TinyCast: Probabilistic Zero-Shot Forecasting with Computed Periodicity

Armin Steinhauser

cs.LGAug 16, 2026

TinyCast: Probabilistic Zero-Shot Forecasting with Computed Periodicity

Authors: Armin Steinhauser

Organizations: RAWS Labs

Abstract

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.

Figures & tables

Figure 1: TinyCast architecture. (a) A single encoder block. (b) The pipeline for one 48-step block: the normalized context and the period-conditioned positional encoding pass through the encoder and decoder to nine quantiles at all block positions in parallel; the dashed arrow is the median feedback that chains blocks. (c) The decoder, whose three readouts compose the per-horizon query

q_{h}

Model	Params $\downarrow$	$\mathrm{nGMASE}\downarrow$	$\mathrm{nWQL}\downarrow$	$\mathrm{nMSIS}\downarrow$
TinyCast (ours)	146 K	0.774	0.545	0.554
Reverso-Nano ( Fu et al., 2026 )	200 K	0.760	(0.661)	(2.035)
Reverso-Small ( Fu et al., 2026 )	550 K	0.726	(0.626)	(1.945)
TTM-R3 ( Ekambaram et al., 2024 )	1.4 M	0.724	0.520	0.501
Reverso ( Fu et al., 2026 )	2.6 M	0.711	(0.610)	(1.905)
Toto-2.0-4m ( Khwaja et al., 2026 )	4.1 M	0.757	0.524	0.455

Table 1: Zero-shot GIFT-Eval; lower is better, best per column in bold among the learned models. All three metrics are ratios to seasonal naive, which scores

1.000

on each. Parenthesized values are point errors for models not emitting predictive distributions.

Figure 2: GIFT-Eval point accuracy (left) and

\mathrm{nWQL}

(right) versus parameter count; lower is better. TinyCast ∗ is the same checkpoint at the firmware profile (Section 4.3 ). Dashed staircase: the Pareto frontier over the census at the host profile, which the static-W8A8 point does not enter.

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 3: Phase binning of the context with a dominant detected period of

p_{1}{=}24

. (a) Context values against position relative to the forecast start,

t{-}L

; the stripe below assigns every position to one of

n_{b}{=}16

phase bins. (b) Cycle template: the mean of the context values sharing a bin. The arrow indicates the phase template selection for the marked future offset

h^{*}

Stage	Module (shape)	Params
input	$\mathrm{Linear}_{\text{in}}$ ( $14{\to}64$ )	960
encoder	depthwise conv ( $10\times(64,1,3){+}\text{bias}$ )	$2,560$
	pointwise $1{\times}1$ ( $10\times(64,64,1){+}\text{bias}$ )	$41,600$
	shared SwiGLU (up $64{\to}128$ , down $64{\to}64$ )	$12,480$
	RMSNorms ( $20\times(64)$ )	$1,280$
	encoder subtotal	57,920

Appendix

Table 2: TinyCast parameter budget:

D{=}64

10

encoder blocks, FFN expansion

1.0

K{=}4

periods,

n_{b}{=}16

phase bins, nine quantile levels.

Optimization
Optimizer	AdamW ( Loshchilov & Hutter, 2019 )
Weight decay	0.01
Gradient clipping	1.0
Precision	bf16-mixed
Random seed	42
Total samples	150 M

Appendix

Table 3: Training configuration of the deployed TinyCast.

Profile	Arithmetic	Symmetrization	Alignment	$\mathrm{nGMASE}$	$\mathrm{nWQL}$	$\mathrm{nMSIS}$
Host	bf16	yes	yes	0.7738	0.5454	0.5541
No alignment	bf16	yes	no	0.7858	0.5567	0.5786
No symmetrization	bf16	no	yes	0.7816	0.5515	0.5638
Single pass	bf16	no	no	0.7935	0.5629	0.5889
Quantization reference	fp32-strict	yes	yes	0.7736	0.5457	0.5535
Single-pass reference	fp32-strict	no	no	0.7918	0.5622	0.5865

Appendix

Table 4: The eight scored configurations: one checkpoint, the same 97 GIFT-Eval configurations, all scored on the host. Lower is better. “Exact” W8A8 calls a host build of the same C integer core sources the firmware executes rather than a fake-quantization emulation, and the board runs the fidelity chain of Appendix E , not the benchmark.

Model	$\mathrm{nGMASE}\downarrow$	$\mathrm{nWQL}\downarrow$	$\mathrm{nMSIS}\downarrow$
TinyCast (ours)	0.774	0.545	0.554
PatchTST	0.849	0.587	0.574
iTransformer	0.893	0.620	0.613
TFT	0.915	0.605	0.656
N-BEATS	0.938	0.816	2.512
DLinear	1.061	0.846	2.841

Appendix

Table 5: Per-dataset supervised models in the pinned snapshot, all 97 configurations, ratios to seasonal naive. Lower is better. These are trained on the series they forecast and are therefore outside the zero-shot census of Table 1 .

				95% CI
	Model	Params	$\Delta$	configs	base datasets
$\mathrm{nGMASE}$	Reverso-Nano	200 K	$+0.0140$ †	$[+0.0030,+0.0245]$	$[-0.0022,+0.0283]$
	Reverso-Small	550 K	$+0.0475$	$[+0.0366,+0.0581]$	$[+0.0322,+0.0613]$
	TTM-R3	1.4 M	$+0.0498$	$[+0.0348,+0.0656]$	$[+0.0290,+0.0695]$
	Reverso	2.6 M	$+0.0626$	$[+0.0479,+0.0782]$	$[+0.0437,+0.0843]$
	Toto-2.0-4m	4.1 M	$+0.0172$ †	$[-0.0081,+0.0382]$	$[-0.0102,+0.0448]$

Appendix

Table 6: Paired bootstrap intervals for every difference in Table 1 with a per-configuration comparator record. Positive

\Delta

means the comparator scores lower and therefore leads. The three StatsForecast baselines are omitted: all are resolved against us, by margins of

0.30

8.08

units. FLAIR is absent for the reason given above, having no per-configuration entry in the snapshot.

\dagger

marks a difference whose cluster interval spans zero. The Reverso rows on

\mathrm{nWQL}

and

\mathrm{nMSIS}

carry the same caveat as in Table 1 : those models emit no predictive distribution, so the quantity differenced is a point error.

Family	Control	Parameters	Steps	$Q$	Encoder
Architecture	dilated-conv base	$340,545$	7,500	1	untied, non-separable, FFN $1.5$
	+ phase binning	$361,089$
	+ recency gate	$393,921$
	substituted-recency arm	$410,241$
Component	architecture family’s best arm	$394,441$	30,000	9	untied, non-separable, FFN $1.5$
	+ future-conv	$445,513$			future-conv stack separable, shared FFN

Appendix

Table 7: Configuration of the three ablation families and of the deployed model. Deltas are valid within a family and absolute scores are not comparable across families.

Q

is the number of quantile levels; the single-quantile families are scored on

\mathrm{nMAD}

, and the component family runs at about a fifth of the deployed sample budget. Every family reads GIFT-Eval-Pretrain and Chronos KernelSynth; the component family adds four locally generated length-4096 KernelSynth shards, which its synthetic-family arm replaces with the four Reverso-family shards the deployed model trains on.

	params	$\mathrm{nGMASE}$	$\Delta$	$\mathrm{nMAD}$	$\Delta$
detector off, recency path substituted	410 K	1.1537	$+0.1312$	0.9774	$+0.1160$
control (dilated-conv base)	340 K	1.0225		0.8614
causal padding	340 K	1.0161	$-0.0064$ †	0.8562	$-0.0052$ †
+ phase binning	361 K	0.9248	$-0.0977$	0.7791	$-0.0823$
+ phase binning + causal	361 K	0.9250	$-0.0975$	0.7886	$-0.0728$
+ phase binning + recency gate	393 K	0.9092	$-0.1133$	0.7694	$-0.0920$

Appendix

Table 8: Architecture family, dilated-conv base at 340 K, 7,500 steps. Lower is better on

\mathrm{nGMASE}

and

\mathrm{nMAD}

, so a negative

\Delta

is an improvement. Arms are not parameter-matched, and each row gives its count.

\mathrm{nMAD}

is the single-quantile point error defined above.

\dagger

marks a delta whose

95\%

paired bootstrap interval over configurations spans zero.

	$\mathrm{nGMASE}$	$\Delta$	$\mathrm{nWQL}$	$\Delta$
control (394 K line)	0.8123		0.5699
+ future-conv correction	0.7972	$-0.0151$	0.5614	$-0.0085$
+ synthetic-family blend	0.8060	$-0.0062$ †	0.5669	$-0.0030$ †
+ synthetic-family blend (tuned dose)	0.8052	$-0.0071$ †	0.5623	$-0.0076$ †
+ gated committing loss	0.8100	$-0.0023$ †	0.5690	$-0.0009$ †
+ future-conv + synthetic families	0.7860	$-0.0263$	0.5529	$-0.0170$

Appendix

Table 9: Component family, 394 K nine-quantile line, 30,000 steps. Lower is better on

\mathrm{nGMASE}

and

\mathrm{nWQL}

, so a negative

\Delta

is an improvement. Arms carry the control’s parameter count except future-conv, which adds

51

\dagger

marks a delta whose

95\%

paired bootstrap interval over configurations spans zero.

	$\mathrm{nGMASE}$	$\Delta$	$\mathrm{nMAD}$	$\Delta$
control (peak LR $3\times 10^{-3}$ , 100 M samples)	0.8562		0.7252
peak LR 1e-3	0.8957	$+0.0395$	0.7460	$+0.0208$
peak LR 2e-3	0.8665	$+0.0103$	0.7300	$+0.0048$ †
peak LR 4e-3	0.8745	$+0.0183$	0.7304	$+0.0052$ †
budget 50 M samples	0.8933	$+0.0371$	0.7479	$+0.0227$
budget 150 M samples	0.8533	$-0.0029$ †	0.7217	$-0.0035$ †

Appendix

Table 10: Optimization family: learning-rate peak and sample budget. Lower is better, so a negative

\Delta

is an improvement.

\mathrm{nMAD}

is a point error, as in Table 8 .

\dagger

marks a delta whose interval spans zero.

	$\mathrm{nGMASE}$	$\Delta$
control (phase binning + recency gate)	0.9092
phase bins, $16$ to $32$	0.9047	$-0.0045$
cross-horizon convolution, width $5$	0.9085	$-0.0007$
encoder kernel width, $3$ to $5$	0.9100	$+0.0008$
gated encoder convolution	0.9178	$+0.0086$
harmonics per period, $1$ to $2$	0.9178	$+0.0086$

Appendix

Table 11: Single-variable overrides on the architecture family’s best arm. All

97

GIFT-Eval configurations; a negative

\Delta

is an improvement.

Group	Intervention	Scored on	Result
1 Computed values	seasonal-naive draft as input value	6-config probe	0.8825
	+ all significant periods	6-config probe	0.8930
	+ linear trend term	6-config probe	0.9178
	control (dilated-conv base)	6-config probe	0.8760
	trend-seasonal decomposition as channels	97 configs	0.9177
2 Learned rule	learned per-period weight, variant 1	97 configs	0.9114

Appendix

Table 12: Interventions aimed at point accuracy, tested and rejected.

\mathrm{nGMASE}

throughout, lower is better. Groups 1 and 2 are scored against an archived control and group 1’s per-configuration results are released. Group 3’s arms have no archived control, and groups 4 to 6 are reported by direction.

Model	Params $\downarrow$	$\mathrm{nMSIS}\downarrow$	$\Delta$	$95\%$ CI
TinyCast (ours)	146 K	0.554
Reverso-Nano	200 K	(2.035)	$-1.4807$	$[-1.6688,-1.3123]$
Reverso-Small	550 K	(1.945)	$-1.3911$	$[-1.5651,-1.2281]$
TTM-R3	1.4 M	0.501	$+0.0528$	$[+0.0219,+0.0843]$
Reverso	2.6 M	(1.905)	$-1.3506$	$[-1.5205,-1.1952]$
Toto-2.0-4m	4.1 M	0.455	$+0.0989$	$[+0.0684,+0.1304]$

Appendix

Table 13: Interval score on GIFT-Eval at the host profile, all

97

configurations, normalized to seasonal naive. Lower is better. Positive

\Delta

means the comparator scores lower and therefore leads. Intervals are paired bootstraps over configurations, and

\dagger

marks a difference whose cluster interval spans zero. Parenthesized values are point errors for models not emitting predictive distributions, as in Table 1 , and their differences carry the same caveat.

Figure 4: Empirical cumulative distribution over all 97 configurations of the relative change from the matched unquantized reference to the quantized host profile, both carrying the two host-side strategies, in

\mathrm{nGMASE}

(left) and

\mathrm{nWQL}

(right), for all configurations (black) and by forecast term (light to dark: 55 short, 21 medium, 21 long). Positive is a degradation and the dashed line is zero change; the panels share one

x

range. Dots mark the median and the P90; the filled marker where a curve reaches one is the worst configuration, named with its change.

Figure 5: The same construction as Figure 4 , but at the firmware profile: the relative change from the single-pass reference to exact static W8A8, with neither sign symmetrization nor period alignment on either side. Lower is better and positive is a degradation.

Model	Params	rel. MASE	rel. WQL
TinyCast	146 K	0.880	0.722
AutoARIMA	–	0.869	0.741
AutoTheta	–	0.859	0.793
AutoETS	–	0.943	0.814
TTM-R2	805 K	1.120	1.134
Chronos-Tiny	8.4 M	0.874	0.703

Appendix

Table 14: Chronos-ZS at the host profile, all

27

tasks, ratios to the published seasonal-naive reference. Lower is better. The statistical methods need no training data and have no position on a parameter axis.

		MASE		WQL
Model	Params $\downarrow$	ratio	win rate	ratio	win rate
TinyCast	146 K	0.819	–	0.658	–
AutoARIMA	0	0.879	0.688	0.746	0.719
AutoTheta	0	0.890	0.650	0.922	0.810
Toto-2.0-4m	4.1 M	0.720	0.190	0.553	0.140
CITRAS-FM	7.2 M ∗	0.707	0.140	0.540	0.080

Appendix

Table 15: fev-bench at the host profile, all

100

tasks. Ratios are to the vendored seasonal-naive reference and lower is better. Win rate is TinyCast’s share of tasks won against that model, computed by the benchmark’s own pairwise function, so it rests on no comparator pool. AutoARIMA returns

96

of the

100

. ∗ CITRAS-FM releases no checkpoint, so its parameter count is the one stated in its paper rather than one we instantiated.

Observed samples	64	128	256	512	1024	2048
Relative MAE	1.013	0.975	0.911	0.845	0.786	0.759

Appendix

Table 16: Cold start: accuracy against the number of observed samples, all

97

configurations rescored on a truncated context at the no-alignment profile, since an alignment factor computed from a truncated context would change the effective context length as history shrinks. Relative MAE, lower is better;

1.0

is parity with seasonal naive.

Figure 6: Zero-shot forecasts at the host profile on ten GIFT-Eval tasks, spanning all seven domains, four sampling frequencies and three forecast terms. Truth (blue), median forecast (orange, dashed), shaded

10

–

90\%

predictive interval, seasonal naive (grey, dotted); the vertical dotted line marks the forecast start and grey bands mark missing observations. Titles give configuration, domain,

\mathrm{nGMASE}

and, where the horizon is only partly drawn, “first

n

H

”;

y

is in each series’ own units. The panel-selection and

x

-range rules are stated below.

Latency
Core call (full $L{=}2048$ re-encode)	4.08 s
Per-position encoder step ( $\times L$ per core call)	1860 $\mu$ s
Decoder (in isolation)	0.20 s
Flash
INT8 matrix and convolution coefficients	138.1 KiB
Complete benchmark image (incl. $8\text{\,}\mathrm{K}\mathrm{i}\mathrm{B}$ context)	365.5 KiB

Appendix

Table 17: Deployment record of the TinyCast static-W8A8 core, with FP32 islands, on an STM32H753 Cortex-M7 at 480 MHz. The RAM rows are not additive: the first

8\text{\,}\mathrm{K}\mathrm{i}\mathrm{B}

of the heap row is already reserved in the linker-section row, and the accounted total removes the overlap.

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