Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning
Authors: Yuanzhao Zhang
William Gilpin
Venue: ICLR 2026 Poster (2026)
Keywords: time series
foundation models
dynamical systems
forecasting
chaos
physics
scientific machine learning
Primary area: learning on time series and dynamical systems
TL;DR: Time series foundation models can be beaten by simple parroting strategies in forecasting dynamical systems

Abstract: Recent time-series foundation models exhibit strong abilities to predict physical systems. These abilities include zero-shot forecasting, in which a model forecasts future states of a system given only a short trajectory as context, without knowledge of the underlying physics. Here, we show that foundation models often forecast through a simple parroting strategy, and when they are not parroting they exhibit some shared failure modes such as converging to the mean. As a result, a naive context parroting model that copies directly from the context scores higher than leading time-series foundation models on predicting a diverse range of dynamical systems, including low-dimensional chaos, turbulence, coupled oscillators, and electrocardiograms, at a tiny fraction of the computational cost. We draw a parallel between context parroting and induction heads, which explains recent works showing that large language models can often be repurposed for time series forecasting. Our dynamical systems perspective also ties the scaling between forecast accuracy and context length to the fractal dimension of the underlying chaotic attractor, providing insight into previously observed in-context neural scaling laws. By revealing the performance gaps and failure modes of current time-series foundation models, context parroting can guide the design of future foundation models and help identify in-context learning strategies beyond parroting.

Published as a conference paper at ICLR 2026
CONTEXT PARROTING: A SIMPLE BUT TOUGH-TO-BEAT BASELINE FOR FOUNDATION MODELS IN SCIENTIFIC
MACHINE LEARNING
Yuanzhao Zhang
William Gilpin
Santa Fe Institute Santa Fe, NM, USA
University of Texas at Austin
Austin, TX, USA
yahang@santafe.com eduu
gilpinEchaos utexas edu
ABSTRACT
Recent time-series foundation models exhibit strong abilities to predict physical systems. These abilities include zero-shot forecasting, in which a model forecasts future states of a system given only short trajectory as context, without knowledge of the underlying physics. Here, we show that foundation models often forecast through simple parroting strategy, and when they are not parroting they exhibit some shared failure modes such as converging to the mean. As a result, a naive context parroting model that copies directly from the context scores higher than leading time-series foundation models on predicting a diverse range of dynamical systems, including www-dimeniional chaos, turbulence, coupled oscillators, and electrocardiograms, at tiny fraction of the computational cost. We draw parallel between context parroting and induction heads, which explains recent works show- ing that large language models can often be repurposed for time series forecasting. Our dynamical systems perspective also tics the scaling between forecast accuracy and context length to the fractal dimension of the underlying chaotic attractor, providing insight into previously observed in-context neural scaling laws. By revealing the performance gaps and failure modes of current time-series foundation models, context parroting can guide the design of future foundation models and help identify in-context learning strategies beyond parroting.
INTRODUCTION
key test of generalization in scientific machine learning (SciML) is zero-shot forecasting: the ability to forecast future states of a new physical system based short context trajectory. Prior SciML approaches primarily focus on developing specialized forecasting models trained specifically on system that needs to be predicted (Brunton et al., 2016; Weinan, 2017; Chen et al., 2018; Pathak et al., 2018; Li et al., 2020; Chen & Tao, 2021; Gauthier et al., 2021; Lim & Zohren, 2021; Karniadakis al., 2021; Levine & Stuart, 2022; Mikhaeil et al., 2022; Brunton al., 2022; Das et al., 2023; Krishnapriyan et al., 2023; Yang et al., 2024; Yu & Wang, 2024; Azizzadenesheli et al., 2024; Brenner al., 2024a;b; Ricci al., 2024; He al., 2025; Cheng et al., 2025; Grigoryeva et al., 2025; Berry Das, 2025). However, the generality of these models is limited by the amount of system-specific data available, motivating the recent development of time-series foundation models (Oreshkin et al., 2021; Garza & Mergenthaler- Mergenthaler-Cannsec., 2023; Rasul et al., 2023; Jin et al., 2023; Zhou et al., 2023; Gruver al., 2024; Dooley al., 2024; Liu et al., 2024b; Woo et al., 2024; Ansari et al., 2024 Goswami et al., 2024; Das et al., 2024; Liang et al., 2024; Shi et al., 2025; Zhai et al., 2024; Liu et al., 2025b), which are trained on vast amounts observed and simulated time series from diverse domains, and which can subsequently perform zero-shot forecasts for any time series-ine series-ineluding those generated by previously-unsee historical data is limited, time-series foundation models outperform classical deep learning models in forecasting chaotic dynamical systems (Zhang & Gilpin, 2024).
dynamical systems. Interestingly, it was recently found that, when available
What mechanisms do time-series foundation models to make zero-shot forecasts, and why they effective for dynamical systems not seen during pre-training? It was recently observed that one such foundation model, Chronos (Ansari et al., 2024), often employs an extremely simple strategy when

---

Published as a conference paper at ICLR 2026
forecasting chaotic systems (Zhang & Gilpin, 2024). The strategy. context parnoting, scans the context for nearly repeating motifs and copies the part of the context following the best-matching motif as its prediction (Fig. 1). This can be viewed as kind of "in-context nearest neighbor" algorithm, which is easy to implement during in-context computation (Garg et al., 2022). How good is context parroting zero-shot forecasting strategy? By comparing it with existing foundation models, what learn about current models' strengths and limitations?
Here, we compare context parroting with diverse set of competitive baselines on the challenging task of forecasting chaotic systems. Our baselines include four state-of-the-ar time-series foundation models: Chronos and Chronos Bolt (Ansari et al., 2024), TimesFM (Das et al., 2024), Time-MoE (Shi et al., 2025), and Moirai (Woo et al.. 2024), as well as a recent foundation model specifically designed for dynamical systems: DynaMix (Hemmer & Durstewitz, 2025). In the Appendix, we also include two classical forecasting methods that are particularly effective in the small-data limit: AutoARIMA (Hyndman & Athanasopoulos, 2018) and simplex projection (Sugihara & May, 1990). The latter represents a classical nonlinear forecasting method conceptually resembling context parroting (Appendix F). We find that parroting outperforms all baselines (including the leading foundation models) in both zero-shot forecast accuracy and inference cost, especially for longer context windows. Our results suggest that current time-series foundation models do not fully utilize the information in the context data, and thus still have significant room for improvement when it comes to SciML tasks.
Our main contributions are:
1. Introduce context parroting as a simple but effective baseline for zero-shot forecasting of dynamical systems, which can guide the design of more informative benchmarks that cannot be solved by simple repetitions and help identify forecasting strategies beyond parroting
2. Show that context parroting outperforms leading time-series foundation models in predicting chaotic systems and reveal common failure modes of many existing foundation models, which can guide the design of better models in the future
3. Explain the in- in-context neural scaling law between forecast accuracy and context length, linking the scaling coefficient to the fractal dimension of the underlying chaotic attractor
2 RELATED WORK
Foundation models for science. Foundation models have recently been introduced for many scientific meahinn-learning tasks (Miller et al., 2024), including partial differential equations (Takamoto et al., 2022; Yang et al., 2023; Rahman et al., 2024; Subramanian et al., 2024; Herde et al., 2024; McCabe al., 2024; Totounferoush al., 2025), neuroscience (Cui et al., 2024; Caro et al., 2023; McKeen et al., 2024), and weather forecasting (Nguyen et al., 2023; Bodnar et al., 2024). However, most of these foundation models remain a black box, and they have not yet provided interpretable strategies for forecasting diverse physical and dynamical processes. Here, we analyze context parroting simple mechanism used by time-series foundation models, noting its strengths and weaknesses as a zero-shot forecasting strategy. This strategy, and the insights gained here, can potentially be applied to other scientific tasks.
In-context neural scaling laws. Neural scaling laws describe the relationship between the per- formance of a neural network and certain resources, such as model size, data size, or the amount of compute (Kaplan et al., 2020; Sorscher et al., 2022; Bahri al., 2024; Yao et al., 2024). Such scaling laws allow practitioners to predict the performance of yet-to-be-trained models based on the available resources and allocate them strategically optimize compute-adjuster accuracy (Hoffmann et al., 2022). When applying LLMs to forecast dynamical systems, Liu et al. (2024a) recently observed an in-context neural scaling law, in which the test loss decreases with the context length following a power law. Here, we show that this in-context neural scaling law can be reproduced when using context parroting to predict dynamical systems, and the scaling coefficient can be linked to invariant property of the underlying dynamic process (the fractal dimension of the chaotic attractor). This finding shows that neural scaling laws are intrinsically linked to invariant properties of the process generating the data, and the theory can potentially be generalized to other models and tasks. For example, can we estimate the "fractal dimension" " of a language from the neural scaling laws of L.LMs (Du & Banaka-Ishin 2025)?
2

---

Published as a conference paper at ICLR 2026
In-context learning and induction heads. Induction heads computational circuits that naturally emerge in simple transformers through training, and they have been hypothesized to underlie much of the in-context learning ability of foundation models (Elhage et al., 2021; Olsson et al., 2022; Von Oswald et al., 2023; Reddy, 2023). In its simplest form, an induction head copies repeating tokens in the context to make predictions. For example, when presented with token stream [A][ ... (A), an induction head will output [ as the next token. Prior works train transformers on minimal Markov chain grammars, and find that, during pretraining, models learn to identify increasingly higher-order k-grams, with different attention heads specializing in copying, lookup, and aggregation (Edelman et al., 2024; Chen al., 2024a). These works imply that pretraining enables models to learn conditional distributions, allowing them to represent sequence distributions seen in the context (Lv et al., 2024; Chen al., 2024b; Keskar et al., 2019; Zekri et al., 2024).
There is a clear parallel between context parroting and induction heads: both are essentially copy-and- paste operations, with context parroting involving the matching of not just one but multiple contiguous tokens. In fact, it is easy to imagine context parroting emerging naturally from combining multiple induction heads. This parallel can potentially explain the unreasonable effectiveness of applying language models trained text time-series tasks without fine-tuning or prompt engineering (Garza & Mergenthaler-Cann Canseeo,,, 2023; Jin et al., 2023; Zhou et al., 2023; Gruver et al., 2024; Liu et al., 2024a). The induction heads formed from training on natural language happen be also effective for predicting time series and can be easily repurposed to implement strategies such as context parroting.
3 CONTEXT PARROTING AS A ZERO-SHOT FORECASTING STRATEGY
Overview of context parroting. In this section motivate and introduce our baseline: context parroting. It was inspired by recent observations that Chronos often predicts chaotic systems by copying directly from the context (Zhang & Gilpin, 2024). An example of Chronos using parroting to forecast a partially- obberred Lorenz system is shown in Fig. 1.
On high level, context parroting uses the last D tokens of the context to query the remaining context. For whatever context sequence that most closely matches the query, the subsequent tokens in the context are copied and used the forecast. Because the length of the motif D can be seen as the number of delayed states in a delay embedding from the lens Takens' embedding theorem (Takens, 2006), also refer to D as the embedding dimension and will use the terms embedding dimension and query length interchangeably. Interpreting D as the embedding dimension is convenient because context parroting can be seen as nearest neighbor algorithm in the D-dimensional delay-embedded space. During the matching process, we exclude the last D motifs to avoid parroting too close to where the prediction starts. Framed in terms of induction heads, the query lookup acts as a copy head, the nearest-neighhor match is a selector, and the exact repetition is the aggregation operation (Chen et al., 2024a). We provide pseudocode for context parroting Algorithm 1.
Algorithm 1 Context Parroting
Input: Context trajectory I1.1. {x1, ......... Fr.), embedding dimension D (i.e., the length of the motif to match), and forecast length H.
Output: Forecast trajectory #1 (I1+1,-..,
for all length- D motif s: Fz-D+1:: the context TT:L-D do
2: compute the Euclidean distance d, between motif and the last motif d1-D+1:E
3: Find the best-matching motif, Sept. with the smallest Euclidean distance
4: Set the first L - Sopt predicted points to be 21+1:21-8aw = Iee and repeat until the forecast length Hl reached
Relationship to classical nonlinear forecasting methods. We show in Appendix F.3 that, in various limits, context parroting is equivalent to two classical algorithms from nonlinear dynamics: the simplex projection technique and the S-map algorithm (Sugihara & May, 1990; Sugihara, 1994). Both approaches have their foundations in Takens' embedding theorem, which states that time-delayed low-dimensional observables derived from nonlinear dynamical system can recover key geometric properties of the underlying high- high-dimensional attractor (Takens, 2006). However, unlike context parroting, which looks for the best matching motif, simplex projection tries to identify multiple
3

---

Published as a conference paper at ICLR 2026
context
forecast
n Aunk
M 1 m/
mmmd
mM my
M 1
MAN mn
MA whhn
MA
by
time
Figure I: Example of a foundation model forecasting chaotic dynamics with context parroting. Here, the foundation model (Chronos) was asked to predict the variable of the Lorenz system based on a short context trajectory with 512 data points. Blue is the prediction and gray is the ground truth. Chronos produced an accurate prediction by simply looking for a motif in the context similar to the motif immediately preceding the prediction (highlighted in yellow) and copying the evolution following the matching motif (highlighted by pink boxes). We distill this context parroting strategy into Algorithm 1 and compare it against time-series foundation models (including Chronos itself).
matching motifs in the context and computes a weighted average as its forecast. This can potentially make simplex projection more sensitive the choice of the embedding dimension D, limiting the method to small embedding dimensions in practice (Chang et al., 2017). Other than simplex projection and S-map, there also exists other zero-shot forecasting strategies from nonlinear dynamics. For example, the Humeer-iddrrowchh method (Farmer & Sidorowich, 1987) looks at multiple nearest neighbors the context and builds a local linear model to make forecasts. An interesting future direction is to compare these methods from nonlinear dynamics with context parroting and time-series foundation models, which might inspire new zero-shot forecasting strategies.
4 METHODS
Datasets. The dysts dataset provides a standardized benchmark of 135 low-dimensional chaotic systems, each defined by set of ordinary differential equations between dimensionality three and six (Gilpin, 2021). The chaotic systems are drawn from different published papers and span fields such as neuroscience, climate science, fluid dynamics, and astrophysics. Every system is annotated with its largest Lyapunov exponent X, an invariant characteristic of the underlying dynamics that quantifies the rate at which small perturbations grow over time. In chaotic systems, even minor errors rapidly compound over a characteristic timescale known as the Lyapunov time, defined as X-1 To normalize the difficulty of predicting different chaotic systems (so results from the 135 systems can be meaningfully compared and combined), we generate trajectory data with a fixed sampling rate of 30 points per Lyapunov time, and also measure the forecast performance in terms of Lyapunov times. To show the relevance of our findings to a broad class of SciML tasks, later we also go beyond low-dimensional chaotic systems and simulated data by benchmarking on real-world datasets from ECG measurements and electronic circuits.
Models. For time-series foundation models, select Chronostase (200M parameters), its variant Chronos-Boltase (205M parameters), Time-MoEhage (200M parameters), TimesFM-220 (500M pa- rameters) and Moirai-2.0umm.. (11M parameters) (Das al., 2024; Ansari al., 2024; 2025; Shi et al., 2025; Liu et al., 2025a). All of these models are pretrained on massive amounts of real-world time series data (hundreds of billions of data points), which are often complemented by synthetic data to improve generalization. We also consider DynaMix. a foundation model pretrained on chaotic dynamical systems (Hemmer & Durstewitz, 2025). These models encompass a wide array of design choices: Time-MoE, TimesFM-2.0, and Moirai-2.0 are decoder-only architectures, Chronos is an encoder-decoder architecture, and DynaMix is an almost-linear RNN trained via teacher forcing (Brenner et al., 2024a). Chronos and Time-MoE use pointwise tokenization, DynaMix implicitly tokenizes pointwise, while TimesFM-22 2.0 and Moirai-2.0 use patching. Time-MoE, DynaMix, and TimesFM-2.00 by default give point forecasts, whereas Chronos, Chronos-Boo and Moirai-2.0 pro- vide probabilistic forecasts with uncertainty quantification. For these models, we use the median prediction when evaluating forecast errors. An important parameter for all foundation models is the
4

---

Published as a conference paper at ICLR 2026
maximum context length Lmax. which varies from 512 data points (Chronos), 1680 (Moirai-2.0), 2048 (TimesFM-2.0), 4096 (Time-MoE), to arbitrary for DynaMix due to its recurrent formulation.
Pipelines. To evaluate different models' ability to zero-shot forecast dynamical systems, generate a chaotic trajectory of length 10 for each of the 135 chaotic systems in dyst s, with a granularity of 30 data points per Lyapunov time. Each trajectory is normalized to have zero mean and unit standard deviation. For a given context length L, we randomly pick a length-Z segment from the chaotic trajectory and provide it to the model as the context. The model's task is to predict the next 300 data points (equivalent to 10 Lyapunov times) solely based on the context. We ask the model to make a univariate forecast on each dimension independently, which then evaluated separately for each dimension. To obtain reliable statistics, we aggregate the results over all 135 chaotic systems, all dimensions, and 20 random initial conditions for each system.
Metrics. In line with previous research (Hyndman & Koehler, 2006; Makridakis et al., 2022; Gilpin, 2021; 2023), we assess forecasting performance using diverse set of complementary metrics.
Symmetric Mean Absolute Percentage Error (sMAPE).
100 T
X
Xe|
sMAPE(X, x) =
X1
X
where the sequence XI, X2,.... XT denotes the ground truth, and &1, .2....; Xy the correspond- ing predictions made by the model. To provide some context to help interpret the sMAPE value, we note that predicting the mean of white noise would give you an sMAPE around 200.
Other than sMAPE, we also show benchmark results using Mean Square Error (MSE) and Mean Absolute Error (MAE), two other metries commonly used in the time series literature.
For chaotic dynamical systems, point forecasts will inevitably fail due to the exponential rate of error accumulation. It is thus equally important for forecasting model to preserve the long-term invariant properties of the chaotic dynamics, such as Lyapunov exponents and the attractor dimension. Here, we compare the structure of true and predicted attractors by calculating the KL Divergence between their distributions.
Kullback-Leible Divergence between Attractors (Dstsp).
P(x)
Datsp DKL(P)))) = Σ P(x) log Q(x)*
xEN
where P and Q represent the true and the predicted attractor, respectively. When estimating Dstap, we follow the methodology Hess et al. (2023): Göring al. (2024). Specifically, we place Gaussian kernels at each point in the true and predicted trajectories and estimate the KI. divergence between these Gaussian mixtures using a sampling- based approximation (Hershey & Olsen, 2007).
In addition, we analyze the frequency content of the predicted trajectories by computing the Power Spectrum. This is estimated using Welch's method. We quantify the accuracy of the spectral reconstruction by calculating the Hellinger distance between the true and predicted power spectra.
In the appendix, we also measure attractor reconstruction accuracy by comparing Correlation Dimension and the rate of divergence using Lyapunov Exponents. The correlation dimension estimates the fractal attractor dimension from a time series by calculating the scaling of the number of attractor points that fall within given radius of each point (Grassberger & Procaccia, 1983).
RESULTS
5.1 CONTEXT PARROTING OUTPERFORMS FOUNDATION MODELS IN FORECASTING CHAOS
Here, we compare context parroting and foundation models in their ability to predict chaotic dynamics. Figure shows each model's forecasting error (measured by sMAPE) as well as their accuracy in attractor reconstruction (measured by KL Divergence). It is clear that context parroting is better than all foundation models tested here in both metrics. In Appendix Fig. 7, we show that this remains true when benchmarked against MSE and MAE. The results for fractal dimension accuracy are shown in
5

---

Published as a conference paper at ICLR 2026
150
1.0
OhronosBot
TimesFM
Attractor KL Divergence
TimeMcE
0.8
Moirai
Error (sMAPE)
DynaMix
Chronos
Parrot
0.4
50
Ansptuile sesor lovg
...
0.0
Parrot ChronosBolt
TimesFM
TimeMoE
Moirai
DynaMix
Chronos
10
10
10'
Forecast Horizon (Lyapunov time)
Figure 2: Context parroting outperforms foundation models in zero-shot forecasting for both short-term point-wise accuracy and long-term attractor reconstruction. Left: Forecast error of each model as a function of the forecast horizon. The context length set 512 for all models. Right: KL Divergence between the predicted attractors and the true attractors (smaller is better). Solid lines represent mean and dotted lines represent median. All results are obtained from 135 chaotic systems in the dysts database, with 20 trajectories from random initial conditions for each system.
Appendix Fig. 8, where parroting, DynaMix, and Chronos significantly outperform other foundation models.
Consistent with Hemmer & Durstewitz (2025), observe that DynaMix preserves long-term geometry-terne termed the "climate" in classical forecasting (Lu et al., 2018). We attribute this capability its recurrent architecture, which often better sustains oscillations over long horizons (Elman, 1990; Durstewitz, 2017). We also note that the efficient recurrent mixture-of-expen allows it achieve competitive performance with small fraction of the active parameters of other models.
design of DynaMix
Among transformer- models, Chronos is the best performer in predicting chaotic systems, which is not surprising given that it often utilizes parroting as key forecasting strategy on this dataset (Zhang & Gilpin, 2024). Chronos's tendency to context parrot arises from its distinet architecture as language model operating on quantized time series. As result, Chronos is trained using cross-entropy loss, which incentivizes preservation of k-gram frequencies and encourages the generation of diverse forecast samples consistent with the dynamical system's 's underlying measure (Yu et al., 2025). In contrast, TimeMoE and TimesFM are trained using mean squared error loss. These models lose diversity and regress to the mean long forecast horizons, thus suppressing oscillations. Representative forecasts from the foundation models are shown in Appendix Fig. 6, which demonstrate that regressing the mean common failure mode for many foundation models when forecasting chaotic systems.
Moreover, the inference cost of context parroting is negligible compared to transformer-basee foundation models, not to mention the substantial GPU time needed to pretrain them. For example, a six orders of magnitude computational gap separates Chronos and context parroting for all context lengths. Combined with the fact that the performance of parroting is not sensitive to the choice of the embedding dimension D (Appendix Fig. 9), these results establish context parroting simple but effective baseline for zero-shot forecasting of dynamical systems.
Given that context parroting by definition outputs periodic prediction, one might suspect that it could fail to truly capture key invariant properties crucial to chaos. For example, the cyclic patterns produced by parroting should have its largest Lyapunov exponent equal to zero. However, parroted trajectories can have positive finite-time Lyapunov exponents, which is the only thing one can practically estimate from finite-lenghh time series. Since parroting can in principle copy an arbitrarily long trajectory, the estimated Lyapunov exponents will approach the ground truth for long enough context. In this sense, parroting is able to capture invariant dynamical properties of chaos such as Lyapunov spectra and power spectra, despite only producing periodic trajectories by definition.
vositive.fimite-time

---

Published as a conference paper at ICLR 2026
Lorenz
Rossler
Prediction
Power Spectrum
Prediction
Power Specirum
DyneMir
Parol
Chrongs
Forecast Hortzon
Frequency
Forecast Horizon
Frequency
Double Pendulum
Chua
Prediction
Power Spactnum
Prediction
Power Spactrum
Demattic
Foreczal Horizon
Frequency
Forecaal Horizon
Frequency
Context parroting best reconstructs the power spectra of chaotic systems despite its predictions being periodic. Predictions of four distinct chaotic systems using the two best- performing models DynaMix and Chronos, relative Parroting. We the context length to L - 2000. Forecasts are generated for 10, 000 points past the end of the context, and the last 2000 timepoints are shown. The power spectrum is estimated using Welch's method on the last 5000 timepoints.
Figure 3:
In Fig. 3, we show that parroting can better capture the power spectrum than Chronos and DynaMix, two foundation models that achieved the lowest attractor KI divergence according to Fig. We demonstrate the same for other invariant properties in Appendix Table 4 and Fig. 11. Moreover, note that as the context length becomes longer, context parroting will be able to parrot increasingly complex patterns with longer periods. This is shown explicitly in Appendix Fig. 12, where parroting captures the power spectrum increasingly better as context length is increased.
Figure 4 further explores the effect of context length on forecast accuracy. We find that longer context windows produce better performance for context parroting, DynaMix, and Chronos. However, Chronos effectively utilize a context length of at most L 512, limitation addressed in later generations models (Ansari et al., 2025). The need to set maximum context length before pretraining a limitation of transformer-based architectures. In contrast, recurrent models like DynaMix, state- space models, and context parroting (Gu et al., 2021), do not share this limitation, allowing them to scale to contexts of arbitrary length during inference.
Interestingly, Chronos outperforms context parroting short contexts, indicating that it employs additional zero-shot learning strategies beyond parroting. We expect that, at short context length, the time series becomes effectively nonstationary, which is the strength of time-series foundation models. For example, Chronos is great at continuing the local trend in the context, which can more effeective strategy than parroting when the length of the context is limited.
Moreover, even when restricted to parroting, the ~ O(L)) operations performed by attention heads in transformers like Chronos have, in principle, sufficient computational complexity dynamically choose the optimal embedding dimension D for each individual time series, giving attention an advantage over parroting algorithms with fixed D. which have the O(D complexity of nearest-neight neighst search. It would be interesting to explicitly identify the mechanisms that enable Chronos outperform parroting in the short-context regime.
7

---

Published as a conference paper at ICLR 2026
Parrot
Chronos
10P
10
Error (sMAPE)
Error (sMAPE)
10
84
4096
128
8182
32768
256
10"
1024
86636
10P
512
2048
1024
10
10a
10 10
10
10
Time (Lyapunov times)
Time (Lyapunov times)
Figure 4: Parroting can better utilize longer context data while Chronos does better for shorter contexts. Each line represents the forecast error for a different context length. The performance of Chronos saturates once the context length exceeds its designed upper limit of 512 data points, whereas the accuracy of context parroting keeps improving for longer context windows. Here we set the embedding dimension D for the parroting algorithm.
5.2 THFORETICAL EXPLANATION OF IN-CONTEXT NEURAL SCALING LAWS
Due to its simplicity and intimate connections to foundation models, context parroting can serve as analytically-tracable model explain some intriguing empirical findings from the literature. Recently, Liu et al. (2024a) reported an in-context neural scaling law for LLMs applied to dynamical systems, which the one-step forecast error decreases algebraically with context length. However, it is unclear where this scaling law came from or why LLMs trained on text can be effective for time series without fine tuning. Here, we show that context parroting naturally gives rise to same in-context scaling law and provides geometric insights into its origin. Given the similarity between parroting and the induction heads implemented by LLMs (Olsson et al., 2022). the geometric explanation we develop next for parroting only applies to time- seresscries foundation models, but can also conceivably be adapted to LLMs and partially explain the observations Liu et al. (2024a).
Brnr Conteet beghhe
Scalling exponent
by dimension
One-step enrr (sMAPE)
Matching mott distance
0.6
Scaling exporant.
10-
100
10-
0.4
10-1
Slope
0.3
10
10
Context length
Context length
correlation dimension, 1/d
Figure 5: Context parroting explains in-context neural scaling laws and links scaling exponents to attractor dimensions. Left: One-step forecast error versus context length. Fach line represents distinct chaotic system and the scaling follows power law. In principle, infinite context length should give parroting infinite accuracy for any deterministic system with a well-defined attractor. Middle: Euclidean distance between the last context point and its nearest neighbor in the delay-embeddingg space, as function of context length. Again, the scaling follows a power law with the same scaling exponent The scaling exponent can be different for each system and is linked to the correlation dimension deor the chaotic attractor through the relation a = 1/dcor- Right: Estimated scaling exponent versus the inverse correlation dimension 1/d where each dot represents chaotic system. For all panels we set the embedding dimension D = 10 for the parroting algorithm.
The left panel in Fig. 5 shows the power law relation between one-step forecast error (measured by sMAPE) and context length for parroting. Longer context lengths improve predictions by allowing the algorithm to find better matching motifs, and thus shadow the ground truth for longer. The middle panel in Fig. 5 shows improving overlap, with the distance between the matching motifs
8

---

Published as a conference paper at ICLR 2026
decreasing algebraically with context length. The matching motif distance E maps linearly to the one-step forecast error e on average: (e) = c()). where c is a system- constant that depends on the largest Lyapunov exponent of the chaotic dynamics. As a result, the power law for the matching motif distance implies the power law for one-step forecast error. Moreover, the two power laws share the same scaling exponent: e xx I_ and f x I. as confirmed by Fig. 5.
Can we predict the scaling coefficient a (how fast the forecast improves with more context data) for any given chaotic system? We link to the geometric invariants of the underlying dynamics, specifically the fractal dimension of the chaotic attractor, as estimated by the correlation dimension:
C(e) C(e
In
deor
lim c,c'
In (5)
where Cee) is the number of point pairs in the attractor that are within given radius from each other. In other words, if plot C(e) against on a log-log plot, deor would be the slope of the plotted line. We assume the chaotic systems are ergodic, so the a sufficiently-long context trajectory represents a random sample of the attractor. Longer context trajectories contain more samples and, for large enough sample sizes, we can show from the definition of the correlation dimension that the expected distance between sample point and its nearest neighbor decreases with context length (i.e., the sample size) -11/drrr For example, for two-dimensional attractor, the distance between random point and its nearest neighbor will decrease as 1/VL. Fractal dimension thus measures the speed at which the distance between neighboring points on an attractor can be reduced by including more samples, and higher dimensionality requires more points to reduce the distance the same extent. Mathematically, we thus expect the Harmer-Sidorowin forecasting method from the nonlinear dynamics community (Farmer Sidorowich, 1987). Indeed, in the right panel of Fig. 5, we observe strong correlation between door and 1/a (Spearman correlation around 0.85), supporting our theoretical argument above.
1/dcor- A similar scaling law has been derived for
We show in Appendix Fig. 10 that the power law scaling persists when aggregated over chaotic systems, across a range of embedding dimension D. Although we focus on deterministic ODEs in Fig. 5, we note that the same power law scaling is expected to hold for discrete maps and weakly- stochastic systems. Explaining the power law for strongly-stoee stochastii systems, such as random Markov chains (Liu et al., 2024a), is a promising direction for future research.
5.3 SCIML TASKS BEYOND LOW- WWWDDIMENSOONAL CHAOTIC SYSTEMS
So far we focused on low-dimensional chaotic systems from the dysts dataset, which enabled systematic comparison between different forecasting models with standardized benchmarks. Here, we show that parroting also outperforms foundation models on a broader class of SciML tasks, including real-world datasets of current scientific interest. Our datasets are: (I) the von Karman vortex street at Reynolds number Re 900, a standard problem in fluid dynamics representing a flow exhibiting intermittency. We generated time series corresponding to the top PCA modes, in order to capture global structure; (2) electrocardiogram recordings (via the QT Database in PhysioNet); (3) 28 coupled electronic circuits measured experimentally from Vera-Ávila et al. (2020)); and (4) 23 Kuramoto oscillatoos coupled through frustrated and nonreciprocal interactions, recently studied in León & Pazó (2025). These are all high-dimensional systems, two generated from simulations and two measured in the real world. For the metrics, we use MAE and MSE to measure pointwise forecast accuracy, and KL Divergence to measure the accuracy in attractor reconstruction. The results are summarized below. Parroting is the only model that ranks in the top three for all tasks and all metrics. Other metrics, such valid prediction time and fractal dimension accuracy, give similar rankings.
Table 1: Performance comparison (MAE @ 50 steps, mean + standard deviation) of forecasting models across SciML tasks. Bold best, italic second and third best.
Task
Parrot
DynaMix
Chronos
Chronos Bolt
TimesFM
TimeMoE
Moirai
Turbulence
0.403=0.210
0.505+0.247
0.431+0.237
0.510=2.114 0.567+0.247
0.394+0.172
0.382+0.189
BCG
0.324
0.77710.241
0.87310:422
0.799 0.72310.259 0.75240.279
0.68410.237
Circuit
0.053=10.00
0,42510.172
0.11110.065
0.34940.122 120
0.19610.090
0.206-10.100 102
0.213-10.093
Kuramoto
0.004=00001
0.07610.002
0.07210.029
0.96140.084
0.624110061
0.070:10011
0.004

---

Published as a conference paper at ICLR 2026
Table 2:
Performance comparison (MSE @ 50 steps) of forecasting models across SciML tasks. Bold- = best, italic = second and third best.
Task
Parrot
DynaMix
Chronos
Chronos Bolt
TimesFM
TimeMoE
Moirai
Turbulence
0.32210.333
0,49010:4530
0.380.10.408
0.044100447
0,403
0.278
0.2781 0.2667
ECG
0.916=0.630
1.06++04488
1.461=10097
0.950+0.581
0.940=0.530
0.893=0.287
0.851=0.4888
Circuit
0.012=0.016 0.297+0.224
0.024=0.030
0.181 122 0.065+0.056
0.076=000080
0.075=00000
Kuramoto
0.001=00.02
0.006=000011
0.009=000077
1.296++0.
0.512+0.096
0.008=00.002
0.001=0.001
Table 3: Performance comparison (KL Divergence between predicted and true attractors) of
forecasting models across SciML tasks, Bold = best, italic = second and third best.
Task
Parrot
DynaMix
Chronos
Chronos Bolt
TimesFM
TimeMoE
Moirai
Turbulence
0.04
0.005
0.04110.046
0.048+00058
0.111:0.072
0.070=00008
0.03010.041
ECG
0.099+0.100 0.065
104
0,253+0.188 0,403=0.367
0.220=0.153
0.944
0.276=#0311
Circuit
0.572=00002
2.940+0.528
0.630=0.118
1.710:#.255
0.383+0.087
0.816:0.200
0.848=0.115
Kuramoto
0.001=000011
1.010+0.150
0.537=0.087
3.116::0.22
4.489=0.363
0.076=00040
0.010=0.011
6 CONCLUSION AND FUTURE DIRECTIONS
We find that simple forecast strategy- context purroting-outperrien on dynamical systems forecasting, a critical task in scientific machine learning. a foundation model cannot beat context parroting, it arguably has failed to learn the underlying physics of the system. This surprssin finding exposes a limitation of current foundation models as general-purposs time-series forecasters and highlights the need to further scale them or fine-tune them for specific domains. also suggests that accurately measuring the performance of foundation models can be difficult for scientific machine learning tasks, because strategies like parroting can effectively game both short- and long-term accuracy metrics. Future work in SciML should measure capabilities that are orthogonal to parroting -uch as inferring unobserved parameters or generalizing to unseen bifurcation regimes (Norton et al., 2025) rather than just competing on reconstruction error.
leading foundation models
Finding a simple but effective baseline for a challenging task can encourage rethinking of the status quo, motivating the development of better model architectures (Arora et al., 2017). For example, context parroting formalizes an explicit baseline to compare against in the time-series domain and can help discover weyond-parroting strategies. Identifying in-context learning strategies beyond parroting can spur the development of next- next-generation foundation models and contribute to the debate on whether (or to what extent) large language models are stochastic parrots (Bender et al., 2021; Mitchell & Krakauer, 2023; Arora & Goyal, 2023; McCoy et al., 2024).
An interesting future direction is to generalize context parroting to deal with non-stationary time series while keeping the simplicity and efficiency of the method. Context parroting assumes the existence of stationary underlying measure; for ergodic deterministic system this implies that conditional probabilities of timepoints are stationary up to any order (Appendix F). However, newer foundation models readily handle simple nonstationarity like baseline drift, implying that modified parroting strategy may be possible in-context (Das et al., 2024). Once generalized, the non-stationary parroting method can replace Naive and Seasonal Naive to serve as more informative baseline for the shot forecasting of general time series (weather, traffic, finance, etc.).
Finally, we want to emphasize that we are not proposing to replace time-series foundation models with context parroting. Instead, the value of parroting is as a simple bascline that can reveal the gaps in current foundation models and guide the design of new ones. When foundation models under perform relative to context parroting, it reveals that they haven't learned to fully utilize the context data. For example, a common failure mode we observed across a range of leading foundation models (TimesFM, TimeMoE, Chronos Bolt) is that they tend to underestimate oscillations in the dynamics and the predictions often quickly converge to the mean (Appendix Fig. 6). It is also interesting to design new interpretable zero-shot forecasting strategies. For example, by combining context parroting with classical forecasting methods from the nonlinear dynamics literature (Farmer & Sidorowich, 1987; Sugihara & May, 1990).
10

---

Published as a conference paper at ICLR 2026
7 ACKNOWLEDGMENTS
YZ acknowledges support from the Omidyar Fellowship and NSF DMS 2436231. WG was supported by NSF DMS 2436233 and NSF CMMI 2440490. This project has been made possible in part by Grant No. DAF2023-3295% from the Chan Zuckerberg Initiative DAF, an advised fund of Silicon Valley Community Foundation. Financial support for this publication results from grant CS-CC DS-CSA-2026-075 from Research Corporation for Science Advancement.
8 REPRODUCIBILITY STATEMENT
A Python implementation of the context parroting algorithm and the benchmarks are available at https: //gi www..ttooy.oo.........o. 2- wwwzzzzzzg///// httpy//-aaaan///rrriiing http//parootnggg
REFERENCES
Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, et al. Chronos: Learning the language time series. arXiv:2403.07815 2024.
Abdul Fatir Ansari, Oleksandr Shchur, Jaris Küken, Andreas Auer, Boran Han, Pedro Mercado, Syama Sundar Rangapuram, Huibin Shen, Lorenzo Stella, Xiyuan Zhang, et Chronos-2: From univariate to universal forecasting. arXiv preprint (5..:22100/882/ 2025.
Sanjeev Arora and Anirudh Goyal. A theory for emergence of complex skills in language models. arXiv:2307. 15936, 2023.
Sanjeev Arora, Yingyu Liang, and Tengyu Ma. A simple but tough- tough-to-beat -o-t baseline for sentence embeddings. International conference on learning representations, 2017.
Kamyar Azizzadenesheli, Nikola Kovachki, Zongyi Li, Miguel Liu-Schiaffini, Jean Kossaifi, and Anima Anandkumar. Neural operators for accelerating scientific simulations and design. Nat. Rev. Phys., pp. 1-9, 2024.
Yasaman Bahri, Ethan Dyer, Jared Kaplan, Jaehoon Lee, and Utkarsh Sharma. Explaining neural scaling laws. Proc. Natl. Acad. Sci. U.S.A., 121(27):e231187812 2024.
Emily M Bender, Timnit Gebru, Angelina McMillan-Maijl Major, and Shmargaret Shmitchell. On the dangers of stochastic parrots: Can language models be too big? In Proceedings of the 2021 ACM conference on fairness, accountability, and transparency, pp. 5100623, 2021.
Tyrus Berry and Suddhasattwa Das. Limits of learning dynamical systems. SIAM Review, 67(1): 107-137, 2025.
Cristian Bodnar, Wessel Bruinsma, Ana Lucic, Megan Stanley, Johannes Brandstetter, Patrick Garvan, Maik Riechert, Jonathan Weyn, Haiyu Dong, Anna Vaughan, al. Aurora: A foundation model of the atmosphere. arXiv:2405. /3063, 2024.
Richard C Bradley. Basic properties of strong mixing conditions. survey and some open questions. Probability Surveys, 2:107-144, 2005.
Manuel Brenner, Florian Hess, Jonas M Mikhaeil, Leonard F Bereska, Zahra Monfared, Po-Chen Kuo, and Daniel Durstewitz. Tractable dendritic mns for reconstructing nonlinear dynamical systems. In International conference on machine learning, pp. 2292-2320. Pmlr, 2022.
Manuel Brenner, Christoph Jürgen Hemmer, Zahra Monfared, and Daniel Durstewitz. Almost-linear mns yield highly interpretable symbolic codes in dynamical systems reconstruction. Advances in Neural Information Processing Systems, 37:36829-3660
2024a.
Manuel Brenner, Elias Weber. Georgia Koppe, and Daniel Durstewitz. Learning interpretable
hierarchical dynamical systems models from time series data. arXiv preprint arXiv:2410.048/1 2024b.
11

---

Published as a conference paper at ICLR 2026
Steven L Brunton, Joshua L Proctor, and J Nathan Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc. Natl. Acad. Sci. U.S.A., 113(15): 3932-3937, 2016.
Steven L Brunton, Marko Budisić, Eurika Kaiser, and J Nathan Kutz. Modern Koopman theory for dynamical systems. SIAM Rev., 64(2):229-33) 2022.
Josue Ortega Caro, Antonio H de O Fonseca, Christopher Averill, Syed A Rizvi, Mattco Rosati, James L Cross, Prateek Mittal, Emanuele Zappala, Daniel Levine, Rahul M Dhodapkar, al. Brainlm: A foundation model for brain activity recordings. bioRxiv, pp. 2023-09, 2023.
Chun- Wei Chang, Masayuki Ushio, and Chih-hao Hsich. Empirical dynamic modeling for beginners. Ecological research, 32:785-796, 2017.
Renyi Chen and Molei Tao. Data-driven prediction of general hamiltonian dynamics via learning maps. In International Conference on Machine Learning, pp. 1717-1727.
PMLR, 2021.
Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud. Neural ordinary differential equations. NeurIPS, 31, 2018.
Siyu Chen, Heejune Sheen, Tianhao Wang, and Zhuoran Yang. Unveiling induction heads: Provable training dynamics and feature learning in transformers. In The Thirtty-ighth Annual Conference on Neural Information Processing Systems, 2024a.
Yanda Chen, Chen Zhao, Zhou Yu, Kathleen McKeown, and He He. Parallel structures in pre-training data yield in-context learning. In 62nd Annual Meeting of the Association for Computational Linguistics, ACI. 2024, pp. 8582-8592. Association for Computational Linguistics (ACL),, 2024b.
Xiaoyuan Cheng, Yi He, Yiming Yang, Xiao Xue, Sibo Chen, Daniel Giles, Xiaohang Tang, and Yukun Hu. Learning chaos in linear way. arXiv preprini arXiv:2503. 14702, 2025.
Wenhui Cui, Woojae Jeong, Philipp Thölke, Takfarinas Medani, Karim Jerbi, Anand A Joshi, and Richard M Leahy. Neuro-gpt: Towards a foundation model for eeg. In 2024 IEEE International Symposium Biomedical Imaging (ISBI), pp. 1-5. IEEE, 2024.
Abhimanyu Das, Weihao Kong, Andrew Leach, Shaan Mathur, Rajat Sen, and Rose Yu, Long-term forecasting with tide: Time-series dense encoder. arXiv:2304.88424 2023.
Abhimanyu Das, Weihao Kong, Rajat Sen, and Yichen Zhou. decoder-only foundation model for time-series forecasting. In Forty-furst International Conference on Machine Learning, 2024.
Samuel Dooley, Gurnoor Singh Khurana, Chirag Mohapatra, Siddartha V Naidu, and Colin White. Forecastpfn: Symthetically-traine zero-shot forecasting. Advances Neural Information Process- ing Systems, 36, 2024.
Xin Du and Kumiko Tanaka-Ishii. Correlation dimension of autoregressive large language models. In The Thirty-ninth Annual Conference on Neural Information Processing Systems, 2025.
Daniel Durstewitz. state space approach for piecewise- linear recurrent neural networks for identifying computational dynamics from neural measurements. PLoS computational biology, 13 (6):1105544) 2017.
Ezra Edelman, Nikolaos Tsilivis, Benjamin Edelman, Eran Malach, and Surbhi Goel. The evolution of statistical induction heads: In-context learning markov chains. Advances in Neural Information Processing Systems, 37:64273-64311 2024.
Nelson Elhage, Neel Nanda, Catherine Olsson, Tom Henighan, Nicholas Joseph, Ben Mann, Amanda Askell, Yuntao Bai, Anna Chen, Tom Conerly, et al. A mathematical framework for transformer circuits. Transformer Circuits Thread, 1(1):12, 2021.
Jeffrey L Elman. Finding structure in time. Cognitive science, 14(2):179 171-211, 1990.
Jianqing Fan and Qiwei Yao. Nonlinear time series: nonparametric and parametric methods. Springer Science & Business Media, 2008
12

---

Published as a conference paper at ICLR 2026
J Doyne Farmer and John J Sidorowich. Predicting chaotic time series. Physical review letters, 59(8): 845, 1987.
Shivam Garg, Dimitris Tsipras, Percy Liang, and Gregory Valiant. What can transformers learn in-context? a case study simple function classes. Advunces neural information processing systems, 35:30583-30553 2022.
Azul Garza and Max Mergenthaler-Cansee.. Timegpt-l, arXiv:2310.03588 2023.
Daniel Gauthier, Erik Bollt, Aaron Griffith, and Wendson AS Barbosa. Next generation reservoir computing. Nat. Commun., 12:5564, 2021.
William Gilpin. Chaos as an interpretable benchmark for forecasting and data-driven modelling. NeurIPS, 34, 2021.
William Gilpin. Model scale versus domain knowledge in statistical forecasting of chaotic systems. Phys. Rev. Research, 5(4):043252, 2023.
Niclas Göring, Florian Hess, Manuel Brenner, Zahra Monfared, and Daniel Durstewitz. Out-of- domain generalization in dynamical systems reconstruction. arXiv:2402.1837) 2024.
Mononito Goswami, Konrad Szafer, Arjun Choudhry, Yifu Cai, Shuo Li, and Artur Dubrawski. Moment: A family of open time-series foundation models. arXiv:2402.03885, 2024.
Peter Grassberger and Itamar Procaccia. Measuring the strangeness of strange attractors. Physica D: nonlinear phenomena, 91-2), 18:18892208 1983.
Lyudmila Grigoryeva, Hannah Lim Jing Ting, and Juan-Pablo Ortega. Infinite-dimensione next- generation reservoir computing. Physical Review E, 11 111(3):03530, 2025.
Nate Gruver, Marc Finzi, Shikai Qiu, and Andrew G Wilson. Large language models zero-shot time series forecasters. Advances in Neural Information Processing Systems, 36, 2024.
Albert Gu, Karan Goel, and Christopher Ré. Efficiently modeling long sequences with structured state spaces. arXiv preprint 1rXiv:2111.00 1.00396, 2021.
Yi He, Yiming Yang, Xiaoyuan Cheng, Hai Wang, Xiao Xue, Boli Chen, and Yukun Hu. Chaos meets attention: Transformers for large-scale dynamical prediction. arXiv preprint arXiv:2504.20858, 2025.
Christoph Jürgen Hemmer and Daniel Durstewitz. True zero-shot inference dynamical systems preserving long-term statistics. Advances in Neural Information Processing Systems, 38, 2025.
Maximilian Herde, Bogdan Raonić, Tobias Rohner, Roger Käppeli, Roberto Molinaro, Em- manuel de Bézenac, and Siddhartha Mishra. Poseidon: Efficient foundation models for pdes. 2rXiv:240S.19101. 2024.
John R Hershey and Peder A Olsen. Approximating the kullback leibler divergence between gaussian mixture models. In 2007 IEEE International Conference on Acoustics, Speech and Signal Concessing-ICASSPPP volume 4, pp. IV-317. IEEE, 2007.
Florian Hess, Zahra Monfared, Manuel Brenner, and Daniel Durstewitz. Generalized teacher forcing for learning chaotic dynamics. In International Conference on Machine Learning, pp. 13017- 13049. PMLR, 2023.
Jordan Hoffimann, Sebastian Borgeaud, Arthur Mensch, Elena Buchatskaya, Trevor Cai, Eliza Rutherford, Diego de Las Casas, Lisa Anne Hendricks, Johannes Welbl, Aidan Clark, al. Training compute-optimal large language models. arXiv:2203. 15556, 2022.
Rob Hyndman and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2018.
Rob J Hyndman and Anne Kochler. Another look at measures of forecast accuracy. International
journal of forecasting, 22(4):679-683 2006.
13

---

Published as a conference paper at ICLR 2026
Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y Zhang, Xiaoming Shi, Pin- Yu Chen, Yux- uan Liang, Yuan-Fana Li, Shirui Pan, et al. Time-LLM: Time series forecasting by reprogramming large language models. arXtv:2310.01728. 2023.
Jared Kaplan, Sam McCandlish, Tom Henighan, Tom Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models. arXiv:2001.08.5 000361, 2020.
George Em Karniadakis, Ioannis G Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. Physics-informed machine learning. Nat. Rev. Phys., 3(6):422 440, 2021.
Nitish Shirish Keskar, Bryan McCann, Lav R Varshney, Caiming Xiong, and Richard Socher. Ctrl: A conditional transformer language model for controllable generation. arXiv preprini arXiv: 2019.
Aditi S Krishnapriyan, Alejandro F Queiruga, N Benjamin Erichson, and Michael W Mahoney. Learning continuous models for continuous physics. Communications Physics, 6(1):119, 2023.
Iván León and Diego Pazó. Dynamics and chaotic properties of the fully disordered kuramoto model. Chaos, 35(7), 2025.
Matthew Levine and Andrew Stuart. A framework for machine learning of model error in dynamical systems. Commun. Am. Math. Soc., 2(07):283-344, 2022.
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations. arXiv:2010.08895, 2020.
Yuxuan Liang. Haomin Wen, Yugi Nie, Yushan Jiang, Ming Jin, Dongjin Song, Shirui Pan, and Qing- song Wen. Foundation models for time series analysis: tutorial and survey. arXiv:2403. 14735, 2024.
Bryan Lim and Stefan Zohren. Time-series forecasting with deep learning: survey. Philosophical Transactions of the Royal Society A, 379(2194):2020020, 2021.
Chenghao Liu, Taha Aksu, Juncheng Liu, Xu Liu, Hanshu Yan, Quang Pham, Doyen Sahoo, Caiming Xiong, Silvio Savarese, and Junnan Li. Moirai 2.0: When less is more for time series forecasting. arXiv:2511.11699 2025a.
Toni JB Liu, Nicolas Boullé, Raphaël Sarfati, and Christopher! J Earls. Llms learn governing principles of dynamical systems, revealing in-context neural scaling law. arXin:2402.00795, 2024a.
Yong Liu, Guo Qin, Xiangdong Huang, Jianmin Wang, and Mingsheng Long. Autotimes: Autore- gressive time series forecasters via large language models. arXiv:2402.02370, 2024b.
Yong Liu, Guo Qin. Zhiyuan Shi, Zhi Chen, Caiyin Yang, Xiangdong Huang, Jianmin Wang, and Mingsheng Long. Sundial: A family of highly capable time series foundation models. (500::2502.008816 2025b.
Zhixin Lu, Brian R Hunt, and Edward Ott. Attractor reconstruction by machine learning. Chaos, 28 (6):061104, 2018
Ang Lv, Ruobing Xie, Xingwu Sun, Zhanhui Kang, and Rui Yan. Language models" grok" to copy. arXiv preprint arXiv:2409.092281, 2024.
Spyros Makridakis, Evangelos Spiliotis, and Vassilios Assimakopoulos. The m5 competition: Background, organization, and implementation. International Journal of Forecasting, 38(4): 1325-1336. 2022.
Michael McCabe, Bruno Régaldo-Sare Saint Blancard, Liam Parker, Ruben Ohana, Miles Cranmer, Alberto Bietti, Michael Eickenberg, Siavash Golkar, Geraud Krawezik, Francois Lanusse, et al. Multiple physics pretraining for spatiotemporal surrogate models. Advances in Neural Information Processing Systems, 37:1 17:1199001-11333 2024.
14

---

Published as a conference paper at ICLR 2026
R Thomas McCoy, Shunyu Yao, Dan Friedman, Mathew D Hardy, and Thomas L Griffiths. Embers of autoregression show how large language models are shaped by the problem they are trained to solve. Proc. Natl. Acad. Sci. U.S.A., 121441):2522222221, 2024.
Kaden McKeen, Laura Oliva, Sameer Masood, Augustin Toma, Barry Rubin, and Bo Wang. Eeg-fi: An open electrocardiogram foundation model. arXiv preprint arXiv:2408.05177 2024.
Jonas Mikhaeil, Zahra Monfared, and Daniel Durstewitz. On the difficulty of learning chaotic dynamics with rnns. Advances in Neural Information Processing Systems, 35:1 15s:11297-113 11312, 2022.
John A Miller, Mohammed Aldosari, Farah Saeed, Nasid Habib Barna, Subas Rana, I Budak Arpinar, and Ninghao Liu. A survey of deep learning and foundation models for time series forecasting. arXiv:2401. 13912, 2024.
Melanie Mitchell and David C Krakauer. The debate over understanding in ai's large language models. Proc. Natl. Acad. Sci. U.S.A., 120(13)ee2115007122) 2023.
Tung Nguyen, Johannes Brandstetter, Ashish Kapoor, Jayesh K Gupta, and Aditya Grover. Climax: A foundation model for weather and climate. arXiv:2301.10333, 2023.
Declan A Norton, Yuanzhao Zhang, and Michelle Girvan. Learning beyond experience: Generalizing to unseen state space with reservoir computing. Chaov, 35(1)), 2025.
Catherine Olsson, Nelson Elhage, Neel Nanda, Nicholas Joseph, Nova DasSarma, Tom Henighan, Ben Mann, Amanda Askell, Yuntao Bai, Anna Chen, et al. In-context learning and induction heads. arXiv:2209.11895, 2022.
Boris N Oreshkin, Dmitri Carpov, Nicolas Chapados, and Yoshua Bengio. Meta-learning framework with applications to zero-shot time-series forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 35, pp. 9242 9250, 2021.
Jaideep Pathak, Brian Hunt, Michelle Girvan, Zhixin Lu, and Edward Ott. Model-free prediction of large spatiotemporally chaotic systems from data: reservoir computing approach. Phys. Rev. Lett., 120 2018
Md Ashiqur Rahman, Robert Joseph George, Mogab Elleithy, Daniel Leibovici, Zongyi Li, Boris Bonev, Colin White, Julius Berner, Raymond A Yeh, Jean Kossaifi, et al. Pretraining codomain attention neural operators for solving multiphysics pdes. arXiv::403. 12553, 2024.
Kashif Rasul, Arjun Ashok, Andrew Robert Williams, Arian Khorasani, George Adamopoulos, Rishika Bhagwatkar, Marin Bilos, Hena Ghonia, Nadhir Vincent Hassen, Anderson Schneider, et al. Lag-llama: Towards foundation models for time series forecasting. arXiv:2310.08278, 2023.
Gautam Reddy. The mechanistic basis of data dependence and abrupt learning in an in-context classification task. arXiv:2312.0333 12.03002, 2023.
Matthew Ricci, Guy Pelc, Zoe Piran, Noa Moriel, and Mor Nitzan. Trendy: Temporal regression of effective non-linear dynamics. arXiv preprint arXiv:2412.03496, 2024.
Michael T Rosenstein, James Collins, and Carlo J De Luca. A practical method for calculating largest Iyapunov exponents from small data sets. Physica D: Nonlinear Phenomena, 65(1-2): 117-134, 1993.
Xiaoming Shi, Shiyu Wang, Yuqi Nie, Dianqi Li, Zhou Ye, Qingsong Wen, and Ming Jin. Time- moe: Billion-scale time series foundation models with mixture of experts. In The Thirteenth International Conference on Learning Representations, 2025.
Ben Sorscher, Robert Geirhos, Shashank Shekhar, Surya Ganguli, and Ari Morcos. Beyond neural scaling laws: beating power law scaling via data pruning. Advances in Neural Information Processing Systems, 35: 1551933319996, 2022.
Shashank Subramanian, Peter Harrington, Kurt Keutzer, Wahid Bhimji, Dmitriy Morozov, Michael W Mahoney, and Amir Gholami. Towards foundation models for scientific machine learning: Charac- terizing scaling and transfer behavior. Advances in Neural Information Processing Systems, 36, 2024.
15

---

Published as a conference paper at ICLR 2026
George Sugihara. Nonlinear forecasting for the classification of natural time series. Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, 348 (1688):477-4955) 1994.
George Sugihara and Robert M May. Nonlinear forecassing as a way distinguishing chaos from measurement error in time series. Nature, 34446266)))67747771, 1990.
Makoto Takamoto, Timothy Praditia, Raphael Leiteritz, Daniel MacKinlay, Francesco Alesiani, Dirk Pflügeer, and Mathias Niepert. Pdebench: An extensive benchmark for scientific machine learning. Advances in Neural Information Processing Systems. 35:1596-1611 2022.
Floris Takens. Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, Warwick 1980: proceedings of a symposium held at the University of Warwick 1979/80, pp- 366-381. Springer, 2006.
Kunio Takezawa. Introduction to nonparametric regression. John Wiley & Sons, 2005.
Amin Totounferoush, Serge Kotchourko, Michael W Mahoney, and Steffen Staab. Paving the way for scientific foundation models: enhancing generalization and robustness in pdes with constraint- aware pre-training. arXiv preprint arXiv:2503. 19081, 2025.
Yao-Hung Hubert Tsai, Shaojie Bai, Makoto Yamada, Louis-Philippe Morency, and Ruslan Salakhut- dinov. Transformer dissection: An unified understanding for transformer's attention via the lens of kernel. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, 2019.
VP Vera-ávila, Ricardo Sevilla-Excoboza, AA Lozano-Sánchez, RR Rivera- and Javier M Buldú. Experimental datasets of networks of nonlinear oscillators: Structure and dynamics during the path to synchronization. Data in brief, 28: 105012, 2020.
Johannes Von Oswald, Eyvind Niklasson, Ettore Randazzo, João Sacramento, Alexander Mordvintsev, Andrey Zhmoginov, and Max Vladymyrov. Transformers learn in-context by gradient descent. In International Conference Machine Learning, pp. 35151-35174. PMLR, 2023.
Walters. An introduction to ergodic theory. Springer- Verlag, 1982.
Weinan. A proposal on machine learning via dynamical systems. Commun. Math. Stat., 1(5):1-11, 2017.
Gerald Woo, Chenghao Liu, Akshat Kumar, Caiming Xiong, Silvio Savarese, and Doyen Sahoo. Unified training of universal time series forecasting transformers. arXiv:2402.02592, 2024.
Liu Yang, Siting Liu, Tingwei Meng, and Stanley Osher. In-context operator learning with data prompts for differential equation problems. Proc. Natl. Acad. Sci. U.S.A., (0339)::2310142220 2023.
Lu Yang, Xiuwen Sun, Boumediene Hamzi, Houman Owhadi, and Naiming Xie. Learning dynamical systems from data: A simple cross-vale cooss-validation perspective, part Sparse kernel flows for 132 chaotic dynamical systems. Physica D: Nonlinear Phenomena, 460:134070, 2024.
Qingren Yao, Chao-Ha Han Huck Yang, Renhe Jiang, Yuxuan Liang, Ming Jin, and Shirui Pan. Towards neural scaling laws for time series foundation models. arXiv:2410.123660 2024.
Annan Yu, Danielle C Maddix, Boran Han, Xiyuan Zhang, Abdul Fatir Ansari, Oleksandr Shchur, Christos Faloutsos, Andrew Gordon Wilson, Michael W Mahoney, and Yuyang Wang. Under- standing the implicit biases of design choices for time series foundation models. arXiv preprint arXiv:2510. 19236, 2025.
Rose Yu and Rui Wang. Learning dynamical systems from data: An introduction to physics-guided deep learning. Proc. Natl. Acad. Sci. U.S.A., 121(27):c2311808122 2024.
Oussama Zekri, Ambroise Odonnat, Abdelhakim Benechehab, Linus Bleistein, Nicolas Boullé, and levgen Redko. Large language models as markov chains. arXiv preprint arXiv:2410.02724 2024.
16

---

Published as a conference paper at ICLR 2026
Zheng-Meng Zhai, Jun- Huang, Benjamin D Stern, and King-Cheng Lai. Reconstructing dynamics from sparse observations with no training on target system. arXiv:2410.21222, 2024.
Yuanzhao Zhang and William Gilpin. Zero-shot forecasting of chaotic systems. arXiv:2409.15771, 2024.
Tian Zhou, Peisong Niu, Liang Sun, Rong Jin, et al. One fits all: Power general time series analysis by pretrained Im. Advances in neural information processing systems, 010443322-433555 2023.
17

---

Published as a conference paper at ICLR 2026
A
SAMPLE PREDICTIONS FROM FOUNDATION MODELS
ground truth
Chronos forecast
15
MIJ my
MU
M
5
wnn
Y
-5
-15
100
200
300
400 time steps
500
600
700
800
ground truth
Chronos Bolt forecast
15
hm
-5
-10
100
200
300
400
500
600
700
800
time steps
ground truth
TimesFM forecast
15
mnn
n
-5
-10
-15
100
200
300
400
500
600
700
800
time steps
ground truth
TimeMoE forecast
15
MUJ
5-
0-
-5
10
-15
100
200
300
400
500
600
700
800
t. time steps
Figure Example forecasts on a chaotic system from foundation models reveal common failure modes. This is the same task as presented in Fig. (predicting the ø variable of the Lorenz system based on a short context trajectory with 512 data points). Chronos does extremely well with parroting strategy. The other models perform comparatively poorly and all exhibit tendency to underestimate the oscillations (c.g., by quickly converging towards the mean). This a general trend that we consistently observe across different chaotic systems and initial conditions.
18

---

Published as a conference paper at ICLR 2026
B BENCHMARKING WITH OTHER METRICS
0.8
1.0
Parrot
Parrot
Chronos
0.7
Chronos
ChronosBolt
ChronosBolt
0.8
TimesFM
0.6
TimesFM
Error (MSE)
TimeMoE
Error (MAE)
TimeMoE
0.6
Moirai
Moirai
DynaMix
0.4
DynaMix Mix
Simplex
Simplex
0.4
AutoARIMA
0.3
AutoARIMA
0.2
0.2
0.0
0.0
10
10 Time (Lyapunov times)
101
10 Time (Lyapunov times)
101
Figure 7: Context parroting outperforms foundation models in zero-shot forecasting. Same setup as Fig. 2, but with the forecast eπror measured by MSE (left) and MAE (right). On top of the foundation models, also include two classical forecasting methods in the comparison: simplex projection (Sugihara & May, 1990) and AutoARIMA (Hyndman & Athanasopoulos, 2018).
3
3
Chronos, 0.85
TimesFM, r- 0,58
DynaMix - 0.70
TimeMoE, r- 0.52
Simplex, 0.76
pred. corr. dim.
pred. corr. dim.
AutcARIMA,
1
2 true corr. dim.
2
3
true corr. dim.
Figure 8: Fractal dimension accuracy for parroting and foundation models. Each point represents the predicted fractal dimension of a chaotic attractor by a model (median of 20 predictions from random initial conditions). The accuracy is measured by the Spearman correlation r between the 135 predicted fractal dimensions and the true fractal dimensions.
C EFFECTS OF EMBEDDING DIMENSION D
Fig. 9 investigates how the choice of the embedding dimension D affects the performance of context parroting. Overall, the valid prediction time stays consistent over a wide range of embedding dimension D. For short context windows, there is slight advantage to small D. For long context windows, larger embedding dimensions are marginally better. This observation suggests potential improvements in the future that choose D adaptively based on factors such context length.
19

---

Published as a conference paper at ICLR 2026
8
7
VPT (Lyap. times)
8
128
5
512
1024
2048
2
16394
32768
1
10
15
20
25
30
Embedding dimension
Figure 9: Effect of the embedding dimension D the forecast accuracy of context parroting. Each curve represents different context length. Results are averaged over 135 chaotic systems in the dysts s database, with 100 trajectories from random initial conditions for each system.
=
D D 5
D 10
D 10
One-step error (sMAPE)
Matching motif distance
D 15
D - 15
D 20
10
D = 20
10
D 25
D = 25
D 30
D 30
10-1
10"
10
10?
10
10
10a
10a
10
Context length
Context length
Figure 10: Scaling laws with context length. Left: One-step forecast error versus context length. The scaling follows a power law for all embedding dimensions D considered. Smaller D is more accurate here because of the one-step forecast error. Larger 1) can be more accurate for longer forecasting horizons. Right: Euclidean distance between the last context motif P1.-D+1:1. and its closest match, as a function of context length. Again, the scaling follows power law for all D.
D INVARIANT PROPERTIES ON LONG FORECAST HORIZONS
next test the performance of parroting for long forecast horizons. We fix the context length L 512 and then generate forecasts of length H 10000 512 9488 (equivalent to over 316 Lyapunov Times). Table shows the results of generating forecasts using the best-performing models from shorter-horizon experiments. For each model, evaluate its global accuracy by calculating (1) the correlation between the fractal dimension of the long forecast, and an estimate generated from the ground truth; the correlation between the largest Lyapunov exponent of the long forecast, and an estimate generated from the ground truth; and (3) the attractor KL-divergence between the long forecast and ground truth (Grassberger Procaccia. 1983; Rosenstein al., 1993; Hess et al., 2023). We find that context parroting performs well on all three metrics.
20

---

Published as a conference paper at ICLR 2026
Metric
Parrot
Chronos
Dynamix
Simplex
Attractor KI. Divergence
0,412 + 0.141 0.679 0.101
0,508 = 0.147
0.546 0.140 0.341 0.072
Fractal Dimension Correlation 0.723 = 0.042
0.120 0.118 0.521 = 0.057
Largest Lyapunov Correlation 0.343 + 0.018 0.269 = 0.1114 0.466 = 0.071 0.343 = 0.085
Table KI. Divergence and correlation invariant properties between predicted and true attractors for different models for long forecast horizons. Error bars are standard deviation across all attractors for the KL Divergence, and uncertainty bounds based on the p p-value for correlations. Bold = best, italic second best.
30
DyraMix
Parrot
20
Count
10
0.08
Lyapunov exponent
Figure 11: Histograms of Lyapunov Exponents. We estimate the Lyapunov exponents from the ground-truth time series, well from long rollouts from parroting and DynaMix, the current- generation foundation model with the best ability to preserve long-term properties. These rollouts generated with context length of 2000 and prediction horizon of 10000, and correspond to estimates from all distinct chaotic systems in dysts.
A
Predicion
Power Spectiun
Opned to
SAA MAMIIII WW/
Oprin 2000 Comeot
0*
07-
Corted
06-
900
2000
2000
Invariant properties predicted by parroting improve with context length. (A) Predictions of single chaotic system, the Lorenz attractor, by the parroting model the context length increased from 100 to 3000. Forecasts are generated for 10, 000 points past the end of the context, and the last 2000 timepoints shown. The power spectrum is estimated using Welch's method on the last 5000 timepoints. (B) The average Hellinger distance between the true and predicted power spectrum
Figure 12:
function context length, averaged over 129 distinct chaotic systems (including the Lorenz attractor). Error bars correspond to standard deviations. The averaged Hellinger distance introduced as long-term metric for chaotic systems Mikhaeil et al. (2022) and Brenner et al. (2022).
21

---

Published as a conference paper at ICLR 2026
E EFFECTS OF NOISE AND SAMPLING RATE
We add Gaussian noise to normalized chaotic trajectories and repeat the original experiments (a noise level of 0.1 translates 10% perturbation each data point on average). The results are consistent across different orders of magnitude in noise, and parroting is consistently the best or the second best all experiments.
Noise level
Parrot
Chronos
Chronos Bolt TimesFM TimeMoE
10
2.17
1.68=0.8
0.79=0.18
1.07:0.19 0.92#1.115
10-2
2.10=10.18
166=0018
0.79
1.05#0.19 0.92 0.8910.17 0.66+t0.11
10
1.04:10.14 0.89=0.15
0.71
Table 5: Valid prediction time across noise levels (higher is better). Bold best, italic second best. Shading highlights best (dark) and second best (light).
Noise level
Parrot
Chronos
Chronos Bolt
TimesFM
TimeMoE
10-3
0.233
0.440:10.228 0.29710.243 0.4913
0.3771:.2211
10 10-2
0.492++.2225 0.286:10.209 0.366 0.509 0.455=0.2224 0.41510.216
0.225=00.20 0.31 0.31/=0.245
0.441#0.228 0.383
10-1
Table 6: MAE @ 1 Lyapunov Time across noise levels (lower is better), Bold best, italic = second best. Shading highlights best (dark) and second best (light).
Noise level
Parrot
Chronos
Chronos Bolt TimesFM
TimeMoE
10 10-3
0.183:10.339
0.26810.367
0.473+0.314
0.394:10.307 0.315#0.273 0.474+0.314
10-2
0.394++0.306 0.318+0.274 0.220-10.346 0.328 0.489+0.314
0.185+
0.282+0.366
10-1
0.407++0.302 0.349
Table 7: MSE @ 1 Lyapunov Time across noise levels (lower is better). Bold best, italic = second best. Shading highlights best (dark) and second best (light).
Noise level Parrot Chronos Chronos Bolt TimesFM TimeMoo
10 10-3
0.73
0.85
0.52
0.58
0.52
10 10-2
0.63
0.77
0.51
0.55
0.45
10-1
0.59
0.57
0.37
0.49
0.16
Table 8: Fractal dimension accuracy (Spearman correlation) across noise levels (higher is better).
Bold = best, italic = second best. Shading highlights best (dark) and second best (light).
Noise level
Parrot
Chronos
Chronos Bolt
TimesFM
TimeMoE
10-3
0.279+00209
0.345++0.298 0.296
0.354+10.220
10-2 2
0.205 0. 0.244
0.344+0.292 0.356+0.229 0.344++.228
10-1
0.141 0.2/8=00.26 0.382+0.314 0.389:10.306 0.433+0.3306
Table KL. Divergence between predicted and true attractors across noise levels (lower better). Bold best, italic second best. Shading highlights best (dark) and second best (light).
In the main text, we set an intermediate granularity of 30 points per Lyapunov time. Below we compare it with results obtained for granularities of 10 points per Lyapunov time and 50 points per Lyapunov time. Granularity does not strongly affect the results or relative model ranking. Parroting is either the best the second best in all experiments. This makes sense, would expect changing
22

---

Published as a conference paper at ICLR 2026
granularity to have similar effect rescaling of time (although with bigger smaller gaps between data points). For example, if we use finer granularity by factor of 2, then we would need to double the context length get the same lookback window.
Granularity
Parrot
Chronos
Chronos Bolt TimesFM TimeMoE
10
4.70
3.9310.59
1.55=0.50 0.79#1.18 0.55+10.10
1.92:00554 1.43=0.26
30
2.15==0.19 1.68+0..1 18
1.07=0.19 0.92+t0.15 0.79#0.11 0.54+0.05
50
0.41=0.11 1.12+0.11
Table 10: Valid prediction time across different granularities (higher is better). Bold = best, italic second best.
Granularity
Parrot
Chronos
Chronos Bolt
TimesFM
TimeMoE
10
0.219 0.204 0.316=02256
0.481 0.4141:.232 0.56710.226
30
0.440= 0.491=0.223 0.270=0.226 0.329=0.241 0.527=0.224
0.233=002211 0.293
0.377#0.211
50
0.448:1.235 0.412#0.193
Table 11: MAE @ Lyapunov Time across different granularities (lower is better). Bold = best, italic second best.
Granularity
Parrot
Chronos
Chronos Bolt
TimesFM
TimeMoE
10
0.163 0.311 0.2911:0.366
0.565+0.314
0.429+-0299
0.349-10.300
30
0.164 0.295 0.268+ 0.367
0.394 0.473+0.314
0.315+0.273
50
0.344 0.310=0.377
0.53610.341 0.426110.311 0.352+1.2222
Table 12: MSE @ Lyapunoy Time across different granularities (lower is better). Bold = best, italic second best.
Granularity Parrot Chronos Chronos Bolt TimesFM TimeMoF
10
0.87
0.82
0.34
0.39
0.36
30
0.80
0.85
0.52
0.58
0.52
50
0.89
0.86
0.41
0.60
0.56
Table 13: Fractal dimension accuracy (Spearman correlation) across different granularities (higher better). Bold best, italic second best.
Granularity
Parrot
Chronos
Chronos Bolt
TimesFM
TimeMoE
10
0.087+0.137 0. 173
0.444+0.326 0.573+0.307
0.467+0.368
30
0.122+0.194 0713+00.200
0.346+0.297
0.345 0.354+0.290
50
0.137+0.207 0.230+0.256
0.406#0.305
0.361+0.323 0.370+0.333
Table 14: KL Divergence between predicted and true attractors across different granularities (lower better). Bold best, italic = second best.
F THEORETICAL PROPERTIES OF CONTEXT PARROTING
F.1 OVERVIEW
Mathematical Formulation. Context parroting corresponds to continuous 1-nearest-neighber search over sequences of length D in the context of length T. It thus corresponds limit of
23

---

Published as a conference paper at ICLR 2026
Nadaraya- Watson model of the time series,
ply q) Lj Ko (q. XJ-(D-1)3) Ko (y, xj+1s++H)
Σjー Ka (q. XJ-(D-1):))
where the query q represents the length- motif immediately preceding the end of the context window. y represents length- H forecast of subsequent values. The forecast sequence y has probability conditioned on the query. The symmetric kernel Ko (u, v) = o K ((u v)/hor has bandwidth in dimension D dim(xx). Assuming mean-squared error as a distance function in sequence space, we Gaussian kernel
Ko (u, v) (2mo2)d/22 exp
2n
We set the second kernel on y in Eq. I to a delta function, in order to output predictions that exactly match sequences from the context, rather than nearby sequences in least-squares sense. We write the conditional mean predictor
L-H H
K₂ (q. z) Dj=D Ko (q. x xj-(D-1)a)
8(q) = Σ ((D-)))(D-I)ss)) Xf+1:jHH w(q.z) = 3=D
Context parroting corresponds to the 1-nearest-neighhor limit a ++ 0.
Context parroting preserves attractor properties at long context lengths. In Appendix F.4, derive the following proposition,
lim Ey(F(y)) [x(F(( Lox
where is the context length for an Nadaraya-Wand Watson estimator p. F(y) is an estimate from forecast sequence y of property F' of an ergodic dynamical system, which has an invariant value Ey [x)] when calculated over the full attractor with underlying measure μ. The query q is an arbitrary sequence of consecutive timepoints from the dynamical system. This proposition states that, when the context sufficiently long, context parroting of an ergodic system preserves invariant values of the underlying dynamics. Context parroting thus represents an effective baseline for dynamical systems forecasting, because, in the limit of long context, it will preserve global properties like conditional distributions of values, Lyapunov exponents, entropy production rates.
F.2 DISCRETE-TOKE, PARROTING
For fully- discreee tokens, thh order Markov chain fit to the context has the form
[ = q) (1ft14HH y)
plylg) Ey #li
(3)
(zz-(D-1)) :
q) A (1ft1gHH =y)
where the overall context has length L, and the Markov chain conditions the H < L future tokens on the D < preceding tokens. The index runs over all contiguous sequences of length D + in the context, E (D I, ..... L - H 2, L H 1}. The vector RD represents the query, and the vector y E R represents the prediction in response to this query. Eq. simply counts the number of token sequences of length D + H that start with given sequence of D query tokens. maximum- likellhoodd estimator derived from this model always samples the sequence y.
likelihood
{MLE(q) = argmax, log log p(yla)
However, this estimator may be unstable due to the appearance of queries q not seen the context, motivating the use of token smoothing, in which Eq. 3 is replaced by the distribution
#(i : (25- = q) A (Iz+IIHH y) +
plylq) = Ey, (# (I)- q) A (#y+1i+H y') +
(4)
with increasing values of the parameter causing predictions to converge uniform sample over possible predictions y. The parameter value a = reduces to no smoothing, while a = 0.5 corresponds to the Jeffreys prior and corresponds Laplace's rule of succession.
24

---

Published as a conference paper at ICLR 2026
F.3 CONTINUOUS-TOKER PARROTING
A more general time series model treats tokens as continuous-valued. Some time series foundation models like Chronos use binning to discretize time series values, allowing the direct of discrete- token architectures (Ansari et al., 2024). However, many time series models assume effective continuity in token values, and we favor continuous formulation in order to highlight connections to dynamical systems theory.
To model continuous-valued tokens directly, we replace the discrete count in $F22 with a kernel- weighted estimate over all past subsequences. Let {x, denote univariate or multivariate time series. Matarayy--aatoonnnnn For context length and prediction horizon H. the Nadaraya- Watson estimate of the conditional density is
ply 9) = Lj=D Kú (q. x)-(D-1)5) KA (y, X5+1:++H)
(S)
Σj= Kn. (q. X)-(D-1)s))
where KA (u, v) h-4K((u- v)/h) is symmetric kernel with bandwidth h in dimension d D dim(x,) for the first kernel, and d H dim(xx) for the second kernel. Assuming mean-squared error as a distance function in sequence space, we use a Gaussian kernel
||u v/1?
(u, v) (2th2)d/2 exp
24
In practice, drop the second kernel y in Eq. 5 in order output a prediction that exactly matches sequences from the context, rather than nearby sequences least-qquares sense. We thus write the conditional mean predictor
L-H (()) = Σ u(q:x)-(D-I)s) X5+1:++H
(6)
I=D
where we have isolated a term corresponding the weight of each sequence,
Kn (q. z) ΣS= K₁ (q. X--(D-1);)
w z)
Nearest-neighbor and global average limits. The bandwidth h plays the role of smoothing parameter (analogous Eq. 4). As h the scheme approximates single-nearest neighbor parrot, while as h oc it converges to global average over all sequences.
Connection attention. If one takes
K(u, v) exp(u (v/r).
then Eq. 6 recovers a simplified form of aettmax-attention, with the temperature hyperparameter controlling smoothness. In this view, the continuous parroting scheme a kernel-regression analogue of discrete k-gram smoothing (Tsai et al., 2019).
neneabr limit. We define the index E {D, D+ L j that produce the k largest values of w(q. x x)-((-1)x)) across all values of We compute simple average these & closest matches
Topk corresponding to subset of the possible values of H 1, L H.. The k elements of Topk correspond to the indices
1 Σ w(q.x)-(D-1)i)) Xf+1i+H
((q)
.jTTopk
yielding --nnarest-neighhors parroting scheme. As increases, this estimator interpolates between exact parroting (k: 1) and global average (k- + T.).
Simplex projection. Simplex projection, a classical forecasting method in nonlinear dynamics, corresponds to the special case H = (single step prediction), h D + in Eq. 7. The condition D + represents the minimal number of affinely independent neighbors needed to triangulate a point in D-dimensional space (Sugihara & May, 1990).
25

---

Published as a conference paper at ICLR 2026
In simplex projection, the query q is interpreted time-delay embedding of the time series observable x. Takens' theorem argues that, under mild conditions, finite number of time delay embeddings of observable drawn from deterministic ergodic system will be diffcomorphic (smoothly mappable) to the full-state dynamics (Takens, 2006). Because simplex projection uses only neighbor identities, and not absolute distances, weight context points, delay embedding is sufficient to calculate the appropriate weights.
S-map forecasts. Another common nonlinear forecasting technique retains all terms in the sum Eq. 6, but instead performs nonlinear weighting of the form
Ka (u, v) exp(-00
vll/d)
where the scale parameter d is determined by the distribution of distances among queries and points in the context. practice, this parameter is often set the mean pairwise distance among all sequences of length D in the context. The optimal value of the hyperparameter 0 increases as the underlying dynamics become more strongly nonlinear Sugihara (1994). We note that, the classical formulation of the S-map, a locally-linear model is fit based all sequences of length D + H seen in the context, while here we use the Nadaraya-Warte Watson estimator in order to emphasize connections to modern kernel regression.
F.4 INVARIANTS OF MOTION
For ergodic dynamical systems in continuous time, there exists a natural measure μ(() such that, for certain observables F(x), the following condition almost surely holds.
/ F(x) - F(x))u((x) constant
B [F] lim
T-+00 T
where the second equality arises from the Birkhoff ergodic theorem (Walters, 1982).
We use the following convention expectation values of sequences and single tokens; the expectation E [x.+T] refers to the expected value of the sequence X given pointwise measure μ. We note that, for deterministic dynamical systems, once a given point is sampled on the attractor with measure u(x,), subsequent points have delta function conditional probability the convention p(x;) (((x:.+)) and we use the measure to refer to both the probability of a given timepoint, sequence of arbitrary length originating from that timepoint.
the first point. Thus, use
Proposition. Under appropriate kernel conditions,
lim E (,,( =x,,, [F()] L
where L is the context length for Nadaraya-Warn Watson estimator p. F(y) is an estimate sequence y of an invariant property of an ergodic dynamical system with measure μ,, and q is an arbitrary sequence of consecutive timepoints from the dynamical system. This proposition states that, when the context is sufficiently long, a Nadaraya-Wand Watson estimator of an ergodic system preserves the invariant values of the underlying dynamics.
Derivation. We start with the definition of the dynamical average.
[F / F(x)dp(x)
Inserting Eq. 5 into this expression,
(x Σ/D Kn (q. Xj- (D-( J K(y)Kr (y, Xz415+H) duly) Σ Kn (q. x)-
We multiply both the numerator and denominator by 1/L and take the limit L + oo, in order to convert the summations expectations,
lim F, (F())]] = E, x FY))Kr x du(y)] 1+00
[, xx.)
26

---

Published as a conference paper at ICLR 2026
where x+- represents the first D points of random lookback window of length D + H sampled from the underlying dynamical system, while x denotes the next H timepoints. In practice, this corresponds to time series of D + H points generated simulating the dynamics starting at point on the attractor randomly-sampled according to the measure j..
If we take the limit h - (exact matching), then the kernel K₁ becomes delta function, yielding
lim lim (P(y)aa = (x( = dl
If the measure μ is ergodic, then the conditional expectation of an invariant F given any query is simply its unconditional expectation,
lim lim F,,(F(y)lqi [x()
h-0 100
F.5 SCALING LAWS LIMITING PREDICTION OF STOCHASTIC SYSTEMS
For stochastic time series X1.7 with autocorrelation given by
[Corr(x,, x(+>)| S Ce a7
with C representing proportionality constant, the expected mean squared error of a forecast scales as
E y ~e-aL L0
Thus, under exponential decay of correlations (mixing), the amount of information about future states length-L context window saturates exponentially quickly Bradley (2005). Thus, forecasts derived from increasingly large context windows converge exponentially quickly to optimal conditional forecasts under the invariant measure p.
Under standard smoothness conditions Fan & Yao (2008); Takezawa (2005), the forecast error also exhibits a standard bias-variance tradeoff the form
E
y |2] O(h)) +
ChL+#
The optimal width of the kernel thus scales as,
hopt (-1((4+++))
27


Reviews:
[{"review_id": "8yBxvDgN94", "reviewer": "Reviewer_xP7T", "summary": "The paper proposes context parroting, a phenomenon observed in recent time series foundation models (FMs), as a tough-to-beat baseline for zero-shot forecasting of physical dynamical systems. The manuscript boils context parroting down to an efficient algorithm that directly copies from the context and is on par with or better than current foundations models such as Chronos. The method is used to explain recent in-context neural scaling laws and connected to the induction heads theory of LLMs. In that, context parroting highlights current failure modes of time series foundation models with the aim to improve future model design.", "questions": "1. “Despite the theoretical correspondence, however, numerically it is challenging to accurately estimate the scaling coefficient α due to noise in the data.” I am confused, in case of controllable benchmark data such as datasets derived from *dysts*, how is noise a problem? Can’t we simply generate data w/o noise?\n2. “Moreover, even when restricted to parroting, Chronos can in principle dynamically choose the optimal embedding dimension D for each individual time series, giving it an advantage over parroting algorithms with a fixed D.” Can the authors explain how Chronos would do this?\n3. Could the authors include an experiment that shows whether the estimated max. Lyapunov exponent converges to the ground truth for increasing context lengths, where $\\lambda_{max}$ is estimated from predicted trajectories only?  And of course predicting for much longer than 10 Lyapunov times, say 100-1000, to really probe the long-term climate of the forecasts of the introduced context parroting algorithm.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is well written and structured and hence easy to follow.\n2. Boiling down the algorithm behind context parroting to a lightweight routine which can be used as a baseline comparison is a great contribution to the field. \n3. Using and comparing the method to existing ideas and routines from dynamical systems theory is great way to gain a more mechanistic understanding of the underlying principles of current time series FMs.", "weaknesses": "The paper should discuss recent work introducing DynaMix [1]. It is a FM for time series based on RNNs and MoE and shows promising performance in forecasting chaotic dynamics from limited context without context parroting. This work also addresses the finding of [2], and shows that while context parroting games short-term forecast metrics, it only produces cyclic patterns in the long-term, rendering the method unable to truly produce the chaotic dynamics underlying the system hinted by the context. An analysis that [1] includes and this paper misses, in my opinion, is one that evaluates invariant measures for long autoregressive roll-outs e.g. by estimating the empirical max. Lyapunov exponent $\\lambda_{max}$ for trajectories pushing $T \\rightarrow \\infty$. [1] clearly shows that Chronos (which is context parroting) only produces $\\lambda_{max} \\approx 0$, indicating cycles (albeit high-order and complex at times). The manuscript should include a thorough discussion on these results and ideally include DynaMix as a comparison FM.\n\n**References**:\n\n[1] Hemmer, Christoph Jürgen, and Daniel Durstewitz. \"True zero-shot inference of dynamical systems preserving long-term statistics.\" arXiv preprint arXiv:2505.13192 (2025).\n\n[2] Zhang, Yuanzhao, and William Gilpin. \"Zero-shot forecasting of chaotic systems.\" arXiv preprint arXiv:2409.15771 (2024).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RFZe5FpfB1", "reviewer": "Reviewer_PSB6", "summary": "This paper shows that simple parroting - the process of identifying the best-matching patterns in history and repeating them as forecast - could beat state of the art time-series foundation models in predicting the evolutions of systems that are deterministic and chaotic. It then observes that simple parroting results in a scaling law between number of time steps and error in prediction quality, which is characteristic of LLMs. Finally, the paper speculates that such in-context parroting mechanism could potentially explain the in-context neural scaling of LLMs.", "questions": "- The theoretical result that the power law coefficient $\\alpha$ should equal $\\frac{1}{d_{correlation}}$ is quite nice. However, the experimental support for this turns out to be quite weak (Fig. 11). Could the authors speculate on why?\n- In Figure 5, context-parroting with more delayed embeddings correspond to curves with higher loss. This is counter-intuitive to me since more delayed embedding should result in better matching of patterns, at least when the context length is sufficiently long. However, this is not what we see in the left panel of Figure 4. Could the authors comment on why? The caption to figure 4 states \"Larger D can be more accurate for longer forecasting horizons\". Could the authors extend on the context length further to see whether algorithms with large D eventually outperform those with lower D?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The paper is well-written. It makes a convincing case for context-parroting as a simple yet non-trivial baseline for zero-shot forecast of chaotic systems.\n- The paper is also very topical as it attempts to elucidate the mechanisms underlying in-context learning of foundation models, though not full achieving a mechanistic interpretation of foundation models.\n- The theoretical analysis bridging the algebraic coefficient of the power law to the embedding dimension of the time series is very insightful, though only speculative.", "weaknesses": "Limited generality. The paper claims to explain the in-context neural scaling law reported in Liu et al. 2024 [1]. However, the in-context neural scaling law of that paper encompasses discrete, stochastic systems such as Markov chains with randomly generated transition matrices, chaotic systems such as the logistic map injected with noise, as well as deterministic ODE systems such as the Lorenz system. On the other hand, this paper (apart from section 5.3) only investigates deterministic systems governed by ordinary differential equations (ODEs). It is unclear whether context parroting could work on stochastic systems, and if so, whether it would result in similar scaling law. The paper defers the theoretical analysis of context parroting on stochastic system to future works, a valid decision in my opinion since the paper is already quite substantial and self-contained as it is. However, I still think the authors should clarify that they are only addressing the in-context neural scaling law that specifically results from learning deterministic chaotic systems governed by ODEs. \n\n[1]: Toni JB Liu, Nicolas Boullé, Raphaël Sarfati, and Christopher J Earls. Llms learn governing principles of dynamical systems, revealing an in-context neural scaling law. arXiv:2402.00795, 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "DmwiuaMFei", "reviewer": "Reviewer_2L3R", "summary": "This paper investigates context parroting, a simple “copying” strategy that mimics motifs from past context, as a surprisingly strong baseline for zero-shot forecasting in scientific machine learning (SciML). The authors show that this trivial method can outperform several state-of-the-art time-series foundation models (Chronos, Chronos-Bolt, TimesFM, Time-MoE) on forecasting chaotic and physical systems. They connect this behavior to induction heads in transformers and to in-context neural scaling laws, deriving a geometric explanation that ties scaling exponents to the fractal dimension of chaotic attractors. The work suggests that many current foundation models rely heavily on parroting-like mechanisms, calling for benchmarks and architectures that go beyond this trivial solution.", "questions": "How does context parroting perform on nonstationary or regime-shifting time series (e.g., climate or economic data)?\n\nCould a hybrid “parrot + predictor” model be constructed to retain parroting’s simplicity while addressing its limitations?\n\nHave you tried comparing against autoregressive baselines (ARIMA, GP kernels, etc.) to quantify parroting’s advantage beyond foundation models?\n\nDoes the observed scaling α ≈ 1/d₍cor₎ persist under noise or partial observability?\n\nCould the parroting mechanism be explicitly detected within transformer attention patterns (e.g., induction heads over repeated motifs)?", "limitations": "", "rating": 10, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "Strong empirical evidence: Extensive benchmarking across 135 chaotic systems and multiple real-world datasets (e.g., ECG, Kuramoto oscillators) convincingly supports the claim that context parroting is competitive or superior to foundation models.\n\nClarity and interpretability: The algorithm is simple, well-motivated, and connected to classic nonlinear dynamics methods (Takens’ embedding, simplex projection).\n\nInsightful theoretical link: The explanation of in-context scaling laws through the fractal dimension of attractors is elegant and potentially generalizable beyond SciML.\n\nCritical perspective: The paper exposes fundamental limitations of current time-series foundation models—especially their tendency to “regress to the mean” and fail to utilize context effectively.\n\nRelevance and timeliness: Given the explosion of foundation models for science, a “simple but tough-to-beat” baseline is highly valuable.", "weaknesses": "Scope of comparison: While the benchmarks are extensive, all compared models are pre-2025 foundations. It’s unclear whether next-generation models (e.g., fine-tuned or physics-aware transformers) would still underperform.\n\nLimited theoretical rigor: The link between fractal dimension and scaling exponent is compelling but heuristic; a more formal derivation or empirical validation of α ≈ 1/d₍cor₎ across systems would strengthen the claim.\n\nPotential overstatement: The claim that parroting “outperforms all foundation models” might be dataset-dependent—some tasks (e.g., short-context nonstationary regimes) still favor Chronos.\n\nComputational fairness: The comparison omits any fine-tuning or adaptation of foundation models; parroting benefits from zero training cost but might not scale as easily to multivariate or stochastic systems.\n\nNo ablation on motif length (D) or distance metrics: Although the authors mention robustness to D, a systematic analysis would clarify when parroting breaks down.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "0Swk6Msf6T", "reviewer": "Reviewer_rUtK", "summary": "# Review for Context Parroting\n\n## Summary\n- This paper presents parroting as a baseline for foundation models in scientific ML. The authors demonstrate that a simple algorithm outperforms foundation models in zero-shot forecasting of chaotic dynamical systems. They perform several analysis, comparing short- and long-time forecasts and motivate the power scaling law in LLMs with respect to one-step error and context length. While the technical contribution is simple, it does demonstrate as a useful baseline for comparing foundation models on forecasting chaotic systems.\n\n## Recommendation\n- Accept given the below feedback and questions are addressed. Particularly, provide a clean repository of code for reproducability (should not be too much effort) and add more comparisons (more models like Moirai and/or LLMTime as well as the classical methods described in the paper, and maybe even comparing sampling strategies).", "questions": "## Questions\n- Can you clarify the difference between fractal dimension, correlation dimension, and scaling coefficient? In the paper it's not clear why fractal dimension and correlation dimension are used separately when they appear to mean the same thing, this makes it slightly confusing.\n- I'm curious how different sampling strategies affect LLM results (eg. beam search, top-p, top-k, etc..). Please clarify if sampling strategy will affect results and how so.\n- I would like to see how off-the-shelf LLMs like Llama perform on this task too (see Gruver (2023)) [[link]](https://proceedings.neurips.cc/paper_files/paper/2023/file/3eb7ca52e8207697361b2c0fb3926511-Paper-Conference.pdf). Was this considered?\n- Classical methods are mentioned and a connection is drawn to parroting, why not just implement them and compare the results? How do those methods compare with parroting?\n- Why not also test multivariate foundation models like Moirai?\n\n## Feedback\n- Elaborate on the parenthetical 'can we estimate the \"fractal dimension\" of a language' and the potential applications there (line 099). Consider moving this to the conclusion (section 6).\n- Provide a direct citation of Takens':\n```\n@inproceedings{takens2006detecting,\n  title={Detecting strange attractors in turbulence},\n  author={Takens, Floris},\n  booktitle={Dynamical Systems and Turbulence, Warwick 1980: proceedings of a symposium held at the University of Warwick 1979/80},\n  pages={366--381},\n  year={2006},\n  organization={Springer}\n}\n```\n\n- Cite the Chronos Time-MoE and TimesFM models in \"Models.\" (line 196)\n- Axes of figure 2 right need to be explained more. What do the widths mean? (line 275)\n- Elaborate more on why Chronos has better correlation dimension that parroting.\n- Line 383, \"This is equivalent to embed\" to \"this is equivalent to embedding\"\n- Figure 4, line 371, \"because the use of the\" -> \"because of the\"\n- Line 379, \"Why do...?\", remove this sentence. Looks unprofessional, just state the answer to the question.\n- Please please please provide code to the broader community! None of this is proprietary and there should be a GitHub.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 2, "strengths": "## Strengths\n- The necessary dynamics backgrounds are explained well and sufficient detail (eg. Lyapunov time)\n- The parroting method is clearly explained.\n- The computational experiment for comparing models is explained clearly.\n- The evaluation metrics sMAPE and KL divergence are clearly explained.\n- The results are compelling and clearly laid out.", "weaknesses": "## Weaknesses\n- The reproducability is lacking. There should be a GitHub page with code that is easily run to recreate the figures and experiments.\n- The authors mention classical forecasting methods like Simplex projection and S-map forecasts and connect it to context parroting, however, these classical methods are not used in any comparisons.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)