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REVIEW 4 major objections 8 minor 37 references

Physics-inspired Energy Transition Neural Network for Sequence Learning

T0 review · 4 major / 8 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper claims that a purely recurrent network whose memory cell mimics atomic energy absorption and release outperforms Transformer-based models on several sequence tasks while using a small fraction of the compute.

desk verdict The paper's core claim—a countdown memory that stores long-term dependencies—is not supported by its own recurrence equations, and the empirical protocol has enough loose ends that the headline result should be treated as unverified. read the letter →

arxiv 2505.03281 v1 pith:MBJL6W7Q submitted 2025-05-06 cs.LG cs.AI

Zhou Wu , Junyi An , Baile Xu , Furao Shen , Jian Zhao This is my paper · ORCID
classification cs.LGcs.AI
keywords recurrentneuralnetworkenergytransitionmodellong-termdependencysequencelearningtimeseriesforecastingself-selectiveinformationmixingtransformeralternativememorymechanism
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to reopen a question most of the field considers settled: whether a purely recurrent architecture, with no attention at all, can rival Transformer-based models on long-term sequence tasks. Its answer is a new recurrent cell, PETNN, whose memory follows the logic of atomic energy transitions — the cell absorbs input as 'energy', holds it for a learned residence time, and dumps it back to a ground state when that time expires. The authors report that PETNN beats the classic recurrent and Transformer baselines on long-horizon forecasting and sentiment classification, ranks among the top performers against recent state-of-the-art forecasting models, and even tops a CNN and LSTM on image classification, all with roughly 0.045M parameters versus the Transformer's 10.54M. If those results hold, the paper's claim that recurrent inductive bias plus a well-designed memory is a competitive foundation architecture, not an obsolete one, would be established. The forecasting numbers carry the authors' own caveat that an unknown NaN problem forced them to drop one embedding in the PETNN and Mamba runs.

What carries the argument

The load-bearing object is the PETNN cell, a recurrent unit carrying three coupled variables: the remaining time $T_t$ (the cell's 'excited-state lifetime'), the cell state $C_t$ (its energy), and the hidden state $S_t$. The time variable is the trip-wire: updated by $T_t = R_t \sigma(T_{t-1} + Z_t) - 1$, it decides when the cell releases everything and snaps back to a learnable ground state $I_t$, selected by the binary switch $m$ when $T_t \le 0$. This hard reset is the mechanism claimed to solve long-term retention: the cell stores information for a duration set by the input itself, rather than by an explicit forget gate, so the memory horizon is learned per neuron instead of being a fixed context window. The second pillar is the hidden-state update $S_t = \sigma((1-Z_w) S_{t-1} + Z_w h_t)$, called self-selective information mixing, which decides how much old state survives into the new hidden state; the ablation study claims this rule beats LSTM-style gating, linear interpolation, and an exponential xLSTM-style gate on the sentiment task.

What would settle it

Run PETNN on the same forecasting benchmarks with horizons pushed to 1,440 and 2,880 steps, or on a long-document language task beyond 600 tokens, and check whether the advantage over Transformer baselines shrinks or training diverges; a second, more direct check is to measure gradient norms through the $T_t$ and $C_t$ paths at those depths and see whether they vanish or explode as the timer update compounds.

Watch

Extended reading notes

Core claim

PETNN's central claim is that a recurrent neuron whose internal dynamics mirror electron energy-level transitions can retain information over long sequences without the vanishing-gradient failure that motivated attention, and that this memory is what lets a pure RNN outperform self-attention models on sequence tasks. Concretely, each cell tracks a remaining time $T_t = R_t \sigma(T_{t-1} + Z_t) - 1$, where $R_t$ is an input-dependent decay rate; when $T_t$ crosses zero, the cell 'emits' its stored state and resets to a learnable ground level $I_t$, while otherwise the energy state accumulates via $C_t = (1-m) C_{t-1} + m I_t + Z_c$. The hidden state is then mixed by the self-selective rule $S_t = \sigma((1-Z_w) S_{t-1} + Z_w h_t)$. On the paper's experiments this recipe reduces MSE and MAE by an average of about 60% relative to Transformer-based forecasting baselines, reaches 89% accuracy on long-text IMDB sentiment classification (against 84% for TextCNN and 83% for LSTM), and achieves the forecasting results with 170M FLOPs and 0.045M parameters where the Transformer baseline uses 1,188M FLOPs and 10.54M parameters.

Load-bearing premise

The whole case rests on the assumption that the neuron's learnable 'timer' — how long it holds a memory before dumping it — stays stable over very long, noisy sequences, but the paper never proves that stability, offering only a loose analogy to a physics decay equation.

Editorial extensions

If this is right

  • A pure recurrent architecture with a cheap cell update can serve as a low-cost alternative to attention for long-horizon forecasting: the paper reports roughly seven times fewer FLOPs and over two hundred times fewer parameters than a Transformer baseline, at comparable or better forecasting error.
  • If the robustness result generalizes, the trip-wire reset gives the model a form of noise immunity: a salient early signal survives long stretches of neutral, irrelevant, and even contradictory text that flips an LSTM's prediction.
  • The model transfers beyond sequences: treating an image as a sequence of rows achieves 99.03% on MNIST in the paper's setup, above a CNN, an LSTM, and a KAN under the same protocol, which the authors take as evidence the cell can be embedded in general architectures.
  • The ablation attributes the model's stability to the self-selective mixing rule: replacing it with LSTM-style gating, linear interpolation, or an exponential gate lowers accuracy or causes training to fluctuate on the IMDB task.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A stress test the paper does not run: push sequence lengths far beyond the 720-step forecasting horizon to see whether the timer update $T_t = R_t \sigma(T_{t-1} + Z_t) - 1$ keeps memories stable or drifts; the paper justifies the update only by a loose continuous-decay analogy, so long-horizon stability is an empirical bet, not a proven property.
  • The physics framing suggests a testable prediction about how the learned parameters organize: if the input-dependent decay $R_t$ and ground level $I_t$ are clustered after training, neurons should segregate into slow 'persistent' channels and fast 'transient' channels — a hierarchical-timescale structure the paper hints at but never measures.
  • The energy-transition vocabulary is generative: importing other atomic phenomena (multi-level transitions, stimulated emission, degeneracy) as new state dynamics is a natural next step the authors gesture at, and each such import gives an immediately testable cell variant against the PETNN baseline.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 8 minor

Summary. The paper proposes PETNN, a recurrent neural network whose update rules are motivated by a physics-inspired "energy transition" analogy. The core model maintains a remaining-time variable T_t, a cell state C_t, and a hidden state S_t; it resets C_t to a ground state when T_t drops below zero, and uses a self-selective mixing rule to update S_t. The authors claim that this mechanism stores long-term dependencies and that PETNN outperforms transformer-based methods on time-series forecasting, text sentiment classification, and image classification, while exhibiting lower complexity. Experiments are run within TSLib for five long-term forecasting datasets, on ACL-IMDB sentiment classification, and on MNIST image classification.

Significance. If the central claims were established, PETNN would be a relevant contribution: a pure recurrent architecture with low FLOPs that competes with transformer-based sequence models on long-term dependency tasks. The paper has useful strengths: the update equations are explicit, the evaluation uses a standard library and standard datasets, and the authors transparently acknowledge the NaN episode that led to a post-hoc architectural change. However, the core memory mechanism is not supported by the equations as written, and the empirical evidence lacks error bars and in one task omits the transformer baseline that the abstract claims to outperform. The physics derivation in Section 3.4 is presented as rigorous but is actually a loose analogy with an ad-hoc modification; the paper needs substantial technical and experimental revision before the claims can be accepted.

major comments (4)
  1. [Section 3.3, Eq. (4); Section 3.4, Eqs. (13)-(14)] The claimed countdown memory is not implemented by the recurrence T_t = R_t * sigma(T_{t-1} + Z_t) - 1. Since sigma is in (0,1), if R_t <= 1 then T_t < 0 at every step and the cell resets on every input, so no excited state is ever held. If R_t > 1, the map can have a positive fixed point (for example, with R_t = 3, T_t tends to about 1.4 rather than decaying to zero), so the variable does not spontaneously count down to the reset threshold. The paper provides no constraint on R_t, no initialization scheme, and no stability or gradient analysis that selects a genuine countdown regime. Moreover, the step from Eq. (13) to Eq. (14) is not an Euler discretization: the coefficient (1 - 1/tau) is replaced by R_t, and a sigmoid and a -1 term are inserted without justification. The central claim that PETNN's memory mechanism stores long-term dependencies is therefore unsupported by the model's own equations.
  2. [Section 3.2, Eq. (3) and Eq. (5); Appendix B, Algorithm 1] The reset switch m is defined inconsistently. The prose says 'set m to 0, if Tt <= 0, otherwise 1', but Eq. (5) states m = 1 if T_t < 0 and m = 0 if T_t >= 0, while Algorithm 1 sets m <- 1 when T_t <= 0. Additionally, Algorithm 1 computes T_t <- R_t * (T_{t-1} + Z_t) - 1 with no sigmoid, unlike Eq. (4). Because m controls whether the cell state is reset or accumulated, these inconsistencies change the model's behavior and make the reported results irreproducible from the text alone.
  3. [Tables 1, 2, 3, 8] All results are reported as single numbers with no error bars or statistical significance tests, even though Appendix C states that 'All experiments are repeated three times.' With a single point estimate per model, the Abstract's claim that 'PETNN outperforms transformer-based methods across various sequence tasks' is not statistically supported. Moreover, Table 3, the text sentiment task, has no Transformer or attention baseline at all, so the claim of outperforming transformer-based methods is not tested on that task. The paper should report means with standard deviations over seeds and add a transformer/attention baseline to the IMDB experiment.
  4. [Section 5.1 and Eq. (8)] The time-series results were produced after removing one embedding because of NaN, described as an 'unknown issue.' This is a post-hoc modification of the model after observing training failure, and the paper does not quantify the effect of the change or compare against the full architecture. A plausible cause is visible in Eq. (8): during a no-reset stretch, C_t = C_{t-1} + Z_c accumulates without normalization and can grow without bound. The paper should report diagnostics for T_t and C_t trajectories, explain the NaN episode, and show that the reported results are stable to the embedding choice. Without this, the empirical wins in Tables 1 and 2 cannot be attributed to the proposed memory mechanism.
minor comments (8)
  1. [Abstract] Typo: 'an effective recurrent structure' should be 'a effective' or, better, 'an effective' is correct, but 'we proposePhysical-inspired' in Section 1 is missing a space.
  2. [Section 3.4] Eq. (12) uses Z_c(t) as the energy injection term, but Eq. (13) uses Z_t; the relationship between these two quantities is never defined.
  3. [Appendix B, Algorithm 1] In the initialization step, R_t is written as W_Rt * X + b_I_t; the bias should presumably be b_R_t rather than b_I_t.
  4. [Eq. (9)] The expression S_{t-1} * (1-m) * C_{t-1} is ambiguous; it should be written using explicit concatenation or bracket notation to make clear which quantities are concatenated.
  5. [Tables 1 and 2] The captions mention results in red and bold, but the tables show no colors; the captions should be updated to match the rendered table, and the per-prediction-length breakdown should be provided so that the average over lengths can be assessed.
  6. [Table 3] The model column contains a formatting artifact, 'T EXT CNN'; this should be corrected.
  7. [Section 5.1] The sentence claiming an average '60%' reduction in MSE/MAE would benefit from a definition of how the average is computed across datasets and prediction lengths, and from a confidence interval.
  8. [Section 6, Figure 4] The figure lacks axis labels and a clear description of how the four update methods were configured; numeric results or a table should accompany the figure.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: PETNN's physics analogy is rhetorical, not a reduction of empirical claims to fitted inputs or self-citations.

full rationale

The central claims of the paper are empirical: PETNN is benchmarked against Transformer-based and SOTA models on held-out test sets, and the parameters (R_t, I_t, gates, and the state updates) are optimized on training data through standard gradient descent. No fitted constant is later renamed as a prediction, and no quantity is derived by definition from the quantity it is supposed to predict. The physics/energy-transition narrative is an analogy used to motivate the update equations; even if the step from Eq. (13) to Eq. (14) is not a faithful discretization and the recurrence's memory behavior is problematic, that is an internal-consistency and correctness concern, not circularity, because the empirical comparisons do not depend on the physics derivation. There are no load-bearing self-citations: the cited physics sources are external background, and the benchmark/code references (e.g., TimesNet/TSLib) are used as a standard evaluation framework rather than to justify the architecture. No uniqueness theorem or prior-work ansatz is invoked to make a design choice forced. Therefore no circular step can be exhibited with the required equation-level reduction, and the appropriate finding is no significant circularity.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central empirical claim relies on standard learned parameters (the gate matrices) plus two hand-designed, physics-flavored components: the input-dependent time-decay R_t and the reset-to-ground-state mechanism. These are not derived from physical theory, despite Sec. 3.4's claim of first-principles rigor; they are architectural choices. The quantum terminology is metaphorical and introduces no new physical entities.

free parameters (6)
  • Time decay network (W_Rt, b_Rt) = learned
    Controls the decay of remaining time T_t; replaces the physical relaxation time tau with a learned input-dependent function (Eq. 2, Eq. 14).
  • Ground-state network (W_It, b_It) = learned
    Sets the cell-state value after reset (Eq. 2, Eq. 7).
  • Update-gate network (W_Zw, b_Zw) = learned
    Mixes previous and candidate hidden states in Eq. (10); behaves like a GRU update gate.
  • Energy-injection and time-increment networks (W_Zc, b_Zc; W_Zt, b_Zt) = learned
    Standard learned projections for cell-state and time updates (Eq. 1).
  • Reset threshold (T_t <= 0) = 0
    Hard-coded threshold for when the cell releases energy and resets (Eq. 5, Algorithm 1).
  • Cell dimension (64 for PETNN in most experiments) = 64
    Chosen by the authors for forecasting and sentiment tasks (Appendix C).
assumptions (4)
  • standard math Sigmoid activation yields values in (0,1), bounding the remaining time T_t to (-1, R_t).
    Used implicitly in Eq. (3) and (4) to keep T_t bounded; this follows from properties of the logistic function.
  • ad hoc to paper The continuous energy-transition ODE is a valid analogue for memory dynamics; discretization with Euler step and subsequent 'refinement' preserves the intended behavior.
    Sec. 3.4 Eq. (12)-(14) replaces tau with learned R_t and inserts sigma and -1; this is an assumption, not a derivation.
  • domain assumption The hard reset to ground state when T_t <= 0 mitigates vanishing gradients better than LSTM-style gates.
    Asserted in Sec. 1 and Sec. 5 but not proven; requires empirical validation, which the paper only partially provides.
  • domain assumption The linear projections W for each gate are sufficient to capture the needed input-state interactions.
    Standard ML assumption; no expressivity analysis is given.

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Cite this review

Pith. "Pith review of Physics-inspired Energy Transition Neural Network for Sequence Learning." pith.science (2026). https://pith.science/paper/MBJL6W7Q

@misc{pith2026250503281,
  author       = {Pith},
  title        = {Pith review of: Physics-inspired Energy Transition Neural Network for Sequence Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MBJL6W7Q}},
  note         = {Machine review of arXiv:2505.03281}
}
read the original abstract

Recently, the superior performance of Transformers has made them a more robust and scalable solution for sequence modeling than traditional recurrent neural networks (RNNs). However, the effectiveness of Transformer in capturing long-term dependencies is primarily attributed to their comprehensive pair-modeling process rather than inherent inductive biases toward sequence semantics. In this study, we explore the capabilities of pure RNNs and reassess their long-term learning mechanisms. Inspired by the physics energy transition models that track energy changes over time, we propose a effective recurrent structure called the``Physics-inspired Energy Transition Neural Network" (PETNN). We demonstrate that PETNN's memory mechanism effectively stores information over long-term dependencies. Experimental results indicate that PETNN outperforms transformer-based methods across various sequence tasks. Furthermore, owing to its recurrent nature, PETNN exhibits significantly lower complexity. Our study presents an optimal foundational recurrent architecture and highlights the potential for developing effective recurrent neural networks in fields currently dominated by Transformer.

Figures

Figures reproduced from arXiv: 2505.03281 by the authors.

Figure 1
Figure 1. Quantum theory explains the energy transition model through the processes of absorption and release. transition can be found in Appendix A. Moreover, we refer interested readers to (Griffiths & Schroeter, 2018). Inspired by this theory, our model captures and retains in￾formative features in a way that resembles energy transition model theory. Just as excited states in energy transition mod￾els are deterministic, de… view at source ↗
Figure 2
Figure 2. A basic neuron in PETNN. The black waveform repre￾sents stored neuronal information over time. When the signal reaches the red dashed line, the neuron releases this information, returning to ground state. 3.1. Physics-inspired Energy Transition Neuron Inspired by the energy transition model, we design a neuron structure. As shown in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Comparision of Different Update Methods. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Visualization of ETTm2 prediction by different models under the input-96-predict-336 setting.The blue lines stand for the ground truth and the orange lines stand for the prediction [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: Visualization of hidden state in last step 15 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]

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Reference graph

Works this paper leans on

37 extracted references · 12 canonical work pages

  1. [1]

    Anderson, O. D. and Kendall, M. G. Time-series. 2nd edn. The Statistician, 25: 0 308, 1976. URL https://api.semanticscholar.org/CorpusID:134001785

    work page 1976

  2. [2]

    xlstm: Extended long short-term memory, 2024

    Beck, M., Pöppel, K., Spanring, M., Auer, A., Prudnikova, O., Kopp, M., Klambauer, G., Brandstetter, J., and Hochreiter, S. xlstm: Extended long short-term memory, 2024. URL https://arxiv.org/abs/2405.04517

    arXiv 2024

  3. [3]

    Learning long-term dependencies with gradient descent is difficult

    Bengio, Y., Simard, P., and Frasconi, P. Learning long-term dependencies with gradient descent is difficult. IEEE Transactions on Neural Networks, 5 0 (2): 0 157--166, 1994. doi:10.1109/72.279181

    doi:10.1109/72.279181 1994

  4. [4]

    Quasi-recurrent neural networks

    Bradbury, J., Merity, S., Xiong, C., and Socher, R. Quasi-recurrent neural networks. arXiv preprint arXiv:1611.01576, 2016

    arXiv 2016

  5. [5]

    O., and Pfister, T

    Chen, S.-A., Li, C.-L., Yoder, N., Arik, S. O., and Pfister, T. Tsmixer: An all-mlp architecture for time series forecasting, 2023. URL https://arxiv.org/abs/2303.06053

    arXiv 2023

  6. [6]

    Learning phrase representations using rnn encoder-decoder for statistical machine translation, 2014

    Cho, K., van Merrienboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., and Bengio, Y. Learning phrase representations using rnn encoder-decoder for statistical machine translation, 2014. URL https://arxiv.org/abs/1406.1078

    arXiv 2014

  7. [7]

    Empirical evaluation of gated recurrent neural networks on sequence modeling, 2014

    Chung, J., Gulcehre, C., Cho, K., and Bengio, Y. Empirical evaluation of gated recurrent neural networks on sequence modeling, 2014. URL https://arxiv.org/abs/1412.3555

    arXiv 2014

  8. [8]

    T., Martin, R

    Connor, J. T., Martin, R. D., and Atlas, L. E. Recurrent neural networks and robust time series prediction. IEEE transactions on neural networks, 5 0 (2): 0 240--254, 1994

    work page 1994

Show all 37 references
  1. [9]

    Cryer, J. D. and Kellet, N. Time series analysis. Springer, 1991

    1991

  2. [10]

    S., Giampaolo, F., Rozza, G., Raissi, M., and Piccialli, F

    Cuomo, S., Di Cola, V. S., Giampaolo, F., Rozza, G., Raissi, M., and Piccialli, F. Scientific machine learning through physics--informed neural networks: Where we are and what's next. Journal of Scientific Computing, 92 0 (3): 0 88, Jul 2022. doi:10.1007/s10915-022-01939-z

    2022 doi

  3. [11]

    The mnist database of handwritten digit images for machine learning research [best of the web]

    Deng, L. The mnist database of handwritten digit images for machine learning research [best of the web]. IEEE Signal Processing Magazine, 29 0 (6): 0 141--142, 2012. doi:10.1109/MSP.2012.2211477

    2012

  4. [12]

    Über einen die erzeugung und verwandlung des lichtes betreffenden heuristischen gesichtspunkt

    Einstein, A. Über einen die erzeugung und verwandlung des lichtes betreffenden heuristischen gesichtspunkt. Annalen der Physik, 322 0 (6): 0 132--148, 1905. doi:https://doi.org/10.1002/andp.19053220607. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.19053220607

    1905 doi

  5. [13]

    Griffiths, D. J. and Schroeter, D. F. Introduction to Quantum Mechanics. Cambridge University Press, 3 edition, 2018

    2018

  6. [14]

    and Dao, T

    Gu, A. and Dao, T. Mamba: Linear-time sequence modeling with selective state spaces, 2024. URL https://arxiv.org/abs/2312.00752

    2024 arXiv

  7. [15]

    Hamilton, J. D. Time series analysis. Princeton university press, 2020

    2020

  8. [16]

    and Schmidhuber, J

    Hochreiter, S. and Schmidhuber, J. Long short-term memory. Neural computation, 9 0 (8): 0 1735--1780, 1997

    1997

  9. [17]

    and Athanasopoulos, G

    Hyndman, R. and Athanasopoulos, G. Forecasting: Principles and Practice. OTexts, Australia, 2nd edition, 2018

    2018

  10. [18]

    Energy transition from molecules to atoms and photons

    Khan, N., Kalair, E., Abas, N., Kalair, A., and Kalair, A. Energy transition from molecules to atoms and photons. Engineering Science and Technology, an International Journal, 22 0 (1): 0 185--214, 2019. ISSN 2215-0986. doi:https://doi.org/10.1016/j.jestch.2018.05.002. URL htt...

    2019 doi

  11. [19]

    Convolutional neural networks for sentence classification, 2014

    Kim, Y. Convolutional neural networks for sentence classification, 2014. URL https://arxiv.org/abs/1408.5882

    2014 arXiv

  12. [20]

    Krizhevsky, A., Sutskever, I., and Hinton, G. E. Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25, 2012

    2012

  13. [21]

    Modeling long-and short-term temporal patterns with deep neural networks

    Lai, G., Chang, W.-C., Yang, Y., and Liu, H. Modeling long-and short-term temporal patterns with deep neural networks. In SIGIR, 2018

    2018

  14. [22]

    Y., and Tegmark, M

    Liu, Z., Wang, Y., Vaidya, S., Ruehle, F., Halverson, J., Soljačić, M., Hou, T. Y., and Tegmark, M. Kan: Kolmogorov-arnold networks, 2024. URL https://arxiv.org/abs/2404.19756

    2024 arXiv

  15. [23]

    The quantum theory of light

    Loudon, R. The quantum theory of light. OUP Oxford, 2000

    2000

  16. [24]

    PeMS. Traffic . http://pems.dot.ca.gov/, 2015

    2015

  17. [25]

    Pennington, J., Socher, R., and Manning, C. D. Glove: Global vectors for word representation. In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pp.\ 1532--1543, 2014

    2014

  18. [26]

    On gravity's role in quantum state reduction

    Penrose, R. On gravity's role in quantum state reduction. General Relativity and Gravitation, 28 0 (5): 0 581--600, May 1996. ISSN 1572-9532. doi:10.1007/BF02105068. URL https://doi.org/10.1007/BF02105068

    1996 doi

  19. [27]

    ElectricityLoadDiagrams20112014

    Trindade, A. ElectricityLoadDiagrams20112014 . UCI Machine Learning Repository, 2015. DOI : https://doi.org/10.24432/C58C86

    2015 doi

  20. [28]

    Tsay, R. S. Analysis of financial time series. John wiley & sons, 2005

    2005

  21. [29]

    N., Kaiser, ., and Polosukhin, I

    Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, ., and Polosukhin, I. Attention is all you need. Advances in neural information processing systems, 30, 2017

    2017

  22. [30]

    General properties of entropy

    Wehrl, A. General properties of entropy. Rev. Mod. Phys., 50: 0 221--260, Apr 1978. doi:10.1103/RevModPhys.50.221. URL https://link.aps.org/doi/10.1103/RevModPhys.50.221

    1978 doi

  23. [31]

    Wetterstation . Weather . https://www.bgc-jena.mpg.de/wetter/, 2014

    2014

  24. [32]

    Etsformer: Exponential smoothing transformers for time-series forecasting, 2022

    Woo, G., Liu, C., Sahoo, D., Kumar, A., and Hoi, S. Etsformer: Exponential smoothing transformers for time-series forecasting, 2022. URL https://arxiv.org/abs/2202.01381

    2022 arXiv

  25. [33]

    Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting, 2022

    Wu, H., Xu, J., Wang, J., and Long, M. Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting, 2022. URL https://arxiv.org/abs/2106.13008

    2022 arXiv

  26. [34]

    Timesnet: Temporal 2d-variation modeling for general time series analysis

    Wu, H., Hu, T., Liu, Y., Zhou, H., Wang, J., and Long, M. Timesnet: Temporal 2d-variation modeling for general time series analysis. In International Conference on Learning Representations, 2023

    2023

  27. [35]

    Are transformers effective for time series forecasting?, 2022

    Zeng, A., Chen, M., Zhang, L., and Xu, Q. Are transformers effective for time series forecasting?, 2022. URL https://arxiv.org/abs/2205.13504

    2022 arXiv

  28. [36]

    Informer: Beyond efficient transformer for long sequence time-series forecasting, 2021

    Zhou, H., Zhang, S., Peng, J., Zhang, S., Li, J., Xiong, H., and Zhang, W. Informer: Beyond efficient transformer for long sequence time-series forecasting, 2021. URL https://arxiv.org/abs/2012.07436

    2021 arXiv

  29. [37]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

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