pith. sign in

arxiv: 2605.19249 · v1 · pith:IZSWDT4Ynew · submitted 2026-05-19 · 💻 cs.LG

Beyond Extrapolation: Knowledge Utilization Paradigm with Bidirectional Inspiration for Time Series Forecasting

Liu Chong , Yingjie Zhou , Hao Li , Pengyang Wang , Qingsong Wen , Ce Zhu This is my paper

Pith reviewed 2026-05-20 07:36 UTC · model grok-4.3

classification 💻 cs.LG
keywords time series forecastingbidirectional inspirationcontinuation proxyinductive biasknowledge utilizationforecasting backbonesgating fusion
0
0 comments X

The pith

Time series forecasters gain from a proxy of post-target trajectory continuations distilled only from training data.

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

The paper claims that most forecasting models map history directly to a target window but miss useful structural signals from how the series would naturally continue afterward. KUP-BI addresses this by building an approximate proxy of that post-target continuation from a library of past training trajectories, then feeding the proxy into any standard backbone through a simple gating fusion. The result supplies an inductive bias toward typical continuation patterns rather than leaving the model to extrapolate solely from its parameters. A reader would care because the method requires no new data or future leakage and adds only modest overhead while lifting accuracy on real tasks such as energy and transport forecasting.

Core claim

By distilling continuation-style knowledge as an approximate post-target continuation proxy from a train-only historical library and integrating it into standard forecasting backbones via a lightweight feature-level gating module, the model obtains bidirectional inspiration that exploits the natural history-target-continuation chain for more stable forecasts without introducing information beyond the training trajectories.

What carries the argument

KUP-BI (Knowledge Utilization Paradigm with Bidirectional Inspiration), which distills an approximate post-target continuation proxy from training trajectories and fuses it with the input stream through feature-level gating to supply a structured inductive bias.

If this is right

  • Forecasting backbones receive a structured inductive bias for typical continuation patterns.
  • Performance improves consistently on six public datasets with only small added overhead.
  • The method avoids any information beyond what is already present in the training trajectories.
  • Forecasts become more stable by following the full natural history-to-target-to-continuation chain.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same proxy-construction step could be tested on non-stationary series to check whether the historical library still yields useful guidance under distribution shift.
  • This library-based bias might complement other sequence models in domains such as video frame prediction where post-frame evolution patterns are informative.
  • Replacing the gating fusion with a learned attention mechanism over the proxy could be compared directly to measure whether the lightweight design is optimal.

Load-bearing premise

That an approximate post-target continuation proxy distilled from a train-only historical library supplies useful structural knowledge for the current input that is not already captured by standard one-way extrapolation and that fusing it via gating improves forecasts without introducing leakage or overfitting.

What would settle it

Train and evaluate the same backbone with the continuation-proxy stream and gating module removed; if accuracy on the six public benchmarks shows no gain or a drop, the value of the bidirectional proxy would be falsified.

Figures

Figures reproduced from arXiv: 2605.19249 by Ce Zhu, Hao Li, Liu Chong, Pengyang Wang, Qingsong Wen, Yingjie Zhou.

Figure 1
Figure 1. Figure 1: Illustration of KUP-BI. (a) Traditional one-way fore￾casting maps the history (input) to the target (output), as the true post-target continuation (PTC) is unavailable at inference time (marked with ×). (b) KUP-BI introduces a continuation-style aux￾iliary stream as an approximate proxy of the PTC, constructed from training trajectories via a PTC proxy estimator, and fuses it with the backbone to provide c… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of KUP-BI. (a) Training-only retrieval library. Each training trajectory is decomposed into a natural chain (Hj , Yj , Fj ) (history, target, and post-target continuation). We convert it into a retrieval entry (H˜ j , Rj ), where the key H˜ j is obtained from the history via last-step offsetting (Han et al., 2025), and the value Rj is produced by applying a ratio oper￾ator to (Hj , Fj ), encoding … view at source ↗
Figure 4
Figure 4. Figure 4: Prediction curves of DLinear and DLinear with KUP-BI under different prediction lengths. 5. Conclusion and Future Work We presented KUP-BI, a knowledge-utilization paradigm that augments time series forecasting with a continuation￾style auxiliary stream. The auxiliary stream is constructed from training-only chains using simple ratio-style trans￾formations, and is fused with the main stream through a light… view at source ↗
Figure 3
Figure 3. Figure 3: examines the sensitivity of KUP-BI to three key hyperparameters on ETTh1 with a DLinear backbone. Effect of Top-k. Varying Top-k among {1, 3, 5, 7, 9} results in nearly unchanged MSE across all horizons, indicating that KUP-BI is largely insensitive to the choice of Top-k. Effect of α. Performance is more sensitive to α, which con￾trols the fusion strength between the historical stream and the auxiliary co… view at source ↗
Figure 5
Figure 5. Figure 5: Sensitivity Analysis of KUP-BI Hyperparameters on DLinear across ETTh1 and ETTh2. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Sensitivity Analysis of KUP-BI Hyperparameters on xPatch across ETTh1 and ETTh2. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
read the original abstract

Time-series forecasting is critical in various scenarios, such as energy, transportation, and public health. However, most existing forecasters rely primarily on one-way inference, \textit{i.e.}, mapping \textbf{history} to \textbf{target}, and overlook the structural information provided by a revised natural chain (``\textbf{history} (model input) -- \textbf{target} (ground-truth output) -- \textbf{post-target continuation}''). The post-target continuation records how trajectories evolve after the target, which can help stabilize forecasting, but it is not observable at inference time. In this work, we aim to obtain an approximate proxy of the post-target continuation for the current input, providing structural knowledge for bidirectional forecasting. This idea is instantiated as KUP-BI (Knowledge Utilization Paradigm with Bidirectional Inspiration), a new time-series modeling paradigm that distills continuation-style knowledge (as an approximate post-target continuation proxy) from a \emph{train-only} historical library and integrates it into standard forecasting backbones. The input stream and the continuation-proxy stream are fused via a lightweight feature-level gating module. This design does not introduce information beyond what is already contained in the training trajectories; instead, it provides a structured inductive bias that helps backbones exploit typical continuation patterns rather than relying solely on parametric extrapolation. Experimental results on six public datasets show that KUP-BI consistently improves the forecasting performance of state-of-the-art models, with small additional overhead.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes KUP-BI, a new modeling paradigm for time series forecasting that distills an approximate post-target continuation proxy from a train-only historical library and fuses it with the input stream via a lightweight feature-level gating module. This is intended to supply a structured inductive bias that helps standard backbones exploit typical continuation patterns rather than relying solely on one-way parametric extrapolation, yielding consistent improvements on six public datasets with small overhead.

Significance. If the central claim is substantiated, the work offers a moderate advance by reframing historical continuation patterns as an explicit inductive bias rather than additional data. The train-only constraint and emphasis on avoiding new information are positive design choices that could generalize across backbones. However, the significance hinges on whether the proxy remains useful under distribution shift, which is not yet demonstrated.

major comments (3)
  1. [§3.2] §3.2 (proxy distillation): the assertion that the continuation-proxy stream supplies no information beyond the training trajectories is load-bearing for the inductive-bias claim, yet the manuscript provides no formal argument or ablation showing that the retrieval/distillation step cannot encode target-window statistics or create circular dependence on the very patterns being predicted.
  2. [§4] §4 (experiments): no evaluation is reported on datasets exhibiting clear non-stationarity or concept drift, leaving the skeptic concern unaddressed; if train-library proxies encode continuation statistics from earlier regimes, fusion via the gating module may degrade rather than stabilize forecasts on shifted test distributions.
  3. [Table 2] Table 2 (or equivalent results table): reported gains are described only qualitatively; without per-dataset MSE/MAE deltas, standard deviations across runs, and an ablation that isolates the proxy stream from the gating module, it is impossible to determine whether the bidirectional component is responsible for the observed improvements or whether they arise from modest capacity increase.
minor comments (2)
  1. [Figure 1] The architectural diagram (presumably Figure 1) would benefit from explicit arrows distinguishing the train-only library retrieval from the inference-time proxy stream to clarify the no-leakage guarantee.
  2. [§3.1] Notation for the continuation proxy (e.g., the symbol used in the gating equations) is introduced late; moving the definition to §3.1 would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback. We address each major comment below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (proxy distillation): the assertion that the continuation-proxy stream supplies no information beyond the training trajectories is load-bearing for the inductive-bias claim, yet the manuscript provides no formal argument or ablation showing that the retrieval/distillation step cannot encode target-window statistics or create circular dependence on the very patterns being predicted.

    Authors: We agree that an explicit demonstration would reinforce the inductive-bias claim. The current design retrieves strictly from the train-only historical library with no access to target or post-target windows at inference or during proxy construction. In the revision we will add a dedicated ablation in §3.2 that compares proxy retrieval under controlled perturbations of target-window statistics and will include a concise argument showing that the distillation step operates exclusively on pre-target history, thereby precluding circular dependence. revision: yes

  2. Referee: [§4] §4 (experiments): no evaluation is reported on datasets exhibiting clear non-stationarity or concept drift, leaving the skeptic concern unaddressed; if train-library proxies encode continuation statistics from earlier regimes, fusion via the gating module may degrade rather than stabilize forecasts on shifted test distributions.

    Authors: We acknowledge that explicit testing under pronounced distribution shift would directly address this concern. While the six public benchmarks already contain realistic non-stationarities, we will augment the experimental section with additional results on datasets known for concept drift (e.g., synthetic regime-shift series and selected real-world streams with documented shifts) to verify that the gating fusion remains beneficial rather than detrimental under such conditions. revision: yes

  3. Referee: [Table 2] Table 2 (or equivalent results table): reported gains are described only qualitatively; without per-dataset MSE/MAE deltas, standard deviations across runs, and an ablation that isolates the proxy stream from the gating module, it is impossible to determine whether the bidirectional component is responsible for the observed improvements or whether they arise from modest capacity increase.

    Authors: We concur that quantitative reporting and targeted ablations are necessary for clarity. The revised manuscript will replace the qualitative description in Table 2 with per-dataset MSE/MAE deltas, report standard deviations over multiple random seeds, and add an ablation that disables the proxy stream while retaining the gating module (and vice versa) to isolate the contribution of the bidirectional inspiration from any capacity increase. revision: yes

Circularity Check

0 steps flagged

No load-bearing circularity; inductive bias from train-only library is self-contained

full rationale

The derivation chain relies on distilling an approximate post-target continuation proxy from a train-only historical library and fusing it via gating to supply a structured inductive bias. This is explicitly framed as not introducing information beyond training trajectories. No equations reduce the claimed improvement to a fitted parameter renamed as prediction, a self-definitional loop, or a self-citation chain that bears the central premise. The train-only constraint and external dataset evaluations keep the approach falsifiable and independent of the target result. Minor score accounts for the self-referential phrasing of the bias claim without any reduction by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Review performed on abstract only; the central claim rests on the domain assumption that historical continuations are representative proxies and on the modeling choice of a lightweight gating fusion.

axioms (1)
  • domain assumption Historical trajectories contain representative continuation patterns usable as proxies for unobserved post-target evolution.
    Invoked when the paper states that the proxy provides structural knowledge distilled from the train-only library.
invented entities (1)
  • continuation-proxy stream no independent evidence
    purpose: Approximate post-target continuation used as second input stream for bidirectional inspiration.
    New data stream introduced and fused via gating; no independent evidence outside the training library is provided.

pith-pipeline@v0.9.0 · 5808 in / 1347 out tokens · 54443 ms · 2026-05-20T07:36:41.452898+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages

  1. [1]

    The Twelfth International Conference on Learning Representations , year=

    Generative Learning for Financial Time Series with Irregular and Scale-Invariant Patterns , author=. The Twelfth International Conference on Learning Representations , year=

    work page

  2. [2]

    2024 , eprint=

    Retrieval Augmented Time Series Forecasting , author=. 2024 , eprint=

    work page 2024

  3. [3]

    Zeng, Wei and Lin, Chengqiao and Liu, Kang and Lin, Juncong and Tung, Anthony K. H. , journal=. Modeling Spatial Nonstationarity via Deformable Convolutions for Deep Traffic Flow Prediction , year=

    work page

  4. [4]

    Science , volume =

    Remi Lam and Alvaro Sanchez-Gonzalez and Matthew Willson and Peter Wirnsberger and Meire Fortunato and Ferran Alet and Suman Ravuri and Timo Ewalds and Zach Eaton-Rosen and Weihua Hu and Alexander Merose and Stephan Hoyer and George Holland and Oriol Vinyals and Jacklynn Stott and Alexander Pritzel and Shakir Mohamed and Peter Battaglia , title =. Science...

    work page 2023

  5. [5]

    Learning Customer Behaviors for Effective Load Forecasting , year=

    Wang, Xishun and Zhang, Minjie and Ren, Fenghui , journal=. Learning Customer Behaviors for Effective Load Forecasting , year=

    work page

  6. [6]

    The Thirty-Fifth

    Haoyi Zhou and Shanghang Zhang and Jieqi Peng and Shuai Zhang and Jianxin Li and Hui Xiong and Wancai Zhang , title =. The Thirty-Fifth

    work page

  7. [7]

    Autoformer: Decomposition Transformers with

    Haixu Wu and Jiehui Xu and Jianmin Wang and Mingsheng Long , booktitle=. Autoformer: Decomposition Transformers with

    work page

  8. [8]

    2008 , publisher=

    Time Series Analysis: Forecasting and Control , author=. 2008 , publisher=

    work page 2008

  9. [9]

    and Zhou, Joey Tianyi , journal=

    Li, Bing and Cui, Wei and Zhang, Le and Zhu, Ce and Wang, Wei and Tsang, Ivor W. and Zhou, Joey Tianyi , journal=. DifFormer: Multi-Resolutional Differencing Transformer With Dynamic Ranging for Time Series Analysis , year=

    work page

  10. [10]

    and Cheng, Xueqi , journal=

    Shao, Zezhi and Wang, Fei and Xu, Yongjun and Wei, Wei and Yu, Chengqing and Zhang, Zhao and Yao, Di and Sun, Tao and Jin, Guangyin and Cao, Xin and Cong, Gao and Jensen, Christian S. and Cheng, Xueqi , journal=. Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis , year=

    work page

  11. [11]

    Forty-second International Conference on Machine Learning , year=

    Patch-wise Structural Loss for Time Series Forecasting , author=. Forty-second International Conference on Machine Learning , year=

    work page

  12. [12]

    Forty-second International Conference on Machine Learning , year=

    TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting , author=. Forty-second International Conference on Machine Learning , year=

    work page

  13. [13]

    International Joint Conference on Artificial Intelligence(IJCAI) , year=

    Transformers in time series: A survey , author=. International Joint Conference on Artificial Intelligence(IJCAI) , year=

    work page

  14. [14]

    2016 , issn =

    Probabilistic electric load forecasting: A tutorial review , journal =. 2016 , issn =. doi:https://doi.org/10.1016/j.ijforecast.2015.11.011 , url =

    work page doi:10.1016/j.ijforecast.2015.11.011 2016

  15. [15]

    Traffic Flow Prediction With Big Data: A Deep Learning Approach , year=

    Lv, Yisheng and Duan, Yanjie and Kang, Wenwen and Li, Zhengxi and Wang, Fei-Yue , journal=. Traffic Flow Prediction With Big Data: A Deep Learning Approach , year=

    work page

  16. [16]

    1998 , publisher=

    Introduction to Approximation Theory , author=. 1998 , publisher=

    work page 1998

  17. [17]

    1993 , publisher=

    Constructive Approximation , author=. 1993 , publisher=

    work page 1993

  18. [18]

    International Conference on Learning Representations , year=

    Reversible Instance Normalization for Accurate Time-Series Forecasting against Distribution Shift , author=. International Conference on Learning Representations , year=

    work page

  19. [19]

    Forty-second International Conference on Machine Learning , year=

    Retrieval Augmented Time Series Forecasting , author=. Forty-second International Conference on Machine Learning , year=

    work page

  20. [20]

    2025 , eprint=

    TS-RAG: Retrieval-Augmented Generation based Time Series Foundation Models are Stronger Zero-Shot Forecaster , author=. 2025 , eprint=

    work page 2025

  21. [21]

    The Twelfth International Conference on Learning Representations , year=

    iTransformer: Inverted Transformers Are Effective for Time Series Forecasting , author=. The Twelfth International Conference on Learning Representations , year=

    work page

  22. [22]

    The Twelfth International Conference on Learning Representations , year=

    Periodicity Decoupling Framework for Long-term Series Forecasting , author=. The Twelfth International Conference on Learning Representations , year=

    work page

  23. [23]

    Forty-second International Conference on Machine Learning , year=

    TimeBase: The Power of Minimalism in Efficient Long-term Time Series Forecasting , author=. Forty-second International Conference on Machine Learning , year=

    work page

  24. [24]

    International Conference on Learning Representations , year=

    TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis , author=. International Conference on Learning Representations , year=

    work page

  25. [25]

    Luo donghao and wang xue , booktitle=. Modern. 2024 , url=

    work page 2024

  26. [26]

    International Conference on Learning Representations , year =

    A Time Series is Worth 64 Words: Long-term Forecasting with Transformers , author =. International Conference on Learning Representations , year =

    work page

  27. [27]

    Nadaraya, E. A. , title =. Theory of Probability & Its Applications , volume =. 1964 , doi =

    work page 1964

  28. [28]

    Watson , journal =

    Geoffrey S. Watson , journal =. Smooth Regression Analysis , urldate =

    work page

  29. [29]

    Bierens, Herman J. , year=. The Nadaraya–Watson kernel regression function estimator , booktitle=

    work page

  30. [30]

    , title =

    Tsybakov, Alexandre B. , title =

    work page

  31. [31]

    A Distribution-Free Theory of Nonparametric Regression , publisher =

    Gy. A Distribution-Free Theory of Nonparametric Regression , publisher =

    work page

  32. [32]

    Proceedings of the 30th International Conference on Neural Information Processing Systems , pages =

    Vinyals, Oriol and Blundell, Charles and Lillicrap, Timothy and Kavukcuoglu, Koray and Wierstra, Daan , title =. Proceedings of the 30th International Conference on Neural Information Processing Systems , pages =. 2016 , isbn =

    work page 2016

  33. [33]

    Meta-Learning in Neural Networks: A Survey , year=

    Hospedales, Timothy and Antoniou, Antreas and Micaelli, Paul and Storkey, Amos , journal=. Meta-Learning in Neural Networks: A Survey , year=

    work page

  34. [34]

    Proceedings of the AAAI Conference on Artificial Intelligence , volume=

    xPatch: Dual-Stream Time Series Forecasting with Exponential Seasonal-Trend Decomposition , author=. Proceedings of the AAAI Conference on Artificial Intelligence , volume=

    work page

  35. [35]

    Noise Reduction in Speech Processing , year=

    Benesty, Jacob and Chen, Jingdong and Huang, Yiteng and Cohen, Israel , title=. Noise Reduction in Speech Processing , year=. doi:10.1007/978-3-642-00296-0_5 , url=

    work page doi:10.1007/978-3-642-00296-0_5

  36. [36]

    Proceedings of the AAAI conference on artificial intelligence , volume=

    Are transformers effective for time series forecasting? , author=. Proceedings of the AAAI conference on artificial intelligence , volume=

    work page

  37. [37]

    The Twelfth International Conference on Learning Representations , year=

    TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting , author=. The Twelfth International Conference on Learning Representations , year=

    work page

  38. [38]

    Zhou, Tian and Ma, Ziqing and Wen, Qingsong and Wang, Xue and Sun, Liang and Jin, Rong , booktitle=

    work page

  39. [39]

    Zhang and Xiaoming Shi and Pin-Yu Chen and Yuxuan Liang and Yuan-Fang Li and Shirui Pan and Qingsong Wen , booktitle=

    Ming Jin and Shiyu Wang and Lintao Ma and Zhixuan Chu and James Y. Zhang and Xiaoming Shi and Pin-Yu Chen and Yuxuan Liang and Yuan-Fang Li and Shirui Pan and Qingsong Wen , booktitle=. Time-. 2024 , url=

    work page 2024

  40. [40]

    Forty-second International Conference on Machine Learning , year=

    LangTime: A Language-Guided Unified Model for Time Series Forecasting with Proximal Policy Optimization , author=. Forty-second International Conference on Machine Learning , year=

    work page

  41. [41]

    Williams , title =

    Billy M. Williams , title =. Transportation Research Record , volume =. 2001 , doi =

    work page 2001

  42. [42]

    and Chouliaras, G

    Vagropoulos, Stylianos I. and Chouliaras, G. I. and Kardakos, E. G. and Simoglou, C. K. and Bakirtzis, A. G. , booktitle=. Comparison of SARIMAX, SARIMA, modified SARIMA and ANN-based models for short-term PV generation forecasting , year=

    work page

  43. [43]

    2023 , issn =

    Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx , journal =. 2023 , issn =. doi:https://doi.org/10.1016/j.ijforecast.2022.03.001 , url =

    work page doi:10.1016/j.ijforecast.2022.03.001 2023

  44. [44]

    Long-term Forecasting with Ti

    Abhimanyu Das and Weihao Kong and Andrew Leach and Shaan K Mathur and Rajat Sen and Rose Yu , journal=. Long-term Forecasting with Ti. 2023 , url=

    work page 2023

  45. [45]

    The Thirty-eighth Annual Conference on Neural Information Processing Systems , year=

    TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables , author=. The Thirty-eighth Annual Conference on Neural Information Processing Systems , year=

    work page

  46. [46]

    THE WEB CONFERENCE 2025 , year=

    Exploiting Language Power for Time Series Forecasting with Exogenous Variables , author=. THE WEB CONFERENCE 2025 , year=

    work page 2025

  47. [47]

    2018 , isbn =

    Lai, Guokun and Chang, Wei-Cheng and Yang, Yiming and Liu, Hanxiao , title =. 2018 , isbn =. doi:10.1145/3209978.3210006 , pages =

    work page doi:10.1145/3209978.3210006 2018

  48. [48]

    PyTorch: An Imperative Style, High-Performance Deep Learning Library , url =

    Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen, Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca and Desmaison, Alban and Kopf, Andreas and Yang, Edward and DeVito, Zachary and Raison, Martin and Tejani, Alykhan and Chilamkurthy, Sasank and Steiner, Benoit and Fang, Lu an...

    work page

  49. [49]

    Akiba, Takuya and Sano, Shotaro and Yanase, Toshihiko and Ohta, Takeru and Koyama, Masanori , booktitle=

    work page

  50. [50]

    Scaling Learning Algorithms Towards

    Bengio, Yoshua and LeCun, Yann , booktitle =. Scaling Learning Algorithms Towards

    work page

  51. [51]

    and Osindero, Simon and Teh, Yee Whye , journal =

    Hinton, Geoffrey E. and Osindero, Simon and Teh, Yee Whye , journal =. A Fast Learning Algorithm for Deep Belief Nets , volume =

    work page

  52. [52]

    2016 , publisher=

    Deep learning , author=. 2016 , publisher=

    work page 2016