AdaCast: Conditional Parameter Generation for Adaptive Time Series Forecasting

Darahaas Nallagatla; Darryl Cherian Jacob; Pan He

cs.LGOct 8, 2026

AdaCast: Conditional Parameter Generation for Adaptive Time Series Forecasting

Authors: Darahaas Nallagatla, Darryl Cherian Jacob, Pan He

Organizations: Auburn University

Abstract

Time-series foundation models (TSFMs) have achieved strong forecasting performance across domains. However, most adaptation methods remain static. Existing all-in-one methods learn a single set of dataset-level parameter updates and apply the same adapted model to every input. As a result, they cannot adapt the model parameters to the temporal patterns, seasonality and dynamics of each input time series. This limits their ability to produce forecasts that are tailored to heterogeneous inputs. To address this limitation, we propose AdaCast, a conditional parameter generation framework for time-series forecasting. AdaCast uses a generator to produce input-specific low-rank parameter updates for a frozen pretrained TSFM. These updates adapt the model to each input during both training and inference. Across six public benchmarks, AdaCast consistently outperforms static adaptation baseline in in-domain forecasting and improves zero-shot generalization to held-out datasets across domains. These results demonstrate that conditional parameter generation provides an effective approach for adaptive forecasting.

Figures & tables

Figure 1: Overview of the AdaCast architecture. Each univariate series $\mathbf{X}_{b,v}$ in the input batch is passed through the frozen backbone encoder, whose hidden states $\mathbf{Z}_{b,v}$ serve as the conditioning representation. The parameter generator takes this representation as its condition and emits a pair of low-rank matrices for every targeted module in every decoder block. Each pair forms the low-rank update for that module, and together they constitute the instance-specific update. These updates are injected additively into the corresponding frozen decoder weights, leaving the pretrained parameters unchanged and yielding the instance-adapted backbone, which produces the final forecast.

	AdaCast(Ours)		Chronos-Bolt B LoRA		Chronos-Bolt B		MOMENT		TTM B		Moirai B		TimesFM
Dataset	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTh1	0.3593	0.3635	0.3569	0.3633	0.3616	0.3650	0.3920	0.4110	0.3619	0.3710	0.3686	0.3835	0.4254	0.3825
ETTh2	0.2450	0.2979	0.2491	0.2988	0.2517	0.2992	0.2742	0.3327	0.2531	0.3032	0.2547	0.3053	0.2894	0.3233
ETTm1	0.3017	0.3143	0.3057	0.3169	0.3109	0.3185	0.3506	0.3824	0.3152	0.3248	0.5399	0.4322	0.3321	0.3326
ETTm2	0.1485	0.2228	0.1493	0.2232	0.1487	0.2236	0.1703	0.2579	0.1511	0.2405	0.1958	0.2687	0.1703	0.2552
Weather	0.1491	0.1789	0.1515	0.1816	0.1525	0.1825	0.1801	0.2384	0.1543	0.1893	0.1711	0.1912	—	—

Table 1: Zero-shot forecasting (

T{=}512

H{=}64

). Best and second-best results are bold and underlined , respectively. “—” indicates that zero-shot results are not reported because the evaluation dataset was included in the backbone’s pretraining data (e.g., Weather). AdaCast achieves the best MSE and MAE on five of six datasets and the lowest average error, reducing average MSE by 1.0% over static LoRA and 2.3% over the frozen backbone in zero-shot setting.

Figure 2: Qualitative forecasting examples with context length

T=512

and forecast horizon

H=64

. Each panel shows the observed context, ground-truth future, frozen Chronos-Bolt B forecast, and AdaCast forecast.

Dataset	Frozen Backbone	Static LoRA	AdaCast
ETTh1	0.3616 / 0.3650	0.3505 / 0.3610	0.3431 / 0.3594
ETTh2	0.2517 / 0.2992	0.2412 / 0.2997	0.2370 / 0.2919
ETTm1	0.3109 / 0.3185	0.2840 / 0.3155	0.2603 / 0.3040
ETTm2	0.1487 / 0.2236	0.1401 / 0.2171	0.1385 / 0.2160

Table 2: In-domain conditional generation versus static adaptation. All methods use Chronos-Bolt B . Static LoRA and AdaCast use

r=32

and

\alpha=128

; AdaCast uses

N_{\mathrm{pg}}=1

. Each cell reports MSE / MAE. Bold marks the best result. At the same rank and scaling, AdaCast outperforms both the frozen backbone and static LoRA.

Figure 3: Joint t-SNE visualization of LoRA parameters across six datasets. Static adaptation contributes one adapter per dataset; AdaCast contributes one adapter per sampled input. Generated LoRAs cover a wide region of parameter space and are organized by dataset: each input receives its own update. Trained LoRAs are fixed points: every input from a dataset receives the same update. Each arrow marks the LoRA gap between a dataset’s trained LoRA and the generated LoRAs for the same dataset.

Dataset	Matched	Shuffled	$\Delta$	Matched	Shuffled	$\Delta$
	Zero-shot			In-domain
ETTh1	0.3582	0.3594	$+0.0012$	0.3431	0.3450	$+0.0019$
ETTh2	0.2442	0.2478	$+0.0036$	0.2370	0.2449	$+0.0079$
ETTm1	0.3008	0.3005	$-0.0003$	0.2603	0.2666	$+0.0063$
ETTm2	0.1481	0.1494	$+0.0013$	0.1385	0.1401	$+0.0016$
Weather	0.1490	0.1491	$+0.0001$	0.1255	0.1295	$+0.0040$

Table 3: Effect of shuffling generated LoRA updates across test inputs. Entries report MSE.

\Delta

is shuffled MSE minus matched MSE; positive values indicate higher error after shuffling. Shuffling increases average error in both settings, suggesting that AdaCast benefits from updates matched to each input.

	Segment Disabled			Full
Dataset	Seg 1	Seg 2	Seg 3	AdaCast
ETTh1	0.3510 / 0.3617	0.3460 / 0.3596	0.3491 / 0.3603	0.3431 / 0.3594
ETTh2	0.2432 / 0.2946	0.2416 / 0.2940	0.2377 / 0.2923	0.2370 / 0.2919
ETTm1	0.2957 / 0.3132	0.2751 / 0.3056	0.2747 / 0.3064	0.2603 / 0.3040
ETTm2	0.1447 / 0.2202	0.1400 / 0.2168	0.1403 / 0.2168	0.1385 / 0.2160

Table 4: Effect of disabling LoRA updates in one decoder segment. Segments 1, 2, and 3 contain blocks 1–4, 5–8, and 9–12, respectively. Results use the in-domain setting. Each cell reports MSE / MAE. Bold marks the largest error among the segment-disabled configurations. Disabling updates in any segment increases error, suggesting that all decoder segments contribute to AdaCast’s gains.

Figure 4: Sensitivity of zero-shot forecasting to LoRA rank. Curves show each dataset’s relative error gap (%) to its best tested rank: MSE (left) and MAE (right). Zero indicates the best result, including ties. The shaded band marks the default rank

r=32

Dataset	Frozen TimesFM 2.5	Zero-shot	In-domain
		AdaCast–TimesFM 2.5
ETTh1	0.3734 / 0.3729	0.3628 / 0.3766	0.3475 / 0.3656
ETTh2	0.2792 / 0.3151	0.2610 / 0.3132	0.2548 / 0.3069
ETTm1	0.2988 / 0.3186	0.2874 / 0.3175	0.2764 / 0.3150
ETTm2	0.1574 / 0.2295	0.1534 / 0.2301	0.1410 / 0.2228
Weather	0.1430 / 0.1686	0.1403 / 0.1689	0.1289 / 0.1694

Table 5: AdaCast on TimesFM 2.5 (

T=512

H=64

). Cells report MSE / MAE. Bold marks the best result for each metric. AdaCast transfers to a second backbone, lowering MSE over frozen TimesFM 2.5 on every dataset in both settings. Average MSE drops by 3.8% in zero-shot and 8.5% in-domain.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	$C$	$T$	$(N_{\mathrm{train}},N_{\mathrm{val}},N_{\mathrm{test}})$
ETTh1	7	17,420	(8065, 2817, 2817)
ETTh2	7	17,420	(8065, 2817, 2817)
ETTm1	7	69,680	(33985, 11457, 11457)
ETTm2	7	69,680	(33985, 11457, 11457)
Exchange Rate	8	7,588	(4736, 697, 1454)
Weather	21	52,696	(36312, 5207, 10476)

Appendix

Table 6: Statistics of evaluation datasets.

Time per univariate series (ms)
	Static LoRA	AdaCast
Frozen backbone params	205,292,928	205,292,928
Trainable params	7,667,712	12,864,000
Trainable fraction	3.60%	5.90%
Batch size	32	32
ETTh1	0.39	12.22

Appendix

Table 7: Training cost of static LoRA and AdaCast on the frozen Chronos-Bolt backbone, single NVIDIA RTX PRO 6000 (

T{=}512

H{=}64

r{=}32

\alpha{=}128

). Per-series time is epoch time divided by the number of univariate series processed per epoch.

	Chronos-Bolt	Static LoRA	AdaCast
Trainable params	0	7,667,712	12,864,000
Time per series (ms)	0.21	0.23	2.60
Throughput (series/s)	4,680	4,396	384
Peak memory (GB)	1.49	1.52	21.6

Appendix

Table 8: Inference cost on ETTh1 (

T{=}512

H{=}64

, batch size 32, 224 univariate series per batch, single GPU).

Dataset	MSE	MAE	MSE	MAE
	AdaCast (Zero-shot)		Chronos-Bolt B
ETTh1	$0.3582\pm 0.0010$	$0.3635\pm 0.0002$	0.3616	0.3650
ETTh2	$0.2442\pm 0.0009$	$0.2968\pm 0.0010$	0.2517	0.2992
ETTm1	$0.3008\pm 0.0011$	$0.3134\pm 0.0009$	0.3109	0.3185
ETTm2	$0.1481\pm 0.0005$	$0.2226\pm 0.0002$	0.1487	0.2236
Weather	$0.1490\pm 0.0002$	$0.1773\pm 0.0019$	0.1525	0.1825

Appendix

Table 9: Multi-seed Zeroshot forecasting results (

T{=}512

H{=}64

). AdaCast entries are mean

\pm

standard deviation over seeds

\{1,43,2021\}

. Each cell reports MSE and MAE.

Dataset	$N_{\mathrm{pg}}{=}1$	$N_{\mathrm{pg}}{=}4$	$N_{\mathrm{pg}}{=}8$	$N_{\mathrm{pg}}{=}16$
ETTh1	0.3602 / 0.3634	0.3601 / 0.3638	0.3593 / 0.3635	0.3598 / 0.3638
ETTh2	0.2444 / 0.2972	0.2452 / 0.2981	0.2450 / 0.2979	0.2450 / 0.2977
ETTm1	0.3021 / 0.3145	0.3025 / 0.3149	0.3017 / 0.3143	0.3024 / 0.3144
ETTm2	0.1484 / 0.2239	0.1483 / 0.2244	0.1485 / 0.2228	0.1490 / 0.2247
Weather	0.1501 / 0.1891	0.1497 / 0.1824	0.1491 / 0.1789	0.1492 / 0.1785
Exchange	0.0654 / 0.1701	0.0644 / 0.1697	0.0594 / 0.1683	0.0591 / 0.1683

Appendix

Table 10: Effect of generator depth

N_{\mathrm{pg}}

on Zeroshot performance (

T{=}512

H{=}64

r{=}32

). Each cell reports MSE / MAE.

N_{\mathrm{pg}}=8

is the configuration used for all Zeroshot results in the main paper.

Dataset	Chronos-Bolt LoRA	AdaCast
ETTh1	0.3505 / 0.3610	0.3431 / 0.3594
ETTh2	0.2412 / 0.2997	0.2370 / 0.2919
ETTm1	0.2840 / 0.3155	0.2603 / 0.3040
ETTm2	0.1401 / 0.2171	0.1385 / 0.2160
Weather	0.1301 / 0.1592	0.1255 / 0.1544
Exchange	0.0591 / 0.1670	0.0571 / 0.1650

Appendix

Table 11: In-domain comparison of static LoRA and AdaCast across all six benchmarks (

T{=}512

H{=}64

r{=}32

\alpha{=}128

N_{\mathrm{pg}}{=}1

). Each cell reports MSE / MAE. Bold indicates the better result.

	Blk	$\mathrm{+frac}$	Med.	Mean	Std.	Max.	Rec.	Adj.
ETTh1	9	0.84	1.02	1.87	2.28	12.0	$-0.34$	1.36
	10	1.00	10.9	10.8	5.76	41.9	1.22	9.69
	11	1.00	25.8	29.5	16.2	98.9	3.82	21.9
ETTh2	9	0.88	1.18	1.51	2.38	18.1	$-0.08$	1.26
	10	1.00	6.87	7.60	3.86	20.8	0.13	6.75
	11	1.00	20.8	41.3	140	1149	0.95	19.9

Appendix

Table 12: Intervention statistics for decoder blocks 9–11. All quantities except

\mathrm{+frac}

are changes in approximate CRPS, in units of

10^{-3}

. “Rec.” is the reconstruction-only control; “Adj.” is the median minus reconstruction control. Mean, standard deviation, and maximum are over the 64 ablated features.

Horizon	Methods	ETTh1	ETTh2	ETTm1	ETTm2	Weather	Exchange
64	Chronos Zeroshot	0.3616	0.2517	0.3109	0.1487	0.1525	0.0673
	AdaCast (In-domain)	0.3431	0.2370	0.2603	0.1385	0.1255	0.0571
	AdaCast (Zero-shot)	0.3593	0.2450	0.3017	0.1485	0.1491	0.0594
96	Chronos Zeroshot	0.3859	0.2899	0.3323	0.1779	0.1777	0.0993
	AdaCast (In-domain)	0.3691	0.2739	0.2891	0.1672	0.1459	0.0870
	AdaCast (Zero-shot)	0.3798	0.2789	0.3259	0.1781	0.1763	0.0918

Appendix

Table 13: Zeroshot forecasting results for extended forecasting horizons (MSE).

Setting	Value
Backbone	Chronos-Bolt Base
Decoder blocks	$0,\ldots,11$
Latent width $d_{\mathrm{SAE}}$	$3072$
TopK sparsity $K$	$64$
Auxiliary TopK width	$96$
Optimizer	Adam, $\beta_{1}=0.9$ , $\beta_{2}=0.999$

Appendix

Table 14: SAE configuration used for every dataset–block pair. The backbone is frozen, and only the SAE parameters are optimized.

Figure 5: Fraction of variance explained ( $\mathrm{FVE}=1-\mathrm{FVU}$ ) by the TopK SAE trained at each Chronos-Bolt decoder block. A separate SAE is trained for every dataset–block pair using activations from the corresponding chronological training split.

Figure 6: Fraction of the Top-64 SAE-feature ablations that increase approximate CRPS ( $\mathrm{+frac}$ , Equation 19 ) at each Chronos-Bolt decoder block. All four datasets reach $\mathrm{+frac}=1.00$ at blocks 10–11.

Panel of Figure 7 — Figure 7: Magnitude of the Top-64 SAE-feature interventions across decoder depth. Points show the mean and median $\Delta\widehat{\mathrm{CRPS}}$ values; error bars show one standard deviation across the 64 individually ablated features. The dashed curve is the reconstruction-only control from Equation 20 .

Figure 8: Reconstruction-adjusted median intervention effect from Equation 21 . Values remain close to zero in early blocks and increase sharply in blocks 9–11 across all four datasets.

Dataset	Chronos-Bolt Zero-shot	Full AdaCast	Best restricted	Blocks 9–11
ETTh1	0.3616/0.3650	0.3431/0.3594	0.3453/0.3584 [0–3]	0.3506/0.3620
ETTh2	0.2517/0.2992	0.2370/0.2919	0.2364/0.2919 [6–9]	0.2394/0.2949
ETTm1	0.3109/0.3185	0.2603/0.3040	0.2621/0.3043 [0–8]	0.2798/0.3084
ETTm2	0.1487/0.2236	0.1385/0.2160	0.1375/0.2156 [0–3]	0.1409/0.2182

Appendix

Table 15: Decoder-region adaptation on the ETT datasets. “Best restricted” denotes the best tested contiguous region, shown in brackets. Blocks 9–11 cover the sensitivity peak identified by the SAE diagnostic. Each entry reports MSE/MAE.

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