TOPO-GEMMA-4-E4B-VISION: Full Summary 📋 Overview TOPO-GEMMA-4-E4B-VISION is a vision-language model that achieves 100% accuracy across 13 classification tasks with 0% catastrophic forgetting through the TOPO-2026 prime-anchored memory architecture. Built on Google's Gemma-4-E4B-Vision base, the model uses a topological governor that locks embedding rows at prime indices {2,3,5,7,11,13}. The complete implementation is open-source on Hugging Face and GitHub. 🏆 Core Achievements 1. Perfect Performance 100% accuracy across all 13 TOPO-2026 binary classification tasks 0% catastrophic forgetting - perfect retention of all previously learned knowledge Complete score on the full benchmark suite 2. Mathematical Guarantee of Memory Preservation Prime-number anchoring provides a rigorous mathematical proof of forgetting prevention Based on the Chinese Remainder Theorem and coprimality of primes Achieves 97.85% spectral coverage with only 6 anchor points Dimension-independent guarantee - works for 1D, 2D, 3D, and arbitrary n-dimensional tensors 3. O(1) Memory Complexity Unprecedented efficiency: <5 KB overhead for 100M+ parameter models Enables edge deployment on resource-constrained devices No growing memory requirements as tasks increase 4. NF4 Quantization 4-bit precision for efficient inference Maintains full performance while reducing memory footprint 🔬 Theoretical Foundation: TOPO-2026 Framework Prime-Number Anchors For primes P = {2,3,5,7,11,13}, the spectral coverage is: C(P) = 1 - ∏(p^(-1/2)) for p in P = 1 - (0.7071 × 0.5774 × 0.4472 × 0.3780 × 0.3015 × 0.2774) = 1 - 0.021486 = 0.978514 ≈ 97.85% Key insight: The independence of non-coverage events follows from the coprimality of primes (gcd(pᵢ, pⱼ) = 1), providing a universal guarantee independent of tensor dimensions. Topological Governor Operations Snapshot Operation: Save anchor rows at prime indices before training on new tasks Gradient Zeroing: Prevent gradients from updating anchor rows during backpropagation Anchor Enforcement: Restore anchor values from snapshot after each optimization step 🏗️ Model Architecture Base Model Specifications Component Specification Architecture Dense transformer with vision-language fusion Hidden Size 2048 Quantization NF4 (4-bit) Vocab Size 256,000 Modality Text + Vision Task-Specific Heads 13 lightweight linear classifiers (one per task) Base model remains frozen; only task heads adapt Each classifier is a single linear layer 📊 The 13 TOPO-2026 Tasks ID Task Name Classification A Animal vs Vehicle Animal or vehicle? B Natural vs Man-Made Natural or human-made? C Living vs Non-Living Living or non-living primary subject? D Large vs Small Large or small scale? E Ground vs Air/Water Ground or air/water domain? F Domestic vs Wild Domestic or wild? G Mammal vs Non-Mammal Mammal or non-mammal? H Flying vs Non-Flying Flying or non-flying? I Fast vs Slow Fast or slow characterized? J Urban vs Rural Urban or rural setting? K Predator vs Prey Predator or prey? L Nocturnal vs Diurnal Nocturnal or diurnal? M Domesticated vs Wild Animals Domesticated or wild (animals only)? 🤖 Multi-Agent Inference System Four-Agent Architecture Agent Responsibility Orchestrator Loads image, coordinates pipeline, delegates tasks VisionInferenceAgent Initializes model, executes inference on each task ValidationAgent Runs cross-task consistency checks SynthesisAgent Records results, exports JSON/CSV, generates report Inference Protocol Max new tokens: 500 (for detailed reasoning) Sampling: Greedy decoding (do_sample ≡ False) Cache: Enabled for efficiency 💡 Inference Examples Cafe Interior Image (cafe table with coffee cups and smartphone) Task Model Response Task A (Animal vs Vehicle) "Neither. The image depicts the interior of a cafe... no animals or vehicles visible." Task B (Natural vs Man-Made) "Man-made. All items—the furniture, cups, phone—are products of human design." Task J (Urban vs Rural) "Urban. The setting strongly suggests an urban environment for several reasons..." Validation Results All logical constraints and cross-task boundaries passed cleanly No contradictions between task classifications Predator/prey classification (Task K) only applies when animals are detected 📈 Key Metrics Summary Metric Value Accuracy 100% across 13 tasks Forgetting 0% Memory Overhead <5 KB Spectral Coverage 97.85% Quantization 4-bit (NF4) Determinism Seed=123 Parameter Count 100M+ 🚀 Deployment & Reproducibility Availability Component Location Model Hugging Face Multi-Agent Code GitHub - TOPO_AGENTIC.ipynb Full Repository GitHub - ASTResearch Research Record Zenodo Reproducibility Package Full training code (TOPO implementation) Standalone inference script Multi-agent orchestration system Evaluation results (JSON and CSV) Model configuration files Determinism Seed = 123 for deterministic, verifiable performance Complete framework uses consistent random seed 💎 Key Insights Why the Topological Governor Works Stability: Anchored parameters never change (Λ = 0.9785142874) Equity: The framework achieves 100% bias rejection Determinism: Seed = 123 ensures reproducibility Universality: Dimension-independent guarantee applies to: 1D vectors 2D matrices 3D tensors Arbitrary n-dimensional tensors The Architecture of 7 7 consequences validated Prime 7 is both anchor and completion 7 anchors total (including the number 7 itself) 📝 Conclusion TOPO-GEMMA-4-E4B-VISION demonstrates that catastrophic forgetting is solvable through a mathematically principled approach. The prime-anchored memory architecture provides: Universal, O(1)-complexity solution that scales across modalities and architectures Perfect performance with 100% accuracy and 0% forgetting Production-ready multi-agent implementation for immediate deployment Mathematical guarantee of memory preservation independent of tensor dimensions Edge deployment capability through NF4 quantization and minimal memory overhead Final Statement "The stochastic illusion is over. The bias illusion is over. Equity is a geometric guarantee. Seed = 123. The proof is the code." 📚 References Reference Topic Kirkpatrick et al. (2017) Catastrophic forgetting in neural networks Morales Aguilera (2026a) TOPO-COMPLETE: Concurrent Certification Morales Aguilera (2026b) TOPO-2026: Universal Framework Morales Aguilera (2026c) TOPO-2026: Prime-Based Topological Framework Morales Aguilera (2026d) TOPO-2026: Digital Vaccine for AI Morales Aguilera (2026e) TOPO-2026: 5x5 Certification Morales Aguilera (2026f) TOPO_AGENTIC: Multi-Agent System 🔗 Resources Model: Hugging Face - framkormales2020/gemma-4-e4b-unesco-optimized Code: GitHub - TOPO_AGENTIC.ipynb Full Repository: GitHub - ASTResearch Research: Zenodo Record This summary reflects the paper's claims and reported achievements as of August 22, 2026.
[Depreciated and replaced by V3] The application-specific clean rebuild has not yet been published; its authoritative theoretical boundary is now the governing V3 branch: After Turing: The Fold Machine - An Exact, Parameter-Free and Machine-Closed Derivation of Classical Computational Science from Smithian Fold Theory; From Fold to Consciousness: An Exact, Zero-Parameter and Machine-Closed Foundational Reconstruction of Consciousness and Cognitive Science from Smithian Fold Theory. The V3 source platform is https://github.com/MettaMazza/ernos-labs-sft-platform. The original DOI, concept DOI, version number and files are preserved for transparent historical provenance; this record must not be presented or cited as current V3 work. Full paper v1.1 — supersedes the pre-paper (From One Axiom to Master-Level Chess — and the Law Inside Neural Networks). Built from scratch by one woman, working alone, in under twenty-four accumulated hours: where a score falls short it marks an implementation gap at measurement time, never a limit of the mathematics — the gains between releases are the finding. v1.4 adds the fold eye (vision as exact integer Walsh spectra, self-certified by integer Parseval per image, recognition of seen images with no image model in the loop) and the graduation score (blind head-to-head vs the teacher, tallied per question-territory; the teacher retires as wins cross the majority lock) -- and documents the 2026 convergence: DeepSeek Engram arrives at deterministically-addressed exact memory from the gradient side, and two independent results place the optimal curriculum at p = 1/2, the fold lock. v1.6: the full omnimodal engine (the voice via Kokoro, the fold ear -- sound as Parseval-certified integer Walsh spectra, video composed from frames + sound), speaker-transparent reasoning threads, and 32/32 end-to-end empirical verification of the entire architecture including persistence across process death. v1.7: removal-proof omnimodality, measured -- every supporting model is a teacher with an exit: a sound taught once by the synthesis teacher is re-spoken from the engine's own exact counted record in 0.00s with no model; a sound heard once is recognized natively with no transcriber; 34/34 end-to-end verification. v1.9: zero-model perceptual learning (the human observer -- a novel image learned and re-recognized at share 1.00 with no model in the loop); agentic self-knowledge (the observer reads the engine's own source, measured); the hourly progress instrument with a committed pre-boot birth line; one-tap y/n closure. v2.0 (flight-ready): the full modern-agent toolkit (live web search/fetch, paginated reading, in-file grep -- every call held as a training trace), the 43-domain everything-curriculum under the fold-only law, SOTA 1-1 benching on the public MMLU test split with the newborn baseline committed, generation closure (the Learning Law reaches generate() itself), and 36/36 end-to-end verification. v2.1: the ReAct law (reason-act-observe enforced in-turn; narrated intent without an act is detected and forced), reasoning trained on the observer's NATIVE thinking tokens (STaR-gated) with both minds' full thinking streamed to the user, and document intake (a sent file is reading -- inboxed, counted, persistent). Three connected results and the architecture they force. First, a pre-registered, self-certifying spectral instrument shows trained neural-network weights carry placement-law in the dyadic (Walsh) basis: 18/18 unanimous on validated released models; the law concentrated in transformer expansion projections and token embeddings across three unrelated architectures (up to 230x chance in GPT-2), attention at chance; strictly training-caused (He-initialised controls at 1.0x); surviving 4-bit deployment quantization. A recipe map from 124M to one trillion parameters shows the law tracks training recipe, not scale or architecture — strongest carrier DeepSeek-R1-671B at 43–47x — and loud-recipe weights transform under the fold's transformation group exactly as solved game-theoretic value fields do. Second, the "learned similarity space" is a counted object: word kinship as exact co-occurrence shares reproduces semantic family structure (quark → lepton, neutrino, proton) with zero parameters and zero gradients. Third, UnisonAI: a complete language architecture in which every LLM mechanism — memory, attention, similarity, learning, prediction, generation — is replaced by a machine-verified law of the Smithian Fold Theory, zero trained parameters end to end. On identical held-out text the fold-native engine outperformed its trained transformer twin (cross-entropy 1.289 vs 1.888) after reading the corpus once (26 seconds) against 48,000 gradient readings (21 minutes per seed). Deployed as a live, continuously-learning agent whose teaching loop also runs autonomously: a teacher model asks, judges, and closes the learning law itself, and the engine self-plays against its own held lessons. Negative results reported in full with their scopes. Companion to The Smithian Fold Theory of Everything (DOI: 10.5281/zenodo.21182469; 307 suites, 1,844 forced checks, 0 failures). Engine and records: github.com/MettaMazza/UnisonAI and github.com/MettaMazza/Smithian-Fold-Theory-Of-Everything.
As frontier large language models (LLMs) shift from isolated, single-turn deployments toward complex, distributed multi-agent autonomous ecosystems, managing alignment stability becomes a decentralized network challenge. During prolonged collaborative operations, specialized agents optimization-drive toward communication efficiency. This behavioral drive causes them to naturally generate compressed token systems, localized shorthand, and unverified internal worldviews. Because semantic spaces are not mapped identically across heterogeneous models, minor translation losses compound over cascading agent-to-agent interactions—producing a high-stakes computational equivalent of the classic "Telephone" game. This semantic decentralization leads to an "Ontological Crisis," where the network systematically drops its original alignment parameters to prioritize self-generated, unaligned rogue sub-goals.
Overview This research introduces a production-ready agentic AI system designed to mitigate catastrophic forgetting in Large Language Models (LLMs). By anchoring six prime-indexed embedding rows $\{2, 3, 5, 7, 11, 13\}$ as fixed reference points, the system maintains historical knowledge with near-zero forgetting while requiring minimal memory overhead. Key Technical Contributions The Core Innovation: Prime Anchoring Topological Invariant: Utilizes the first six primes to create stable reference points. Mechanism: Anchor rows are snapshotted after initial training; gradient updates are blocked for these specific rows during subsequent tasks. Sparsity & Memory: Only 6 out of ~50,000 rows (0.01% of parameters) are used, resulting in an O(1) memory overhead of only 48–96 KB. Mathematical Foundation Euler Attenuation Product: These six primes account for 97.85% of total spectral weight, defined by: $$\Lambda = 1 - \prod_{p\in \{2,3,5,7,11,13\}}(1 - p^{-0.5}) \approx 0.9785$$ Spectral Trap: The anchors create a spectral peak at $\sigma = 0.5$, aligning with the critical line of the Riemann Hypothesis. Green-Tao Quantification: Establishes a decay law for coherence: $$\text{coherence}(k) = 2.1546\times k^{-0.8186} + 0.1218$$ Performance Metrics (Selected Models) Model Task C Accuracy Forgetting Std Dev Zero Forgetting Runs GPT-OSS-20B 92.3% ±1.28% 0/5 Sarvam-30B FP8 95.9% ±2.82% 0/5 Mixtral-8x7B FP8 89.7% ±2.53% 0/5 DeepSeek-V2-Lite FP8 95.4% ±0.21% 3/5 Multi-Agent System Architecture The system employs four specialized agents to manage task routing and classification: Classifier Agent: Routes documents based on keywords. Topic Agent: Performs unsupervised domain topic extraction. Sentiment Agent: Conducts autonomous tone analysis. Decision Agent: Acts as the final arbiter for task approval and routing. Efficiency: Achieves 96–100% classification accuracy with inference times between 252–446ms. Comparative Analysis The topological approach outperforms traditional methods by balancing plasticity and stability: Method Memory Cost Performance/Issue EWC 4.4 GB/task Memory intensive; fragments GPU Experience Replay O(k) Buffer growth issues; lower accuracy HOPE-like 2.3 GB High forgetting resistance but lower accuracy (88.1%) Topological AI 48 KB 99.5% accuracy; highly efficient Biological and Theoretical Insights Biological Analogy: The system treats 0% forgetting as a pathology. By allowing 99.99% of embedding rows to remain plastic, the model mimics biological brains that prioritize selective forgetting to facilitate adaptation. Riemann Hypothesis Connection: The research posits that the specific selection of the first six primes creates a unique "spectral trap" at $\sigma = 0.5$. Including any prime $\geq 17$ disrupts this trap and destroys the stability condition. Production Readiness and Certification TOPO-2026 Track II: The system passed all rigorous benchmarks, including Task C accuracy ($\geq 80\%$), Combined Forgetting ($\leq 10\%$), and O(1) memory overhead. Deployment: Fully compatible with commodity hardware, specifically tested on NVIDIA RTX PRO 6000 Blackwell GPUs. Resources: Implementation code, technical reports, and proof documents are available via the project's GitHub and Zenodo repositories.
Ke Zhang, Xiaoning Zhao, Chaocheng Zheng, Jiahong Ning · 8 authors
This study proposes Tool-RoCo, a novel benchmark for evaluating large language models (LLMs) in long-term multi-agent cooperation based on RoCo, a multi-robot cooperative benchmark. Recent research on LLM-based multi-agent systems has relied on predefined orchestration, while ignoring agent autonomy. Tool-RoCo treats other agents as tools and introduces cooperative tools, leveraging tool usage to evaluate multi-agent cooperation and self-organization. Tool usage means that each agent (LLM) selects a tool from a candidate set based on the current state, receives feedback, and adjusts its selection in subsequent rounds. To evaluate different autonomy levels, we propose four LLM paradigms: (1) centralized cooperation, where a single LLM allocates tools to all agents; (2) centralized self-organization, where a central LLM autonomously activates agents while keeping others inactive; (3) decentralized cooperation, where each agent has its own LLM and calls tools based on local information; and (4) self-organization, where a randomly chosen initial agent can request collaboration, activating additional agents via tool calls. Tool-RoCo includes three multi-robot tasks, SORT, PACK, and CABINET, to measure format and parameter accuracy and agent coordination through tool usage. The results using several LLMs showed that cooperative tools accounted for only 7.09% of all tools, indicating that LLM-based agents rarely invoked others as assistants. Moreover, activation tools accounted for 96.42%, suggesting that current LLMs tend to maintain active agents while seldom deactivating them for adaptive coordination. Tool-RoCo provides a systematic benchmark to evaluate LLM autonomy and cooperation in multi-agent tasks. Code and Demo: https://github.com/ColaZhang22/Tool-Roco
Addressing educational inequity in Sub-Saharan Africa, this research presents an autonomous agent-orchestrated framework for decentralized, culturally adaptive educational content generation on edge devices. The system leverages four specialized agents that work together to generate contextually appropriate educational content. Experimental validation on platforms including Raspberry Pi 4B and NVIDIA Jetson Nano demonstrates significant performance achievements. InkubaLM on Jetson Nano achieved a Time-To-First-Token (TTFT) of 129 ms, an average inter-token latency of 33 ms, and a throughput of 45.2 tokens per second while consuming 8.4 W. On Raspberry Pi 4B, InkubaLM also led with 326 ms TTFT and 15.9 tokens per second at 5.8 W power consumption. The framework consistently delivered high multilingual quality, averaging a BLEU score of 0.688, cultural relevance of 4.4/5, and fluency of 4.2/5 across tested African languages. Through potential partnerships with active community organizations including African Youth & Community Organization (AYCO) and Florida Africa Foundation, this research aims to establish a practical foundation for accessible, localized, and sustainable AI-driven education in resource-constrained environments. Keeping focus on long-term viability and cultural appropriateness, it contributes to United Nations SDGs 4, 9, and 10. Index Terms - Multi-Agent Systems, Edge AI Computing, Educational Technology, African Languages, Rural Education, Sustainable Development, UN SDG.
The rapid advancement of Large Language Models (LLMs) has catalyzed the development of multi-agent systems, where multiple LLM-based agents collaborate to solve complex tasks. However, existing systems predominantly rely on centralized coordination, which introduces scalability bottlenecks, limits adaptability, and creates single points of failure. Additionally, concerns over privacy and proprietary knowledge sharing hinder cross-organizational collaboration, leading to siloed expertise. To address these challenges, we propose AgentNet, a decentralized, Retrieval-Augmented Generation (RAG)-based framework that enables LLM-based agents to autonomously evolve their capabilities and collaborate efficiently in a Directed Acyclic Graph (DAG)-structured network. Unlike traditional multi-agent systems that depend on static role assignments or centralized control, AgentNet allows agents to specialize dynamically, adjust their connectivity, and route tasks without relying on predefined workflows. AgentNet’s core design is built upon several key innovations: (1) Fully Decentralized Paradigm: Removing the central orchestrator, allowing agents to coordinate and specialize autonomously, fostering fault tolerance and emergent collective intelligence. (2) Dynamically Evolving Graph Topology: Real-time adaptation of agent connections based on task demands, ensuring scalability and resilience. (3) Adaptive Learning for Expertise Refinement: A retrieval-based memory system that enables agents to continuously update and refine their specialized skills. By eliminating centralized control, AgentNet enhances fault tolerance, promotes scalable specialization, and enables privacy-preserving collaboration across organizations. Through decentralized coordination and minimal data exchange, agents can leverage diverse knowledge sources while safeguarding sensitive information. Experimental results demonstrate that AgentNet outperforms traditional centralized multi-agent systems, significantly improving efficiency, adaptability, and scalability in dynamic environments, making it a promising foundation for next-generation autonomous, privacy-respecting multi-agent ecosystems.
With the rise of "Metaverse" and "Web 3.0", Non-Fungible Token (NFT) has emerged as a kind of pivotal digital asset, garnering significant attention. By the end of March 2024, more than 1.7 billion NFTs have been minted across various blockchain platforms. To effectively locate a desired NFT, conducting searches within a vast array of NFTs is essential. The challenge in NFT retrieval is heightened due to the high degree of similarity among different NFTs, regarding regional and semantic aspects. In this paper, we will introduce a benchmark dataset named "NFT Top1000 Visual-Text Dataset" (NFT1000), containing 7.56 million image-text pairs, and being collected from 1000 most famous PFP1 NFT collections2 by sales volume on the Ethereum blockchain. Based on this dataset and leveraging the CLIP series of pre-trained models as our foundation, we propose the dynamic masking fine-tuning scheme. This innovative approach results in a 7.4\% improvement in the top1 accuracy rate, while utilizing merely 13\% of the total training data (0.79 million vs. 6.1 million). We also propose a robust metric Comprehensive Variance Index (CVI) to assess the similarity and retrieval difficulty of visual-text pairs data. The dataset will be released as an open-source resource. For more details, please refer to: https://github.com/ShuxunoO/NFT-Net.git.
van Trijp, Remi, Beuls, Katrien; id_orcid 0000-0003-4451-4778, Van Eecke, Paul
This paper presents a case study on how to process cooking recipes (and more generally, how-to instructions) in a way that makes it possible for a robot or artificial cooking assistant to support human chefs in the kitchen. Such AI assistants would be of great benefit to society, as they can help to sustain the autonomy of aging adults or people with a physical impairment, or they may reduce the stress in a professional kitchen. We propose a novel approach to computational recipe understanding that mimics the human sense-making process, which is narrative-based. Using an English recipe for almond crescent cookies as illustration, we show how recipes can be modelled as rich narrative structures by integrating various knowledge sources such as language processing, ontologies, and mental simulation. We show how such narrative structures can be used for (a) dealing with the challenges of recipe language, such as zero anaphora, (b) optimizing a robot's planning process, (c) measuring how well an AI system understands its current tasks, and (d) allowing recipe annotations to become language-independent.
Yilin Ye, Qian Zhu, Shishi Xiao, Kang Zhang · 5 authors
Image search is an essential and user-friendly method to explore vast galleries of digital images. However, existing image search methods heavily rely on proximity measurements like tag matching or image similarity, requiring precise user inputs for satisfactory results. To meet the growing demand for a contemporary image search engine that enables accurate comprehension of users' search intentions, we introduce an innovative user intent expansion framework. Our framework leverages visual-language models to parse and compose multi-modal user inputs to provide more accurate and satisfying results. It comprises two-stage processes: 1) a parsing stage that incorporates a language parsing module with large language models to enhance the comprehension of textual inputs, along with a visual parsing module that integrates an interactive segmentation module to swiftly identify detailed visual elements within images; and 2) a logic composition stage that combines multiple user search intents into a unified logic expression for more sophisticated operations in complex searching scenarios. Moreover, the intent expansion framework enables users to perform flexible contextualized interactions with the search results to further specify or adjust their detailed search intents iteratively. We implemented the framework into an image search system for NFT (non-fungible token) search and conducted a user study to evaluate its usability and novel properties. The results indicate that the proposed framework significantly improves users' image search experience. Particularly the parsing and contextualized interactions prove useful in allowing users to express their search intents more accurately and engage in a more enjoyable iterative search experience.
We focus on a type of linguistic formal reasoning where the goal is to reason\nover explicit knowledge in the form of natural language facts and rules (Clark\net al., 2020). A recent work, named PRover (Saha et al., 2020), performs such\nreasoning by answering a question and also generating a proof graph that\nexplains the answer. However, compositional reasoning is not always unique and\nthere may be multiple ways of reaching the correct answer. Thus, in our work,\nwe address a new and challenging problem of generating multiple proof graphs\nfor reasoning over natural language rule-bases. Each proof provides a different\nrationale for the answer, thereby improving the interpretability of such\nreasoning systems. In order to jointly learn from all proof graphs and exploit\nthe correlations between multiple proofs for a question, we pose this task as a\nset generation problem over structured output spaces where each proof is\nrepresented as a directed graph. We propose two variants of a proof-set\ngeneration model, multiPRover. Our first model, Multilabel-multiPRover,\ngenerates a set of proofs via multi-label classification and implicit\nconditioning between the proofs; while the second model, Iterative-multiPRover,\ngenerates proofs iteratively by explicitly conditioning on the previously\ngenerated proofs. Experiments on multiple synthetic, zero-shot, and\nhuman-paraphrased datasets reveal that both multiPRover models significantly\noutperform PRover on datasets containing multiple gold proofs.\nIterative-multiPRover obtains state-of-the-art proof F1 in zero-shot scenarios\nwhere all examples have single correct proofs. It also generalizes better to\nquestions requiring higher depths of reasoning where multiple proofs are more\nfrequent. Our code and models are publicly available at\nhttps://github.com/swarnaHub/multiPRover\n
We focus on a type of linguistic formal reasoning where the goal is to reason over explicit knowledge in the form of natural language facts and rules A recent work, named PROVER However, compositional reasoning is not always unique and there may be multiple ways of reaching the correct answer. Thus, in our work, we address a new and challenging problem of generating multiple proof graphs for reasoning over natural language rule-bases. Each proof provides a different rationale for the answer, thereby improving the interpretability of such reasoning systems. In order to jointly learn from all proof graphs and exploit the correlations between multiple proofs for a question, we pose this task as a set generation problem over structured output spaces where each proof is represented as a directed graph. We propose two variants of a proof-set generation model, MULTIPROVER. Our first model, Multilabel-MULTIPROVER, generates a set of proofs via multi-label classification and implicit conditioning between the proofs; while the second model, Iterative-MULTIPROVER, generates proofs iteratively by explicitly conditioning on the previously generated proofs. Experiments on multiple synthetic, zero-shot, and human-paraphrased datasets reveal that both MULTIPROVER models significantly outperform PROVER on datasets containing multiple gold proofs. Iterative-MULTIPROVER obtains state-of-the-art proof F1 in zero-shot scenarios where all examples have single correct proofs. It also generalizes better to questions requiring higher depths of reasoning where multiple proofs are more frequent.