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TinyCast: Probabilistic Zero-Shot Forecasting with Computed Periodicity

Armin Steinhauser

arXiv:2608.15767v1cs.LGcs.AI

TL;DR

TinyCast addresses how small a probabilistic zero-shot forecaster can be while remaining usable across unseen series and constrained devices. It computes periodicity explicitly and models the remainder with an attention-free architecture, defining the probabilistic size-accuracy frontier at 146,505 parameters.

  • Problem

    The open question is how to achieve general probabilistic zero-shot forecasting at a size suitable for deployment across varying devices, sites, and signals.

  • Method

    TinyCast detects dominant periods without parameters, folds context by phase, and uses an attention-free convolutional encoder with a quantile decoder.

  • Results

    146,505 parameters define the probabilistic size-accuracy frontier; every zero-shot model scoring better carries at least 1.4 M parameters.

  • Takeaways & Limitations

    Convolutional and matrix-multiplication mixing enables static INT8 export and end-to-end embedded forecasting without per-signal fitting.

  • Takeaways & Limitations

    TinyCast is univariate, uses neither covariates nor cross-series structure, and degrades silently when inputs leave its pretraining regime.

Abstract

from arXiv · show

We introduce TinyCast, an attention-free zero-shot forecaster that emits a predictive distribution from 146,505 parameters, on the premise that at this size the periodic structure of a context is worth computing rather than learning. A zero-parameter spectral detector supplies the dominant periods, the context is folded on their phase, and a dilated convolutional encoder and a block-autoregressive quantile decoder model the rest. It is smaller than every zero-shot entry on the GIFT-Eval board whose parameter count can be established. On probabilistic accuracy it defines the size-accuracy frontier. Among zero-shot entries declaring no test-data leakage it is the only one below 1.4M parameters that emits a predictive distribution, and every entry scoring better carries at least that budget. On Chronos-ZS and fev-bench every neural model ahead of it carries at least 28 times its parameters. Because the mixing path is convolutions and matrix multiplications only, it exports to static INT8 and forecasts end to end on an embedded device without per-signal fitting.

1 Introduction

TinyCast asks how small a probabilistic zero-shot forecaster can be, replacing learned seasonality with computed periodicity in a 146,505-parameter model. It targets generality without per-signal fitting and runs end to end on embedded hardware.

  • Motivation: Time series foundation models forecast unseen series zero-shot, addressing the human cost of fitting, validating, and maintaining one specialist per signal.Per-dataset models can use fewer than 1,000 parameters, but the stated gap is generality at that size.
  • Architecture: TinyCast computes periodicity rather than learning it, folding the context on the phase of detected periods.This preserves learned capacity for structure that fixed computation does not deliver at the target budget.
  • Deployment: INT8 execution forecasts end to end on embedded hardware from one firmware image, without a host, network, or per-signal fitting.The model uses fixed-window working memory and learned operations limited to convolutions, matrix multiplications, normalization, and elementwise gates.
  • Size and accuracy: 146,505 parameters make TinyCast smaller than every zero-shot GIFT-Eval entry with an established parameter count.It is trained once, zero-shot, on GIFT-Eval-Pretrain and synthetic data.
  • Size and accuracy: 1.4 M parameters is the threshold below which TinyCast is the only no-test-leakage zero-shot entry emitting a predictive distribution.Every Table 1 model with a better probabilistic score carries at least 1.4 M parameters; ahead of TinyCast, every neural model on Chronos-ZS and fev-bench carries at least 28 times its parameters.

2 Related work

TinyCast is positioned at the intersection of pretrained zero-shot forecasting, attention-free sequence mixing, and constrained-hardware forecasting. Its distinguishing approach is to measure periodicity directly from each context without parameter cost or signal metadata, while using convolutional mixing for deployment.

  • Scope: TinyCast is compared within forecasting across pretrained zero-shot models, attention-free mixers, and constrained-hardware systems.Classification and representation-learning models are outside the comparison.
  • Time series foundation models: Pretrained zero-shot forecasters span decoder-only and encoder transformers, state-space encoders, and tabular or PFN-based predictors, avoiding parameter updates.TinyCast is trained on Chronos’s KernelSynth corpus and evaluated against its zero-shot task.
  • Compact zero-shot models: TinyCast’s closest compact comparator, Reverso, interleaves long convolutions with DeltaNet linear-recurrence layers and trains sizes from 200 K to 2.6 M.Unlike approaches that reach periodic structure through attention or patching, TinyCast measures it from the context at no parameter cost.
  • Explicit periodicity: FlowState reads a period from dataset metadata, whereas TinyCast detects the period from the series for signals without metadata.This contrast is presented as the basis for TinyCast’s usability on previously unseen signals.
  • Attention-free mixing: TinyCast uses a dilated causal convolution stack, extending receptive fields through local kernels alone without relying on attention.State-space models and TiRex’s recurrent xLSTM backbone also stream in constant memory, while the passage identifies the dilated stack as a distinct mixing design.
  • On-device forecasting: On-device time-series forecasters are typically bespoke models trained for one signal, assuming that signal and a labeled history are known at programming time.TinyML work supplies efficient kernels and tiny-model design, but fixed-task objectives do not transfer when the target signal is unknown at design time.

3 Methodology

TinyCast allocates 146,505 parameters around computed periodicity: deterministic detection and positional features feed an attention-free convolutional encoder and block-autoregressive quantile decoder. It normalizes each context, forecasts 48-step blocks with median feedback, and trains under scheduled sampling with a gated committing term.

  • Architecture: 146,505 parameters define four components: zero-parameter periodicity detection, deterministic positional encoding, dilated-convolution encoding, and future-position decoding.The design computes structure exposed by the context rather than learning it.
  • Decoder and rollout: p=48 future positions receive nine nominal quantiles in parallel from pooled, phase-binned, and future-convolution readouts, with completed-block medians feeding later blocks.Arbitrary horizons therefore compose block-autoregressively, and inference re-encodes after appending each block median.
  • Periodicity detection: Four period slots retain significant integer periods after DC removal, FFT periodogram testing at α=0.05, Bonferroni correction, and rounding.Failed slots are zeroed; the cap permits co-existing cycles such as daily and weekly seasonality.
  • Encoder: L=2048 is encoded by depthwise-separable causal convolutions with kernel size Kc=3 and dilations from 1 to 512, yielding a receptive field of 2047.Residual SwiGLU feed-forwards and RMS normalization complete each encoder block without downsampling.
  • Training: λ=0.3 weights a gated committing term added to the nine-quantile pinball loss, and scheduled sampling rolls out four autoregressive blocks during training.The committing term activates when repeating the metadata-derived last cycle would outperform the median on the window.

4 Experiments

TinyCast is evaluated against zero-shot and statistical baselines across GIFT-Eval, Chronos-ZS, and fev-bench, where its 146,505-parameter model extends the point-accuracy size frontier and leads the probabilistic size-accuracy frontier. Ablations identify computed periodicity and phase binning as major contributors, while static INT8 preserves performance sufficiently for embedded deployment.

  • Benchmark results: 0.545 nWQL makes TinyCast the probabilistic size-accuracy frontier, while every lower-scoring Table 1 model uses at least 1.4 M parameters.TTM-R3 uses 1.4 M parameters for 0.520 nWQL, and FlowState-9.1M uses 9.1 M for 0.502.
  • Benchmark results: 0.880 relative MASE and 0.722 relative WQL on Chronos-ZS make TinyCast’s predictive distribution lead every method requiring no training data.AutoARIMA and AutoTheta exceed TinyCast on point accuracy by one to two percent, the only such case across the three benchmarks.
  • Benchmark results: 0.819 relative MASE and 0.658 relative WQL on fev-bench put TinyCast ahead of every statistical baseline, while stronger released models use 28×–62× more parameters.Its primary scaled quantile-loss skill score is 0.304 [0.247, 0.364], but task disjointness is not established.
  • Ablations: Computed periodicity improves the shipped recipe from 0.7814 to 0.7743 nGMASE and from 0.5483 to 0.5441 nWQL at the same 146,505-parameter budget.The detector is parameter-free; phase binning contributes −0.098 nGMASE over the dilated-convolution base, and adding the recency gate reaches −0.113.
  • Deployment: Static W8A8 over all 97 configurations reaches 0.790 nGMASE and 0.553 nWQL, while the firmware profile with all deployment constraints reaches 0.833 and 0.581.Quantization degrades the matched unquantized reference by 2.14% and 1.26%; the firmware model uses 138.1 KiB of INT8 weights and returns nine quantiles.

5 Discussion

TinyCast’s discussion argues that computed periodicity enables a strong probabilistic accuracy frontier at very small scale, while the same constrained architecture supports deployment on integer runtimes. It also identifies limitations in streaming efficiency, missing multivariate structure, ablation comparability, and evaluation evidence.

  • Computed periodicity: Measured-period folding is the largest contributor in TinyCast’s ablations, supporting the premise that computing seasonality preserves capacity for other functions.Removing the detector while retraining the shipped budget performs worse, despite the detector using no parameters.
  • Accuracy frontier: TinyCast extends probabilistic accuracy scaling downward and defines the size-accuracy frontier, making its result more consequential for usable forecasts than point accuracy alone.Probabilistic forecasts indicate how much to trust outputs for control loops and alarm thresholds.
  • Deployment: The parameter constraint yields a deployment-friendly architecture using dilated convolutions and only integer-runtime-compatible learned operations.Learned operations are convolutions, matrix multiplications, normalization, and elementwise gates.
  • Limitations: Limitations include repeated full-context encoding at every call, weaker reduced-budget streaming accuracy, and the absence of covariate and cross-series information.The model is univariate; streaming would require causal normalization and window-invariant positional encoding.
  • Limitations: Evidence is limited because ablation families use their own budgets, while GIFT-Eval informed design choices and Chronos-ZS provides the untouched process test.Ablation deltas bound component benefits at the shipped configuration rather than directly measuring them there.

6 Conclusion · A Architecture, training and inference details

TinyCast concludes that a 146,505-parameter probabilistic zero-shot forecaster can compute dominant periodicity rather than learn it, while restricting learned operations to enable embedded deployment. The conclusion also emphasizes that emitting uncertainty intervals expands the practical questions hardware deployments can address.

  • 6 Conclusion: 146,505 parameters define TinyCast as a probabilistic zero-shot forecaster that computes dominant context periods spectrally at no parameter cost.The context is folded on the detected periods’ phase, preserving learned capacity for structure fixed computation does not supply.
  • 6 Conclusion: TinyCast is smaller than every zero-shot GIFT-Eval entry whose parameter count can be established.
  • 6 Conclusion: Convolutions, matrix multiplications, normalization, and elementwise gates replace global mixing under the model’s tight parameter budget.
  • 6 Conclusion: Static integer-graph execution on an embedded device follows from restricting the model to those learned operations.
  • 6 Conclusion: At this parameter scale, TinyCast distinguishes itself by reporting how far to trust each forecast step rather than emitting only one value per step.This enables control loops and alarm thresholds to act on intervals rather than single numbers.
  • A Architecture, training and inference details: The appendix supplies the mathematical details and formal definitions underlying the architectural choices introduced in Section 3.

A.1 Architecture

TinyCast computes dominant periods from the context, folds encoder representations by phase, and combines them with positional and pooled features for probabilistic decoding. Its causal convolutional architecture emits nine de-normalized quantiles while supporting arbitrary horizons and deployment-safe processing.

  • Periodicity detector: The detector retains the K=4 largest significant local periodogram maxima at α=0.05, while failed slots are set to zero.It searches periods from 2 through L/2 and admits only strict local maxima.
  • Encoder: The encoder stacks dilated separable convolutions and SwiGLU feed-forwards with residual additions, RMS normalization, and causal padding.Causal padding preserves length and ensures each output depends only on past samples.
  • Decoder: Phase folding averages encoder states sharing each detected period’s phase bin, producing per-slot templates for the phase readout.With undetected periods, max(pk, 1) sends all positions to bin 0, so the slot contributes its whole-context average rather than being masked.
  • Decoder: The six-block future-convolution correction uses causal padding, preventing future-label leakage while refining a phase-based draft.The draft is an input to the correction network rather than a forecast, and the released decoder can emit arbitrary horizons in one pass.
  • Decoder: The decoder combines positional encoding, pooled context, phase templates, and future-convolution corrections before a residual SwiGLU and linear head emit nine quantiles.The quantiles use nominal decile levels τ ∈ {0.1, 0.2, . . . , 0.9} and are de-normalized using stored context statistics.

A.2 Training · A.3 Inference · B Evaluation protocol and comparators

TinyCast is trained with block-autoregressive quantile supervision, gated seasonal copying, and carefully controlled data, seeds, and compute. At inference, host-only preprocessing supports evaluation, while the unconstrained quantile head remains INT8-friendly but may require sorting.

  • A.2 Training: Four 48-step blocks are rolled out autoregressively, with each block predicted in parallel and its median probabilistically committed to the next context.The commitment probability ramps from zero to 0.5; otherwise the target block is used, and Wfc-out is zero-initialized so correction starts at zero.
  • A.2 Training: The base objective is a nine-quantile pinball loss augmented by a metadata-derived seasonal copy of the last cycle.The rounded seasonality is ⌊24/s⌉, clipped to [2, L/2].
  • A.2 Training: λ = 0.3 weights the gated seasonal term, which is evaluated only at the median and becomes silent when the median matches or beats the copy.The base loss continues supervising all nine quantiles.
  • A.2 Training: Eight RTX 3090 GPUs trained the deployed run for 7.8 h, or about 62 accelerator-hours, using bf16 mixed precision and torch.compile.The environment used PyTorch 2.10.0, CUDA 12.8, Python 3.12, and PyTorch Lightning.
  • A.2 Training: 0.0009 nGMASE and 0.0022 nWQL are the spreads across the three repeated runs used to measure training variance.Every arm uses seed 42 except shipped-recipe repeats at seeds 43 and 44; all runs average the same eight checkpoints.
  • A.3 Inference: Host evaluation applies sign symmetrization and canonical-period alignment, whereas neither transformation is carried by the firmware.Alignment requires the dominant spectral peak to satisfy the stated k ∈[2, 16] condition and the canonical cycle to be absent.
  • B Evaluation protocol and comparators: The scored configurations use host builds of the same C integer core sources executed by the firmware for exact W8A8 evaluation.The board uses the fidelity chain of Appendix E rather than the benchmark.
  • A.3 Inference: The quantile head is unconstrained, preserving a single INT8-friendly matrix multiplication and an independent median for block feedback.Although training targets the true non-crossing quantiles, finite-sample crossings still occur and are more frequent on one path.

B.1 Evaluation protocol … C Ablations and negative results

The paper evaluates TinyCast under benchmark-native protocols and defines a restricted, auditable zero-shot comparator census. It reports reproducible scoring, resource-axis accounting, supervised-model exclusions, and paired uncertainty intervals, while no passage supplied here describes Section C’s ablations or negative results.

  • B.1 Evaluation protocol: Scores use each benchmark’s own harness, test windows, and prediction lengths, with bf16 autocast and a released strict-FP32 path.Multivariate targets are converted to univariate only where required.
  • B.1 Evaluation protocol: The leaderboard’s CRPS column is reported as nWQL because it aggregates weighted quantile loss over each model’s finite quantile grid.The paper therefore uses nWQL throughout rather than continuous ranked probability score.
  • B.1 Evaluation protocol: Table 4 isolates the costs of removing inference strategies, symmetrization, alignment, and quantization through four specified contrasts.The quantized-host comparison uses an unquantized fp32-strict reference under the quantized path’s arithmetic.
  • B.1 Evaluation protocol: Comparator results come from publishers’ own per-configuration files, re-aggregated under GIFT-Eval’s rule or vendored unchanged for Chronos-ZS and fev-bench.Models without per-configuration results are excluded from the census, while aggregate-only results are retained at those aggregates.
  • B.2 Comparator census: The census admits zero-shot models with published per-configuration GIFT-Eval results, declared no test-data leakage, and at most 10 M parameters.Zero-shot means forecasting an evaluation series without fitting to it, regardless of the leaderboard’s differing model_type boundary.
  • B.2 Comparator census: Parameter counts use released checkpoints when available and papers otherwise, producing discrepancies such as Reverso-Small at 550,161 learnable parameters and YingLong-6m at 7,319,566.Non-learned FFT constants are excluded from Reverso-Small’s recount.
  • B.2 Comparator census: TinyCast’s 0.774, 0.545 and 0.554 lead all eight covered per-dataset supervised models on all three metrics, although supervised models remain outside the zero-shot census.An uncovered xLSTM-Mixer reports 0.510 on the board’s probabilistic metric, ahead of TinyCast.
  • B.3 Comparator intervals: Table 6 provides paired bootstrap intervals from 20,000 replicates, using either 97 configurations or the 28 base datasets, with positive deltas indicating comparator leads.The delta is defined as TinyCast’s score minus the comparator’s score.

C.1 Ablation setup

The ablation compares three configuration families with the deployed model under shared benchmark-data exclusions and no benchmark test-base exposure. It also identifies five architectural differences and family-specific scoring and data-budget conditions.

  • Data and configuration controls: All families inherit Appendix A exclusions from cached GIFT-Eval-Pretrain, so none saw a benchmark test base.The exclusions are applied when GIFT-Eval-Pretrain is cached.
  • Data and configuration controls: 5 fields distinguish the deployed configuration from the architecture family’s causal phase-binning arm: FFN expansion, feed-forward tying, convolution factorization, future-conv readout, and quantile levels.These are the stated configuration differences between the deployed model and that ablation arm.
  • Family definitions and scoring: Q is the number of quantile levels, while single-quantile families are scored on nMAD and the component family uses about a fifth of the deployed sample budget.Every family reads GIFT-Eval-Pretrain and Chronos KernelSynth; the component family additionally uses four locally generated length-4096 KernelSynth shards.

C.2 The ablation tables

The ablation tables distinguish point-error nMAD from nine-quantile probabilistic metrics and report architecture, component, and optimization effects with paired-bootstrap uncertainty. They also show that canonical-period alignment is weakly identified while multiplicity correction covers the 36 table deltas and leaves delta statuses unchanged when redundant nMAD columns are removed.

  • Metric definitions: Single-quantile arms report nMAD, which is exactly median absolute deviation and is not comparable to nine-quantile nWQL.nMAD is formed and normalized like nWQL but measures point error.
  • Architecture family: 0.131 nGMASE is the cost of replacing the detector with a phase-free recency path on the 340 K, 7,500-step architecture line.The 95% paired-bootstrap interval is [0.085, 0.189], and the arm combines detector and capacity effects because it has 410 K parameters versus 340 K.
  • Component family: 0.0297 is the component-family nMSIS improvement from the longer training rollout, with a 95% CI of [0.0171, 0.0433].The improvement occurs on 58 of 97 configurations; under clustering, the interval is [0.0163, 0.0435].
  • Canonical-period alignment: 2 of 97 configurations change under canonical-period alignment, while bootstrap replicates return exactly zero in 13.2% of draws.Under clustering, replicates omit the affected dataset in 36.0% of draws, with an achieved two-sided level of 0.72 on both metrics.

C.3 Detector evidence · C.4 Capacity, size and single-setting sweeps

The detector frequently identifies usable periodic structure, and its choices materially improve forecasting, especially when the selected periods provide adequate window occupancy. Capacity sweeps indicate that phase binning is more efficient than other measured additions, while a roughly half-sized model preserves accuracy.

  • C.3 Detector evidence: 84% of initial contexts trigger the detector, which fills 2.9 of four period slots on average and returns checkable true periods for hourly and daily series.This statistic covers initial contexts only, although deployment reruns detection after each rollout.
  • C.3 Detector evidence: 0.753 nGMASE is achieved on 71 configurations firing above 90% of windows, versus 0.841 on 10 configurations firing below 50%.Seven low-firing configurations have no benchmark-declared seasonality, so the split may partly reflect intrinsically harder series.
  • C.3 Detector evidence: +0.0071 nGMASE and +0.0042 nWQL are the detector-off contrasts against the mean of three shipped-recipe runs.The corresponding 97-configuration bootstrap intervals are [−0.0004, +0.0148] and [−0.0006, +0.0088].
  • C.3 Detector evidence: 0.0751 nGMASE is lost when detector output is suppressed, while fixed and shuffled substitutions score 0.8597 and 0.8414 against controls of 0.8489 and 0.8488.The shuffled draw is only barely better, indicating that applying detector outputs to the wrong series recovers little value.
  • C.3 Detector evidence: 0.136 versus 0.005 in log ratio is the cost of canonical-period substitution on sub-hourly/hourly versus daily-or-coarser configurations, a 0.131 contrast.The canonical period is correct in both groups, so window occupancy explains part, but not all, of the difference.
  • C.4 Capacity, size and single-setting sweeps: 33 K additional parameters for the recency gate yield 0.0156 nGMASE, making this capacity use about a tenth as efficient per parameter as phase binning.The estimate has a 95% CI of [−0.0255, −0.0067] over configurations.
  • C.4 Capacity, size and single-setting sweeps: 225,865 parameters, 49% fewer than the 445,513-parameter future-conv control, produce 1.0085× point and probabilistic accuracy on the shared 43 configurations.The point-accuracy 95% CI is [0.9697, 1.0450], and the probabilistic-accuracy interval is [0.9892, 1.0321].
  • C.4 Capacity, size and single-setting sweeps: 32 phase bins are the only one-variable override improving the best arm, by 0.0045; the other six settings either reduce accuracy or remain within noise.Table 11 reports these overrides across all 97 GIFT-Eval configurations, with negative ∆ indicating improvement.

C.5 Negative results … D.2 Quantization spread

The tested point-accuracy interventions were rejected or limited to specific training budgets, while additional benchmark measurements expose interval-quality, coverage, and quantization costs. TinyCast is over-confident overall, with degradation worsening at shorter deployment profiles.

  • C.5 Negative results: Computed periods help as encoder-indexed coordinates, whereas computed forecasts supplied as values cause regression to grow with the amount of prior supplied.The convolutional stack models level and seasonality in value space better than the hand-computed baseline.
  • C.5 Negative results: Table 12 records single-run, reduced-budget probes of point-accuracy interventions that were tested and rejected.These results characterize the architecture at this scale and need not generalize.
  • C.5 Negative results: Both learned per-period weighting variants were worse than the hard rule and no rule, so neither appears in the deployed configuration.The rejected variants replaced a hard window-selection rule with learned weights.
  • C.5 Negative results: 0.009 per flag at 30,000 steps versus a joint cost of 0.0161 at 150,000 steps shows that the hard rule and wider fixed cross-horizon convolution helped reduced-budget training but hurt shipped-budget accuracy.The two flags changed together, so attribution is joint.
  • C.5 Negative results: A per-series Bayesian fit that looks strong on a balanced interior-window probe falls behind the amortized model under the exact GIFT-Eval protocol, limiting apparent in-context-learning headroom.The oracle gate’s per-series advantage also does not correlate with the tested identifiability statistics.
  • D.1 Interval quality and coverage: 0.554 is TinyCast’s mean scaled interval score, while pooled nominal 80% intervals capture only 68.0% of actuals, indicating over-confidence.Coverage is 83.0% short term, 67.4% medium term, and 60.0% long term.
  • D.1 Interval quality and coverage: 1.75% is the quantized host profile’s interval-score cost, compared with 12.7% for the firmware profile against the host profile.The firmware profile reaches 0.6243 versus 0.5541 for the host profile; interval score degrades about twice as fast as nGMASE and nWQL.
  • D.2 Quantization spread: 5.18% nGMASE and 3.29% nWQL are firmware quantizer costs, versus 2.14% and 1.26% at the host profile.Firmware nGMASE degrades on 87 of 97 configurations, compared with 79 at the host profile.

D.3 Secondary benchmarks in full … E.1 Setup and operating point

Across secondary benchmarks and inference tests, TinyCast’s performance depends on task structure, history length, and forecast feedback, while its reported wins and losses reveal clear seasonal and calibration limits. The paper also documents qualitative forecast coverage and a static-W8A8 deployment setup that retains floating-point non-affine operations.

  • D.3 Secondary benchmarks in full: 14 of Chronos-ZS’s 27 tasks have seasonal periods of four steps or fewer, while 10 declare none, limiting the phase fold’s leverage.Chronos-ZS is described as the least favorable benchmark for computed periodicity because many tasks offer little usable seasonal structure.
  • D.3 Secondary benchmarks in full: 0.913 relative MASE on short-season tasks trails AutoARIMA’s 0.856 and AutoTheta’s 0.851, while 0.846 on the other 13 leads 0.885 and 0.867.The passage characterizes this as a tendency rather than a rule because declared periods do not explain every task.
  • D.4 Inference behavior: 39 of 44 recursive configurations improve interval score when sampled quantiles replace medians as feedback, by 0.087 nMSIS.The 53 configurations with horizons no longer than one block are bit-identical because nothing is fed back.
  • D.4 Inference behavior: 0.058 remains the gain from 512 to 1024 samples, whereas the 1024-to-2048 gain falls to 0.027, indicating graceful cold-start recovery rather than detector-only dependence.The rescoring is on relative MAE, anchored to a full-context value of 0.759 without canonical-period alignment.
  • D.5 Wins and losses against seasonal naive: 90 of 97 GIFT-Eval configurations, 22 of 27 Chronos-ZS configurations, and 83 of 100 fev-bench configurations beat seasonal naive on point accuracy.Losses cluster in weekly, monthly, and annual configurations, which score 0.873 nGMASE against 0.758 elsewhere.
  • D.5 Wins and losses against seasonal naive: 80% is the widest central predictive interval available from nine quantiles, so 95% and 99% alarm thresholds cannot be produced.This limitation follows directly from the forecast head’s quantile design.
  • D.6 Qualitative forecasts: Figure 6 samples ten GIFT-Eval forecasts across seven domains, four sampling frequencies, and three forecast terms, using truth, median forecasts, and 10–90% intervals.Panel selection is based on domain-proportional allocation and evenly spaced nGMASE order statistics.
  • E.1 Setup and operating point: Static-W8A8 export freezes per-output-channel weight and per-tensor activation scales, while RMSNorm, SiLU products, normalization, bias additions, and period detection remain floating-point.The detector runs in FP64 and the remaining non-affine operations run in FP32.

E.2 Measured performance · E.3 Fidelity · E.4 Limits and projections

TinyCast’s embedded core achieves measured end-to-end forecasting on a Cortex-M7, with bounded memory and INT8 arithmetic, while cross-hardware tests show close numerical fidelity. Portability is demonstrated for the encoder, and streaming inference is projected to reduce forecast latency substantially, though the projection was not implemented or timed.

  • E.2 Measured performance: 4.08 s is required to re-encode the context and decode one 48-step forecast block on the 480 MHz Cortex-M7.The encoder contributes 3.8 s, while the decoder and quantile readout contribute about 0.27 s.
  • E.2 Measured performance: 310.1 KiB is the activation-arena footprint, comprising 256.5 KiB of encoder rings and phase-fold context plus a 53.6 KiB decoder-plan peak.The firmware image occupies 17.8% of flash, and INT8 coefficients are below the one-byte-per-parameter estimate because biases and normalization scalars use higher precision.
  • E.2 Measured performance: 89 million multiply-accumulates per second are sustained at 480 MHz, with throughput limited by FP32 islands and non-matrix runtime operations.The datasheet specifies 110 mA typical run-mode current under the stated revision-V, VOS0 conditions.
  • E.3 Fidelity: 432 outputs on the fixed test input all lie within 3 ULP of the host static-W8A8 reference, with a maximum absolute deviation of 9.5 × 10−7.173 outputs are bit-identical, and repeated boots reproduce the board record exactly.
  • E.3 Fidelity: 55.4% of 13,824 outputs across 32 contexts are bit-identical, while period detection is identical everywhere and the pooled median relative deviation is zero.Half the contexts agree within 14 ULP throughout; benchmark-workload contexts have a 47% bit-identical rate and a strictly positive median relative deviation.
  • E.3 Fidelity: 22.8% of the output range is the worst-case deviation under adversarial stress, versus 16.1% on held-out real series and 15.4% on benchmark-workload contexts.The deviations arise from near-zero outputs and FP32 one-ULP changes crossing INT8 bin boundaries.
  • E.4 Limits and projections: 7.73 ms per position is achieved by the unchanged streaming encoder on a 150 MHz Cortex-M33 within roughly 230 KiB, at 1.30× the Cortex-M7’s cycle count.The full model exceeds that device’s 520 KB SRAM, so the result demonstrates encoder portability rather than full-model deployment.
  • E.4 Limits and projections: 0.27 s is the projected decoder-and-readout cost for streaming forecasts, about 15× below the measured 4.08 s windowed call.The streaming variant would ingest samples at 1.86 ms per position, but no such firmware was linked or timed.
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