I’ve written a couple times about Fibonacci numbers and certificates. Here the certificate is auxiliary data that makes it faster to confirm that the original calculation was correct. This post puts some timing numbers to this. I calculated the 10 millionth Fibonacci number using code from this post. n = 10_000_000 F = fib_mpmath(n) This took 150.3 seconds. As I’ve discussed before, a number f is a Fibonacci number if and only if 5f² ± 4 is a […]

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arXiv:2405.00081v5 Announce Type: replace-cross Abstract: We introduce the concept of an imprecise Markov semigroup (mathbf Q). It is a tool that allows us to represent ambiguity around both the transition probabilities and the invariant measure of a continuous-time Markov process via a collection of Markov semigroups, each associated with a (possibly different) Markov process. We use techniques from topology, geometry, and probability to analyze ergodic limits under model uncertainty encoded by (mathbf Q). We establish long-term bounds that […]

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Most stablecoins are backed by either fiat reserves or crypto assets, a model that’s proven functional but fundamentally limited. Tharwa is building something different: a stablecoin collateralized by a diversified portfolio of real-world assets, UAE real estate, gold, oil, treasury bills, managed by AI-driven rebalancing algorithms. It’s an ambitious technical stack that attempts to solve the yield problem plaguing dollar-pegged stablecoins while maintaining stability through diversification rather than overcollateralization. Saeed Al Fahim, founder of Tharwa and member of […]

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Recurrent neural networks (RNNs) can be interpreted as discrete-time state-space models, where the state evolution corresponds to an infinite-impulse-response (IIR) filtering operation governed by both feedforward weights and recurrent poles. While, in principle, all parameters including pole locations can be optimized via backpropagation through time (BPTT), such joint learning incurs substantial computational overhead and is often impractical for applications with limited training data. Echo state networks (ESNs) mitigate this limitation by fixing the recurrent dynamics and training only […]

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Molecule representation learning is crucial for understanding and predicting molecular properties. However, conventional atom-centric models, which treat chemical bonds merely as pairwise interactions, often overlook complex bond-level phenomena like resonance and stereoselectivity. This oversight limits their predictive accuracy for nuanced chemical behaviors. To address this limitation, we introduce textbf{DeMol}, a dual-graph framework whose architecture is motivated by a rigorous information-theoretic analysis demonstrating the information gain from a bond-centric perspective. DeMol explicitly models molecules through parallel atom-centric and bond-centric […]

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arXiv:2601.19041v1 Announce Type: new Abstract: Heatmap-based non-autoregressive solvers for large-scale Travelling Salesman Problems output dense edge-probability scores, yet final performance largely hinges on the decoder that must satisfy degree-2 constraints and form a single Hamiltonian tour. Greedy commitment can cascade into irreparable mistakes at large $N$, whereas MCTS-guided local search is accurate but compute-heavy and highly engineered. We instead treat the heatmap as a soft edge prior and cast decoding as probabilistic tour construction under feasibility constraints, where […]

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arXiv:2601.20867v1 Announce Type: new Abstract: Prompt tuning has achieved remarkable progress in vision-language models (VLMs) and is recently being adopted for audio-language models (ALMs). However, its generalization ability in ALMs remains largely underexplored. We observe that conventional prompt tuning for ALMs also suffers from the Base-New Tradeoff, and we identify that this issue stems from the disrupted semantic structure of the embedding space. To address this issue, we propose Semantically Expanded Prompt Tuning (SEPT)-a plug-and-play framework that explicitly […]

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arXiv:2602.00866v1 Announce Type: new Abstract: The Controller Area Network (CAN) bus provides a rich source of vehicular signals increasingly leveraged for applications in automotive and auto insurance domains, including collision detection, predictive maintenance, and driver risk modeling. Despite this potential, existing pipelines largely train isolated task-specific models on raw CAN data, with only limited efforts exploring decoded signals. Such fragmentation prevents shared representation learning and limits cross-task generalization. By contrast, natural language processing (NLP) and computer vision (CV) […]

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arXiv:2506.05544v2 Announce Type: replace Abstract: This paper introduces the MPS (Model Prediction Set), a novel framework for online model selection for nonstationary time series. Classical model selection methods, such as information criteria and cross-validation, rely heavily on the stationarity assumption and often fail in dynamic environments which undergo gradual or abrupt changes over time. Yet real-world data are rarely stationary, and model selection under nonstationarity remains a largely open problem. To tackle this challenge, we combine conformal inference […]

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This is the story of the United Space Ship Enterprise. Assigned a five year patrol of our galaxy, the giant starship visits Earth colonies, regulates commerce, and explores strange new worlds and civilizations. These are its voyages… and its adventures. — ROUGH DRAFT 8/2/66, before the Star Trek opening narration reached its final form Tags: screen-writing, science-fiction

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