Chronos Architectures

• Chronos Architectures are a suite of systems that leverage temporal sensitivity to enhance embedded OS, ML models, HPC solvers, and instrumentation.
• They employ innovative methods including formal verification, multi-timer scheduling, group attention, and secure federated protocols to boost performance and accuracy.
• Demonstrated improvements include up to 10× overhead reduction in RTOS, 20–30 point forecasting skill gains, and advanced sensitivity in gravitational-wave detection, guiding future research.

Chronos Architectures comprise a family of technical systems, models, and frameworks spanning embedded real-time operating systems, numerical linear algebra (AMG), large-scale pretrained time-series models, debugging-focused LLMs, gravitation-wave observatories, secure federated learning, and temporally-aware multi-agent coordination. These systems are unified by an acute sensitivity to temporal structure—whether in concurrency, signal forecasting, security, or marketplace valuation—implemented through bespoke software, hardware, or algorithmic innovations.

1. Real-Time Operating Systems: eChronos and Multi-Timer Scheduling

eChronos is a preemptible, formally-verified RTOS targeting embedded MCUs, originally built for proprietary ISAs (ARM, PowerPC) and later ported to RISC-V (Singhal et al., 2019). The architecture exhibits strict layering: generic APIs (task, timer, queue), architecture-specific backends (e.g., context-switch-RISC-V, interrupt-event-RISC-V), statically-allocated task stacks (no MMU), and fixed-priority preemptive scheduling using a ready bitmap scanned by CLZ-style instructions.

Porting to RISC-V required:

• Replacing ARM/PowerPC SVC opcodes with ECALL/EBREAK,
• Marshaling arguments via x10–x17 in line with the RISC-V ABI,
• Refactoring all linker "edata" dependencies not present on RISC-V,
• Rewriting inline-assembly shims to RISC-V,
• Harnessing exception vectors (mtvec) for interrupt entry.

The RTOS implements context-switching by saving all callee-saved registers, PC, and SP via context-switch-RISC-V, and manages software synchronization (mutexes, semaphores) with atomic disabling of mie (machine-interrupt-enable) through CSR operations. Functional verification was achieved via execution on the Spike emulator, although no cycle-accurate or WCET figures were supplied.

Theoretical concurrency and responsiveness of eChronos are formalized via a controlled Owicki-Gries model in Isabelle/HOL (Andronick et al., 2015). The model introduces pseudo-variables such as EIT (enabled interrupts), AT (active task), and ATStack (context stack), and details guarded entry/exit for ISRs and SVC handlers, enforcing correct, preemptible interleaving and reflecting the real hardware's mask and scheduling semantics.

The CHRONOS multi-timer framework extends traditional RTOS tick scheduling by partitioning periodic tasks over m hardware timers, each operated at the GCD of its assigned subset to reduce unnecessary tick interrupts (Heider et al., 3 Mar 2025). The mapping is formalized as MIQCP:

$$\min\;\sum_{j=1}^m f_j\,u_j,\quad f_j = \frac{1}{P_j}$$

subject to assignment and divisibility constraints, where $P_j$ is the GCD of periods assigned to timer $j$.

Implemented in FreeRTOS on the ESP32-S3, CHRONOS multi-timer strategies achieve up to $10\times$ peak and $6\times$ average reductions in bookkeeping overhead relative to single-timer baselines, by maximizing per-subset GCD and efficiently managing per-timer delayed task lists.

2. Pretrained Time-Series Models: Chronos and Chronos-2

The Chronos and Chronos-2 architectures represent a class of universal, zero-shot time-series foundation models leveraging large-scale transformer-based backbones for probabilistic forecasting (Ansari et al., 2024, Ansari et al., 17 Oct 2025, Zhai et al., 23 Apr 2025, Berthelier et al., 12 May 2026). Chronos tokenizes real-valued signals via mean-scaling and quantization, converting values $x_t$ into a fixed-size discrete vocabulary through

$\tilde x_t = \frac{x_t-m}{s}$

with vocabulary bin centers $c_1 < \dots < c_B$ and corresponding quantizer $q(x)$.

Forecasting is reframed as a next-token prediction problem solved by a T5/GPT-2 transformer:

$$\ell(\theta) = -\sum_{h=1}^{H+1}\sum_{i=1}^{|V_{ts}|} 1_{[z_{C+h+1}=i]}\log p_\theta (z_{C+h+1}=i|\dots)$$

Chronos-2 introduces a novel Group Attention mechanism, alternating time-attention (across time for each series/group) and group-attention (across series/covariates at each time index). For each transformer block, group attention is defined as:

$P_j$0

where group id $P_j$1 determines attention sharing within series groups or among targets and covariates.

Chronos-2 is pretrained on both real and synthetically multivariate time-series, employing TSI/TCM univariate generators and "multivariatizers" to induce cross-series dependencies. Zero-shot inference leverages in-context learning: specifying the groupings $P_j$2 and providing covariate/target compositions directly in the input.

Benchmark results demonstrate state-of-the-art performance in univariate, multivariate, and covariate-informed settings across fev-bench, GIFT-Eval, and Chronos Benchmark II (Ansari et al., 17 Oct 2025). The architecture gains most in covariate-rich scenarios, achieving 20–30 point skill improvements over previous foundation models.

A key limitation is exposed in controlled experiments: Chronos-2's "covariate as extra series" dual-attention architecture underperforms purely tabular in-context regression models on tasks with strong instantaneous covariate-target mappings and short horizons (Berthelier et al., 12 May 2026). Future design directions indicated include cross-attention fusion heads, mixture-of-experts for simple arithmetic, and feature-cross embeddings for covariates.

3. Chronos in Numerical Linear Algebra and High-Performance Computing

Chronos is also the name of a classical algebraic multigrid (AMG) solver framework tailored for large-scale, sparse systems on massively parallel machines (Isotton et al., 2021). The architecture uses C++/MPI+OpenMP and organizes computation as follows:

• DSMat: Distributed block-CSR storage, partitioned by row-blocks for per-rank locality.
• AMG components: strength-of-connection options (classical, strong-coupling, affinity), PMIS coarsening, multiple prolongation strategies (distance-one, extended, BAMG, hybrid via least-squares), aFSAI smoothing.
• Coarse-grid solves: Cholesky factorization for small $P_j$3, with aggregation to a single rank.
• Communication: Non-blocking MPI halo exchanges fully overlap with local SpMV.
• Object-oriented design: Uniform MatrixProd interface allows composable replacement of sparse kernels.

Chronos achieves 2–6x speedup in total time compared to BoomerAMG and PETSc-GAMG on diffusion and elasticity problems with hundreds of millions of DOFs, sustaining over 80% parallel efficiency up to 512 MPI ranks. The main architectural strengths are the parallel, block-wise storage, efficient Overlap/CSR exploitation, and flexible, high-quality coarsening/interpolation (Isotton et al., 2021).

4. Chronos Architectures in Machine Debugging and Conversational Agents

Kodezi Chronos-1 is a repository-scale, debugging-focused LLM whose architecture integrates Adaptive Graph-Guided Retrieval (AGR), Persistent Debug Memory (PDM), and a seven-layer fix-test-refine pipeline (Khan et al., 14 Jul 2025). AGR dynamically constructs a multi-signal (AST, dependency, test, call-graph, etc.) code graph and adaptively grows context via multi-hop neighborhood expansion scored by:

$P_j$4

Working in concert with PDM (a graph+vector memory system updated on commit/CI events), Chronos-1 executes a fix-test-refine loop where retrieved context and patterns are input to a debug-tuned LLM, which proposes fixes validated in a sandboxed test runner. Performance on practical debugging benchmarks is a clear outlier: 67.3% fix accuracy (5,000 scenarios), 80.33% on SWE-bench Lite, with 4–5x improvements over generic LLMs and sharp reductions in iteration/time (Khan et al., 14 Jul 2025). Limitations remain for hardware-specific and highly dynamic language errors.

Chronos also defines a temporal-memory conversational agent framework combining structured event extraction (S-V-O tuples with timestamp ranges) and dense+grep retrieval from dual calendars (event, turn) (Sen et al., 17 Mar 2026). At query time, dynamic prompting conditions retrieval and reasoning on the dialogue question, and a ReAct-style agent orchestrates multi-hop tool use over both calendars. Empirical results show Chronos achieves 92.6–95.6% accuracy on long-range memory tasks, with ablation identifying the event calendar as critical for temporal reasoning.

5. Chronos in Physical Instrumentation and Secure Learning

The CHRONOS observatory is a sub-hertz, cryogenic gravitational-wave detector deploying cross-shaped sapphire torsion bars as test masses suspended via high-Q fibers and read out by triangular Sagnac speed-meter cavities (Inoue et al., 10 Mar 2026, Tanabe et al., 7 Apr 2026). Key architectural features are:

• Cryogenic operation (8–10K) with multi-stage shields and active vibration isolation,
• Quantum non-demolition speed-meter readout, which suppresses radiation-pressure noise at low frequencies and enables probing the stochastic GW background at 0.1–10 Hz,

$P_j$5

• State-of-the-art noise budget, reaching strain sensitivities of $P_j$6 at 2 Hz.

The instrument is optimized for detection of intermediate-mass black-hole mergers and primordial stochastic backgrounds inaccessible to LIGO/Virgo/KAGRA or LISA (Inoue et al., 10 Mar 2026, Tanabe et al., 7 Apr 2026).

A separate line in secure federated learning, CHRONOS, leverages ARM TrustZone enclaves to decouple heavy key-exchange from active gradient aggregation via a phase-decoupled protocol: per-epoch ECDH, Shamir-secret sharing of ephemeral keys, and single AES-CTR-based mask per round. Secure World monotonic counters enforce mask freshness, while dropout recovery reconstructs missing masks from peer-held Shamir shares. This architecture achieves a 74% reduction in active-phase latency vs. synchronous Secure Aggregation for 20 clients, with only 632 B per-device secure storage (Dang, 21 Apr 2026).

In privacy-preserving data marketplaces, CHRONOS organizes three architectural layers: (i) index routing with neural ODE-decayed shortcuts, (ii) event-conditioned Shapley valuation using BOCPD-driven changepoints, and (iii) EXP3-IX DP budget scheduling. Key expressions include a monotone-envelope Poisson recall bound and per-seller DP Shapley value release, enabling competitive recall/QPS/ε tradeoffs for knowledge graph query systems (Chandra, 22 May 2026).

6. Comparative Table of Chronos Architectures

Application Domain	Key Architectural Elements	Distinctive Technical Features
Embedded RTOS	Layered modular kernel, RISC-V backend	Preemptive scheduling, formal OG concurrency, MIQCP mapping
Time-Series Foundation	Group Attention transformer, patching, quantiles	In-context learning, robust scaling, universal forecasting
HPC AMG	Block-CSR DSMat, aFSAI smoother, PMIS coarsening	Near-ideal scaling, hybrid prolongation, operator complexity
Debugging LLM	Graph-guided retrieval, persistent memory, 7-layer	Multi-hop context expansion, sandbox validation, high recall
Gravitational-Wave Det.	Torsion-bar, cryo-mirrors, Sagnac speed-meter	Quantum noise suppression, sub-Hz regime, active ISO
Secure FL	TEE ECDH+Shamir setup, idle/active-phase split	OS-compromise resilience, O(ND) masking, DP-dropout recover
Data Marketplace	ODE-decay index, event Shapley val, DP-scheduler	Tight recall bounds, per-epoch DP release, EC-MPV mechanism

7. Significance and Future Directions

Chronos architectures demonstrate a cross-disciplinary convergence on temporally-informed structures, where the precise encoding, partitioning, or augmentation of time-related features is foundational to correctness, efficiency, scalability, or privacy. In embedded systems, these principles translate to responsiveness and formally verified safety; in time-series models, to universal generalization and strong covariate integration; in scientific instrumentation, to sensitivity gains through quantum measurement design; and in multi-agent systems, to differentially-private value accounting resilient to structural temporal drift.

Open research directions center on explicit fusion/attention mechanisms for covariate exploitation in foundation models (Berthelier et al., 12 May 2026), further integration of temporal-logic formalism with real hardware (Andronick et al., 2015), runtime scalability of multi-timer RTOS partitioning (Heider et al., 3 Mar 2025), and DP/ODE-driven index evolution for privacy-aware marketplaces (Chandra, 22 May 2026). Across all applications, the success of Chronos designs underscores the centrality of temporal modeling and synchronization—whether in simulating, controlling, predicting, or collaborating within dynamic environments.