Papers

Multi-teacher on-policy distillation (MOPD) aims to combine the strengths of RL-trained teachers in a single student, but how teacher signals affect parameter changes remains underexplored. We study Qwen3-1.7B with four domain teachers trained with RL from the same initialization as the student, comparing gradients, optimizer updates, and task learning curves, with additional SmolLM3-3B diagnostics. We find that several factors influence teacher signals. First, loss averaging implicitly weights responses: token averaging favors longer responses, and equalizing domain contributions retains this weighting within domains. Second, Adam's first moment reduces differences in parameter updates: the cosine similarity is 0.83 between teachers and 0.96 between averaging rules, despite differences in raw gradients. Third, BF16 rounding hides small changes: about 97% of FP32 master weights differ from initialization, but only 7–11% of BF16 weights do. Finally, the top-64 intersection KL gradient closely matches Qwen's full-vocabulary gradient, but the effect on task performance depends on averaging: mathematics accuracy is 2.6 points higher than with sampled-token policy-gradient (PG) under response averaging and 2.1 points lower under global token averaging.

We study the problem of learning the dense Sachdev–Ye–Kitaev (SYK) Hamiltonian from copies of its Gibbs state. Existing algorithms for Hamiltonian learning typically rely on geometric locality or bounded interaction degree and therefore do not apply to SYK, where each quartic interaction overlaps with $\Theta(n^3)$ others. We show that this obstruction can be overcome by exploiting the random mean-field structure of the model. At any constant temperature, we prove that with high probability over the SYK couplings, the entire Hamiltonian can be learned to inverse-polynomial accuracy using polynomially many samples. Furthermore, when the inverse temperature is restricted to be a sufficiently small constant, we construct a quasipolynomial-time learning algorithm which is qualitatively different from the sample-efficient algorithm.

In 1993, Ruzsa showed that for every $k \geq 2$, there exists a constant $C$ such that every subset $A \subseteq [N]$ of size at least $C N^{1/k}$ contains $2k$ distinct elements $a_1, \ldots, a_k, b_1, \ldots, b_k \in A$ such that $a_1 + \cdots + a_k = b_1 + \cdots + b_k$. We strengthen this result by proving that the elements $a_1, \ldots, a_k, b_1, \ldots, b_k$ can be chosen to have the additional property that $\{a_1, \ldots, a_k, b_1, \ldots, b_k\}$ has $2^{2k}-1$ distinct subset sums, with the only coincidence being that $\{a_1, \ldots, a_k\}$ and $\{b_1, \ldots, b_k\}$ have the same sum. Our proof also applies to any finite Abelian group of odd order $N$, and it provides a corresponding supersaturation result: that whenever $|A| \geq CN^{1/k}$, there are at least $\Omega(|A|^{2k}/N)$ choices for $a_1, \ldots, a_k, b_1, \ldots, b_k \in A$ satisfying these properties. We prove a slightly weaker statement for Abelian groups of even order. We also apply our methods to the vector space setting and prove the following $\mathbb F_q$-analogue of the Bondy-Simonovits Theorem on the extremal number of even cycles in graphs: Any rank-$n$, simple, $\mathbb F_q$-representable matroid with no circuit of size exactly $2k$ has size at most $C q^{n/k}$ for some constant $C$ depending only on $q$ and $k$. When $q=2$, this is best possible up to the constant $C$ for all $k \geq 2$. Our methods also apply to the original graph setting and give a new proof of the Bondy-Simonovits Theorem and its supersaturation version.

Correlations across channel uses can improve quantum communication rates, making optimization over arbitrarily large blocks a central difficulty in determining quantum capacity. We show how full permutation invariance limits this advantage for every finite-dimensional memoryless channel. The optimized coherent information per use converges to the single-use maximum and consequently attains its supremum at a finite block length. Thus finite-block superadditivity remains possible, while the asymptotic optimization reduces to a single channel use. We also establish a strong converse for pure-source entanglement generation with permutation-invariant inputs: at any fixed rate above the single-use coherent-information maximum, the fidelity tends to zero. Beyond these communication bounds, we identify a common structure underlying completely bounded norms and the sandwiched Rényi channel quantities governing discrimination against a replacer and entanglement-assisted communication. De Finetti reduction and permutation covariance yield systematic alternative proofs of their known multiplicativity and additivity results within a shared variational framework. We further show that, for permutation-invariant inputs, correlations cannot sustain an asymptotic reduction in output entropy per use below the single-use minimum. This entropy limit holds for Rényi orders greater than one and for the von Neumann entropy, extending the role of symmetry from communication bounds to the control of output entropy.

Protein function annotation needs to know which predictions to distrust, not only what a model predicts. We ask whether tissue-specific interaction structure carries that information. Our candidate signal is effective resistance, used previously to relieve over-squashing by rewiring. Across 24 tissue-specific interactomes it is dominated by inverse degree, and the degeneration deepens as the co-expression filtered network grows, with a Spearman correlation of -0.955. The residual departure from that limit exceeds degree-preserving null graphs in all 24 networks. Controlling for predictive entropy, degree, annotation cardinality, local structure and feature-only difficulty, the residual explains additional per-node loss in 19 of 24 held-out networks once a permutation floor is subtracted, at every depth, and the effect strengthens monotonically with depth. The increment reaches 0.37% of the variance the controls leave unexplained, 5.6 times a permutation floor, against 1.5 times when the model is retrained in a degree-preserving null world. Selective prediction improves negligibly. The signal is reproducible; degree degeneration bounds it.

We show that the canonical embeddings of the Jiang–Su algebra $\mathcal Z$ into the universal unital free product $\mathcal Z \ast_{\mathbb C}\mathcal Z$ are not approximately unitarily equivalent. This answers a question appearing in one of the $99$ problems list of Schafhauser, Tikuisis, and White. By contrast, we prove that any two such embeddings into a selfless $\mathrm{C}^\ast$-algebra are strongly asymptotically unitarily equivalent.

Ablate a component of a language model, and other components often appear to adjust and compensate. This phenomenon, termed self-repair, has been observed repeatedly, but its mechanism remains unclear. The most systematic study to date concluded that self-repair is noisy and unlikely to have a single explanation. We argue that it has one: a gain already present before any ablation. Any intervention on a causally important component can be viewed as a point on a coordinate axis $\lambda$, the signed strength of a counterfactual contrast. Hence, conventional ablation methods are uncalibrated points on this axis. We show that the causal repair response for a fine-grained unit $r$ is governed by an affine law, $E_r(\lambda)=\mathrm{own}_r+\gamma_r\lambda$. The slope $\gamma_r$ is a fixed coefficient that consistently influences the model, with or without ablation, and its sign determines whether the unit counteracts or reinforces the removed signal. On a factual-verdict task across four models from distinct families (Gemma, Qwen, LLaMA, and Mistral), we identify components including MLP neurons, OV neurons, and singular directions that follow this affine law, 68 of 81 downstream directions in all. Moreover, we can anticipate the magnitude of $\gamma_r$ from the fixed weights. On the IOI circuit of GPT-2 Small, seven of the ten heads the intervention can reach follow the law, and all seven are counterweights. From this perspective, what may appear as self-repair is a counterweight performing its usual operation when the contrastive signal emerges at the core.

The power and limitations of classical simulation are central to understanding quantum computational advantages. A leading simulation paradigm is based on coherent decomposition into classically tractable free states where the decomposition rank determines the simulation complexity. Proving strong lower bounds on this number is a notoriously difficult and mathematically rich problem, as exemplified by the qubit stabilizer rank problem. Here, we study the Gaussian version of this problem in both bosonic and fermionic systems and establish robust exponential lower bounds on Gaussian rank. In particular, we prove that for every pure non-Gaussian state on finitely many modes, with definite parity in the fermionic case, the approximate border Gaussian rank of its tensor powers grows at least exponentially at any fixed norm error below one. Our proofs combine reduction to four modes with Majorana spectral bounds for fermions, and Gaussian postselection with an entropy-based rank bound for bosons. As concrete examples, we derive explicit exponential lower bounds for the four-mode fermionic GHZ state and the bosonic single-photon state. The bosonic results require no assumption on the energy of the target state. Our results show that non-Gaussianity universally entails exponential Gaussian decomposition complexity, setting fundamental limitations on decomposition-based classical simulation of bosonic and fermionic systems.

The Ahlfors–Weill construction explicitly extends a univalent function $f$ with Schwarzian norm less than $1/2$ to a quasiconformal homeomorphism of the Riemann sphere, an extension that can be understood geometrically through Epstein surfaces. For asymptotically conformal curves, the uniformization map can be extended to a larger disk, and Loewner theory can be used to verify that this extension is quasiconformal. In this paper, we construct a local quasireflection with such an extension. Using this local quasireflection, we modify classical estimates of Ahlfors and show that domains bounded by asymptotically conformal curves have asymptotically similar hyperbolic and quasihyperbolic metrics. Furthermore, by combining these estimates with a geometric reinterpretation of the extension through Epstein surfaces, we show that the Epstein-Poincaré surfaces of the complementary domains are arbitrarily close to one another near the curve.

Robots operating in the physical world will increasingly need to coordinate with other robots, particularly in manipulation tasks where an object may be too large or heavy for a single robot to carry alone. Physical limitations caused by hardware degradation or actuator faults can restrict the actions a robot can reliably execute, yet these limitations may be unknown to its partner. We study whether a helper can infer a robot partner's physical constraints from observing it coordinate with another robot, then use the inferred capability to coordinate with the same partner on a new task. This is difficult because a demonstration shows what the constrained robot did, but not what it could have done. In physically coupled tasks, the other robot may also compensate for its limitations, making those limitations difficult to identify from the constrained robot's behavior alone. Our key insight is that these constraints shape the joint behavior of the team, making the actions of both robots informative about the constrained partner's capability. We introduce Watch, Infer, Coordinate, a benchmark spanning three physically coupled manipulation settings, together with an inference approach that scores candidate constraints using observed joint behavior. Across all three settings, our method substantially improves constraint inference and zero-shot coordination, approaching an oracle with access to the true constraints.

We present a technique for computing Drell-Yan lepton pair production at particle-level that achieves N$^3$LO and approximate N$^4$LL$'$ accuracy at small to moderate transverse momentum, tree-level precision for $Z+4$, $5$, and $6$ jets, and approximate NLO EW precision at high transverse momentum. A crucial non-perturbative input, the Collins-Soper kernel, is obtained from continuum-limit lattice QCD results. High-precision theory results are recast into strictly positive event weights using an information-theoretic approach based on the maximum entropy principle.

We propose an extension of the cosmological-state construction of Antonini, Sasieta and Swingle (AS$^2$) to three or more holographic CFTs. Each CFT resides on the asymptotic boundary of an AdS page, and all pages are glued along a common interface by imposing the multiway junction conditions. The associated states are prepared by Euclidean evolution with a multilinear insertion. In appropriate heavy insertion limit the bulk geometry develop a closed universe in the center and we refer the state in this limit as a booklet cosmological state. Extending the effective Gaussian assumption used in AS$^2$, we model the three-page insertion by a circular complex Gaussian random tensor, yielding a tripartite Haar state in flat energy windows. In this Gaussian model of the cosmology-to-boundary map, each arm is a network branch associated with one boundary CFT. In the simplest example of three pages with three equal output Hilbert-space dimension $b$, we show that a prescribed code of dimension $K$ is approximately recoverable from any two arms, with vanishing error and high probability as $K/b\to0$.

Quantum impurity models are paradigmatic models of interacting quantum matter, as well as key computational primitives for modern electronic-structure methods. They describe a small subsystem of interacting fermions coupled to a large, noninteracting bath. We perform a comprehensive study of the computational complexity of simulating impurity models, delineating the boundary between classical and quantum tractability for this class of problems. Our main finding is that static properties of quantum impurity models can be calculated efficiently on a classical computer. Specifically, we give classical algorithms that (1) estimate the ground-state energy to additive precision $\delta$ in time $\mathrm{poly}(n,\delta^{-1})$, and (2) estimate the partition function at inverse temperature $\beta$ to relative precision $\delta$ in time $\mathrm{poly}(n,\beta,\delta^{-1})$, where $n$ is the system size. These results improve the previous best-known complexity for ground-state energy estimation from quasipolynomial to polynomial time, while establishing for the first time rigorous polynomial-time guarantees for simulating impurity models in thermal equilibrium. On the other hand, we find that simulating dynamical properties of impurity models is hard for classical computers but easy on a quantum computer. As a canonical example, we show that computing their nonequilibrium Green's functions captures the full power of quantum computation, even at finite temperature. Taken together, our results rule out superpolynomial quantum speedups for computing static properties, but provide an avenue for quantum advantage in simulating impurity physics out of equilibrium.

We introduce a technique for studying state preparation complexity in the quantum $p$-spin model on $n$ qubits, a disordered quantum spin system with random interactions on every set of $p$ qubits. We reduce the task of proving state preparation lower bounds to bounding the local profile complexity of the class, a quantity derived from the metric entropy of the set of vectors recording each state's expectation values against all weight-$p$ Pauli strings. We show that, for sufficiently large fixed $p$, any class with local profile complexity $O(n^2)$ remains separated from the ground-state energy by $\Omega(\sqrt n)$, a gap on the leading energy scale. When the profile complexity is $o(n^2)$, we prove the stronger conclusion that the class cannot outperform a benchmark class of simpler states at leading order. Product states always provide such a benchmark. Our framework strengthens known bounds and covers classes beyond the reach of previous methods. These include examples where circuit lightcones extend across the entire system, preventing an application of standard arguments. We obtain an $\Omega(n^2/\log n)$ gate lower bound for preparing near-ground states and depth–width tradeoffs, allowing arbitrary one- and two-qubit gates and arbitrarily many discardable ancillas. We also derive lower bounds on entanglement depth and matrix product state bond dimension, and energy obstructions for forward and reverse magic at every fixed level of Parham's magic hierarchy (arXiv:2504.19966). For Clifford circuits doped with $T$-gates, we obtain sharper energy comparisons using product stabilizer states as a more restrictive benchmark. The proof combines an adaptation of a nonsymmetric quantum de Finetti theorem (arXiv:1810.12197) with metric-entropy bounds for the Gaussian process indexed by the local profiles of states in the class.

What is the maximum number of rainbow triangles in an edge-colored graph with $m$ edges and $r$ colors? Using entropic techniques, we prove an upper bound of $C_rm^{3/2}$ rainbow triangles with $C_r=\sqrt{\frac{2(r-2)}{9r}}$; this constant is best possible whenever there exists an affine plane of order $r-1$. We also show that constructions attaining at least $(C_r-\varepsilon_r)m^{3/2}$ rainbow triangles must exhibit an affine plane structure, which further improves the upper bound if no such affine plane exists. We also consider the problem of counting properly edge-colored cliques of larger sizes. Surprisingly, if the number $r$ of colors is odd, this count is instead maximized by blowups of a properly edge-colored $K_{r+1}$.

We establish the uniqueness of the soliton vector field of a complete shrinking gradient Kähler-Ricci soliton up to pushforward by biholomorphism.

Coding agents solve repository-level software engineering tasks through long trajectories of code inspection, search, editing, and testing. As a task progresses, earlier exploration becomes stale, so managing context is more than avoiding overflow: an agent must decide when to compact, what working state to preserve, and how to continue from it. We introduce AutoCompact, which trains a coding agent to make these decisions as part of its policy. To collect training data, we run the base agent on coding tasks and use a judge to review its compaction decisions, summaries, and actions after compaction. Flawed outputs are replaced with corrected ones before being executed in the environment, so each trajectory continues from the corrected decisions. We use these trajectories for supervised fine-tuning, then jointly optimize coding and compaction through reinforcement learning with task-success rewards. Experiments on SWE-bench Verified and SWE-PolyBench Verified show that AutoCompact improves pass rates over the base model by an absolute 9.2% and 5.0%, respectively. The improvements hold across all evaluated inference budgets, with a 256K context window that never overflows and with a 16K window whose overflow triggers fallback compaction.

How can a world model continuously observe regions beyond the actor's current view? Video world models simulate how an environment evolves from an agent's actions, yet remain actor-centric. Once an object leaves the actor's view, they lose direct evidence of its evolution, often failing to preserve its state and dynamics upon re-entry. To address this, we introduce World Observer, which decouples observing from acting by jointly generating a perspective actor for the agent-centric view with one or more panoramic observers that watch selected world regions. This allows objects that leave the actor's view to remain visually evolving in an observer, so their updated states are reflected when they re-enter. We ground the actor and observers by warping from a shared panoramic source for explicit geometric correspondence, and introduce an Observer Sink of high-resolution perspective references to restore fine appearance upon re-entry. Since the observers are decoupled from the actor, they can be placed freely across the scene, extended to multiple locations for broader coverage, and driven by control signals to steer out-of-view evolution. To evaluate out-of-view evolution, we further introduce world-space metrics and a benchmark spanning real and synthetic scenes. World Observer substantially improves out-of-view dynamics while remaining competitive in visual fidelity, camera control, and 3D adherence.

Vision-language models (VLMs) and vision-language-action models (VLAs) have recently driven rapid progress in general-purpose robots, yet most progress has focused on single-robot settings. Extending these capabilities to multi-robot systems remains challenging because robots must coordinate long-horizon behaviors while maintaining reliable, fine-grained execution. We introduce DuoMind, a distributed hierarchical framework for multi-robot coordination through semantic communication. Each robot uses a VLA-based action model for low-level execution and a VLM-based orchestrator for high-level reasoning and inter-agent coordination. At each planning step, the orchestrator at each robot reasons over the task instruction, local observations, and messages received from other robots. It then generates low-level instructions for the action model and semantic messages for peer robots. This architecture exploits the complementary strengths of pretrained models by combining the semantic reasoning capabilities of VLMs with the precise action-generation capabilities of VLAs. To address the scarcity of benchmarks for multi-robot coordination, we further develop RoboPoly, a benchmark comprising long-horizon manipulation tasks that require coordinated, closed-loop execution under distributed control. Experiments on RoboPoly and RoboTwin demonstrate that DuoMind improves multi-robot task performance, while ablation studies confirm the contributions of hierarchical orchestration and semantic communication. More details are available on our project page.

Precise control over camera and object motion is essential for professional video production. Existing methods control objects only coarsely, through image-plane cues that are ambiguous in depth and rotation or through 3D tracks and blobs that lack complete geometry and lose consistency across viewpoint changes. We introduce 4Director, a video world model conditioned on an explicit 4D scene representation: each object is reconstructed once from the input image as a canonical mesh and moved by one prescribed rigid transformation per frame. This representation provides an intuitive 3D control interface and prevents unobserved geometry from being regenerated independently in every frame. We render the controlled scene as a depth video and introduce a Motion Adapter that transforms this geometric scaffold into video while synthesizing view-consistent appearance, illumination, and non-rigid dynamics. For training, we construct RealCOD-Rigid, a new dataset of 20,774 clips annotated with rigid 3D scenes by our automatic pipeline. We further introduce Identity-Gated IoU (IG-IoU), which jointly evaluates adherence to prescribed object motion and preservation of object identity. Experiments demonstrate that 4Director consistently outperforms prior methods in visual quality and in camera and object control.

Intrinsic rewards are designed to guide exploration in reinforcement learning by assigning value to an agent's experience, for example through prediction error or learning progress. However, maximizing these rewards need not produce the most informative experience available. We propose a formal criterion for exploration that compares policies by the counterfactual information they acquire: how well their histories can substitute for experience under alternative policies. We construct a single, simple environment in which specified count-based, prediction-error, empowerment, and information-gain objectives have maximizing policies that are Pareto-suboptimal at acquiring counterfactual information. We explain these failures and establish conditions under which existing intrinsic rewards successfully encourage optimal exploration. We also construct an objective that assigns a higher value whenever exploration strictly improves under our criterion.

We consider the problem of sampling from Gibbs distributions on matrix spaces whose potential energies are neither convex nor globally gradient-Lipschitz. We introduce a family of non-quadratic kinetic energies that lead to a new underdamped Langevin system with momentum preconditioning, in which the gradient of the kinetic energy acts as a smooth spectral taming of the momentum. We prove that, under these relaxed assumptions on the potential, the resulting dynamics leaves the target Gibbs measure invariant, and we establish exponential convergence to equilibrium in a weighted total variation distance. Finally, we show that the corresponding Euler-Maruyama discretization admits moment bounds that are uniform in time, without any modification of the potential gradient, which ensures the stability of the resulting sampling algorithm.

Hamiltonian learning provides a systematic framework for reconstructing unknown quantum dynamics. However, existing protocols typically assume direct measurement access to the entire system. With fast single-qubit control and a connected reference backbone, we show that a single measurable qubit suffices to learn all $O(N)$ independent parameters of a bounded-degree two-body Hamiltonian on $N$ qubits at the Heisenberg limit. Crucially, our protocol uses robust SWAP gates synthesized by quantum signal processing, enabling coherent transfer of states evolving under distant Hamiltonian parameters to the measurable qubit. This transfer requires no prior calibration of the Hamiltonian parameters of the intermediate links. A parallel learning architecture achieves total query time $\widetilde{O}(N)$ for an $N$-qubit chain, while retaining Heisenberg-limited precision scaling. On the chain, these scalings match the fundamental precision and information-propagation lower bounds up to logarithmic factors. The framework further extends to arbitrary bounded-degree interaction graphs. Our results establish a scalable route to learning an extensive number of many-body Hamiltonian parameters through only a local measurement interface.

The aim of the paper is to provide an extension of the averaging method to the periodic problem for quasilinear differential equations $(\phi(t,u'))' = \varepsilon f(t,u,u',\varepsilon)$, $u(0) = u(T)$, $u'(0) = u'(T)$, where $u$ and $u'$ take values in a Banach space $X$ and $\phi$ is a suitable homeomorphism between a neighborhood of $0$ in $X$ and $X$. The approach follows from a given extension of the averaging method to first order systems of the form $u' = g(t,v)$, $v' = h(t,u,v)$, $u(0) = u(T)$, $v(0) = v(T)$, in a product of Banach spaces, obtained from a direct application of the implicit function theorem in Banach spaces to an equivalent problem. We prove that every nondegenerate zero of the corresponding averaged equation generates, for sufficiently small nonzero values of the parameter, a unique nearby periodic solution. An application is given to an infinite system of coupled forced pendulums with relativistic acceleration.

We develop an abstract averaging method for equations $Mx=\varepsilon N(x,\varepsilon)$ in Banach spaces. The method applies when the equation can be separated into an averaged compatibility condition and a nonlinear complementary problem, and it allows the principal operator $M$ to be genuinely nonlinear. We prove that every nondegenerate zero of the corresponding averaged equation generates, for all sufficiently small nonzero values of $\varepsilon$, a nearby solution. Under a suitable small Lipschitz condition this solution is locally unique, while in the differentiable case it belongs to a unique local $C^1$ branch. The framework contains the abstract linear Fredholm averaging theory as a special case, but also covers quasilinear problems for which the principal operator has no invertible linearization at the reference state. We also determine the leading asymptotic profile of the solutions. Applications are given to a vector $p$-Laplacian Duffing system and to a nonsmooth problem in a Hilbert space.

In this work we study the robustness of $\mathsf{QAC}^0$ with respect to error tolerance and modifications to its gate-set. First, we investigate whether the non-zero error typically allowed for $\mathsf{QAC}^0$ circuits computing Boolean functions is truly necessary. We show that the error inherent in the parallel $W$-test of \cite{grier_morris_wu} can be eliminated entirely via a novel application of exact amplitude amplification in the many-copies context. Consequently, we find that $\mathsf{QAC}^0$ can exactly simulate $\mathsf{TC}^0$ with polynomially many copies of the classical input and that for every fixed prime $p$ exact $\mathsf{QAC}^0$, $\mathsf{EQAC}^0$, can compute total Boolean functions outside of $\mathsf{AC}^0[p]$. Second, we ask to what extent the computational power of $\mathsf{QAC}^0$ follows from the fact that arbitrary single-qubit gates may be used at any point in the circuit. We find that $\mathsf{QAC}^0$ is in fact robust to restrictions on which single-qubit gates are permitted: every $\mathsf{QAC}^0$ circuit can be approximately implemented by a $\mathsf{QAC}^0$ circuit consisting of just generalized Toffoli, $S$, and Hadamard gates. Moreover, this approximating circuit can be constructed efficiently from a classical description of the original circuit.

Long-horizon autoregressive video generation is limited by a finite context window. When an object or scene falls out of context, its fine-grained visual details may be lost and difficult to recover upon reappearance. To retain access to such visual details, we introduce MosaiChunk, a spatio-temporal memory mechanism that composes a mosaic of selected historical key-value (KV) entries across space and time. Our approach is motivated by the observation that a frozen video generator can directly consume such non-contiguous historical KV and recover the corresponding visual content. We therefore keep the generator fixed and learn only a lightweight router that determines which historical sections to include in the mosaic under a fixed active-memory budget. We further introduce RememBench, a benchmark of long-horizon revisits with prompt-driven text-to-video (T2V) and camera-driven image-to-video (I2V) splits. Our experiments show that MosaiChunk consistently improves revisit consistency over both sliding-window inference and whole-chunk retrieval under matched memory budgets, across both T2V and I2V settings.

We establish a natural generalization of the Hörmander condition for the multiplication of Besov distributions using the global wavefront set framework of Coriasco, Johansson, and Toft. Using this condition, we relate the microlocal perspective on multiplication of distributions to the classical paraproduct decomposition of pointwise multiplication arising in the paradifferential calculus of Bony.

This paper addresses simultaneous input and output constraint satisfaction for a class of multi-input linear time-invariant systems with state feedback and integral action. A control barrier function (CBF)-based governor modifies the reference command while preserving the nominal feedback controller. Necessary and sufficient conditions are derived under which the governor is feasible at every state of a prescribed operating set and ensures simultaneous input and output constraint satisfaction, forward invariance, and bounded closed-loop solutions. The paper also shows that these conditions need not be met for certain choices of the CBF governor parameters due to conflicts between input and output constraints. A systematic design procedure is proposed that first searches for feasible free parameters and, if necessary, proposes a relaxation in the input constraint that restores feasibility. A companion paper provides numerical examples and counterexamples illustrating these results.

Large language model (LLM) agents increasingly rely on persistent external sources to solve sequences of knowledge-intensive tasks. Existing methods improve how source content is accessed and organized, while agent-memory systems preserve reusable knowledge from prior interactions, but repeated use of the same source is still largely treated as repeated access rather than an opportunity to progressively improve understanding of that source. We study source learning: developing reusable source-specific competence over a persistent authoritative source. We represent this competence with a persistent source model that captures reusable understanding of the source, including how its knowledge is structured, interpreted, and applied. To construct and progressively refine such models, we propose SourceLearn, which combines two complementary learning mechanisms. Self-Directed Source Learning identifies what remains incompletely understood and adaptively revisits the source, while Task-Guided Source Learning uses downstream experience to reveal local representational gaps and recurring needs in how source knowledge should be organized. In both cases, learning signals determine what should be reconsidered, while persistent updates are reconstructed from the authoritative source. Across five benchmarks and three LLM backends, SourceLearn achieves the best performance in 13 of 15 settings, with gains of up to 22.6 points over Hybrid RAG and substantial overall improvements over static source representations and experience-based memory baselines.