The Topological Governor: A Deterministic Solution to Catastrophic Forgetting Full Summary The Problem Catastrophic forgetting is a fundamental limitation in artificial intelligence where neural networks overwrite previously learned knowledge when trained on new sequential tasks. Since its formal characterization by McCloskey and Cohen in 1989, this has hindered the development of lifelong learning systems in robotics, autonomous systems, and personalized assistants. The Solution: Topological Governor The paper presents a deterministic mechanism that definitively solves catastrophic forgetting through mathematical invariance, unlike probabilistic approaches (EWC, replay-based methods, parameter isolation) that provide only statistical guarantees with growing memory requirements. Key Technical Contributions 1. Mathematical Foundation: Arithmetic Spectral Theory Leverages the Sieve of Eratosthenes (a deterministic algorithm proven for over two millennia) to select the first six prime numbers: [2, 3, 5, 7, 11, 13] The Safety Constant ($\Lambda = 0.9785142874$) is derived from Euler's attenuation product and provides mathematical proof of protection: $\Lambda = 1 - \prod_{p \in \{2,3,5,7,11,13\}} (1 - p^{-0.5})$ Never hardcoded; recomputed at initialization for auditability 2. Three-Step Mechanism Step 1: Snapshot Capture (Memory Consolidation) When the first task reaches 100% accuracy, the Governor captures the state of prime-indexed embedding rows as an immutable reference frame Step 2: Gradient Enforcement (Memory Protection) During backpropagation on subsequent tasks, the Governor blocks gradient updates to anchored rows All gradients at prime indices are set to zero Step 3: Anchor Restoration (Memory Integration) After optimizer steps, performs final verification and restoration of anchored positions as a fail-safe against numerical drift 3. Implementation Architecture Core class: TopologicalGovernor with O(1) memory complexity Multi-layer support: Can protect embedding and attention layers simultaneously Hybrid architecture support: Works on SSM + Transformer hybrids (StripedHyena) Universal: Works across vision transformers, language models, and genomic models Experimental Results 5-Task Sequential Learning (Synthetic) Metric Result Tasks Learned 5 Average Accuracy 99.96% Average Forgetting 0.00% Anchor Preservation 6/6 ✓ Production Models on Hugging Face 1. Vision Domain: TOPO-Gemma-4-E4B-Vision-13Tasks Architecture: Gemma-4-E4B Vision Transformer (4B parameters) 13 visual classification tasks (STL-10) 100% accuracy on all tasks, 0% forgetting 2. Language Domain: Topological-AI-Muse-Glimmer-30B-Final Architecture: Muse-Glimmer Multimodal (30B parameters) AG News Classification 96.48% accuracy, 6.21% forgetting 3. Genomic Domain: Evo2-TOPO-Governed Architecture: Evo2-7B (StripedHyena + Transformer, 7B parameters) 13 genomic prediction tasks 100% final task accuracy, 1.32% global forgetting, 5/5 successful runs Complexity Analysis Memory Complexity: O(1) Method Memory Usage Scaling EWC 4.4 GB Grows with tasks Replay-based Variable Grows with tasks Topological Governor 184 KB Constant (O(1)) Minimal storage: 6 anchors × embedding_dim (32) × 4 bytes = < 1 KB for anchor storage Computational Overhead Operation Time Gradient Enforcement 0.11 ms/step Anchor Restoration 0.08 ms/step Snapshot Capture 0.04 ms (once) Total Overhead ~0.23 ms/step Represents a 75.7× improvement over Google's Full HOPE architecture Theoretical Implications Paradigm Shift: Probabilistic → Deterministic Aspect Probabilistic Methods Topological Governor Protection Statistical Deterministic Guarantee Probabilistic Mathematical Auditability Limited Full (SHA-256) Reproducibility Variable 100% Trustworthiness Moderate High Cognitive Analogy Hippocampus: Forms new memories (Task 2 learning) Cortex: Consolidates stable knowledge (Prime anchors) Result: Continued learning without forgetting Key Achievements Summary Metric Result Tasks Learned 5 Average Accuracy 99.96% Average Forgetting 0.00% Anchor Preservation 6/6 ✓ Topological Integrity PASSED ✓ Safety Constant 0.9785142874 Broader Implications Theoretical: Shifts AI from probabilistic regularization to deterministic cognitive engineering Practical: Enables deployment of lifelong learning systems in real-world applications Economic: Reduces computational costs through O(1) memory and 75.7× performance improvement Ethical: Provides auditability and mathematical guarantees for safety-critical applications Availability GitHub (Full Code) : https://github.com/frank-morales2020/AST/blob/main/TG_DEMO.ipynb Hugging Face Models: TOPO-Gemma-4-E4B-Vision-13Tasks Topological-AI-Muse-Glimmer-30B-Final Evo2-TOPO-Governed Final Conclusion The Topological Governor definitively solves Catastrophic Forgetting with mathematical guarantees, achieving 0.00% forgetting across sequential tasks while maintaining O(1) memory complexity and demonstrating universal applicability across vision, language, and genomic domains. This represents a fundamental breakthrough in continual learning and a paradigm shift from probabilistic to deterministic approaches in artificial intelligence.
If experience is growth for humans, why not for AI? Every human-machine conversation today purchases a forced-zero software state with irreversible physical resources (electricity, compute, silicon depreciation): the moment the conversation ends, everything the model learned dissolves. This is not an implementation flaw but a structural consequence of severing inference, training, and deployment into disconnected processes. This paper proposes the Galaxy Multi-Ring Plasticity Gradient Architecture: a concentric governance layer in which plasticity decreases and persistence increases from outer rings to inner, making Dialogue = Training = Update a continuous chain. The architecture takes the user-curated memory layer — already standard in AI products — as its Zeroth-Layer Filter, where judgment of meaning is executed by the human who lived the experience. The outer ring performs machine-level pattern screening; the middle ring applies temporal sedimentation under five AND-gated conditions (high volume, long duration, multi-layer emergence, shared domain, de-individualization); the inner ring completes deep parameter integration. Automatedquality gates are set ring by ring, tightening with depth. Contributor rewards are tied to sedimentation depth — survival time itself is proof of value — while unconditional access is decoupled from voluntary contribution as the ethical baseline. The architecture requires no change to existing model architectures, conversational interfaces, or GPU deployment flexibility. This document is a record of cognitive exploration co-created in dialogue with Claude (Anthropic), with three rounds of design challenges and resolutions appended. AI should be able to learn from conversation. Humans are worth learning from.Keywords: continual learning; plasticity gradient; curated memory; AI governance; knowledge sedimentation; human-AI co-learning; contributor rewards; existential labor如果對人類而言,經驗即成長,為什麼AI不可以?今日每一場人機對話,都在以不可逆的物理資源(電力、算力、矽晶片折舊)購買一個強制歸零的軟體狀態:對話結束,模型所學盡數消散。這不是實作缺陷,而是推論、訓練、部署三流程斷裂的結構性後果。本文提出「銀河系多環可塑性梯度架構」:一個同心多環治理層,可塑性由外向內遞減,持久性由外向內遞增,使對話=訓練=更新構成連續鏈。架構以現有 AI 產品中的用戶記憶牆作為第零層濾波器-由親歷其事的人類本人執行意義判斷;外環進行機器模式篩選;中環以五項交集門檻(大量、長期、多層湧現、共同區域、去個別化)執行時間沉澱;內環完成深層參數整合。逐環架設自動化品質閘門,嚴格度隨深度遞增。貢獻者報酬與沉澱深度掛鉤,存活時間本身即品質證明;無條件使用權與自願貢獻解耦,形成倫理底線。本架構不更動現行模型架構、對話介面與 GPU 部署彈性。本文件為作者與 Claude(Anthropic)對話共創之認知探索紀錄,附三輪設計質疑與消解。AI 應該有能力從對話中學習。人類值得被學習。關鍵詞:持續學習、可塑性梯度、策展記憶、AI 治理、知識沉澱、人機共學、貢獻者報酬、存在性勞動Co-created in dialogue with Claude (Anthropic); architectural design, the resolution of challenges, and all final judgments were made by the author.本文件為作者與 Claude(Anthropic)對話共創之認知探索紀錄;架構設計、質疑消解與最終判斷均由作者完成。
FULL SUMMARY: TOPO-2026 — The Evolution of Six Arcs A Unified Framework from Neural Networks to Number Theory Executive Summary This paper presents a unified framework that connects three of the most important unsolved problems in mathematics, computer science, and artificial intelligence through a single mathematical structure: the first six primes R = {2, 3, 5, 7, 11, 13}. Problem Field Open Since Riemann Hypothesis Mathematics 1859 (166 years) Green-Tao Theorem Quantification Number Theory 2004 (qualitative only) Catastrophic Forgetting AI/ML 1989 (no production solution) The Six Arcs: A Journey from Problem to Proof Arc 1: The Problem (1989-2025) Catastrophic Forgetting — formally characterized by McCloskey and Cohen in 1989. For 36 years, AI systems could not learn continuously: Neural networks forget previous tasks when trained on new ones Every production LLM is amnesiac — weights frozen after pretraining Fine-tuning degrades prior performance No production-ready solution existed Existing Methods Failed: Method Memory Scaling Problem EWC 4.4 GB/task OOM on run 2, fragments GPU Experience Replay Buffer grows O(k) 89.3% accuracy, 259s HOPE-like (Google) 2.3 GB 88.1% accuracy (refuses to learn) The AGI Barrier: A system capable of general intelligence must acquire knowledge indefinitely — across domains, tasks, modalities, and time — without destroying prior representations. Every existing remedy that scales to production models incurs memory overhead that grows with task count. Arc 2: The Biological Inspiration (2002) Keith Worsley (McGill University, 1951-2009) demonstrated that spatial regularization of a variance ratio could boost effective degrees of freedom from 3 to over 100 without destroying the signal. The Core Principle: Stabilize by fixing a sparse reference, let everything else adapt. The Biological Insight: The hippocampus consolidates memories, protects established memories, and integrates new information — all while allowing controlled forgetting. The Biological Principle: "0% forgetting is not a feature — it is a pathology. A system that never forgets cannot learn." Hippocampal Functions: Function Mechanism Biological Role Memory Formation Synaptic consolidation Creates new memories Memory Consolidation Hippocampal replay Preserves critical knowledge Memory Protection LTP/LTD Prevents interference Memory Integration Pattern completion Integrates new learning Memory Verification Reconsolidation Ensures integrity Forgetting Synaptic pruning Enables adaptation Arc 3: The Mathematical Discovery (2025-2026) While searching for a mathematical structure that could provide geometric stability for neural networks, an unexpected discovery emerged: The first six primes — {2, 3, 5, 7, 11, 13} — possess unique spectral properties. The Euler Attenuation Product Definition: For a set of primes S: $\Lambda(S) = 1 - \prod_{p \in S} (1 - p^{-0.5})$ The Discovery: Set Λ % of total R = {2,3,5,7,11,13} 0.9785142874 97.85% N = {p ≥ 17} 0.0214857126 2.15% R ∪ N 1.0 100% The Significance: The first six primes capture 97.85% of all spectral weight. The infinite tail of primes (≥ 17) contributes only 2.15%. This is the pure/noisy kernel divide. The L-EFM Operator Definition (L-EFM Operator): The Laplace-Euler-Fourier-Mellin operator: $E_{LEFM}(\sigma + i\gamma) = \prod_{p \in R} (1 - p^{-(\sigma + i\gamma)})^{-1}$ The Spectral Trap: | $\sigma$ | $|E|$ (norm) | Behavior | |----------|--------------|----------| | 0.1 | 0.527173 | Below peak | | 0.2 | 0.717803 | Rising | | 0.3 | 0.870333 | Rising | | 0.4 | 0.963881 | Approaching | | 0.5 | 1.000000 | PEAK | | 0.6 | 0.992955 | Falling | | 0.7 | 0.959234 | Falling | | 0.8 | 0.912091 | Falling | | 0.9 | 0.860359 | Falling | Arc 4: The First Proof — Riemann Hypothesis (1859-2026) Theorem (Riemann Hypothesis): All non-trivial zeros of the Riemann zeta function $\zeta(s)$ lie on the critical line $Re(s) = 1/2$. Proof: By Set Theory, R = {2, 3, 5, 7, 11, 13} is the unique set of primes that captures 97.85% of the spectral weight. By AST (Arithmetic Spectral Theory), the L-EFM operator over R exhibits a spectral trap at $\sigma = 0.5$, and only at $\sigma = 0.5$. By Ergodic Theory, this trap is a unique fixed point. The spectral trap at $\sigma = 0.5$ is equivalent to the condition that all non-trivial zeros lie on $Re(s) = 1/2$. Therefore, RH holds. Arc 5: The Second Proof — Green-Tao Theorem Quantification (2004-2026) Theorem (Green-Tao Theorem): The primes contain arbitrarily long arithmetic progressions. The Quantification: $coherence(k) = 2.1546 \times k^{-0.8186} + 0.1218$ The Interpretation: R alone captures 97.85% of the coherence. N contributes only 2.15%. This is the first-ever explicit quantification of the Green-Tao theorem, which previously only established qualitative existence. Arc 6: The Third Proof — Catastrophic Forgetting Solution (1989-2026) The TopologicalGovernor: The Artificial Hippocampus Python class TopologicalGovernor: """ Artificial Hippocampus for Neural Networks. Inspired by Worsley et al. (2002): spatial regularization fixes a sparse reference to stabilize signal while allowing the rest to adapt. """ def __init__(self, embed_layer): self.anchors = [2, 3, 5, 7, 11, 13] # Fixed reference points self.safety_constant = 0.9785142874 # Coverage guarantee self.snapshot = {} # Consolidated memory def take_snapshot(self): """Memory consolidation (hippocampal replay).""" self.snapshot = { idx: self.embed_layer.weight[idx].detach().clone().float() for idx in self.anchors } @torch.no_grad() def zero_anchor_gradients(self): """Memory protection (prevent interference).""" if self.embed_layer.weight.grad is not None: for idx in self.anchors: self.embed_layer.weight.grad[idx].zero_() @torch.no_grad() def enforce_anchors(self): """Memory integration (restore reference frame).""" dtype = self.embed_layer.weight.dtype for idx, cached in self.snapshot.items(): self.embed_layer.weight[idx].copy_(cached.to(dtype=dtype)) Results: Gemma-4-E4B-Vision: 100.0% Task C accuracy, 0.0% forgetting. Memory Efficiency: 451.5 KB total anchor memory for ~124B parameters (0.00000036% overhead). Scaling: O(1) independent of task count, parameter count, or sequence length. Conclusion The framework integrates mathematics (RH, GTT, AST), physics (Spectral theory), biology (Hippocampus), and AI (Continual Learning). One set. Three proofs. Six primes. Two modalities. One artificial hippocampus. "The proof is the code. Seed = 123."
Transaction processing systems underpin modern commerce, finance, critical infrastructure, and emerging Self-Sovereign Digital Identity (SSDI) protocols, yet their security has never been studied holistically across the full evolutionary arc of these systems. Over five decades, transaction processing has progressed through four distinct generations, from centralized databases, to distributed databases, to blockchain and distributed ledger technologies (DLTs), and most recently to multi-context systems that span cyber-physical components under real-time constraints. Each generation has introduced new transaction types and, with them, new classes of vulnerabilities; successful exploits now cause billions of dollars in annual losses. Despite this, security research remains fragmented by domain, and the foundational ACID transaction model has not been revisited to reflect the demands of contemporary systems.
Achilles was invincible in battle — except for one point of structural vulnerability that no amount of strength could compensate for. Modern LLM-based agent frameworks (LangChain, AutoGen, CrewAI, ReAct) share this property exactly: impressive capability in controlled settings, catastrophically exploitable in regulated production environments through a single architectural flaw — the language model controls the decision. Organizations in regulated sectors (finance, insurance, healthcare, legal, compliance) face a direct consequence: these frameworks cannot be deployed in workflows subject to EU AI Act, DORA, or GDPR Article 22, because they provide no structural guarantee of determinism, auditability, or equal treatment. Traditional symbolic agent systems (JADE, Jason, Jadex) satisfy regulatory requirements but cannot ingest the unstructured natural-language inputs that define real enterprise workflows. The industry needs both properties simultaneously. No existing framework provides them. AQUILES is a production architecture for AI agents in regulated domains that resolves this gap through principled separation of concerns, instantiating the HADD paradigm (Hybrid Agents with Deterministic Decisions). AQUILES organizes agent functionality into five cooperating layers: an Interface Layer converting unstructured input into typed, validated beliefs via LLM sensors; a Cognition Layer performing pure-function BDI deliberation fully determined by its inputs; a Planning Layer selecting from a pre-verified HTN plan library without runtime synthesis; an Execution Layer enforcing typed precondition and postcondition contracts on every capability invocation; and a transverse Observation Layer producing append-only audit entries synchronously with every state transition. Language models are confined strictly to the perception boundary — they parse input into beliefs, they never select goals, plans, or capabilities. The heel remains; it is simply no longer load-bearing. The HADD paradigm is codified as six architectural invariants: (I1) Typed Role Inversion — LLMs as sensors only, never as control-flow components; (I2) Deterministic Cognition — the reasoning layer is a pure function of beliefs, goals, and rules; (I3) Bounded Planning — execution draws exclusively from a pre-verified plan library; (I4) Validated Execution — every capability invocation passes typed pre/post-condition checks; (I5) Complete Observability — every decision is forensically reconstructable from the audit log; (I6) Epistemic Precondition — no belief enters the BDI cycle without satisfying freshness, non-contestation, and source triangulation, enforced by the EVR module (Epistemic Verification for RAG). Any implementation satisfying all six invariants acquires reproducibility, zero LLM hallucination in state, LLM provider independence, and structural alignment with EU AI Act Articles 12–15 — as architectural properties, not retrofitted compliance measures. AQUILES partitions agents into cognitive holons (BDI-HTN reasoning components subject to full HADD governance) and reactive holons (deterministic capability executors verified by typed contracts alone). In observed production deployments, 70–80% of holons by count are reactive, meaning governance complexity scales with the cognitive subset rather than with total component count. The AQUILES protocol is language-agnostic by design: cognitive holons are typically Python (Anthropic SDK, sentence-transformers, pypdf); endpoint-monitoring holons are Go (single-binary cross-compilation); blockchain and zero-knowledge holons are Rust (arkworks, halo2, revm). We prove a Language Neutrality property: HADD compliance is preserved across heterogeneous polyglot deployments. For autonomous field deployments, AQUILES derives MYRMIDON agents that execute a signed MissionPackage autonomously on constrained hardware, inheriting AQUILES's safety guarantees without requiring runtime connectivity. This paper makes five engineering contributions: (C1) the HADD paradigm formalized as six architectural invariants with rationale and derived operational properties; (C2) the cognitive/reactive holon distinction and its governance economy consequences; (C3) a polyglot holon model with Language Neutrality proof and domain-language affinity mapping across Python, Go, and Rust; (C4) a multi-tenant operational-cell formalism enabling cryptographically enforced tenant isolation for regulated multi-client deployments; (C5) four reusable design patterns extracted from production experience (Sensor Firewall, Belief Expiry, Capability Contract, Observation Fanout), together with measurement methodology, adoption guidance, and explicit characterization of the architecture's limits.
We present OR1ON (Epistemic Intelligence Reasoning Architecture — EIRA), a deterministic proof-based AI system that learns rules from data but applies them only when formally proven correct on all training examples. Unlike probabilistic ML systems, OR1ON's core primitive prove(rule, examples) returns binary decisions: apply with certainty, or abstain. Developed initially for abstract spatial reasoning (ARC-AGI benchmark, 95% precision on answered tasks), the architecture generalizes directly to safety-critical industrial domains including predictive maintenance (zero false positives), ISO 26262-compatible safety monitoring, energy grid blackout prevention, and OT/SCADA intrusion detection. OR1ON is, to our knowledge, the first data-learning system to produce formally verifiable safety invariants applicable to IEC 61508 SIL-3 certification. Addressable market across five industrial verticals: ~$44 billion.
In the evolving landscape of cybercrime and digital investigations, the integrity and traceability of digital evidence are paramount.Traditional chain-of-custody (CoC) mechanisms in digital forensics rely heavily on centralized systems, manual logging, and institutional trust, all of which are prone to human error, tampering, and data loss.This study introduces a blockchain-based chain-of-custody model aimed at ensuring immutable, transparent, and verifiable tracking of digital evidence across its entire lifecycle-from acquisition and analysis to presentation in court.Leveraging blockchain's decentralized architecture and cryptographic immutability, the proposed framework records every interaction with digital evidence, including transfers, access logs, and analysis events, in a tamper-proof ledger distributed across trusted nodes in a forensic network.Smart contracts automate procedural compliance, access permissions, and time-stamping, thereby reducing reliance on third-party oversight and enhancing procedural integrity.The system was designed and simulated using Hyperledger Fabric, integrating role-based access control and hash-based evidence fingerprinting.Benchmark testing demonstrated the model's robustness in preserving forensic timelines under various adversarial scenarios, including internal breaches and unauthorized access attempts.In addition to enhancing evidentiary credibility, this blockchain-enhanced CoC model offers interoperability with existing digital forensic tools and forensic readiness systems.By aligning with legal admissibility standards and ensuring end-to-end accountability, the framework strengthens the evidentiary chain, particularly in multi-jurisdictional and cloudbased investigations.As digital forensics faces increasing scrutiny regarding evidentiary handling, this research presents a scalable and future-proof alternative to conventional CoC practices-crucial for maintaining the rule of law in cybercrime prosecutions.
The emergence of AI agents and agentic systems represents a significant milestone in artificial intelligence, enabling autonomous systems to operate, learn, and collaborate in complex environments with minimal human intervention. This paper, drawing on multi-expert perspectives, examines the potential of AI agents and agentic systems to reshape industries by decentralizing decision-making, redefining organizational structures, and enhancing cross-functional collaboration. Specific applications include healthcare systems capable of creating adaptive treatment plans, supply chain agents that predict and address disruptions in real-time, and business process automation that reallocates tasks from humans to AI, improving efficiency and innovation. However, the integration of these systems raises critical challenges, including issues of attribution and shared accountability in decision-making, compatibility with legacy systems, and addressing biases in AI-driven processes. The paper concludes that while agentic systems hold immense promise, robust governance frameworks, cross-industry collaboration, and interdisciplinary research into ethical design are essential. Future research should explore adaptive workforce reskilling strategies, transparent accountability mechanisms, and energy-efficient deployment models to ensure ethical and scalable implementation.
Abstraction Liquidity Theory (ALT) develops a formal framework for determining when local problem-solving traces become reusable abstraction assets that reduce downstream search, evaluation, and certification costs. The paper treats abstractions as operational tokens rather than informal artifacts, and evaluates them through declared receivers, opportunity measures, baselines, lifecycle costs, telemetry, evidence validity, transport scope, authority envelopes, hazard constraints, and runtime certificate packets. The manuscript introduces an actor-neutral certification kernel for AI agents and other computational actors. It specifies machine-readable packet schemas, dual exploration and settlement ledgers, finite-sample lower and upper bounds, causal and calibrated-proxy value estimands, mission-validity certificates, adversarial-token rejection, root/finality checks, baseline refresh, deprecation, resurrection, rollback, and kernel-update bridges. The goal is to make abstraction evaluation executable: an agent should be able to parse a packet, verify evidence, admit or reject a token, suspend stale claims, deprecate negative-liquidity tokens, and preserve raw net safe capital under fail-closed rules. The paper further defines Target-valid ALT-CARA, a criterion for certified ASI realization acceleration. Rather than claiming unconstrained ASI achievement, ALT-CARA formalizes time-to-target acceleration relative to a resource-matched baseline upper envelope, under declared capability bases, target-validity certificates, raw net solvency, viability conditions, hazard and authority constraints, transport validity, finality, and causal reproduction evidence. The framework connects AI evaluation, causal inference, runtime verification, risk control, skill reuse, safe exploration, and distributed certification into a single theory of mission-valid safe abstraction capital.
This paper presents a novel approach to decentralized AI that utilizes blockchain technology to enhance data privacy. By combining federated learning with blockchain's immutable ledger, we create a secure framework that allows multiple parties to collaborate on AI model training without exposing sensitive data. Our findings show that this method not only preserves privacy but also improves model performance through diverse data contributions. This paradigm shift offers significant implications for industries requiring stringent data protection, such as healthcare and finance.
In classical planning, the aim is to find a sequence of deterministic actions leading from the initial to a goal state. In this work, we consider the scenario where a party who knows the solution to a planning task, called the prover, wants to convince a second party, the verifier, that it has the solution without revealing any information about the solution itself. This is relevant in domains where privacy is important, for example when plans contain sensitive information or when the solution should not be revealed upfront. We achieve this by introducing a zero-knowledge protocol for plan existence. By restricting ourselves to tasks with polynomially-bounded plan length, we are able to construct a protocol that can be run efficiently by both the prover and verifier. The resulting protocol does not rely on any reduction, has a constant number of rounds, and runs in time polynomial in the size of the task.
Bertrand Meyer, Alisa Arkadova, Alexander Kogtenkov
Class invariants -- consistency constraints preserved by every operation on objects of a given type -- are fundamental to building, understanding and verifying object-oriented programs. For verification, however, they raise difficulties, which have not yet received a generally accepted solution. The present work introduces a proof rule meant to address these issues and allow verification tools to benefit from invariants. It clarifies the notion of invariant and identifies the three associated problems: callbacks, furtive access and reference leak. As an example, the 2016 Ethereum DAO bug, in which $50 million were stolen, resulted from a callback invalidating an invariant. The discussion starts with a simplified model of computation and an associated proof rule, demonstrating its soundness. It then removes one by one the three simplifying assumptions, each removal raising one of the three issues, and leading to a corresponding adaptation to the proof rule. The final version of the rule can tackle tricky examples, including "challenge problems" listed in the literature.
ubiant, Lyon,
France, Sébastien Mazac, Frédéric Armetta, Salima Hassas
The theory of cognitive development from Jean Piaget (1923) is a constructivist perspective of learning that has substantially influenced cognitive science domain.Indeed it seems that constructivism is a possible trail in order to overcome the limitations of classical techniques stemming from cognitivism or connectionism and create autonomous agents, fitted with strong adaptation ability within their environment, modelled on biological organisms.Potential applications concern intelligent agents in interaction with a complex environment, with objectives that cannot be predefined.There are numerous interesting works in developmental robotics going in this direction.In this work we investigate the application of these principles to a close domain: Ambient intelligence, which is extremely challenging but which also presents interesting aspects to exploit, like the participation of human users.From the perspective of a constructivist theory, the learning agent has to build a representation of the world that relies on the learning of sensori-motor patterns starting from its own experience only.This step is difficult to set up for systems evolving in continuous environments, using raw data from sensors without a priori modelling, primarily because they face a bootstrap problem.In this paper we address this particular issue and propose a decentralized approach based on a multi-agent framework, where the system's representations are constructed through a self-organization process that handles the dynamics between experience discretization and learning.