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Arbor is a multi-agent framework that introduces structured tree search as a cognition layer for autonomous agents operating in large, stateful action spaces. Prior autonomous optimization systems operate on isolated targets with stateless evaluation. Arbor instead maintains an explicit search tree of scored hypotheses that serves as the shared working memory across agents, evolving with every measurement, treating failures as diagnostic signal that reshapes subsequent exploration, and expanding as prior successes shift the bottleneck distribution. We validate Arbor on full-stack LLM inference optimization, a domain where achieving peak performance has historically required coordinated effort from engineering teams across the application, framework, compiler, kernel, and hardware stack. Arbor pairs an Orchestrator agent, which drives optimization by delegating to Domain Specialists across the inference stack, with a Critic agent that safeguards stability through root-cause analysis, introspection, and measurement validation -- a checks-and-balances architecture where neither agent can unilaterally drive the system. Agent capabilities are decomposed into hard skills (domain expertis

The \emph{linear vertex arboricity} of a graph is the smallest number of sets into which the vertices of a graph can be partitioned so that each of these sets induces a linear forest. Chaplick et al. [JoCG 2020] showed that, somewhat surprisingly, the linear vertex arboricity of a graph is the same as the \emph{3D weak line cover number} of the graph, that is, the minimum number of straight lines necessary to cover the vertices of a crossing-free straight-line drawing of the graph in $\mathbb{R}^3$. Chaplick et al. [JGAA 2023] showed that deciding whether a given graph has linear vertex arboricity 2 is NP-hard. In this paper, we investigate the parameterized complexity of computing the linear vertex arboricity. We show that the problem is para-NP-hard with respect to the parameter maximum degree. Our result is tight in the following sense. All graphs of maximum degree 4 (except for $K_4$) have linear vertex arboricity at most 2, whereas we show that it is NP-hard to decide, given a graph of maximum degree 5, whether its linear vertex arboricity is 2. Moreover, we show that, for planar graphs, the same question is NP-hard for graphs of maximum degree 6, leaving open the maximum-degr

The $n$-dimensional lattice polytopes $\mathcal{Q}_{n,k}$ obtained by intersecting the $n$th dilate of the standard $n$-dimensional simplex in $\mathbb{R}^n$ with the half-spaces $x_i \le 1$ for $1 \le i \le k$ form an interesting special case of Chapoton's arbor polytopes. They interpolate between the $n$th dilate of the standard $n$-dimensional simplex and the standard $n$-dimensional cube in $\mathbb{R}^n$. This paper provides an explicit combinatorial interpretation of the $h^\ast$-polynomial of $\mathcal{Q}_{n,k}$, as the ascent enumerator of certain words, and partly confirms some of Chapoton's conjectures on the lattice point enumeration of arbor polytopes in this special case. More specifically, the Ehrhart polynomial of $\mathcal{Q}_{n,k}$ is shown to be magic positive, by means of a new combinatorial parking model for cars, and the real-rootedness of its $h^\ast$-polynomial is deduced. The polynomial whose coefficients count the lattice points of $\mathcal{Q}_{n,k}$ by the number of their nonzero coordinates is shown to be gamma-positive and a combinatorial interpretation of the $h^\ast$-polynomial of any arbor polytope is conjectured.

Text and image conditioned 3D models now generate convincing assets, but they still offer little direct control over the space an object should occupy or avoid. In authoring, this spatial intent is often known before generation starts. A chair should fit a seating envelope, a prop should leave clearance for motion, or a part should expose a contact surface. Prompts and image views are poor carriers for such constraints, requiring the need for an explicit control interface. We present Arbor, a trainable attachment for text conditioned latent 3D generation. Arbor introduces constraint meshes as a native 3D control interface. The interface uses hull regions where geometry should exist, avoidance regions that should remain empty, and touch regions the object should contact. Unlike completion or whole object scaffold control, these meshes are not target evidence. They are local typed requirements and can include regions where no surface should appear. Arbor keeps this signal as geometry by converting constraint meshes into tokens and learning a routed attachment inside a frozen denoiser. Each latent region can therefore receive the part of the constraint that matters for its spatial loc

This paper proves four conjectured generating series, due to Chapoton, which concern invariants of posets and polytopes associated with a specific sequence of arbors. Two of these conjectures provide closed-form formulas for the generating series of the Zeta polynomial and the generating series of the M-triangle of the poset, respectively. The remaining two conjectures pertain, respectively, to the Ehrhart polynomial and the Laplace transform of the volume function of the associated arbor polytope.

Arboreal categories were introduced as an axiomatic framework for game comonads, which provide a comonadic view on many model-comparison games in logic. We demonstrate the inadequacy of the axiom stating that paths are connected. We then propose the notion of ``tree-connectedness'' to address this deficiency, and show that all the essential properties of arboreal categories that we are aware of remain valid under this new definition. Furthermore, we show that the path functor is a Street fibration.

We construct a category $\OrdFor$ as an arboreal extension of $Δ_{\mathrm{epi}}\subseteqΔ$, whose morphisms are ordered forests composed by grafting. We define a full functor $π\colon \OrdFor\toΔ_{\mathrm{epi}}^{op}$ extracting the semisimplicial shadow. For every complete category $\mathcal C$, this induces a fully faithful functor from semisimplicial objects in $\mathcal C$ to $\mathcal C$-valued presheaves on $\OrdFor$, with right adjoint given by right Kan extension. We show that if weak equivalences of arboreal objects are detected by this right adjoint, then their Gabriel--Zisman localization is equivalent to that of semisimplicial objects. For bicomplete cofibrantly generated model categories, under the usual acyclicity hypothesis for right-induced transfer, the corresponding model structure on arboreal objects is Quillen equivalent to the Reedy model structure on semisimplicial objects.

LLM-based search agents are trained predominantly with outcome-only reward, leaving the search process itself unsupervised. This signal degenerates on outcome-homogeneous groups where all sampled trajectories share the same correctness, yielding zero within-group advantage and no gradient. Existing process supervision either trains a costly verifier or generates per-query rubrics that are inconsistent across queries and discarded after one use. We propose ARBOR (Adaptive Rubric Buffer for Online Reward), a reusable process-reward framework that maintains a rubric memory shared across queries. Query-local drafts induced from contrastive trajectories are admitted, consolidated into cross-query common rubrics, and retired as the policy evolves. A small active subset of common rubrics scores trajectories via sparse pairwise judging, and the resulting scores are added to the base reward, providing process-level gradient even when outcome reward is uniform. ARBOR consistently outperforms GRPO and DAPO baselines on four multi-hop QA benchmarks, raising average LLM-judge accuracy by up to 4.2 points and converting up to 42% of otherwise-zero-gradient training groups into informative ones.

Horizontal gene transfer (HGT) is an important process in bacterial evolution. Current phylogeny-based approaches to capture it cannot however appropriately account for the fact that HGT can occur between bacteria living in different ecological niches. Due to the fact that arboreal networks are a type of multiple-rooted phylogenetic network that can be thought of as a forest of rooted phylogenetic trees along with a set of additional arcs each joining two different trees in the forest, understanding the combinatorial structure of such networks might therefore pave the way to extending current phylogeny-based HGT-inference methods in this direction. A central question in this context is, how can we construct an arboreal network? Answering this question is strongly informed by finding ways to \textit{encode} an arboreal network, that is, breaking up the network into simpler combinatorial structures that, in a well defined sense uniquely determine the network. In the form of triplets, trinets and quarnets such encodings are known for certain types of single-rooted phylogenetic networks. By studying the underlying tree of an arboreal network, we compliment them here with an answer for

Large language models struggle to maintain strict adherence to structured workflows in high-stakes domains such as healthcare triage. Monolithic approaches that encode entire decision structures within a single prompt are prone to instruction-following degradation as prompt length increases, including lost-in-the-middle effects and context window overflow. To address this gap, we present Arbor, a framework that decomposes decision tree navigation into specialized, node-level tasks. Decision trees are standardized into an edge-list representation and stored for dynamic retrieval. At runtime, a directed acyclic graph (DAG)-based orchestration mechanism iteratively retrieves only the outgoing edges of the current node, evaluates valid transitions via a dedicated LLM call, and delegates response generation to a separate inference step. The framework is agnostic to the underlying decision logic and model provider. Evaluated against single-prompt baselines across 10 foundation models using annotated turns from real clinical triage conversations. Arbor improves mean turn accuracy by 29.4 percentage points, reduces per-turn latency by 57.1%, and achieves an average 14.4x reduction in per-t

The study of arboreal Galois representations (that is, Galois groups arising from iteration of polynomial and rational functions) originated with work of Odoni in the 1980s. Beginning in the early 2000s it underwent a period of renewed interest, which continues to this day. Written in 2007, this survey article gives a sense of the subject from the early days of this renewal. It is presented here as a document of historical interest -- precisely as originally written -- and because some recent work has referenced specific pieces of it. It was written as an informal document, and not intended to be published. Much, though not all, of the content overlaps with the 2013 survey article ``Galois representations from pre-image trees: an arboreal survey" of the author.

Starting from the data of an arbor, which is a rooted tree with vertices decorated by disjoint sets, we introduce a lattice polytope and a partial order on its lattice points. We give recursive algorithms for various classical invariants of these polytopes and posets, using the tree structure. For linear arbors, we propose a conjecture exchanging the Ehrhart polynomial of the polytope with the Zeta polynomial of the poset for the reverse arbor. The general motivation comes from the action of a transmutation operator acting on M -triangles, which should link the posets considered here with some kinds of generalized noncrossing partitions and generalized associahedra. We give some evidence for this relationship in several cases, including notably some polytopes, namely halohedra and Hochschild polytopes.

We introduce a new matroid (graph) invariant, the arboricity polynomial. Given a matroid, the arboricity polynomial enumerates the number of covers of the ground set by disjoint independent sets. We establish the polynomiality of the counting function as a special case of a scheduling polynomial, i.e. both in terms of quasisymmetric functions and via Ehrhart theory of the normal fan of the matroid base polytope. We show basic properties of the polynomial and demonstrate that it is not a Tutte invariant. Namely, the arboricity polynomial does not satisfy a contraction / deletion recursion.

Computational neuroscience has traditionally focused on isolated scales, limiting understanding of brain function across multiple levels. While microscopic models capture biophysical details of neurons, macroscopic models describe large-scale network dynamics. Integrating these scales, however, remains a significant challenge. In this study, we present a novel co-simulation framework that bridges these levels by integrating the neural simulator Arbor with The Virtual Brain (TVB) platform. Arbor enables detailed simulations from single-compartment neurons to populations of such cells, while TVB models whole-brain dynamics based on anatomical features and the mean neural activity of a brain region. By linking these simulators for the first time, we provide an example of how to model and investigate the onset of seizures in specific areas and their propagation to the whole brain. This framework employs an MPI intercommunicator for real-time bidirectional interaction, translating between discrete spikes from Arbor and continuous TVB activity. Its fully modular design enables independent model selection for each scale, requiring minimal effort to translate activity across simulators. Th

For a Weinstein manifold, we compare and contrast the properties of admitting an arboreal skeleton and admitting Maslov data. Both properties are implied by the existence of a polarization, for which a basic obstruction is that the odd Chern classes are 2-torsion. In a similar spirit we establish cohomological obstructions to the existence of arboreal skeleta and to the existence of Maslov data, exhibiting concrete examples to illustrate their failure. For instance, we show that complements of smooth anti-canonical divisors in complex projective space may fail to admit either arboreal skeleta or Maslov data. We also exhibit an example of a Weinstein manifold which admits Maslov data but does not admit an arboreal skeleton.

Arboreal networks are multi-rooted phylogenetic networks whose underlying graph is a tree. We give an encoding of stack-free arboreal networks in terms of triplets and the novel concept of a duet. This yields a polynomial time algorithm to construct these networks from complete triplet and duet systems. The classification results show correctness and lead to a natural metric on these multi-rooted networks.

Arboreal categories, introduced by Abramsky and Reggio, axiomatise categories with tree-shaped objects. These categories provide a categorical language for formalising behavioural notions such as simulation, bisimulation, and resource-indexing. In this paper, we strengthen the axioms of an arboreal category to exclude `branching' behaviour, obtaining a notion of `linear arboreal category'. We then demonstrate that every arboreal category satisfying a linearisability condition has an associated linear arboreal subcategory related via an adjunction. This identifies the relationship between the pebble-relation comonad, of Montacute and Shah, and the pebbling comonad, of Abramsky, Dawar, and Wang, and generalises it further. As another outcome of this new framework, we obtain a linear variant of the arboreal category for modal logic. By doing so we recover different linear-time equivalences between transition systems as instances of their categorical definitions. We conclude with new preservation and characterisation theorems relating trace inclusion and trace equivalence with different linear fragments of modal logic.

A network $N$ on a finite set $X$, $|X|\geq 2$, is a connected directed acyclic graph with leaf set $X$ in which every root in $N$ has outdegree at least 2 and no vertex in $N$ has indegree and outdegree equal to 1; $N$ is arboreal if the underlying unrooted, undirected graph of $N$ is a tree. Networks are of interest in evolutionary biology since they are used, for example, to represent the evolutionary history of a set $X$ of species whose ancestors have exchanged genes in the past. For $M$ some arbitrary set of symbols, $d:{X \choose 2} \to M \cup \{\odot\}$ is a symbolic arboreal map if there exists some arboreal network $N$ whose vertices with outdegree two or more are labelled by elements in $M$ and so that $d(\{x,y\})$, $\{x,y\} \in {X \choose 2}$, is equal to the label of the least common ancestor of $x$ and $y$ in $N$ if this exists and $\odot$ else. Important examples of symbolic arboreal maps include the symbolic ultrametrics, which arise in areas such as game theory, phylogenetics and cograph theory. In this paper we show that a map $d:{X \choose 2} \to M \cup \{\odot\}$ is a symbolic arboreal map if and only if $d$ satisfies certain 3- and 4-point conditions and the gr

Arboreal Gas is a type of (unrooted) random forest on a graph, where the probability is determined by a parameter $β>0$ per edge. This model is essentially equivalent to acyclic Bernoulli bond percolation with a parameter $p=β/(1+β)$. Additionally, Arboreal Gas can be considered as the limit of the $q$-states random cluster model with $p=βq$ as $q\to 0$. A natural question arises regarding the existence and performance of the weak limit of Arboreal Gas as the graph size goes to infinity. The answer to this question relies on the negative correlation of Arboreal Gas, which is still an open problem. This paper primarily focuses on the negative correlation of Arboreal Gas and provides some results for specific graphs.