In the AI era, no data or system is fully secure. A single error can compromise critical infrastructure1, risking data leaks2, asset loss3, and even the takeover of entire systems4.
Adversaries are already using AI agents to target mission-critical operations, with incidents reported across national security5, finance6, and infrastructure7—against which current cyber-protection solutions are largely ineffective.
Logical Intelligence unites internationally recognized security experts and world-class mathematicians to deliver a new kind of intelligence—built on a non-autoregressive, energy-based learning architecture (LI-1.0) that guarantees correct answers with no hallucinations for formal reasoning. This is the foundation for defending mission-critical systems against rapidly evolving AI threats8.
Autoregressive (AR) traditional LLMs (Claude, ChatGPT-5, DeepSeek) are not reliable for formal reasoning because of hallucinations and long, costly compute times, since they generate responses on a token-by-token basis. At the natural-language level, AR models have been adequate, but in deeper mathematical work, they are fundamentally brittle. By-token architectures have a central vulnerability: one misstep can derail the entire reasoning process, with no internal mechanism for error recognition or recovery9.
Logical Intelligence has solved the problem of hallucinations in formal reasoning and now offers this intelligence—backed by an expert team—to protect mission-critical systems. Our LI-1.0 reasoning model supports key cybersecurity activities, including threat prevention (zero-day vulnerabilities) by formal verification of critical systems (including those requiring zero-knowledge proofs).
Why current models fall short for mathematical reasoning and correctness-seeking tasks
Large language models today are primarily autoregressive. This means they build their response one token at a time, with each new token being a statistical prediction based on the sequence that came before it. For prose, this is a powerful technique, allowing models to generate fluent and coherent text. For mathematical reasoning, however, this approach is fundamentally brittle. The model is not performing logical deduction; it is completing a pattern. It acts as an expert linguistic improviser, not a logician deriving a conclusion.
This architectural choice creates a critical vulnerability: a single incorrect token generated early in a reasoning chain — whether a flawed calculation or a subtle logical misstep — can irreversibly derail the entire process. The model has no internal mechanism to recognize this error. Instead, it continues to generate the most probable next tokens based on the now-flawed history, leading to a cascade of errors that invalidates the final answer. There is no structured backtracking or recovery.
This fundamental limitation manifests in several well-documented technical failures:
- Lack of Verifiability and Compositionality: An autoregressive model produces a flat string of tokens, not a symbolic structure. An intermediate step, like 'x2=4⟹x=2', is simply a likely sequence of characters, not a formal logical implication that can be independently verified. Because these intermediate steps are not verifiable objects, they cannot be reliably reused, composed into larger proofs, or checked hierarchically. This fundamentally limits the scalability of the model's reasoning.
- Brittleness in Multi-Step Reasoning: While techniques like Chain-of-Thought (CoT) prompt models to "show their work," they only encourage a reasoning-like output format without enforcing logical validity. This brittleness is evident in benchmark performance. As the number of required reasoning steps increases, accuracy plummets10.
- Inefficient Search: The linear, forward-only generation process is a highly inefficient method for exploring a solution space. Unlike a human mathematician or a formal proof assistant, which can explore various branches of a proof, backtrack from dead ends, and apply lemmas, an LLM is largely committed to its initial path. This prevents the kind of structured exploration required to solve complex, novel problems.
We protect your safety-critical systems
In the first half of 2025, crypto investors lost nearly $2.5 billion to scams and hacks, with major incidents like the $223M Cetus Protocol breach and $197M Euler Finance exploit leading the damage11,12,13. These attacks exploited smart contract vulnerabilities and flash-loan logic errors, exposing deep weaknesses in current DeFi infrastructure.
| Rank | Category | Incidents |
|---|---|---|
| #1 | Logic Errors | 23 |
| #2 | Access Control | 17 |
| #3 | Phishing | 8 |
| #4 | Flash Loan Attack | 7 |
| #5 | Lack of Input Validation | 5 |
| #6 | Reentrancy | 4 |
| #7 | Private Key Leak | 4 |
| #8 | Price Oracle Manipulation | 3 |
| #9 | Other | 3 |
| #10 | Rug Pull | 3 |
The scale and frequency of these exploits highlight the urgent need for stronger, verifiable security tools in crypto systems backing up human efforts.
Our architecture LI-1.0 enables AI to audit, revise, scale with complexity, and verify like a superintelligent mathematical expert, delivering faster, more reliable, and mathematically-provably correct solutions where failure isn’t an option.
We address the core limitations of current reasoning models by introducing a novel architecture that combines non-autoregressive reasoning, energy-based modeling (EBM), and a proprietary integration layer optimized for formal verification tools like Lean4 which leaves no room for mathematical mistakes.
Non-autoregressive reasoning allows for global refinement and revision of intermediate steps, enabling the model to correct earlier mistakes and maintain coherent, valid reasoning chains. By incorporating energy-based inference techniques — such as iterative refinement, MCMC sampling, and parallel sampling — we enable the system to backtrack, evaluate, and globally adjust candidate solutions. This approach mirrors human problem-solving: proposing full reasoning trajectories, evaluating their consistency, and refining the best ones. It also allows us to scale inference in parallel, unlike strictly sequential chain-of-thought (CoT) reasoning, which becomes a bottleneck in long proofs or complex plans. This not only improves accuracy but also significantly reduces inference time delivering results several orders of magnitude faster (and hence cheaper).
Finally, our architecture is more data-efficient. EBMs can be trained using solution-only or weak supervision (e.g., test-time rewards, constraints, or external verifiers), reducing dependence on expensive, curated CoT datasets — which often contain noisy or misleading reasoning traces. With better data efficiency we can train models for domains with scarce data availability, such as formal verification.
We’re rebuilding the foundations of logical intelligence—unlocking true reasoning you can trust and verify. Any human-AI workload that needs guarantees of correctness will require Logical Intelligence.
Endnotes
[1] "Attacking Artificial Intelligence: The Case for a National AI Safety Board." Belfer Center for Science and International Affairs, Harvard Kennedy School, 2024. ↑
[2] "Weaponized AI: A New Era of Threats." Ash Center for Democratic Governance and Innovation, Harvard Kennedy School, 2024. ↑
[3] "CertiK's Hack3d Report: $2.3 Billion Lost to Scams, Hacks, and Exploits in 2024." GlobeNewswire, 2 Jan. 2025. ↑
[4] Heller, Nathan. "How to Keep AI from Killing Us All." Berkeley News, 9 Apr. 2024. ↑
[5] Kolodi, Roman, “From CIA to C(AI): Using Artificial Intelligence as a Shield and Sword in Cyberespionage”, 2020. ↑
[6] Miao, Jeff. "Investors Have Lost Nearly USD 2.5B on Crypto Scams, Hacks." Investopedia, 6 Feb. 2025. ↑
[7] "AI Agents Tip the Scales in Cybersecurity." World Economic Forum, 5 June 2025. ↑
[8] "One Token to Rule Them All: The Alarming Vulnerability of LLM as a Judge." GopenAI Blog, 2025. ↑
[9] "Artificial Intelligence for Analysis: The Road Ahead." Center for the Study of Intelligence, Central Intelligence Agency, 2023. ↑
[10] Shojaee, Parshin, et al. The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity. Apple Machine Learning Research, 5 June 2025. ↑
[11] Arghire, Ionut ”$223 Million Stolen in Cetus Protocol Hack“ Security Week. ↑
[12] Chainalysis Team. “$197 Million Stolen: Euler Finance Flash Loan Attack Explained [UPDATED 4/6/23].” Chainalysis Blog, 15 Mar. 2023, updated 6 Apr. 2023. ↑
[13] Aaron McDade. “Investors Have Lost Nearly $2.5 Billion on Crypto Scams, Hacks So Far in 2025: Report.” Investopedia, 1 July 2025. ↑
[14] SolidityScan Web3 Hack Hub. ↑