LAGRANGE

2025 was a pivotal year for Lagrange. We set out to transform cryptography from theory into strategic infrastructure, bringing verifiable AI to defense, aerospace, and government systems where correctness cannot be assumed. Here's the year in review: 👇 lagrange.dev/blog/lagranges…

Checking in from @nvidia GTC in San Jose. A few themes showing up everywhere: • AI focus is shifting from model training to real-world deployment • Agentic systems are moving from answering questions to taking action • NVIDIA is expanding beyond chips toward the full stack - hardware, software, and infrastructure Seeing companies like @QuantinuumQC, @EvidenceOpen , and @Infleqtion pushing the boundaries of compute makes one thing clear: As AI moves into real products, the conversation is shifting from performance to reliability, control, and verification.

Autonomous systems are advancing faster than our ability to verify them. Drone swarms. Autonomous vehicles. Edge AI targeting. The systems making decisions are evolving quickly. The systems proving those decisions were correct are not.

Brian Novell 📮 brian@lagrange.dev

The team at Lagrange joins fellow trailblazers in AI at Nvidia's GTC this week. Reach out to Head of BD @BrianNovell to link up.

Drone swarms aren’t an AI problem. They’re a distributed systems problem. Model quality doesn't matter if coordination collapses under latency, jamming or partial connectivity.

Major DeepProve milestone. We completed a refactor of our proving system to support elliptic curves. The result: • 30% faster proving times • Increased parallelization • Architecture built for post-quantum cryptography Performance matters. Security at scale matters even more.

Trust once meant policy, hierarchy, and hope. That doesn’t scale to AI. Defense systems can’t just follow orders, they must be able to prove they are.

Defense systems can’t just follow orders. They must be able to prove they are compliant. In high-stakes autonomous situations, instruction isn't enough. Verification is.

Zero-knowledge isn't just privacy technology. It’s infrastructure for trustworthy autonomy. It enables powerful systems to prove correctness without exposing sensitive internals. Verifiability and resilience aren’t tradeoffs. With modern cryptography, they scale together.

Oversight used to keep systems in check. Now proofs can. Cryptography makes machines accountable without exposing everything. Zero-knowledge guarantees turn former black boxes into verifiable systems. Deterrence in the age of AI means provable integrity.

The old model of defense relied on secrecy and hierarchy. The next will rely on proofs and verification. Defense AI can’t run on “trust me”. The strongest defense systems won’t be the most secret. They’ll be the most provable.

Cryptography turns “trust me” into “prove it.” That’s the upgrade defense AI can’t skip.

Learn more about how DeepProve makes this possible: lagrange.dev/blog/deepprove…

Generative AI is flooding the internet with music, video, art, and text. The problem isn’t creativity. It’s attribution. Without proofs, we can’t tell who made what, or who owns it. Remix culture doesn’t fail because people create. It fails when provenance disappears. DeepProve makes authorship cryptographically provable at the content layer.

Decision-makers like the comfort of a “brain.” Centralized control feels safe: • Visibility • Override capability • Clear accountability But centralized systems create single points of failure. Distributed autonomy increases resilience. Accountability has to be reconstructed from system behavior, not command visibility.

AI systems can be 99% accurate. When those systems take action, that 1% gap isn’t a rounding error. It’s a liability. The real barrier to AI deployment isn’t model performance. It’s the gap between probabilistic confidence and institutional certainty. Internally, we call this the chasm of AI adoption. Verification is what closes it.

Full blog post + research paper lagrange.dev/blog/making-ha…

Most zk systems become inefficient when math stops being polynomial. Real systems aren’t purely polynomial. They rely on: sin, exp, sigmoid or erf Today we’re introducing research that makes non-polynomial functions efficient to prove in zk-SNARKs. The result: • Up to 256× lower error • Up to 20× better prover performance If we want verifiable AI in the real world, we must be able to prove the math real systems actually use. Hard math just became provable. Full paper ↓

More autonomy → less direct oversight. More oversight → less resilience. You can’t maximize both. As AI systems move into defense, finance, and infrastructure, this tradeoff stops being theoretical. It becomes architectural. Oversight shifts from control to verification