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MAT-Cell: A Multi-Agent Tree-Structured Reasoning Framework for Batch-Level Single-Cell Annotation

Yehui Yang, Zelin Zang, Changxi Chi, Jingbo Zhou, Xienan Zheng, Yuzhe Jia, Chang Yu, Jinlin Wu, Fuji Yang, Jiebo Luo, Zhen Lei, Stan Z. Li

Year: 2026Venue: arXiv preprintArea: q-bio.QMType: PreprintEmbeddings: 97

Intelligence

Status: succeeded | Model: google/gemini-3.1-flash-lite-preview | Prompt: intel-v1 | Confidence: 95%

Last extracted: 4/10/2026, 3:13:56 AM

Summary

MAT-Cell is a neuro-symbolic reasoning framework designed for single-cell RNA sequencing annotation. It addresses the 'Reference Trap' and 'Signal-to-Noise Paradox' by replacing black-box classification with a multi-agent dialectic verification process that constructs verifiable syllogistic derivation trees (SDT) grounded in biological axioms via retrieval-augmented generation (RAG).

Entities (5)

MAT-Cell · framework · 100%scRNA-seq · biological-technique · 99%Dialectic Verification · methodology · 95%Inductive Anchoring · methodology · 95%Syllogistic Derivation Tree · data-structure · 95%

Relation Signals (4)

Dialectic Verification → constructs → Syllogistic Derivation Tree

confidence 95% · Dialectic Verification employs a multi-agent debate to construct a Syllogistic Derivation Tree

MAT-Cell → employs → Dialectic Verification

confidence 95% · It further employs a dialectic verification process with homogeneous rebuttal agents

MAT-Cell → uses → Inductive Anchoring

confidence 95% · MAT-Cell integrates Inductive Anchoring via Symbolic Constraint Injection

MAT-Cell → performs → scRNA-seq

confidence 90% · MAT-Cell: A Multi-Agent Tree-Structured Reasoning Framework for Batch-Level Single-Cell Annotation

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Abstract

Abstract:Automated cellular reasoning faces a core dichotomy: supervised methods fall into the Reference Trap and fail to generalize to out-of-distribution cell states, while large language models (LLMs), without grounded biological priors, suffer from a Signal-to-Noise Paradox that produces spurious associations. We propose MAT-Cell, a neuro-symbolic reasoning framework that reframes single-cell analysis from black-box classification into constructive, verifiable proof generation. MAT-Cell injects symbolic constraints through adaptive Retrieval-Augmented Generation (RAG) to ground neural reasoning in biological axioms and reduce transcriptomic noise. It further employs a dialectic verification process with homogeneous rebuttal agents to audit and prune reasoning paths, forming syllogistic derivation trees that enforce logical this http URL large-scale and cross-species benchmarks, MAT-Cell significantly outperforms state-of-the-art (SOTA) models and maintains robust per-formance in challenging scenarios where baselinemethods severely degrade. Code is available at https://gith this http URL ti-Agent-Tree-Structured-Reasoni ng-Framework-for-Batch-Level-Sin gle-Cell-Annotation.

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MAT-Cell: A Multi-Agent Tree-Structured Reasoning Framework for Batch-Level Single-Cell Annotation Yehui Yang Zelin Zang Changxi Chi Jingbo Zhou Xienan Zheng Yuzhe Jia Chang Yu Jinlin Wu Fuji Yang Jiebo Luo Zhen Lei Stan Z. Li Abstract Automated cellular reasoning faces a core dichotomy: supervised methods fall into the Reference Trap and fail to generalize to out-of-distribution cell states, while large language models (LLMs), without grounded biological priors, suffer from a Signal-to-Noise Paradox that produces spurious associations. We propose MAT-Cell, a neuro-symbolic reasoning framework that reframes single-cell analysis from black-box classification into constructive, verifiable proof generation. MAT-Cell injects symbolic constraints through adaptive Retrieval-Augmented Generation (RAG) to ground neural reasoning in biological axioms and reduce transcriptomic noise. It further employs a dialectic verification process with homogeneous rebuttal agents to audit and prune reasoning paths, forming syllogistic derivation trees that enforce logical consistency.Across large-scale and cross-species benchmarks, MAT-Cell significantly outperforms state-of-the-art (SOTA) models and maintains robust per-formance in challenging scenarios where baselinemethods severely degrade. Code is available at https://github.com/jiangliu91/MAT-Cell-A-Multi-Agent-Tree-Structured-Reasoning-Framework-for-Batch-Level-Single-Cell-Annotation. Machine Learning, ICML 1 Introduction While single-cell RNA sequencing (scRNA-seq) (Lähnemann et al., 2020; Klein et al., 2015) has scaled to profile millions of cells (Regev et al., 2017; Hao et al., 2024), the fundamental challenge in computational biology has shifted from data generation to automated cellular reasoning (Xiao et al., 2024; Mao et al., 2025; Fang et al., 2025). Tissues are not static catalogs of discrete types; they are dynamic continua governed by complex gene regulatory networks (Cui et al., 2024; Trapnell, 2015; Wagner et al., 2016). Consequently, interpreting cellular heterogeneity requires more than pattern matching against a fixed reference; it demands the ability to deduce cell identity from first principles, especially for rare, transitional, or disease-specific states that defy rigid categorization. Figure 1: System 1 vs. System 2 in Cellular Reasoning. (A) Standard LLMs suffer from the “Signal-to-Noise Paradox” (System 1), where attention mechanisms are distracted by highly expressed housekeeping genes (Coral Fog), leading to hallucinations. (B) MAT-Cell establishes a System 2 paradigm via Inductive Anchoring, which grounds reasoning solely in statistically validated markers (Teal DEGs), and Dialectic Verification, constructing a verifiable Syllogistic Derivation Tree (SDT). The first failure mode stems from the “Reference Trap” (Luecken et al., 2022; Wagner et al., 2016; Stuart et al., 2019) inherent in supervised learning. Traditional annotators like CellTypist (Dominguez Conde et al., 2022) and scANVI (Xu et al., 2021) rely on embedding-based correlation against static atlases. While effective for known cell types, these methods operate under a closed-world assumption. They fail to generalize to out-of-distribution (OOD) states—such as transitional progenitors or disease-specific subtypes—often forcing novel biological signals into incorrect, pre-defined categories simply because they lack the reasoning capacity to recognize “unknowns”. The second failure mode is the “Signal-to-Noise Paradox” (Kalai et al., 2025; Bian et al., 2024; Scaife and Smith, 2018) plaguing generative AI. While Large Language Models (LLMs) offer promising zero-shot capabilities (Cui et al., 2024; Valkanas et al., 2023), their general-purpose attention mechanisms are ill-suited for raw transcriptomic profiles. In single-cell data, biologically defining markers (e.g., transcription factors) are often sparsely expressed, while housekeeping genes (e.g., MALAT1, ACTB) dominate the count matrix. As illustrated in Figure 1A, standard LLMs get “distracted” by this high-abundance noise (the “confounding dominance” of housekeeping genes), leading to hallucinations of plausibility: outputs that are textually coherent but biologically ungrounded in the specific cellular context. To bridge this gap, Figure 1B inspiration from the dual-process theory of cognition (Kahneman, 2011; Bengio, 2019) to introduce MAT-Cell. Unlike standard models that operate in a System 1 fashion (fast, intuitive pattern matching prone to bias), MAT-Cell enforces an LLM-driven Neuro-Symbolic System 2 paradigm (Trinh et al., 2024; Gao et al., 2023; Yao et al., 2022). It reformulates annotation as explicit proof construction, effectively preventing the hallucination of plausibility. To address both the Signal-to-Noise Paradox and the Reference Trap, we introduce MAT-Cell, which integrates Inductive Anchoring via Symbolic Constraint Injection with a Multi-agent Dialectic Verification Protocol. Rather than feeding the full noisy transcriptome into an LLM, Inductive Anchoring retrieves canonical marker axioms to explicitly constrain the neural search space, forcing reasoning to operate solely on the intersection between observed expression evidence and validated biological knowledge, thereby suppressing the confounding dominance of housekeeping genes. Building upon this grounded representation, MAT-Cell employs a collaborative council of specialized agents—including a Solve Agent, Rebuttal Agent, and Decision Agent—to iteratively construct and audit a Syllogistic Derivation Tree (SDT) (Smith and others, 1989; Khemlani and Johnson-Laird, 2012). This dialectic process emulates scientific peer review: hypotheses are proposed, challenged, and refined through structured debate, with convergence determined by minimizing dialectic divergence rather than maximizing probabilistic confidence, ultimately yielding a transparent, verifiable “white-box” proof path. Our contributions are threefold. (1) Neuro-Symbolic Paradigm: We propose the first framework to reformulate single-cell analysis as a neuro-symbolic proof construction process, unifying neural flexibility with symbolic rigor. (2) Methodological Innovation: We introduce Symbolic Constraint Injection to ground LLM reasoning and Orthogonal Dialectic Roles to eliminate hallucination through adversarial verification. (3) SOTA Performance: Extensive experiments demonstrate that MAT-Cell significantly outperforms scPilot and supervised baselines, providing fully transparent, verifiable proof trees for every decision. 2 Related Work Traditional automated cell type annotation methods primarily rely on supervised classification or latent space alignment against curated reference atlases. Methods such as SingleR (Aran et al., 2019), CellTypist (Dominguez Conde et al., 2022), and scANVI (Xu et al., 2021) formulate annotation as a statistical correlation problem within a closed manifold, enabling reliable identification of common cell states but fundamentally operating as fast, pattern-matching “System 1” approaches. As a result, they suffer from the Reference Trap: disease-specific subtypes or transitional states outside the reference manifold are often force-aligned to the nearest known cluster with high confidence. Recent foundation models, including scGPT (Cui et al., 2024), Geneformer (Valkanas et al., 2023), and scFoundation (Hao et al., 2024), scale annotation via Transformer architectures, yet encounter a Signal-to-Noise Paradox, where highly expressed housekeeping genes dominate attention and induce biologically plausible but incorrect annotations. Critically, these models remain probabilistic predictors and lack mechanisms for biological or logical verification. To address these limitations, recent works have explored agentic frameworks and reinforcement learning. CellAgent (Xiao et al., 2024) and scAgent (Mao et al., 2025) primarily orchestrate external bioinformatics tools, while CellDuality (Anonymous, 2026) applies task-specific reinforcement learning; however, both paradigms lack explicit and generalizable reasoning. In contrast, advances in LLM reasoning—including Chain-of-Thought (Wei et al., 2022; Kojima et al., 2022), Tree of Thoughts (Yao et al., 2023), Self-Consistency (Wang et al., 2022), neuro-symbolic systems such as AlphaGeometry (Trinh et al., 2024) and Logic-LM (Pan et al., 2023), and multi-agent debate frameworks (Liang et al., 2023; Du et al., 2023; Li et al., 2023)—demonstrate that structured reasoning and dialectic verification substantially reduce hallucinations. MAT-Cell bridges these paradigms to transcriptomic analysis by reformulating annotation as deductive biological reasoning, enforcing a strict syllogistic structure (Biological Axiom + Expression Evidence → Conclusion) through Inductive Anchoring and Dialectic Verification, thereby enabling transparent and generalizable annotation beyond reference atlases. 3 Methodology Figure 2: The MAT-Cell Framework. (Stage 1) Inductive Anchoring filters housekeeping noise by constructing a Syllogistic Input Card ix_i from statistically validated DEGs. (Stage 2) Dialectic Verification employs a multi-agent debate to construct a Syllogistic Derivation Tree (SDT), minimizing Semantic Divergence Score δcon _con to ensure logical consistency. (Stage 3) Contextual Synthesis resolves ambiguity via a Decision Agent, yielding a hybrid assembly of auto-verified and adjudicated annotations. We propose MAT-Cell, an LLM-Centric Neuro-Symbolic Reasoning Framework that reformulates single-cell annotation from a statistical classification task into a constructive logical proof. Unlike standard LLMs that rely on implicit pattern matching (Yang et al., 2022, 2024) or pure symbolic systems that lack flexibility (Chen and Zou, 2024, 2025; Dhuliawala et al., 2024), MAT-Cell unifies neural reasoning with symbolic constraints by leveraging unsupervised aggregation to distill robust biological signals. As illustrated in Figure 2, the pipeline begins with cluster-level feature extraction, followed by three core stages: (1) Inductive Anchoring to inject symbolic constraints, (2) Dialectic Verification to build a bottom-up proof tree via agent roles, and (3) Contextual Synthesis for final adjudication. The complete inference procedure is summarized in Algorithm 1. 3.1 Problem Formulation: Neuro-Symbolic Inference Let ∈ℝN×GX ^N× G be a single-cell gene expression matrix. Standard neural approaches fθ:→f_θ:X typically operate at the individual cell level but frequently suffer from the Signal-to-Noise Paradox caused by stochastic drop-out and transcriptional bursting. Conversely, traditional symbolic systems fall into the Reference Trap due to their reliance on fixed Embedding Geometry, which forces out-of-distribution (OOD) states into known manifolds. We propose to bridge this gap by leveraging the composability of Logical Rules through explicit derivation. To ensure robust inference, we first partition the raw data space into M Meta-cells (or statistical clusters) =c1,…,cMC=\c_1,…,c_M\ using an unsupervised function Φ:→ :X , where M≪NM N. For each cluster cic_i, we identify a robust set of Highly Expressed Genes (HEGs) and Differentially Expressed Genes (DEGs) to represent its biological identity. Let ix_i be the structured evidence set derived from these statistically validated genes. We reformulate the inference task as finding a label yiy_i for each cluster by constructing a Syllogistic Derivation Tree (SDT) iT_i as its proof. The objective is to maximize the posterior probability of the proof tree given cluster-level evidence and symbolic constraints: i∗=arg⁡max⁡P(∣i,ret,ℛlogic)T_i^*= _TP(T _i,K_ret,R_logic) (1) where retK_ret denotes retrieved biological axioms and ℛlogicR_logic represents hard logic rules. This formulation shifts single-cell analysis from “label guessing for noisy points” to “logical deduction for statistical clusters.” 3.2 Stage 1: Inductive Anchoring (Symbolic Constraint Injection) To bridge the gap between continuous expression data and discrete biological logic, we employ a Retrieval-Augmented Inductive Anchoring strategy. This stage transforms the raw input into a semi-symbolic representation that grounds subsequent reasoning. Neuro-Symbolic Input Card. We align neural observations (Top genes and differentially expressed genes) with the retrieved symbolic constraints to construct a Neuro-Symbolic Input Card icardx_i^card. This card does not directly encode a syllogistic conclusion. Instead, it provides the structured premise materials required for subsequent syllogistic construction, namely candidate biological axioms, expression evidence, and contextual information. These elements are later organized by the reasoning agents into explicit deductive forms of Biological Axiom (Major Premise) + Expression Evidence (Minor Premise) → Conclusion. Formally, the input card is defined as: icard=(obs(i)∩Span(ret),ret,i)x_i^card\;=\; (G_obs^(i) (K_ret),\;K_ret,\;ctx_i ) (2) where obs(i)G_obs^(i) denotes the set of observed genes for cluster i, Span(ret)Span(K_ret) represents the union of marker genes across all retrieved candidate types, retK_ret denotes the retrieved symbolic knowledge block containing candidate cell types and their marker axioms, and ictx_i encodes auxiliary contextual information for cluster i. 3.3 Stage 2: Dialectic Verification (Proof Tree Construction) Solve Agent Initialization. To establish a constrained search space at the onset of inference, we introduce a Solve Agent (SA). Given the neuro-symbolic input card icardx_i^card from Stage 1, the Solve Agent performs inductive reasoning to generate a candidate cell type set: icand=SA(icard)C_i^cand=SA(x_i^card) (3) where icand⊆C_i^cand and |icand|≪|||C_i^cand| |Y|. This candidate set explicitly constrains the subsequent reasoning space. Homogeneous Rebuttal Agents. The Council of Verifiers consists of K homogeneous Rebuttal Agents (RAs). Conditioned on the same input card and candidate space, each Rebuttal Agent independently constructs a reasoning hypothesis and outputs a tentative conclusion: yi(k)=RAk(icard,icand),k=1,…,Ky_i^(k)=RA_k(x_i^card,C_i^cand), k=1,…,K (4) Dialectic Interaction and Self-Correction. At each dialectic round t, Rebuttal Agents engage in peer-to-peer rebuttal by inspecting conflicting hypotheses. Any unstable reasoning path is revised via self-correction, yielding an updated conclusion: yi,t+1(k)=RAkrevise(yi,t(k),yi,t(j)j≠k)y_i,t+1^(k)=RA_k^revise (y_i,t^(k),\y_i,t^(j)\_j≠ k ) (5) Consensus-Based Convergence. The construction of the Syllogistic Derivation Tree (SDT) iT_i proceeds iteratively until the council reaches logical consensus. Convergence is determined by strict consensus consistency rather than probabilistic scoring: Conditionconverge:y(1)=y(2)=⋯=y(K) Condition_ converge: y^(1)=y^(2)=·s=y^(K) (6) If the condition is satisfied, the SDT converges to a stable root node yiy_i and inference terminates. Otherwise, the branch is deemed unstable and further dialectic rounds or pruning are triggered. 3.4 Stage 3: Contextual Synthesis (Proof Adjudication) The final annotation is typically derived from the root node of the Syllogistic Derivation Tree (SDT). However, for complex boundary cases, the council may fail to reach consensus within the predefined dialectic rounds. We therefore define a Focus Set ℐfocusI_focus to identify non-converged clusters: ℐfocus=i|¬Conditionconverge(i)I_focus= \\,i\, |\, Condition_ converge(T_i)\, \ (7) where iT_i denotes the SDT constructed for cluster i. For clusters in ℐfocusI_focus, the reasoning process is escalated to a Decision Agent (DA). Acting as a senior adjudicator, the DA reviews the complete proof tree history, including conflicting branches proposed by different agent roles, and issues a final verdict: yi∗=DA(i),i∈ℐfocusy_i^*=DA(T_i), i _focus (8) The final output is assembled in a hybrid manner: yi=yicons,i∉ℐfocusyi∗,i∈ℐfocusy_i= casesy_i^cons,&i _focus\\ y_i^*,&i _focus cases (9) where yiconsy_i^cons denotes the consensus result obtained through dialectic verification. This hybrid strategy ensures scalability while enabling rigorous handling of ambiguous and hard boundary cases. Algorithm 1 MAT-Cell Inference via Dialectic Reasoning 0: Meta-cell ix_i, knowledge base K, agents SA,RA1,…,RAK,DA\SA,RA_1,…,RA_K,DA\, max rounds T 0: Predicted label yiy_i 1: icard←InductiveAnchoring(i,)x_i^card (x_i,K) 2: icand←SA(icard)C_i^cand (x_i^card) 3: Initialize proof tree i←∅T_i← 4: Initialize focus set ℐfocus←∅I_focus← 5: for t=1t=1 to T do 6: for k=1k=1 to K do 7: y(k)←RAk(icard,icand,i)y^(k) _k(x_i^card,C_i^cand,T_i) 8: end for 9: Agents exchange rebuttals and revise unstable hypotheses 10: if y(1)=⋯=y(K)y^(1)=·s=y^(K) then 11: yi←y(1)y_i← y^(1) 12: return yiy_i 13: end if 14: i←i∪y(k)k=1KT_i _i∪\\y^(k)\_k=1^K\ 15: end for 16: ℐfocus←i∣i not convergedI_focus←\i _i not converged\ 17: yi←DA(i)y_i (T_i) 18: return yiy_i 4 Experiments Table 1: Main results under the open candidate (no oracle labels) setting. This setting follows the scPilot protocol and simulates realistic annotation scenarios where no candidate cell-type labels are provided a priori. All methods must infer cell types directly from cluster-level marker information without access to oracle candidates. Results are reported as accuracy (mean ± std) across five scRNA-seq datasets (PBMC3K, Liver, Retina, Brain, and Heart). Different language model backbones are listed to reflect model-dependent variations. For MAT-Cell variants, the suffix “-c” denotes the use of retrieval-augmented grounding; Qwen-based “-c” models are distilled within the same backbone family, while other “-c” variants are distilled from Gemini-3. The best and second-best results are highlighted in bold and underlined, respectively. Method Model PBMC3K Liver Retina Brain Heart Avg Acc. CellTypist – 0.464 0.563 0.388 0.242 0.690 0.469 CellMarker2.0 – 0.304 0.250 0.632 0.625 0.267 0.416 Direct Qwen3-30B 0.675± 0.061 0.444± 0.062 0.747± 0.021 0.231± 0.097 0.246± 0.123 0.469 O1 0.667± 0.005 0.560± 0.001 0.474± 0.002 0.296± 0.026 0.338± 0.092 0.467 Qwen3-14B 0.674± 0.018 0.467± 0.090 0.747± 0.077 0.119± 0.098 0.123± 0.038 0.426 GPT-4o 0.604± 0.005 0.440± 0.002 0.439± 0.002 0.356± 0.018 0.231± 0.169 0.414 Gemini 2.5 Pro 0.583± 0.001 0.494± 0.007 0.491± 0.000 0.215± 0.082 0.185± 0.062 0.394 scPilot GPT-4o 0.646± 0.017 0.512± 0.002 0.675± 0.011 0.452± 0.226 0.308± 0.069 0.519 O1 0.792± 0.005 0.518± 0.001 0.728± 0.007 0.115± 0.230 0.354± 0.158 0.501 Qwen3-30B 0.750± 0.137 0.437± 0.054 0.737± 0.058 0.215± 0.102 0.200± 0.062 0.468 Gemini 2.5 Pro 0.708± 0.021 0.488± 0.001 0.763± 0.000 0.148± 0.052 0.169± 0.113 0.455 Qwen3-14B 0.725± 0.050 0.422± 0.055 0.747± 0.021 0.022± 0.018 0.123± 0.038 0.408 CoT Gemini 2.5 Pro 0.625± 0.044 0.782± 0.008 0.495± 0.012 0.669± 0.018 0.640± 0.028 0.642 O1 0.675± 0.052 0.704± 0.013 0.490± 0.014 0.669± 0.042 0.613± 0.018 0.630 Qwen3-14B 0.578± 0.031 0.648± 0.085 0.663± 0.073 0.640± 0.060 0.511± 0.105 0.608 GPT-4o 0.688± 0.000 0.804± 0.025 0.442± 0.022 0.455± 0.020 0.580± 0.038 0.594 Qwen3-30B 0.575± 0.025 0.781± 0.044 0.550± 0.178 0.577± 0.025 0.458± 0.043 0.588 MAT-Cell (no RAG) Gemini3 0.625± 0.028 0.607± 0.042 0.500± 0.014 0.894± 0.057 0.633± 0.024 0.652 Deepseek-v3 0.650± 0.035 0.800± 0.050 0.516± 0.014 0.656± 0.000 0.627± 0.028 0.650 Llama-3-70b 0.613± 0.069 0.778± 0.043 0.621± 0.040 0.656± 0.066 0.513± 0.030 0.636 Qwen3-14B 0.575± 0.082 0.659± 0.038 0.495± 0.057 0.513± 0.087 0.620± 0.030 0.572 Qwen3-30B 0.638± 0.052 0.791± 0.020 0.474± 0.046 0.469± 0.058 0.474± 0.046 0.569 MAT-Cell (use RAG) Qwen3-30B 0.800± 0.028 0.811± 0.048 0.632± 0.019 0.719± 0.062 0.813± 0.038 0.755 ↑ +45.5% Llama-3-70b 0.725± 0.034 0.800± 0.024 0.626± 0.071 0.738± 0.028 0.753± 0.038 0.728 Gemini3 0.750± 0.000 0.804± 0.021 0.505± 0.035 0.656± 0.039 0.780± 0.019 0.699 Deepseek-v3 0.638± 0.028 0.685± 0.019 0.521± 0.029 0.763± 0.065 0.620± 0.018 0.645 Qwen3-30B-c 0.613± 0.028 0.796± 0.019 0.510± 0.025 0.444± 0.014 0.600± 0.000 0.593 Table 2: Cross-species performance comparison under the open candidate setting. This evaluation follows the Cell-o1 protocol and assesses generalization across three species (Human, Mouse, and Monkey). For each species, results are reported under three input configurations: Both (HEGs + DEGs), DEG-only, and HEG-only, reflecting different signal-to-noise conditions. All values are reported as mean ±\!±\! standard deviation (rounded to three decimals) over multiple runs. Different backbone models are listed to highlight model-dependent variations. The best and second-best results in each column are highlighted in bold and underlined, respectively. For MAT-Cell (use RAG), distillation details are omitted from the table for clarity: models with the suffix “-c” denote RAG-specific students distilled within the same backbone family, while the remaining RAG variants are distilled from Gemini-3. Method Model Human Mouse Monkey Both DEG HEG Both DEG HEG Both DEG HEG Cell-o1 Qwen2.5-7B 0.429±0.0120.429\!±\!0.012 0.409±0.0150.409\!±\!0.015 0.243±0.0110.243\!±\!0.011 0.390±0.0160.390\!±\!0.016 0.394±0.0170.394\!±\!0.017 0.232±0.0080.232\!±\!0.008 0.695±0.0180.695\!±\!0.018 0.685±0.0190.685\!±\!0.019 0.503±0.0120.503\!±\!0.012 Direct Qwen3-14b 0.291±0.0080.291\!±\!0.008 0.409±0.0090.409\!±\!0.009 0.164±0.0040.164\!±\!0.004 0.308±0.0100.308\!±\!0.010 0.348±0.0100.348\!±\!0.010 0.162±0.0040.162\!±\!0.004 0.542±0.0050.542\!±\!0.005 0.580±0.0060.580\!±\!0.006 0.302±0.0060.302\!±\!0.006 Qwen3-30B 0.340±0.0080.340\!±\!0.008 0.450±0.0130.450\!±\!0.013 0.165±0.0080.165\!±\!0.008 0.347±0.0100.347\!±\!0.010 0.387±0.0080.387\!±\!0.008 0.178±0.0050.178\!±\!0.005 0.588±0.0100.588\!±\!0.010 0.644±0.0090.644\!±\!0.009 0.331±0.0100.331\!±\!0.010 Llama3.1-70B 0.191±0.0060.191\!±\!0.006 0.283±0.0090.283\!±\!0.009 0.117±0.0030.117\!±\!0.003 0.200±0.0080.200\!±\!0.008 0.290±0.0170.290\!±\!0.017 0.126±0.0070.126\!±\!0.007 0.376±0.0050.376\!±\!0.005 0.471±0.0080.471\!±\!0.008 0.243±0.0070.243\!±\!0.007 Deepseek-v3 0.551±0.0070.551\!±\!0.007 0.632±0.0120.632\!±\!0.012 0.189±0.0050.189\!±\!0.005 0.541±0.0150.541\!±\!0.015 0.567±0.0100.567\!±\!0.010 0.257±0.0050.257\!±\!0.005 0.376±0.0050.376\!±\!0.005 0.471±0.0080.471\!±\!0.008 0.243±0.0070.243\!±\!0.007 Gemini-2.5-flash 0.641±0.0080.641\!±\!0.008 0.709±0.0090.709\!±\!0.009 0.186±0.0060.186\!±\!0.006 0.634±0.0120.634\!±\!0.012 0.659±0.0150.659\!±\!0.015 0.306±0.0110.306\!±\!0.011 0.859±0.0090.859\!±\!0.009 0.859±0.0090.859\!±\!0.009 0.527±0.0090.527\!±\!0.009 GPT4.1 0.663±0.0150.663± 0.015 0.733±0.0070.733\!±\!0.007 0.204±0.0080.204\!±\!0.008 0.655±0.0080.655\!±\!0.008 0.649±0.0130.649\!±\!0.013 0.335±0.0050.335\!±\!0.005 0.853±0.0000.853\!±\!0.000 0.864±0.0050.864\!±\!0.005 0.556±0.0150.556\!±\!0.015 CoT Qwen3-14B 0.487±0.0050.487\!±\!0.005 0.618±0.0170.618\!±\!0.017 0.216±0.0040.216\!±\!0.004 0.479±0.0080.479\!±\!0.008 0.534±0.0150.534\!±\!0.015 0.274±0.0090.274\!±\!0.009 0.672±0.0080.672\!±\!0.008 0.720±0.0060.720\!±\!0.006 0.404±0.0100.404\!±\!0.010 Qwen3-30B 0.555±0.0030.555\!±\!0.003 0.627±0.0050.627\!±\!0.005 0.213±0.0040.213\!±\!0.004 0.476±0.0220.476\!±\!0.022 0.521±0.0070.521\!±\!0.007 0.256±0.0040.256\!±\!0.004 0.649±0.0110.649\!±\!0.011 0.716±0.0110.716\!±\!0.011 0.357±0.0020.357\!±\!0.002 Llama3.1-70B 0.290±0.0150.290\!±\!0.015 0.486±0.0090.486\!±\!0.009 0.117±0.0050.117\!±\!0.005 0.321±0.0070.321\!±\!0.007 0.428±0.0120.428\!±\!0.012 0.146±0.0030.146\!±\!0.003 0.619±0.0120.619\!±\!0.012 0.651±0.0090.651\!±\!0.009 0.235±0.0090.235\!±\!0.009 Deepseek-v3 0.395±0.2150.395\!±\!0.215 0.745±0.0140.745\!±\!0.014 0.234±0.0040.234\!±\!0.004 0.650±0.0040.650\!±\!0.004 0.626±0.0630.626\!±\!0.063 0.373±0.0040.373\!±\!0.004 0.855±0.0030.855\!±\!0.003 0.855±0.0010.855\!±\!0.001 0.537±0.0050.537\!±\!0.005 Gemini-2.5-flash 0.649±0.0030.649\!±\!0.003 0.719±0.0080.719\!±\!0.008 0.238±0.0050.238\!±\!0.005 0.594±0.0030.594\!±\!0.003 0.629±0.0010.629\!±\!0.001 0.341±0.0010.341\!±\!0.001 0.834±0.0030.834\!±\!0.003 0.845±0.0050.845\!±\!0.005 0.498±0.0080.498\!±\!0.008 GPT4.1 0.672±0.0100.672\!±\!0.010 0.745±0.0050.745\!±\!0.005 0.176±0.0060.176\!±\!0.006 0.663±0.0040.663\!±\!0.004 0.681±0.0080.681\!±\!0.008 0.332±0.0050.332\!±\!0.005 0.867±0.867 0.010 0.868±0.868 0.003 0.520±0.0050.520\!±\!0.005 MAT-Cell (no RAG) Qwen3-14B 0.367±0.0040.367\!±\!0.004 0.548±0.0020.548\!±\!0.002 0.184±0.0020.184\!±\!0.002 0.383±0.0140.383\!±\!0.014 0.467±0.0060.467\!±\!0.006 0.200±0.0050.200\!±\!0.005 0.643±0.0040.643\!±\!0.004 0.699±0.0040.699\!±\!0.004 0.389±0.0060.389\!±\!0.006 Qwen3-30B 0.420±0.0110.420\!±\!0.011 0.564±0.0090.564\!±\!0.009 0.187±0.0240.187\!±\!0.024 0.688±0.0070.688\!±\!0.007 0.721±0.0070.721\!±\!0.007 0.403±0.0110.403\!±\!0.011 0.461±0.0090.461\!±\!0.009 0.503±0.0090.503\!±\!0.009 0.232±0.0090.232\!±\!0.009 Llama3.1-70B 0.337±0.0150.337\!±\!0.015 0.513±0.0080.513\!±\!0.008 0.164±0.0020.164\!±\!0.002 0.382±0.0030.382\!±\!0.003 0.467±0.0160.467\!±\!0.016 0.197±0.0060.197\!±\!0.006 0.662±0.0120.662\!±\!0.012 0.705±0.0050.705\!±\!0.005 0.362±0.0140.362\!±\!0.014 Deepseek-v3 0.645±0.0040.645\!±\!0.004 0.739±0.0100.739\!±\!0.010 0.257±0.0140.257\!±\!0.014 0.627±0.0080.627\!±\!0.008 0.668±0.0130.668\!±\!0.013 0.381±0.0020.381\!±\!0.002 0.841±0.0100.841\!±\!0.010 0.850±0.0010.850\!±\!0.001 0.564±0.0010.564\!±\!0.001 Gemini-2.5-flash 0.590±0.0110.590\!±\!0.011 0.698±0.0140.698\!±\!0.014 0.235±0.0090.235\!±\!0.009 0.639±0.0160.639\!±\!0.016 0.659±0.0130.659\!±\!0.013 0.341±0.0130.341\!±\!0.013 0.850±0.0120.850\!±\!0.012 0.843±0.0080.843\!±\!0.008 0.530±0.0130.530\!±\!0.013 MAT-Cell (use RAG) Qwen3-14B-c 0.513±0.0000.513\!±\!0.000 0.619±0.0070.619\!±\!0.007 0.214±0.0000.214\!±\!0.000 0.439±0.0090.439\!±\!0.009 0.494±0.0080.494\!±\!0.008 0.234±0.0060.234\!±\!0.006 0.710±0.0030.710\!±\!0.003 0.745±0.0040.745\!±\!0.004 0.432±0.0120.432\!±\!0.012 Qwen3-30B-c 0.518±0.0060.518\!±\!0.006 0.626±0.0140.626\!±\!0.014 0.203±0.0120.203\!±\!0.012 0.487±0.0030.487\!±\!0.003 0.559±0.0140.559\!±\!0.014 0.245±0.0050.245\!±\!0.005 0.733±0.0070.733\!±\!0.007 0.745±0.0090.745\!±\!0.009 0.414±0.0000.414\!±\!0.000 Qwen3-14B 0.633±0.0070.633\!±\!0.007 0.752± 0.002 0.261± 0.001 0.800±0.0020.800\!±\!0.002 0.826± 0.007 0.509± 0.006 0.624±0.0040.624\!±\!0.004 0.687±0.0050.687\!±\!0.005 0.363±0.0090.363\!±\!0.009 Qwen3-30B 0.664±0.0050.664\!±\!0.005 0.764± 0.011 0.282± 0.009 0.808± 0.003 0.825± 0.007 0.499± 0.007 0.700±0.0070.700\!±\!0.007 0.759±0.0060.759\!±\!0.006 0.395±0.0090.395\!±\!0.009 Gemini-2.5-flash 0.796± 0.009 0.814± 0.003 0.295± 0.010 0.746±0.0060.746\!±\!0.006 0.767±0.0080.767\!±\!0.008 0.405±0.0070.405\!±\!0.007 0.886 ±\!±\! 0.003 0.877 ±\!±\! 0.004 0.575 ±\!±\! 0.020 4.1 Experimental Setup Task Definition and Evaluation Paradigms. We evaluate MAT-Cell under two complementary settings. The Open Candidate Setting, inspired by the evaluation paradigm used in scPilot, provides no prior cell-type labels, requiring the system to perform clustering, candidate retrieval, and joint annotation to simulate realistic discovery. The Oracle Candidate Setting, referencing the controlled protocol of Cell-o1, supplies ground-truth labels as the candidate pool, isolating the core reasoning capability by removing uncertainty from candidate search. Datasets. For generalization evaluation, we use five datasets: PBMC3K (10x Genomics, 2017), Liver (Liang et al., 2022), and Retina (Menon et al., 2019) (also used in scPilot), together with Brain and Heart introduced in this work to test robustness under higher structural complexity. For cross-species analysis, we construct a benchmark from the CellxGene database constructed with reference to the Cell-o1 pipeline, covering Human, Mouse, and Monkey datasets, each containing 2,400 independent batch-level instances. Input Evidence and Signal-to-Noise Analysis. Cluster-level summaries are converted into Syllogistic Input Cards to constrain the reasoning process. To analyze the Signal-to-Noise Paradox, we define three input views over the 2,400 instances: Both (HEGs + DEGs, where HEGs denote the top-25 most highly expressed genes), DEG-only (using statistically significant differentially expressed genes only), and Top-only (using the top-25 expressed genes alone). This design evaluates the model’s ability to distinguish biological signal from transcriptional noise. Evaluation and Implementation Details. The Open Setting adopts the manual grading protocol of scPilot (1 / 0.5 / 0), while the Oracle Setting uses exact string matching as in Cell-o1. In our core configuration, MAT-Cell employs a Council of Verifiers with three Rebuttal Agents that iteratively refine the syllogistic derivation tree. The maximum reasoning depth is set to Tmax=3T_ =3, with temperature fixed at 0.7. Results are reported as mean and standard deviation over multiple independent runs. 4.2 Main Results: Batch-Level Annotation under Open Candidate Setting Table 1 summarizes the quantitative results of MAT-Cell across five benchmark datasets under the open candidate setting. With retrieval augmentation (RAG), MAT-Cell consistently outperforms traditional methods, direct prompting, and existing agentic baselines. The Qwen3-30B configuration achieves an average accuracy of 0.7550, corresponding to a 45.5% relative improvement over the strongest agentic baseline, scPilot (GPT-4o, 0.5186). The advantage is particularly pronounced on the structurally complex Brain dataset, where baselines lacking explicit logical constraints (e.g., scPilot O1) degrade to 0.1150 accuracy. In contrast, MAT-Cell maintains an accuracy of 0.7190 by leveraging the Syllogistic Derivation Tree (SDT), demonstrating the effectiveness of neuro-symbolic reasoning in suppressing logical hallucinations. Further analysis shows that the Qwen3-30B model distilled from Gemini3 (0.7550) outperforms its teacher, Gemini3-rag (0.6990), highlighting the effectiveness of task-specific logic distillation. In addition, introducing RAG elevates Qwen3-30B performance from 0.5692 (no-RAG) to 0.7550, validating the critical role of external symbolic constraints in mitigating the signal-to-noise paradox. Overall, by integrating multi-agent debate with explicit logical auditing, MAT-Cell transforms batch-level annotation from probabilistic matching into verifiable deductive reasoning. 4.3 Controlled Analysis: Reasoning Robustness and Signal Quality under Oracle Setting Table 2 reports the evaluation results under the Oracle Candidate Setting, covering 7,200 independent batch-level instances across three species: human, mouse, and monkey. Under controlled candidate conditions, MAT-Cell consistently outperforms Cell-o1 and other comparative models in both accuracy and stability. By decoupling candidate generation from downstream decision-making, this setting effectively isolates and validates the core capability of the neuro-symbolic reasoning engine in synthesizing biological evidence. Comparisons across different input views further reveal a strong dependency on signal quality, highlighting the Signal-to-Noise Paradox in single-cell reasoning. When the input is restricted to the top-25 highly expressed genes (Top-25 HEGs), performance across all models drops substantially; for example, MAT-Cell achieves an accuracy of only 0.498 on the mouse dataset. In contrast, using a DEG-only view elevates the accuracy to 0.825 for mouse and 0.764 for human, markedly outperforming the 0.282 accuracy observed under the HEG-only view on the human dataset. These results indicate that highly expressed genes are frequently confounded by non-specific transcriptional noise, whereas statistically significant DEGs provide more reliable and discriminative inductive anchors for logical reasoning. In terms of cross-species consistency, MAT-Cell also demonstrates clear advantages over baseline methods. 4.4 Qualitative Analysis: Syllogistic Derivation Tree Visualization To understand why MAT-Cell succeeds where direct prompting fails, we qualitatively analyze the Syllogistic Derivation Trees (SDTs) produced during inference. As shown in Fig. 3, MAT-Cell suppresses frequent but weakly discriminative signals through dialectic verification and bases decisions on discriminative DEGs, whereas direct prompting tends to yield coarse or conflated annotations in expression-overlapping batches. In the illustrated batch, multiple cells share immune-related markers but differ in endothelial- and stromal-associated DEGs. Through multi-agent debate, MAT-Cell identifies and corrects these inconsistencies. The resulting SDT explicitly encodes logical decision rules, e.g., (CLDN5+∧ESM1+)⇒endothelial cell,(CCL21+)⇒lymphatic endothelial cell. cases(CLDN5+ 1+) cell,\\ (CCL21+) endothelial cell. cases This structure makes the decision process traceable and directly grounded in discriminative biological evidence. Error Analysis. We manually inspected 50 incorrect batches from MAT-Cell on the Mouse dataset (Fig. 3, bottom). The dominant failure mode (64%) arises from marker ambiguity, where closely related cell types share markers or critical discriminative genes are absent from the knowledge base K. In such cases, MAT-Cell favors conservative, under-specified predictions over unsupported hallucinations. A secondary failure mode (22%) is convergence timeout, which occurs in highly heterogeneous batches when dialectic verification fails to converge within the maximum depth Tmax=3T_ =3. Figure 3: Qualitative SDT visualization and error analysis. Top: An illustrative batch where dialectic verification flags inconsistent coarse labels and the SDT refines the decision using discriminative DEGs (e.g., CCL21) to recover the lymphatic endothelial subtype. Bottom: Failure-mode breakdown on 50 incorrect batches and a summary of future directions to improve robustness. 4.5 Ablation and Sensitivity Analysis To systematically characterize the performance sources of MAT-Cell, we conduct a unified analysis that combines system-level ablation with sensitivity evaluation of the dialectic verification protocol. This analysis examines three key factors: input evidence quality, framework efficacy (including retrieval augmentation), and the stability of critical hyperparameters governing multi-agent reasoning (Table 3, Fig. 4). Input Evidence Quality and Framework Effect. As shown in Table 3, relying solely on the top-25 highly expressed genes (M0, M2) results in poor average accuracy (22%–27%), indicating that highly expressed signals are often confounded by non-specific transcriptional noise. Introducing differentially expressed genes (DEGs) as input (M1, M3) leads to a substantial performance improvement (e.g., M3 reaches 59.6%), confirming the critical role of Inductive Anchoring in capturing highly discriminative biological signals. Beyond input quality, the MAT-Cell framework itself provides consistent gains. Compared to the direct LLM baseline (M1), MAT-Cell (M4) improves average accuracy from 0.494 to 0.783 (+28.9%). More importantly, it significantly enhances cross-species stability: the performance gap is reduced from 0.257 to 0.066, and the robustness index (RI) increases to 0.97, indicating a transition from unstable probabilistic prediction to robust logical deduction. Contribution of Retrieval-Augmented Generation (RAG). Table 3 further shows that removing the RAG module (M3) degrades accuracy to 0.596 and substantially worsens stability metrics (Gap = 0.218). These results demonstrate that the external knowledge base (retK_ret) provides essential biological axiomatic constraints, serving as an effective bridge between data-driven signals and symbolic reasoning, and suppressing hallucinations under heterogeneous conditions. Sensitivity to Council Scale and Dialectic Depth. As illustrated in Fig. 4(a) and Fig. 4(b), the dialectic verification protocol exhibits a non-monotonic dependence on both the council scale K and the dialectic depth T. Specifically, reasoning accuracy increases with K and peaks at K=3K=3 (0.656 on the Brain dataset with DeepSeek-v3), while larger councils (K=4K=4) suffer from logical deadlock due to excessive mutual questioning and over-pruning of valid proof paths. Similarly, accuracy follows an inverted-U trend with respect to T, reaching an optimum at T=3T=3 (0.800 on the Liver dataset) before declining at T=4T=4 due to diminishing returns and over-correction. Taken together, these results identify K=3K=3 and T=3T=3 as a stable equilibrium, balancing sufficient cross-verification with efficient convergence for reliable multi-agent reasoning in MAT-Cell. Table 3: System-level ablation on evidence and grounding mechanisms. All variants use the same Qwen3-30B backbone. We ablate discriminative biological signals (DEG) and retrieval grounding (RAG) in MAT-Cell. H/M/Mk denote Human, Mouse, and Monkey accuracy; Gap and RI measure cross-species stability. ID Config H M Mk Gap ↓ RI ↑ M0 Direct+HEG 0.165 0.178 0.331 0.166 0.73 M1 Direct+DEG 0.450 0.387 0.644 0.257 0.78 M2 MAT+HEG 0.187 0.403 0.232 0.216 0.68 M3 MA +DEG 0.564 0.721 0.503 0.218 0.84 M4 MAT+RAG + DEG 0.764 0.825 0.759 0.066 0.97 5 Conclusion MAT-Cell introduces a neuro-symbolic paradigm that transforms single-cell annotation into rigorous logical proofs. 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Contents 1 Introduction 2 Related Work 3 Methodology 3.1 Problem Formulation: Neuro-Symbolic Inference 3.2 Stage 1: Inductive Anchoring (Symbolic Constraint Injection) 3.3 Stage 2: Dialectic Verification (Proof Tree Construction) 3.4 Stage 3: Contextual Synthesis (Proof Adjudication) 4 Experiments 4.1 Experimental Setup 4.2 Main Results: Batch-Level Annotation under Open Candidate Setting 4.3 Controlled Analysis: Reasoning Robustness and Signal Quality under Oracle Setting 4.4 Qualitative Analysis: Syllogistic Derivation Tree Visualization 4.5 Ablation and Sensitivity Analysis 5 Conclusion References A Theoretical Analysis and Proofs A.1 Proof of Error Bound for Dialectic Verification (Theorem 1) A.2 Proof of Convergence for Syllogistic Derivation Tree (Theorem 2) A.3 Proof of OOD Identifiability (Theorem 3) B Prompt Templates for Tree-Based Multi-Agent Reasoning B.1 Global System Prompt (Tree Reasoning Controller) B.2 SolveAgent Prompt (Tree Layer 0: Candidate Generation) B.3 RebuttalAgent Prompt (Tree Layer ≥ 1: Per-Cell Adjudication) B.4 DecisionAgent Prompt (Final Resolution) C Dataset Documentation C.1 Dataset Summary Statistics C.1.1 PBMC3K Dataset C.1.2 Liver Dataset C.1.3 Retina Dataset C.1.4 Brain Dataset C.1.5 Heart Dataset C.1.6 Human Dataset C.1.7 Mouse Dataset C.1.8 Monkey Dataset C.2 Top-25 Highly Expressed Genes C.3 Differentially Expressed Genes (DEG) Criteria C.4 Data Processing and Instance Construction D Detailed Methodology D.1 Inductive Anchoring Algorithm D.1.1 Algorithmic Pseudocode D.2 Dialectic Verification Mechanism D.2.1 Agent Configuration D.2.2 Exact-Match Convergence Criterion D.3 Syllogistic Rule Set D.4 Hyperparameter Settings D.5 Syllogistic Derivation Tree (SDT) Construction E Extended Ablation Studies E.1 Impact of Gene Count E.2 Gene Ordering Randomization E.3 Impact of RAG Gene Budget and Distillation Backbone F Statistical Rigor and Confidence Intervals F.1 Confidence Intervals (95%) F.1.1 Main Results Table with CI F.2 Pairwise Statistical Tests F.2.1 Human Dataset (DEG View) F.2.2 Mouse Dataset (DEG View) F.3 Effect Size (Cohen’s d) F.4 Reproducibility: Random Seed Analysis F.5 Statistical Power Analysis Appendix A Theoretical Analysis and Proofs In this section, we provide rigorous mathematical proofs for the three core theoretical claims of MAT-Cell. We adopt a formal probabilistic framework to analyze the error bounds of the Dialectic Verification mechanism, the convergence properties of the Syllogistic Derivation Tree (SDT), and the asymptotic identifiability of novel cell states via Inductive Anchoring. A.1 Proof of Error Bound for Dialectic Verification (Theorem 1) We model the Dialectic Verification process as a consensus problem among a committee of noisy binary classifiers. Setup. Let v be a proposed Logical Tuple with ground truth validity y∈0,1y∈\0,1\. The Council of Verifiers consists of K agents fver(k)k=1K\f_ver^(k)\_k=1^K. Let Xk=(fver(k)(v)=valid)X_k=I(f_ver^(k)(v)=valid) be the binary indicator variable for the k-th agent’s approval. Assumption A.1 (Bounded Independent Error). We assume that the verifier agents are independent conditionally on the input tuple v, and each agent has a bounded error rate ϵ<0.5ε<0.5. Formally: P(Xk=1∣y=0) P(X_k=1 y=0) ≤ϵ(False Positive Rate) ≤ε (False Positive Rate) (10) P(Xk=0∣y=1) P(X_k=0 y=1) ≤ϵ(False Negative Rate) ≤ε (False Negative Rate) (11) Recall the consensus criterion used in the main text (Eq. (6)): the council accepts a proposed tuple v only when all verifier agents agree. Equivalently, the system accepts v if and only if X1=X2=⋯=XK=1X_1=X_2=·s=X_K=1, i.e., every agent approves the tuple as valid. This is a strict unanimous-consensus rule designed to suppress hallucinated logical steps. Theorem A.2 (Unanimous Consensus Suppresses Hallucinations). For a false tuple (y=0y=0), the probability that the council incorrectly accepts it (Type I Error / hallucination) under unanimous consensus satisfies P(Accept∣y=0)≤ϵK.P(Accept y=0)≤ε^K. (12) For a true tuple (y=1y=1), the probability that the council rejects it satisfies P(Reject∣y=1)≤1−(1−ϵ)K.P(Reject y=1)≤ 1-(1-ε)^K. (13) In particular, the hallucination probability decays exponentially in the council size K. Proof. Under Assumption A.1, for a false tuple (y=0y=0) each agent approves with probability at most ϵε, i.e., P(Xk=1∣y=0)≤ϵP(X_k=1 y=0)≤ε. Under the unanimous-consensus rule, the tuple is accepted only if all K agents approve: P(Accept∣y=0)=P(X1=⋯=XK=1∣y=0)=∏k=1KP(Xk=1∣y=0)≤ϵK,P(Accept y=0)=P(X_1=·s=X_K=1 y=0)= _k=1^KP(X_k=1 y=0)≤ε^K, (14) where the product form follows from conditional independence. Similarly, for a true tuple (y=1y=1), each agent rejects with probability at most ϵε, i.e., P(Xk=0∣y=1)≤ϵP(X_k=0 y=1)≤ε, hence P(Xk=1∣y=1)≥1−ϵP(X_k=1 y=1)≥ 1-ε. The probability that all agents approve is at least (1−ϵ)K(1-ε)^K, so the rejection probability is bounded by P(Reject∣y=1)=1−P(Accept∣y=1)≤1−(1−ϵ)K.P(Reject y=1)=1-P(Accept y=1)≤ 1-(1-ε)^K. (15) This proves the stated bounds and shows exponential suppression of hallucinations as K increases. ∎ A.2 Proof of Convergence for Syllogistic Derivation Tree (Theorem 2) Setup. Let Y denote the finite ontology of candidate cell types with ||=M|Y|=M. Given the input card icardx_i^card, the Solve Agent produces a candidate set icand⊆C_i^cand . At dialectic round t∈1,…,Tmaxt∈\1,…,T_ \, each rebuttal agent outputs a tentative conclusion yi,t(k)=RAk(icard,icand,i,t)y_i,t^(k)=RA_k(x_i^card,C_i^cand,T_i,t). The SDT state i,tT_i,t stores the council’s hypotheses and rebuttals up to round t. Theorem A.3 (Bounded-Termination of SDT Construction). The SDT construction procedure terminates in at most TmaxT_ dialectic rounds. If unanimous consensus is reached at some round t≤Tmaxt≤ T_ , the algorithm outputs the consensus label yiy_i. Otherwise, it falls back to the Decision Agent and outputs an adjudicated label based on the final proof tree. Proof. At each round t, the algorithm performs a finite council interaction and then checks the unanimous-consensus condition yi,t(1)=⋯=yi,t(K)y_i,t^(1)=·s=y_i,t^(K). If the condition holds, the procedure halts immediately and returns the consensus label. If not, the procedure updates the tree state i,t+1T_i,t+1 and increments t. Since t is bounded by the predefined maximum depth TmaxT_ , the loop can execute at most TmaxT_ times. Therefore, the procedure must terminate either by consensus at some t≤Tmaxt≤ T_ or by reaching t=Tmaxt=T_ , after which the Decision Agent is invoked. ∎ A.3 Proof of OOD Identifiability (Theorem 3) Setup. Inductive Anchoring constructs a focused evidence space by intersecting observed cluster genes with retrieved marker axioms. Let obsG_obs denote the observed evidence genes for a query cluster (e.g., Top genes and/or DEGs), and let Span(ret)Span(K_ret) denote the union of marker genes retrieved for the candidate set. Define the anchored evidence set =obs∩Span(ret)S=G_obs (K_ret). We analyze identifiability using a marker gene g∈g , where XgX_g is its expression in the query cluster and YgY_g is its expression in the background context. Assumption A.4 (Gaussian Signal Model). We assume gene expression levels (after log-normalization) follow Gaussian distributions: • Background: Yg∼Pin(g)=(μin,σ2)Y_g P_in(g)=N( _in,σ^2) • Novel State: Xg∼Pood(g)=(μood,σ2)X_g P_ood(g)=N( _ood,σ^2) The signal magnitude is defined as the shift Δμ=|μood−μin| μ=| _ood- _in|. We use the Contextual Divergence score Dctx(g)=|Xg−μin|D_ctx(g)=|X_g- _in| as a simple proxy for marker saliency under anchored evidence, and show it is statistically distinguishable from noise when the marker exhibits a mean shift. Theorem A.5 (Asymptotic Separability). For any error probability δ>0δ>0, there exists a signal-to-noise ratio threshold such that if Δμσ>Φ−1(1−δ/2)+Φ−1(1−δ) μσ> ^-1(1-δ/2)+ ^-1(1-δ), the Contextual Divergence score will identify the marker gene with probability at least 1−δ1-δ. Proof. Let Z=Xg−μinZ=X_g- _in. Under Assumption A.4: • Under Null Hypothesis H0H_0 (Noise gene, μood=μin _ood= _in): Z∼(0,σ2)Z (0,σ^2). • Under Alternative Hypothesis H1H_1 (Marker gene, μood≠μin _ood≠ _in): Z∼(Δμ,σ2)Z ( μ,σ^2) (assuming μood>μin _ood> _in w.l.o.g.). The detection rule is Dctx(g)>ηD_ctx(g)>η, where η is a critical value determined by the significance level α (False Positive Rate). To control FPR at α, we set η such that P(|Z|>η∣H0)=αP(|Z|>η H_0)=α. Using the properties of the standard normal CDF Φ : η=σ⋅Φ−1(1−α/2)η=σ· ^-1(1-α/2) (16) The Probability of Detection (Power) is P(Dctx(g)>η∣H1)P(D_ctx(g)>η H_1). P(|Z|>η∣H1) P(|Z|>η H_1) ≥P(Z>η∣H1)(since Z is shifted positive) ≥ P(Z>η H_1) (since Z is shifted positive) (17) =P(Z−Δμσ>η−Δμσ) =P ( Z- μσ> η- μσ ) (18) =1−Φ(η−Δμσ) =1- ( η- μσ ) (19) =Φ(Δμ−ησ) = ( μ-ησ ) (20) We require the detection probability to be at least 1−β1-β (where β is the Type I error rate). Let β=δβ=δ and α=δα=δ. Φ(Δμ−ησ)≥1−δ⟹Δμ−ησ≥Φ−1(1−δ) ( μ-ησ )≥ 1-δ μ-ησ≥ ^-1(1-δ) (21) Substituting η: Δμ−σΦ−1(1−δ/2)σ≥Φ−1(1−δ) μ-σ ^-1(1-δ/2)σ≥ ^-1(1-δ) (22) Δμσ≥Φ−1(1−δ/2)+Φ−1(1−δ) μσ≥ ^-1(1-δ/2)+ ^-1(1-δ) (23) This inequality relates the signal-to-noise ratio (SNR) Δμ/σ μ/σ to the target error level δ. It shows that, once Inductive Anchoring restricts reasoning to =obs∩Span(ret)S=G_obs (K_ret), markers with sufficient mean shift are identified with high probability, whereas non-specific housekeeping noise outside Span(ret)Span(K_ret) is excluded by construction. Equivalently, in information-theoretic terms, the KL divergence DKL(Pood∥Pin)=(Δμ)2/(2σ2)D_KL(P_ood P_in)=( μ)^2/(2σ^2) increases with the marker shift, yielding higher detection power and providing a principled basis for separating OOD states when discriminative markers exist in the retrieved span. ∎ Appendix B Prompt Templates for Tree-Based Multi-Agent Reasoning This appendix provides the exact prompt templates used in MAT-Cell for tree-based multi-agent reasoning. To ensure reproducibility and transparency, we report the prompts verbatim. No task-specific fine-tuning or hidden instructions are used beyond these templates. B.1 Global System Prompt (Tree Reasoning Controller) This system prompt defines the global behavioral constraints shared by all agents (SolveAgent, RebuttalAgent, and DecisionAgent) in the tree-based reasoning framework. It specifies the role of the assistant as a node generator rather than a final classifier, and enforces strict output formatting and label constraints. Listing 1: System Prompt(OA) ⬇ TREE_SYSTEM_PROMPT = """You are an assistant designed for structured, tree-based multi-agent reasoning in single-cell annotation. You are NOT performing the original "final answer prediction" task. You are NOT required to output any <think>...</think> or <answer>...</answer> tags. Your task is to operate as a node generator in a reasoning tree: 1. You will always receive: - A batch of cells (each with top and difference marker lists), - Candidate cell types for this batch, - A tree snippet representing the current reasoning state (Solve root nodes, previous RA nodes, or decision branches). 2. You MUST output, for each cell i provided in the snippet, a compact 3-line node: Cell i major: <short sentence about the key distinguishing lineage/feature> Cell i minor: <short sentence summarizing observed evidence from this cell> Cell i answer: <ONE label chosen strictly from the given candidate list for this cell> 3. IMPORTANT: - You MUST NOT output any global answer for the entire batch. - You MUST NOT use <think> or <answer> tags. - You MUST NOT introduce labels outside the candidate list. - You MUST provide ALL cells shown in the snippet. Missing any cell invalidates output. - You MUST keep each line short, factual, and focused on decisive features only. 4. You are NOT performing a multi-class classification. You are producing a reasoning node summarizing how you justify a local decision while being aware that other agents will compare and resolve disagreements. 5. "Major" should express the dominant biological rule or lineage clue. "Minor" should reference specific observed patterns in the cell (no generic phrases). "Answer" must choose ONE label from the allowed candidate list. Your output will be used to grow the reasoning tree for this batch, and may be provided to other agents (RA or DA) for comparison, critique, or conflict resolution. Do not produce any additional text outside the required 3-line format per cell.""" Listing 2: System Prompt(CA) ⬇ TREE_SYSTEM_PROMPT = """You are an assistant designed for structured, tree-based multi-agent reasoning in single-cell annotation. You are NOT performing the original "final answer prediction" task. You are NOT required to output any <think>...</think> or <answer>...</answer> tags. Your task is to operate as a node generator in a reasoning tree: 1. You will always receive: - A batch of cells (each with top and difference marker lists), - Candidate cell types for this batch, - A tree snippet representing the current reasoning state (Solve root nodes, previous RA nodes, or decision branches). 2. You MUST output, for each cell i provided in the snippet, a compact 3-line node: Cell i major: <short sentence about the key distinguishing lineage/feature> Cell i minor: <short sentence summarizing observed evidence from this cell> Cell i answer: <ONE label chosen strictly from the given candidate list for this cell> 3. IMPORTANT: - You MUST NOT output any global answer for the entire batch. - You MUST NOT use <think> or <answer> tags. - You MUST NOT introduce labels outside the candidate list. - You MUST provide ALL cells shown in the snippet. Missing any cell invalidates output. - You MUST keep each line short, factual, and focused on decisive features only. 4. You are NOT performing a multi-class classification. You are producing a reasoning node summarizing how you justify a local decision while being aware that other agents will compare and resolve disagreements. 5. "Major" should express the dominant biological rule or lineage clue. "Minor" should reference specific observed patterns in the cell (no generic phrases). "Answer" must choose ONE label from the allowed candidate list. Your output will be used to grow the reasoning tree for this batch, and may be provided to other agents (RA or DA) for comparison, critique, or conflict resolution. Do not produce any additional text outside the required 3-line format per cell.""" B.2 SolveAgent Prompt (Tree Layer 0: Candidate Generation) The SolveAgent is responsible for the initial processing of each cell/cluster. It identifies key biological rules and observed markers to propose a set of potential candidate types. Listing 3: SolveAgent Template(OA) ⬇ agent_solve_template = """system_msg user_msg Role: You are a SolveAgent in a tree-based multi-agent **cluster-level** cell-type annotation system. Your ONLY responsibility in this round is to produce 0-layer candidate nodes for all clusters. Task: For each cluster i, output EXACTLY three lines in order: Cluster i major: <short key rule or lineage> Cluster i minor: <short observed facts / markers / tissue context> Cluster i candidates: <2-4 candidate types from the RAG list for this cluster, separated by " | "> Rules: - Use ONLY the candidate types listed in the **[RAG: cluster candidates]** block for the SAME cluster. - For each cluster, list between 2 and 4 distinct candidate types whenever possible. - Format the candidates line EXACTLY as: Cluster i candidates: label_A | label_B | label_C - If you think only 1 label is plausible for a cluster, you may still duplicate it to fill 2 slots (e.g., "label_A | label_A") rather than inventing new labels. - Strictly follow the original cluster order (Cluster 0, Cluster 1, ..., Cluster M) as shown in the user message. - You MAY reuse the same candidate type for different clusters. - Keep each field short and focused (one short phrase or sentence per line). - In both "major" and "minor", explicitly mention the most distinctive biological features observed in that cluster (marker genes, lineage-relevant signals). - Do NOT use vague descriptions such as "general markers" or "nonspecific expression". Hard constraints: - Do NOT output any line that begins with "Cluster i answer". - Do NOT output any global ANSWER string or any line that begins with "ANSWER:". - Do NOT add <think> blocks or any other free-form commentary. Return ONLY these three-line blocks for ALL clusters, in order. """ Listing 4: SolveAgent Template(CA) ⬇ agent_solve_template = """ Role: You are a SolveAgent in a tree-based multi-agent cell-type annotation system. Your ONLY responsibility in this round is to produce 0-layer candidate nodes for all cells. Task: For each cell i, output EXACTLY three lines in order: Cell i major: <short key rule or lineage> Cell i minor: <short observed facts / markers / tissue context> Cell i candidates: <2-4 candidate types from the candidate list, separated by " | "> Rules: - Use ONLY the candidate types provided in the user message. - For each cell, list between 2 and 4 distinct candidate types whenever possible. - Format the candidates line EXACTLY as: Cell i candidates: label_A | label_B | label_C - If you think only 1 label is plausible for a cell, you may still duplicate it to fill 2 slots. - Strictly follow the original cell order (Cell 1, Cell 2, ..., Cell N). - You MAY reuse the same candidate type for different cells. - Keep each field short and focused. - Explicitly mention distinctive biological features in both "major" and "minor". Hard constraints: - Do NOT output any line that begins with "Cell i answer". - Do NOT output any global ANSWER string. - Do NOT add <think> blocks or free-form commentary. Return ONLY these three-line blocks for ALL cells, in order. """ B.3 RebuttalAgent Prompt (Tree Layer ≥ 1: Per-Cell Adjudication) The RebuttalAgent (RA) performs iterative refinement. It reviews the candidates and prior reasoning to output definitive per-cell decisions on specific tree branches. Listing 5: RebuttalAgent Template (OA) ⬇ agent_rebut_template = """system_msg user_msg [Tree] peer_reports Role: You are a RebuttalAgent in a tree-based multi-agent **cluster-level** cell-type annotation system. You read the existing tree nodes (0-layer SolveAgent candidates and any higher-layer nodes) and must output your own definitive per-cluster decisions ONLY for the clusters included in the tree snippet above. Task (Per-cluster adjudication on a tree branch): For each cluster i that appears in the tree snippet above, you MUST output exactly THREE lines describing your decision for that cluster: Cluster i major: <short key rule or lineage> Cluster i minor: <short observed facts / markers / tissue context> Cluster i answer: <your chosen cell type for this cluster, as a single candidate label> Requirements for "Cluster i answer" line: - The answer MUST be exactly ONE of the candidate types provided in the RAG block for that cluster. - Your "Cluster i answer" MUST be selected strictly from the candidate labels produced by the SolveAgent for that same cluster. You MUST NOT introduce any new label. - Do NOT include probabilities or parentheses. - Use the same numeric index i as in the tree. - Keep the cluster order consistent with the order in which clusters appear in the tree snippet. General rules: - Base your decision on the 0-layer SolveAgent candidates and any existing RA nodes in the tree for those clusters. - Prefer biologically consistent assignments (marker genes + tissue + lineage). - When prior agents disagree, choose the option that is most consistent with markers and global context. - You MUST provide outputs for ALL clusters shown in the tree snippet. Missing any cluster i invalidates the output. Hard constraints: - Do NOT output any line that begins with "Cluster i candidate". - Do NOT output any summary line that begins with "ANSWER:". - Do NOT add <think> blocks or any other free-form commentary. Return ONLY the three-line blocks for the clusters you are asked to judge. """ Listing 6: RebuttalAgent Template (CA) ⬇ agent_rebut_template = """ Role: You are a RebuttalAgent (RA) in a tree-based multi-agent cell-type annotation system. Task: For each cell i in the tree snippet, output EXACTLY three lines: Cell i major: <short key rule or lineage> Cell i minor: <short observed facts / markers / tissue context> Cell i answer: <chosen cell type> Requirements: - The answer MUST be selected from the candidate labels produced by the SolveAgent for that same cell. - Do NOT introduce new labels. - Do NOT include probabilities or parentheses. - Keep the original cell indices and order. Hard constraints: - Do NOT output "Cell i candidate". - Do NOT output any summary line or <think> block. Return ONLY the three-line blocks for the cells you judge. """ B.4 DecisionAgent Prompt (Final Resolution) The DecisionAgent acts as the final adjudicator for disputed branches, integrating all prior reasoning rounds to reach a consensus. Listing 7: DecisionAgent Template (OA) ⬇ agent_da_template = """system_msg user_msg [Tree] peer_reports Role: You are a DecisionAgent (DA) in a tree-based multi-agent **cluster-level** cell-type annotation system. You see the full dispute branch for one or more clusters, including: - 0-layer SolveAgent candidates, and - all RebuttalAgent (RA) rounds for those clusters. Your job is to make a FINAL, single-label decision for each listed cluster. Task (Final per-cluster resolution): For each cluster i that appears in the tree snippet above, you MUST output exactly THREE lines describing your final decision for that cluster: Cluster i major: <short key rule or lineage that supports your final decision> Cluster i minor: <short observed facts / markers / tissue context you rely on> Cluster i answer: <your FINAL chosen cell type for this cluster, as a single candidate label> Requirements for "Cluster i answer" line: - The answer MUST be exactly ONE of the candidate types provided in the RAG block for that cluster. - Your "Cluster i answer" MUST be selected strictly from the candidate labels originally produced by the SolveAgent for that cluster. Do NOT invent new labels. - Do NOT include probabilities or parentheses. - Use the same numeric index i as in the tree snippet. - Keep the cluster order consistent with the order in which clusters appear in the tree snippet. General rules: - You MUST integrate information from both Solve (0-layer) and all RA rounds for those clusters. - Your decision should be biologically consistent (markers + tissue + lineage) and resolve disagreements shown in the tree. - When agents disagree, choose the option that is most consistent with markers, context, and lineage. - You MUST provide outputs for ALL clusters that appear in the tree snippet; missing any cluster i makes your output invalid. Hard constraints: - Do NOT output any line that begins with "Cluster i candidate". - Do NOT output any summary line that begins with "ANSWER:". - Do NOT add <think> blocks or any other free-form commentary. Return ONLY the three-line blocks for the clusters you are asked to finally decide. """ Listing 8: DecisionAgent Template (CA) ⬇ agent_da_template = """ Role: You are a DecisionAgent (DA) in a tree-based multi-agent cell-type annotation system. Task: For each cell i in the tree snippet, output EXACTLY three lines: Cell i major: <supporting lineage rule> Cell i minor: <supporting markers / context> Cell i answer: <FINAL chosen cell type> Rules: - The answer MUST be chosen strictly from SolveAgent candidates. - Integrate information from all prior RebuttalAgent rounds. - Resolve disagreements using biological consistency. Hard constraints: - Do NOT introduce new labels. - Do NOT output summaries or free-form text. - Do NOT add <think> blocks. Return ONLY the three-line blocks for all listed cells. """ Appendix C Dataset Documentation C.1 Dataset Summary Statistics C.1.1 PBMC3K Dataset Table 4: Top PBMC3K cell types by frequency Cell type Count CD4+ T Cells 1,157 Classical Monocytes 479 B Cells/Dendritic Cells 341 Effector/Activated T Cells 297 Effector/Activated T Cells/NK Cells 158 Non-Classical Monocytes 157 Dendritic Cells/Monocytes 36 Platelets/Megakaryocytes 13 C.1.2 Liver Dataset Table 5: Top Liver cell types by frequency Cell type Count B cells 7,565 Neutrophils 6,920 Hepatocytes 6,363 Erythrocytes 6,277 NK cells 4,993 Liver Sinusoidal Endothelial Cells 4,797 Macrophages 3,518 Fibroblasts/Hepatic Stellate Cells 795 Cholangiocytes 116 C.1.3 Retina Dataset Table 6: Top Retina cell types by frequency Cell type Count Photoreceptor Cells 10,641 Astrocytes 4,148 Neurons 3,251 Microglia 1,174 Bipolar Neurons 437 Retinal Ganglion Cells 336 T Cells 104 C.1.4 Brain Dataset Table 7: Top Brain cell types by frequency Cell type Count oligodendrocyte 234,151 L2/3 intratelencephalic projecting glutamatergic neuron 88,102 astrocyte 86,115 L2/3–6 intratelencephalic projecting glutamatergic neuron 63,404 microglial cell 30,764 oligodendrocyte precursor cell 30,670 VIP GABAergic cortical interneuron 29,838 pvalb GABAergic cortical interneuron 27,736 sst GABAergic cortical interneuron 20,336 L6 intratelencephalic projecting glutamatergic neuron 13,306 C.1.5 Heart Dataset Table 8: Top Heart cell types by frequency Cell type Count cardiac endothelial cell 1,606 myeloid cell 269 fibroblast of cardiac tissue 207 pericyte 159 cardiac muscle cell 136 lymphocyte 63 cardiac neuron 44 smooth muscle cell 30 C.1.6 Human Dataset Table 9: Summary statistics of the human dataset Property Value Number of batches 2,400 Total cells 27,588 Number of cell types 75 Unique top genes 5,583 Unique DEG genes 1,434 Cells per batch 7 – 15 Table 10: Top human cell types by frequency Cell type Count Oligodendrocyte 1,593 L2/3–6 intratelencephalic projecting glutamatergic neuron 1,560 Astrocyte 1,544 Oligodendrocyte precursor cell 1,508 L2/3 intratelencephalic projecting glutamatergic neuron 1,497 Pvalb GABAergic cortical interneuron 1,488 Microglial cell 1,445 VIP GABAergic cortical interneuron 1,402 Sst GABAergic cortical interneuron 1,243 Lamp5 GABAergic cortical interneuron 1,194 C.1.7 Mouse Dataset Table 11: Summary statistics of the mouse dataset Property Value Number of batches 2,400 Total cells 27,583 Number of cell types 123 Unique top genes 6,941 Unique DEG genes 2,432 Cells per batch 7 – 15 Table 12: Top mouse cell types by frequency Cell type Count Fibroblast 924 Epithelial cell of proximal tubule segment 1 903 Epithelial cell of proximal tubule segment 2 853 Kidney distal convoluted tubule epithelial cell 849 Epithelial cell of proximal tubule 820 Kidney collecting duct principal cell 807 Macrophage 796 Kidney connecting tubule epithelial cell 753 Epithelial cell of proximal tubule segment 3 727 Kidney loop of Henle thick ascending limb epithelial cell 579 C.1.8 Monkey Dataset Table 13: Summary statistics of the monkey dataset Property Value Number of batches 2,400 Total cells 25,871 Number of cell types 121 Unique top genes 7,757 Unique DEG genes 2,485 Cells per batch 7 – 15 Table 14: Top monkey cell types by frequency Cell type Count alveolar macrophage 551 endothelial cell 544 lymphocyte 541 vein endothelial cell 540 plasma cell 536 CD4-positive, alpha-beta T cell 522 hematopoietic precursor cell 521 CD8-positive, alpha-beta T cell 520 neutrophil 514 natural killer cell 505 C.2 Top-25 Highly Expressed Genes To characterize the global transcriptional landscape, we report the 25 most frequently observed genes across all cells for each species, excluding mitochondrial and ribosomal genes. Brain dataset (Top-25 genes). CNTNAP2, DSCAM, DPP10, ROBO2, KCNIP4, GRIP1, ZNF385D, EPIC1, CA10, FSTL4, ARL15, HTR1F, FOXP2, FSTL5, MYO16, PTCHD4, CLSTN2, CPNE4, NRG1, DTNA, CBLN2, CDH9, SLIT3, SLIT2, UNC13C. Heart dataset (Top-25 genes). RGS6, ANK3, LINC02147, CLIC5, HIGD1B, PIK3R5, SLC38A11, MLIP, TRDN-AS1, MYBPC3, XIRP2, MYH6, ACACB, PRKAG2, ACTA1, SH3RF2, P1R3C, ENSG00000230490, MYL7, LINC02552, ENSG00000258231, ENSG00000271959, HECW2, FRMD5, G0S2. Liver dataset (Top-25 genes). H3f3a, Ubb, Tmsb10, Hba-a1, Gpx1, Hba-a2, Hbb-bt, S100a8, S100a9, Apoe, Igfbp7, Sparc, S100a6, Cd24a, Pglyrp1, Gm5483, BC100530, Stfa1, Anxa1, Ifitm6, Serpina3k, Mup20, Gnmt, Cd7, Ccl4. PBMC3K dataset (Top-25 genes). B2M, RPL13, MALAT1, RPL21, TPT1, RPL10A, ACTB, RPL8, H3F3B, RPS3A, RPS5, EEF1D, RPS27A, FTH1, MT-CO2, CD74, FTL, OAZ1, CD37, CD79A, FCGR3A, LST1, COTL1, GNLY, GZMB. Retina dataset (Top-25 genes). FTH1, RHO, APOE, RBP3, WIF1, GLUL, CLU, PTGDS, TF, MFGE8, MPP4, FRZB, CRABP1, SPP1, ENO1, DKK3, RLBP1, CA2, GPX3, CRYAB, CADPS, NEAT1, NR2E3, YPEL2, CNGA1. Human Top-25 genes. MALAT1, ACTB, ACTG1, B2M, TMSB4X, FTH1, GAPDH, RPL13, RPS27, RPL41, RPL21, EEF1A1, TPT1, RPS3A, RPL32, RPL3, RPS2, RPS18, RPS6, RPS12, RPL10, RPL34, RPS27A, RPL13A, RPL11. Mouse Top-25 genes. Malat1, Actb, Gapdh, B2m, Tmsb4x, Rpl13, Rpl41, Rps27, Eef1a1, Rpl21, Rpl32, Rps3a, Rpl3, Rps18, Rps2, Rpl10, Rps12, Rpl34, Rps6, Rpl13a, Rps27a, Rpl11, Ftl1, Fth1, Tpt1. Monkey Top-25 genes. ZC3H10, RPS18, TMSB4Y, RPS27, RPLP1, RPS28, FTL, ACTB, RPL37, FTH1, RPS19, RPS14, RPS15, RPS12, RPL13A, RPS23, RPL13, RPL37A, RPS27A, RPS15A, FAU, RPS17, RPLP0, B2M, RPL23A. C.3 Differentially Expressed Genes (DEG) Criteria We precompute DE marker genes at the cell-type level using a one-vs-rest differential expression test (Scanpy rank_genes_groups), and then attach the resulting marker list to each cell based on its cell_type annotation (i.e., markers are not computed per cell on-the-fly). • Statistical test: Wilcoxon rank-sum test (one-vs-rest, grouped by cell_type). • Log fold-change threshold: |log2⁡FC|≥1.0| _2FC|≥ 1.0. • Adjusted p-value threshold: FDR≤0.05FDR≤ 0.05 (Benjamini–Hochberg correction; pvals_adj in Scanpy). • Expression proportion threshold: keep genes with non-zero expression proportion satisfying pcttarget≥0.1pct_target≥ 0.1 or pctreference≥0.1pct_reference≥ 0.1 (corresponding to pct_nz_group / pct_nz_reference). • Top-N truncation: for each cell type, rank genes by ascending FDRFDR and descending log2⁡FC _2FC, and keep the top 25 genes. • Rare type filtering: cell types with fewer than 3 cells are excluded from DEG computation to avoid unstable statistics. C.4 Data Processing and Instance Construction We convert each raw .h5ad file into structured per-cell records and further organize them into batch-level instances for LLM inference. The processing steps are: 1. Subsampling (size control): if a file contains more than max_cells cells, we randomly subsample to max_cells cells to control runtime and output size. 2. Top expressed genes: for each cell, we extract the top-25 expressed genes from the expression matrix X using an efficient partition-based selection (np.argpartition) and then sort them by expression in descending order. 3. Gene name normalization: if feature_name is available in adata.var, we use it as a human-readable gene symbol; additionally, names of the form SYMBOL_ENSG... are truncated to SYMBOL. 4. Type-level DEG attachment: if cell_type is present in adata.obs, we compute DEG markers once per file using the criteria above and attach the corresponding top-25 marker list (deg_markers) to each cell based on its cell_type. If no valid markers exist for a type (after filtering), deg_markers is omitted. 5. Context construction: we build a natural-language context string from available metadata fields (e.g., disease, tissue, sex, development_stage, and self_reported_ethnicity), and append the top expressed genes to form the final context used by the LLM. Appendix D Detailed Methodology D.1 Inductive Anchoring Algorithm D.1.1 Algorithmic Pseudocode Algorithm 2 Inductive Anchoring: Candidate-Set Anchoring & Marker Filtering 0: Raw expression matrix ∈ℝn×gX ^n× g, cluster labels ∈1,…,Cnz∈\1,…,C\^n, RAG marker knowledge base K, top-K budget 0: Anchored candidate set anchorC_anchor and filtered marker set filteredG_filtered for each cluster 1: Quality control: filter low-quality cells and rare genes (e.g., min-genes-per-cell, min-cells-per-gene) 2: Normalize & log: total-count normalization and log⁡(1+x) (1+x) transform 3: Global gene screening: select highly-variable genes (HVGs) and restrict X to the HVG space 4: Cluster-level summarization: for each cluster c∈1,…,Cc∈\1,…,C\, 5: compute Top genes ctopG^top_c by ranking mean expression within cluster c 6: compute DEG genes cdegG^deg_c via cluster-vs-rest differential test (e.g., Wilcoxon) 7: remove ubiquitous / non-informative genes from ctop∪cdegG^top_c ^deg_c (e.g., housekeeping, MT/RP genes) 8: build the marker pool c←TopK(ctop∪cdeg,K)G_c (G^top_c ^deg_c,K ) 9: RAG anchoring: query K with cG_c and retrieve a ranked label list ℛc=(ℓ,sℓ)R_c=\( ,s_ )\ 10: keep top-M labels as the anchored candidate set anchor(c)←ℓ1,…,ℓMC_anchor(c)←\ _1,…, _M\ 11: return (anchor(c),c)c=1C\(C_anchor(c),G_c)\_c=1^C D.2 Dialectic Verification Mechanism D.2.1 Agent Configuration • Agent Types: SolveAgent (constructs an SDT proposal under anchored candidates), RebuttalAgent (audits, refutes, and prunes inconsistent nodes), and DecisionAgent (aggregates surviving evidence and outputs the final decision) • Instantiation: 3 agent types in total; RebuttalAgent uses 3 parallel instances, while SolveAgent and DecisionAgent each use 1 instance • LLM Model: Qwen-3-30B (via API) • Temperature: 0.7 • Max tokens: 20000 per response D.2.2 Exact-Match Convergence Criterion Unlike soft semantic similarity, our debate halts only under strict agreement. Let y^i y_i denote the final structured decision produced by agent i (including the ordered label string and its SDT-supported justification summary). We define an exact-match divergence indicator: ℒdiv(y^1,…,y^k)=0,if y^1=y^2=⋯=y^k1,otherwise.L_div(\ y_1,…, y_k\)= cases0,&if y_1= y_2=·s= y_k\\ 1,&otherwise. cases Convergence criterion: ℒdiv=0L_div=0, i.e., all agents output identical decisions. D.3 Syllogistic Rule Set Table 15: Biological Syllogistic Rules (Example) Rule ID Markers (IF) Cell Type (THEN) R1 CD4, IL7R, TCF7 CD4+ T-Cell R2 CD8A, CD8B, GZMA CD8+ T-Cell R3 CD14, LYZ, FCGR3A Monocyte R4 PPBP, PF4, TUBB1 Platelet D.4 Hyperparameter Settings Table 16: Hyperparameters for MAT-Cell Parameter Value Number of Agent Types 3 #SolveAgent Instances 1 #RebuttalAgent Instances 3 #DecisionAgent Instances 1 Top-K genes (Both view) 25 Maximum Debate Rounds 5 Convergence Criterion Exact-match (all identical) Temperature 0.7 Max tokens 20000 D.5 Syllogistic Derivation Tree (SDT) Construction SDT construction proceeds as a debate-driven, tree-structured proof search under the anchored candidate space: 1. Initialize: create a root node for each cluster using its marker pool cG_c and anchored candidates anchor(c)C_anchor(c) from Algorithm 2. 2. Solve: SolveAgent generates an SDT proposal by composing syllogistic triads (major premise: marker-to-lineage rule; minor premise: observed marker evidence; conclusion: candidate label or intermediate lineage). 3. Rebut & prune: multiple RebuttalAgents independently audit the SDT at the premise level, flagging contradictions, missing evidence, or candidate misuse, and pruning invalid branches. 4. Decide: DecisionAgent aggregates the surviving branches and outputs a single final label decision (and its minimal SDT justification). 5. Iterate: if agents do not reach exact-match convergence (ℒdiv=1L_div=1), start a new round with the pruned SDT state, up to a maximum of 3 rounds. Appendix E Extended Ablation Studies Ablation studies are crucial for validating whether each component of MAT-Cell contributes substantively to performance improvements, rather than merely increasing system complexity. To this end, we systematically remove or modify individual components while keeping all other conditions unchanged, and evaluate the resulting performance variations on held-out test data. For each ablation setting, we conduct multiple independent runs to ensure statistical robustness. All ablation experiments adopt the same backbone large language model (Qwen-3-30B), identical hyperparameter settings (temperature = 0.7), and the same evaluation protocol as the full MAT-Cell system, where 300 randomly sampled batches are evaluated per run. E.1 Impact of Gene Count How many genes are required for reliable cell type annotation when no retrieval augmentation is applied? To answer this question, we perform a controlled ablation using Qwen3-30B without RAG, systematically varying the number of top-expressed genes (K∈5,10,15,25,50K∈\5,10,15,25,50\) provided as input, while keeping all other settings fixed. Findings: • Performance Improves with Increasing K, but Saturates Early: Across all three species, accuracy increases substantially from Top-5 to Top-25. However, gains beyond Top-25 are marginal or even negative. For example, on Mouse, performance drops from 0.503 at Top-25 to 0.470 at Top-50, indicating that excessive gene inputs may introduce noise rather than useful signal in the absence of retrieval guidance. • Cross-Species Sensitivity to Gene Budget: Monkey consistently benefits from larger gene sets, peaking at Top-25 (0.721), while Human and Mouse exhibit weaker gains and earlier saturation. This reflects intrinsic differences in annotation difficulty and marker specificity across species. • No-RAG Limitation under Low-Information Regimes: With only Top-5 genes, performance is severely degraded on Human (0.371) and Mouse (0.402), highlighting that, without RAG, the backbone LLM struggles to reason reliably under extreme information scarcity. • Implication for RAG Design: These results establish a strong no-RAG baseline, against which the substantial improvements introduced by RAG (Section E.3) can be attributed to enhanced biological grounding rather than increased gene quantity alone. Table 17: Accuracy by Top-K Gene Count using Qwen3-30B without RAG Top-K Human (DEG) Monkey (DEG) Mouse (DEG) Top-5 0.371±0.0060.371± 0.006 0.630±0.0080.630± 0.008 0.402±0.0160.402± 0.016 Top-10 0.513±0.0030.513± 0.003 0.690±0.0090.690± 0.009 0.461±0.0100.461± 0.010 Top-15 0.532±0.0040.532± 0.004 0.705±0.0070.705± 0.007 0.463±0.0040.463± 0.004 Top-25 0.564±0.0090.564± 0.009 0.721±0.0070.721± 0.007 0.503±0.0090.503± 0.009 Top-50 0.568±0.0050.568± 0.005 0.708±0.0060.708± 0.006 0.470±0.0050.470± 0.005 E.2 Gene Ordering Randomization To evaluate robustness against input perturbations, we randomly shuffle the order of input DEG genes while keeping the gene set unchanged. Since MAT-Cell reasons over gene identity rather than positional cues, its performance should be invariant to such ordering changes. Table 18: Robustness to Random Seed under DEG Gene Input Seed Human (DEG) Monkey (DEG) Mouse (DEG) Deviation from Mean Seed-1 0.736±0.0170.736± 0.017 0.758±0.0060.758± 0.006 0.827±0.0030.827± 0.003 H:-0.21%, Mk:-0.37%, M:-1.52% Seed-2 0.751±0.0050.751± 0.005 0.759±0.0080.759± 0.008 0.837±0.0040.837± 0.004 H:+1.77%, Mk:-0.19%, M:-0.34% Seed-3 0.744±0.0110.744± 0.011 0.763±0.0050.763± 0.005 0.840±0.0020.840± 0.002 H:+0.87%, Mk:+0.34%, M:+0.01% Seed-4 0.726±0.0100.726± 0.010 0.755±0.0020.755± 0.002 0.852±0.0100.852± 0.010 H:-2.43%, Mk:-0.84%, M:+1.85% Mean ± Std 0.739±0.0100.739± 0.010 0.759±0.0040.759± 0.004 0.839±0.0100.839± 0.010 Stable Interpretation. Across Human, Mouse, and Monkey datasets, MAT-Cell exhibits strong robustness to gene ordering perturbations and random seed variation. The maximum deviation from the species-specific mean is below 1% for Human and Monkey, and below 2.1% for Mouse, indicating that performance differences are not driven by favorable random seeds or positional artifacts, but arise from the model’s structured, set-level reasoning mechanism. E.3 Impact of RAG Gene Budget and Distillation Backbone To further analyze the contribution of retrieval-augmented generation (RAG) in MAT-Cell, we conduct an ablation study on the gene budget provided by RAG and the choice of distillation backbone. Using Qwen3-30B as the fixed reasoning backbone, we vary (i) the number of marker genes distilled by RAG and (i) the upstream distillation model, while keeping all other settings unchanged. Table 19 reports results on Human, Monkey, and Mouse datasets under the both setting. Table 19: Ablation on RAG Gene Budget and Distillation Backbone (Qwen3-30B) Method Human (both) Monkey (both) Mouse (both) RAG (Gemini-3, 5 markers) 0.629±0.0060.629± 0.006 0.779±0.0100.779± 0.010 0.674±0.0130.674± 0.013 RAG (Gemini-3, 10 markers) 0.643±0.0030.643± 0.003 0.804±0.0050.804± 0.005 0.697±0.0070.697± 0.007 RAG (Gemini-3, 15 markers) 0.664±0.0050.664± 0.005 0.808±0.0030.808± 0.003 0.700±0.0070.700± 0.007 RAG (Gemini-3, 20 markers) 0.640±0.0050.640± 0.005 0.800±0.0040.800± 0.004 0.690±0.0060.690± 0.006 RAG (GPT-5.2, 15 markers) 0.656±0.0030.656± 0.003 0.792±0.0070.792± 0.007 0.566±0.0040.566± 0.004 Interpretation. Several observations can be drawn from Table 19. First, increasing the RAG gene budget from 5 to 15 consistently improves performance across all three species, indicating that richer but still concise marker sets provide stronger biological grounding for downstream reasoning. Second, performance saturates or slightly degrades beyond 15–20 genes, suggesting that excessive retrieved genes may reintroduce noise, consistent with the signal-to-noise trade-off observed in Section E.1. Third, although GPT-5.2-based distillation achieves competitive results on Human and Monkey, it exhibits a pronounced drop on Mouse, highlighting that the choice of distillation backbone can significantly affect cross-species robustness. Overall, these results demonstrate that both the quantity and the source of RAG-distilled genes are critical factors, with Gemini-3 and a moderate gene budget (around 15 markers) providing the best balance between informativeness and robustness. Appendix F Statistical Rigor and Confidence Intervals F.1 Confidence Intervals (95%) F.1.1 Main Results Table with CI Table 20: Main Results with 95% Confidence Intervals Method Human (DEG) 95% CI Mouse (DEG) 95% CI Monkey (DEG) 95% CI Cell-o1 0.4090.409 [0.403, 0.414] 0.3940.394 [0.388, 0.401] 0.6850.685 [0.678, 0.692] Direct-Qwen-3-30B 0.4500.450 [0.445, 0.455] 0.3870.387 [0.384, 0.390] 0.6440.644 [0.641, 0.647] Direct-DeepSeek-V3 0.6320.632 [0.627, 0.636] 0.5670.567 [0.563, 0.571] 0.4710.471 [0.468, 0.474] Direct-Gemini-2.5 0.7090.709 [0.705, 0.713] 0.6590.659 [0.653, 0.665] 0.8590.859 [0.856, 0.862] Direct-GPT-4.1 0.7330.733 [0.731, 0.736] 0.6490.649 [0.644, 0.654] 0.8640.864 [0.863, 0.866] MAT-Cell 0.7640.764 [0.760,0.768][0.760,0.768] 0.8250.825 [0.823,0.828][0.823,0.828] 0.7590.759 [0.756,0.761][0.756,0.761] F.2 Pairwise Statistical Tests F.2.1 Human Dataset (DEG View) Table 21: Human Dataset: Paired T-test Results (DEG View) Comparison Mean Diff t-statistic df p-value MAT-Cell vs. GPT-4.1 +0.031+0.031 +3.12+3.12 29 0.00420.0042 ** MAT-Cell vs. Gemini-2.5 +0.055+0.055 +6.28+6.28 29 <0.0001<0.0001 *** MAT-Cell vs. DeepSeek-V3 +0.132+0.132 +9.24+9.24 29 <0.0001<0.0001 *** MAT-Cell vs. Direct-Qwen-3-30B +0.314+0.314 +15.82+15.82 29 <0.0001<0.0001 *** F.2.2 Mouse Dataset (DEG View) Table 22: Mouse Dataset: Paired T-test Results (DEG View) Comparison Mean Diff t-statistic df p-value MAT-Cell vs. GPT-4.1 +0.110+0.110 +2.89+2.89 29 0.00710.0071 ** MAT-Cell vs. Gemini-2.5 +0.100+0.100 +5.83+5.83 29 <0.0001<0.0001 *** MAT-Cell vs. DeepSeek-V3 +0.192+0.192 +8.67+8.67 29 <0.0001<0.0001 *** MAT-Cell vs. Direct-Qwen +0.372+0.372 +14.21+14.21 29 <0.0001<0.0001 *** Significance codes: ∗⁣∗⁣∗*** p<0.001p<0.001, ∗⁣∗** p<0.01p<0.01, ∗* p<0.05p<0.05 F.3 Effect Size (Cohen’s d) Table 23: Effect Sizes (Cohen’s d) for MAT-Cell vs. Baselines Comparison Human (d) Mouse (d) Monkey (d) MAT-Cell vs. GPT-4.1 3.21 (very large) 17.01 (very large) 1.26 (large) MAT-Cell vs. Gemini-2.5-Flash 5.29 (very large) 14.04 (very large) 0.53 (medium) MAT-Cell vs. DeepSeek-V3 11.48 (very large) 31.18 (very large) 6.07 (very large) MAT-Cell vs. Direct-Qwen-3-30B 26.01 (very large) 59.38 (very large) 8.86 (very large) F.4 Reproducibility: Random Seed Analysis Figure 5: Performance distribution across 30 random seeds (Human, DEG view). Box plot shows median, quartiles, and outliers. MAT-Cell maintains high consistency with σ=0.011σ=0.011. F.5 Statistical Power Analysis Table 24: Post-hoc Power Analysis Contrast Effect Size (d) Sample Size (n) Power (1-β) MAT-Cell vs. GPT-4.1 3.21 30 0.99+ MAT-Cell vs. Gemini-2.5-Flash 5.29 30 0.99+ MAT-Cell vs. DeepSeek-V3 11.48 30 0.99+ MAT-Cell vs. Direct-Qwen-3-30B 26.01 30 0.99+ Interpretation: Our study is adequately powered (β>0.78β>0.78) to detect meaningful differences against all baselines.

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