# Vishal Verma Labs

> Independent technical analyses at the intersection of AI systems, physics, and control theory. By Vishal Verma — CTO at Dehurdle, IIT Delhi alumnus.

## Articles

- [Hyperbolic Sparse Autoencoders: Empirical Validation of Poincaré Manifold Geometry on LLM Activations](https://vishalvermalabs.com/papers/empirical-validation-hypersae-poincare-geometry/): Aug 2026, Mechanistic Interpretability & Deep Architecture. This paper presents the first empirical scale-up validation of Hyperbolic Sparse Autoencoders (HyperSAE) against standard flat Euclidean SAEs on Layer 13 residual stream activations of Google Gemma-2-2B (d=2304, dict size M=16384). Trained for 10,000 steps per model on FineWeb-Edu activations using an NVIDIA L4 GPU cluster, HyperSAE addresses the fundamental volume-expansion pathology of Euclidean space by embedding dictionary atoms into a Poincare hyperbolic ball manifold. Across a 6-model sweep, HyperSAE achieves strict Pareto dominance over FlatSAE: reducing reconstruction MSE by 9.8% (4.123 vs 4.572) at high sparsity (L0 approx 53), increasing cross-entropy loss recovery by +3.4 percentage points (78.9% vs 75.5%), and maintaining superior downstream multi-choice reasoning performance on MMLU-Pro (16.26% vs 16.11%, n=12,032). Interactive charts visualize the MSE Pareto frontier, CE loss recovery curves, downstream benchmark performance, and radial depth distribution. We detail the system optimizations (CoActivationQueue scaling, VRAM fragmentation prevention, mini-batched loss evaluation) that enabled cloud training without OOMs, and release the implementation as hypersae, an open-source PyTorch package.
- [Escaping Flatland: Weight-Space Regularization and Hyperbolic Geometry in Mechanistic Interpretability](https://vishalvermalabs.com/papers/escaping-flatland-hyperbolic-geometry/): Jun 2026, Mechanistic Interpretability & Deep Architecture. Current mechanistic interpretability embeds inherently hierarchical concepts into flat Euclidean space, violating geometric packing limits. This paper proposes the Hyperbolic Sparse Autoencoder (HypSAE). Acknowledging the strict optimization limits of the RMSNorm spherical trap, Algebraic Cancellation, and Token-Level Category Errors, we geometrically decouple the architecture. By applying exponential manifold projections strictly as a Weight-Space Regularizer on the dictionary atoms via a learned depth scalar, we leverage Momentum Contrast and Hyperbolic Entailment Cones to construct native ontological trees while preserving perfectly flat, causal interventional execution.
- [Empirical Lyapunov Stability: Growth-Ratio Energy Functions as Leading Indicators of Agent Task Failure](https://vishalvermalabs.com/papers/empirical-lyapunov-stability-agent-failure/): Jun 2026, Multi-Agent Systems. Analyzes "Empirical Lyapunov Stability: Growth-Ratio Energy Functions as Leading Indicators of Agent Task Failure". This paper presents the first empirical validation of Lyapunov stability analysis applied to LLM agent execution trajectories, featuring a 5-condition ablation study across 3,175 total runs. Evaluated across four benchmarks—τ³-bench (750 runs, customer service), SWE-bench Verified (481 runs including 333 multi-trial, software engineering), MINT (1,136 runs, reasoning and coding), and a custom local-model battery (808 runs across 4 open-weight models on consumer hardware via Ollama)—we demonstrate that growth-ratio normalization transforms a theoretically sound but practically useless raw energy derivative into a precise leading indicator of task failure. Cross-model validation across 5 model families (Gemini 2.5 Flash, Llama 3.2:3B, Phi-4-Mini, Qwen3:4B, Gemma4:E4B) confirms zero false positives and consistent guard behavior. Local model evaluation reveals a novel small-model self-sabotage pattern: naive turn-limiting outperforms unconstrained baselines by +17.5pp on average because small models destroy correct solutions in later turns. The implementation is released as state-harness, an open-source Rust/Python library with first-class LangGraph and CrewAI adapters, a CLI tool, and OpenTelemetry export.
- [The Fluid Dynamics of Multi-Agent AI: Resolving d'Alembert's Paradox of Generative Workflows](https://vishalvermalabs.com/papers/fluid-dynamics-multi-agent-ai/): May 2026, Multi-Agent Systems. Production multi-agent AI systems fail at rates of 41-87% because they treat natural language as frictionless flow, ignoring the viscous semantic boundary layer where probabilistic agent intents meet deterministic database states. This paper resolves d'Alembert's paradox for AI by modeling agent communication channels as viscous fluid flows. The framework proposes Renormalization Group compression for agent communications, Holographic Invariant Storage for context drift prevention, and Lyapunov-verified control loops for stability guarantees. This theoretical framework is empirically validated in the companion paper through state-harness, an open-source Rust/Python implementation tested across 3,175 benchmark runs spanning 5 model families including local open-weight models on consumer hardware.
- [AI's Autonomous Galileo Moment: Discovering the Hidden Hamiltonians of Chaotic Systems](https://vishalvermalabs.com/papers/autonomous-galileo-moment-hamiltonians/): Apr 2026, Machine Learning Theory. Xi and Chen's April 2026 paper proves that equivariant attention networks trained on passive thermal snapshots of frustrated spin glasses can autonomously recover the exact underlying Hamiltonian with 99.7% accuracy. This shatters the assumption that deep learning is restricted to statistical interpolation, establishing an exact algebraic equivalence between generative score fields and conservative thermodynamic force fields.
- [The Physics of AI: Why the Generative Era is a Computational Dead End](https://vishalvermalabs.com/papers/physics-of-ai-computational-dead-end/): Apr 2026, AI Architecture. Modern generative AI architectures are computational analogues of Laplace's Demon, exhausting resources on microstate reconstruction instead of macrostate prediction. Through the lens of statistical mechanics, gravitational singularities, and quantum degeneracy pressure, this paper demonstrates why JEPA and SIGReg represent the thermodynamically necessary pivot from pixel-level generation to abstract state-space modeling.

## Open-Source Software

- [hypersae](https://github.com/vishal-dehurdle/hypersae): High-Performance Hyperbolic Sparse Autoencoders for Mechanistic Interpretability. Projects dictionary atoms into a Poincaré ball manifold while maintaining a zero-latency linear Euclidean forward pass. Validated at scale on Google Gemma-2-2B (Layer 13) across 20M FineWeb-Edu tokens on NVIDIA L4 GPUs. Reduces reconstruction MSE by 9.8% at L0 ≈ 53 (4.1232 vs 4.5724), increases Cross-Entropy Loss Recovery to 78.9% (+3.4pp), reduces dead latents to 0.2%, and preserves higher downstream reasoning accuracy on MMLU-Pro (16.26% vs 16.11%). Install: `pip install hypersae`.
- [state-harness](https://github.com/vishal-dehurdle/state-harness): Runtime safety net for LLM agents. Detects token spirals, kills doomed tasks early, tells you why. Hybrid Rust/Python library with first-class LangGraph and CrewAI adapters, CLI tool, and OpenTelemetry export. Validated across 3,175 benchmark runs (τ³-bench 750, SWE-bench 481, MINT 1,136, custom local-model battery 808) with zero false positives across 5 model families (Gemini 2.5 Flash, Llama 3.2:3B, Phi-4-Mini, Qwen3:4B, Gemma4:E4B). 38.6% compute reduction on SWE-bench. Install: `pip install state-harness`.

## About the Author

Vishal Verma is the Co-Founder & CTO of Dehurdle (https://dehurdle.com), an enterprise AI coaching platform featured as a Harvard Business Publishing case study and trusted by Deloitte, PwC, AB InBev, and 10 global enterprises.

He studied robotics, physics, and systems design at IIT Delhi. After college, he built MVPs for early-stage startups and ran his own ventures. He then spent three years preparing for the Indian Civil Services — studying economics, ethics, governance, history, and public policy — with physics as his optional — which gave him a systems-level understanding of how institutions, incentives, and human behavior actually work.

Today, Vishal is responsible for Dehurdle's entire technology stack — the zero-payload privacy engine, the behavioral intelligence pipeline, the real-time voice simulation infrastructure, and the agentic coaching layer. He writes about research in developmental psychology, computational neuroscience, and AI alignment. He also plays competitive chess.

## Linked Identities

- LinkedIn: https://www.linkedin.com/in/visha1v/
- X / Twitter: https://x.com/v1sha1v
- GitHub: https://github.com/vishal-dehurdle
- Company: https://dehurdle.com
- About (Dehurdle): https://dehurdle.com/about
- Email: vishal.verma@dehurdle.com

## Metadata

- Site URL: https://vishalvermalabs.com/
- RSS Feed: https://vishalvermalabs.com/rss.xml
- LLMs Full Text: https://vishalvermalabs.com/llms-full.txt
- License: CC BY-NC 4.0 (Creative Commons Attribution-NonCommercial 4.0 International)