the role of design smoothness in the minimax estimation of conditional average treatment effects at a fixed covariate point. For design densities bounded above and away from zero, without further regularity, we derive upper and lower risk bounds with an arbitrarily small gap in the convergence-rate exponent. Under uniform design, we obtain matching upper and lower bounds at interior points in the regime of low nuisance smoothness. These results show that rough covariate designs can lead to slower rates than uniform designs, even under the same smoothness assumptions on the treatment effect and nuisance functions, highlighting the role of the covariate distribution in pointwise causal estimation.

Long legal documents are often represented as single retrieval units, which can dilute relevant content and limit retrieval effectiveness. This study investigates structural segmentation as a document representation strategy to improve Brazilian legal document retrieval. Using the hierarchical structure of legal acts, we represent each document as a collection of chunks. We evaluate four representation strategies: a multi-layered hierarchy representation and three simplified versions based on core chunks (articles and non-normative document components), with varying contextual details. We test these strategies on two publicly available Brazilian legal datasets containing normative acts and legislative proposals, using both lexical and dense retrieval models. Results show that structural segmentation improves dense retrieval compared with whole-document indexing, despite substantially increasing the number of indexed units. However, it does not consistently benefit lexical retrieval. Finally, we find that full hierarchicy representation is not necessary: core chunks enriched with document metadata yield comparable or better results.

Accurate uncertainty quantification is critical for many time series forecasting applications, and recent studies have increasingly adopted generative models to capture predictive uncertainty. Existing approaches often combine deterministic forecasting with generative modeling to improve predictive performance. However, their joint training is typically unstable because the deterministic model is embedded within the generative process, resulting in deep computational graphs and changing the probability transport path. In this work, we propose DV-Flow, a unified flow-matching formulation that incorporates the deterministic predictor as a parallel velocity component rather than as the endpoint of the transport path. This design enables stable end-to-end optimization while subsuming several existing formulations as special cases, allowing direct comparisons among them. Extensive experiments on six real-world datasets demonstrate that DV-Flow consistently improves probabilistic forecasting performance over strong baselines. Our code is available at https://github.com/tufts-ml/dv-flow-time-series.

For a locally finitely generated Grothendieck category, we characterise the Gorenstein injective covering property by several equivalent conditions, including closure under coproducts. To complete this characterisation, we construct a countable commutative Noetherian Cohen–Macaulay local ring of dimension one for which this property fails, answering negatively Iacob's question Question 1 whether character modules of Gorenstein injective modules over left Noetherian rings are Gorenstein flat. Using this characterisation, we prove that for Noetherian schemes the covering property is Zariski-local. Moreover, assuming that $\mathcal{GI}(\mathrm{QCoh}(X))$ is a covering class, we establish compatible adjunctions and recollements for homotopy categories of injectives and totally acyclic injective complexes under open restriction. However, this property is not stalk-local: we construct a commutative Noetherian ring $S$ such that $\mathcal{GI}(S_{\mathfrak{p}})$ forms a covering class for all prime ideals $\mathfrak{p}$, but $\mathcal{GI}(S)$ do not form a covering class.

We extend Uhlenbeck's classical results on the generic properties of Laplacian eigenfunctions. In particular, we find a residual set of $C^k$ domains in $\mathbb{R}^n$, $k > n$, such that the nodal set of any Dirichlet eigenfunction intersects the boundary orthogonally along a $C^{k-1}$ embedded submanifold, whenever the intersection is non-empty. This is achieved by analyzing the boundary asymptotics of Dirichlet eigenfunctions via homogeneous harmonic polynomials and comparing their respective nodal sets. Along the way, we give a complete proof that generic Euclidean domains have simple Dirichlet eigenfunctions with zero as a regular value in the interior and zero as a regular value of the boundary normal derivative. In the special case of planar domains, a different argument provides one-parameter families of perturbed domains with the desired properties.

We prove the Labastida–Mariño–Ooguri–Vafa conjecture for oriented links with arbitrary integer framings. Consequently, the framed reformulated invariants have finite integral LMOV expansions for every integer framing vector.

An embodied agent must prioritise among competing bodily needs. In active inference, it can respond to an urgent need by increasing the precision of information about that need or by increasing its preference for outcomes that relieve it. We compare these two interventions, separately and together, in a foraging gridworld with three lethal needs, and ask how each changes survival, perception and the body model the agent learns. Precision sharpens interoceptive posteriors and improves survival. Preference reweighting keeps bodily states further from their lethal boundaries and changes the states from which the agent learns, so its learned model covers fewer need levels, with lower quality across all levels but slightly higher quality on the levels it visits. An experiment on 72 further layouts does not establish the predicted preference benefit on difficult layouts, but both interventions improve average survival there and their interaction is positive. Survival alone therefore gives an incomplete account of how a model prioritises needs and learns about its body.

Searching text-rich knowledge graphs requires following relations while examining textual evidence. Predefined graph interfaces constrain what evidence agents can access, even when they write code to combine tool calls or process retrieved subgraphs. We propose direct knowledge graph interaction (DKGI), a harness in which language model agents create graph access tools directly over complete node and edge files. The agent writes Python code to follow relations, combine node sets, and select textual evidence, interleaving execution with shell search and file inspection. This lets agents process large node sets in bulk while returning selected text for the model to assess. Execution feedback guides tool creation and revision, while the evolving tools determine what evidence the agent gathers next. On benchmark datasets spanning three domains, training-free DKGI exceeds the strongest published baseline by at least 6.7 Hit@1 points on every graph, even with a minimal harness. Controlled ablations show the benefits of multi-turn programming over shell-only access and predefined graph tools, while trajectories show agents revising code to extend searches or address errors. These findings highlight the value of allowing tool creation and tool use to co-evolve during graph search. Our code and data are available at https://github.com/leopoldwhite/DKGI.

Visual agents must turn video observations into timely decisions to track progress and choose what to do next. Building on the emerging System One paradigm, we introduce VideoJev, a family of models that cast video understanding and interaction as structured decision tasks. We adapt pretrained multimodal large language models (MLLMs) by replacing autoregressive answer decoding with a shared head that scores temporal intervals and textual options against video evidence. These scores yield event spans or answer choices, unifying temporal grounding and multiple-choice video question answering. This combines the semantic flexibility of MLLMs with efficient decisions that agents can use directly. As an interaction unfolds, new goals and intermediate results prompt further queries about the same visual history. VideoJev therefore reuses visual computation through Cached inference for queries as they arrive and Joint inference for multiple queries in a single forward pass. Across three temporal grounding benchmarks, VideoJev-4B and VideoJev-35B-A3B improve mean mIoU over their backbones by 6.7 and 10.8 points, respectively, with measured inference speedups of $2.8$-$3.1\times$. On four video QA benchmarks, both achieve performance comparable to their backbones in Thinking mode, with measured inference speedups exceeding $100\times$. These results offer a unified, reusable decision interface for composing structured visual judgments into complex, open-ended workflows.

Controlling an acting LLM agent means deciding, at each step of a long-horizon task, whether to trust its next action, abstain, or hand off to a human. That decision needs a per-step confidence signal predicting whether the current rollout will eventually succeed. The agent's own self-reported verbalized confidence is the natural candidate, but existing reinforcement learning methods calibrate it against the correctness of a decision at the current step. We propose a method to calibrate it against the eventual outcome of a multi-step episode: under GRPO, the group of rollouts for a task supplies success labels, and a proper scoring rule scores each step's confidence against the realized outcome. In offline RL on recorded trajectories of a Qwen2.5-7B agent in ALFWorld, TextWorld, and WebShop environments, the AUROC of step confidence against episode outcome rises from near chance to 0.68-0.85, and the top-10% of steps the agent is most confident about succeed ~4.3x more often than average. In online RL on the live ALFWorld agent, four calibration rewards improve early-step AUROC, expected calibration error goes from 0.42 to below 0.12, and selective execution improves over both the untrained agent and a format-only RL control, without degrading task success. We also introduce an evaluation protocol that separates episode depth, task difficulty, and attempt-level foresight, which shows where the gain lies: the trained agent recognizes from its first step which tasks it will fail, while telling a succeeding attempt from a failing one at the same task is harder, with some early-window signal emerging on TextWorld.