Papers › Adaptive Rational Activations to Boost Deep Reinforcement Learning

Adaptive Rational Activations to Boost Deep Reinforcement Learning

18 Feb 2021arXiv:2102.09407archive 2025-07-28

Quentin Delfosse, Patrick Schramowski, Martin Mundt, Alejandro Molina, Kristian Kersting

Latest insights from biology show that intelligence not only emerges from the connections between neurons but that individual neurons shoulder more computational responsibility than previously anticipated. This perspective should be critical in the context of constantly changing distinct reinforcement learning environments, yet current approaches still primarily employ static activation functions. In this work, we motivate why rationals are suitable for adaptable activation functions and why their inclusion into neural networks is crucial. Inspired by recurrence in residual networks, we derive a condition under which rational units are closed under residual connections and formulate a naturally regularised version: the recurrent-rational. We demonstrate that equipping popular algorithms with (recurrent-)rational activations leads to consistent improvements on Atari games, especially turning simple DQN into a solid approach, competitive to DDQN and Rainbow.

PaperPDFCodeCode Syntology ran

In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.

For agents, Syntology's MCP tool lists every function and class Syntology harvested from this paper and whether it ran (how to connect): get_harvested_code_for_paper(arxiv_id="2102.09407")

Code

Syntology Ran 6 of 6 code samples harvested from 1 repository linked to this paper; 0 have no recorded run. Of those that ran: 6 ran · fixture could not drive it.

By repository: official repository: 3 samples from 1 repository, 3 ran; 3 identical to code first harvested elsewhere. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.

ml-research/rational_activations officialmentioned in papermentioned on GitHubpytorch report
ml-research/rational_rl officialmentioned in papermentioned on GitHubpytorch report
ml-research/rational_sl officialmentioned in papermentioned on GitHubpytorch report
k4ntz/activation-functions officialmentioned in paperpytorch report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

6 samples harvested; 6 ran; 0 honoured the contract we drafted; 0 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.

6ran · fixture could not drive it

Licence: 3 of the 6 samples are pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.

Harvested from k4ntz/activation-functions. Some samples are identical code Syntology first harvested from another repository; for those, this paper's copy is not located and its licence is not recorded. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.

Each sample ends with its code_sha256, Syntology's identity for that exact code. An agent fetches the stored sample with Syntology's MCP tool get_code(code_sha256="…") (how to connect); click an identity to copy that call.

Repository labels, per sample. official repository: The archive marks this repository official for the paper. named in the paper: The archive records that the paper mentions this repository; it is not marked official. community (archive-listed): In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper. found in paper text by Syntology: Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted. community: Not in the archive's code links for this paper; a community repository Syntology harvested. Samples from a repository marked official are listed first. Licence labels name the repository's licence as recorded at harvest. “Pointer only” means Syntology does not serve that copy's text, for one of four reasons: no licence file was found; the licence was not identified; the licence is recorded as permissive but that copy's record is not marked cleared; or the licence is outside the permissive list Syntology serves text under (MIT, Apache-2.0, BSD and similar). Some licences outside that list permit redistribution, such as WTFPL, and GPL-3.0 under its conditions; they are simply not on the list. Hover a licence label for the reason. File links open the file on GitHub at the default branch, which may have changed since the harvest.

Rational_PYTORCH_A_F k4ntz/activation-functions/activations/torch/rationals/rational_pytorch_functions.py official repository ran · fixture could not drive it fingerprinted MIT (permissive) · 6e9f17d4218ef85b · report
Rational_PYTORCH_B_F k4ntz/activation-functions/activations/torch/rationals/rational_pytorch_functions.py official repository ran · fixture could not drive it fingerprinted MIT (permissive) · b2ce1b13b9074606 · report
Rational_PYTORCH_C_F k4ntz/activation-functions/activations/torch/rationals/rational_pytorch_functions.py official repository ran · fixture could not drive it fingerprinted MIT (permissive) · 960dbf127ba74109 · report
Rational_PYTORCH_A_F identical code first harvested elsewhere ran · fixture could not drive it fingerprinted licence of this copy not recorded · 39ec3d1f9d97cc5c · report
Rational_PYTORCH_B_F identical code first harvested elsewhere ran · fixture could not drive it fingerprinted licence of this copy not recorded · 15a510212432a6c3 · report
Rational_PYTORCH_C_F identical code first harvested elsewhere ran · fixture could not drive it fingerprinted licence of this copy not recorded · 6e3e9a40d8b5f9f7 · report

Tasks

Atari GamesDeep Reinforcement LearningGeneral Reinforcement LearningImage ClassificationReinforcement LearningReinforcement Learning (RL)reinforcement-learning

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Atari Games Atari 2600 Asterix Rational DQN Average Score 18109 #30 of 49 Archive leaderboard report
Atari Games Atari 2600 Asterix Recurrent Rational DQN Average Score 12621 #37 of 49 Archive leaderboard report
Atari Games Atari 2600 Battle Zone Recurrent Rational DQN Average Score 25749 #30 of 47 Archive leaderboard report
Atari Games Atari 2600 Battle Zone Rational DQN Average Score 23403 #35 of 47 Archive leaderboard report
Atari Games Atari 2600 Breakout Recurrent Rational DQN Average Score 336 #40 of 58 Archive leaderboard report
Atari Games Atari 2600 Breakout Rational DQN Average Score 316 #41 of 58 Archive leaderboard report
Atari Games Atari 2600 Enduro Rational DQN Average Score 1043 #30 of 48 Archive leaderboard report
Atari Games Atari 2600 Enduro Recurrent Rational DQN Average Score 957 #31 of 48 Archive leaderboard report
Atari Games Atari 2600 James Bond Recurrent Rational DQN Average Score 1137 #22 of 45 Archive leaderboard report
Atari Games Atari 2600 James Bond Rational DQN Average Score 1122 #23 of 45 Archive leaderboard report
Atari Games Atari 2600 Kangaroo Recurrent Rational DQN Average Score 5266 #28 of 47 Archive leaderboard report
Atari Games Atari 2600 Kangaroo Rational DQN Average Score 2941 #31 of 47 Archive leaderboard report
Atari Games Atari 2600 Pong Recurrent Rational DQN Average Score 18.13 #40 of 52 Archive leaderboard report
Atari Games Atari 2600 Pong Rational DQN Average Score 18.04 #41 of 52 Archive leaderboard report
Atari Games Atari 2600 Q*Bert Rational DQN Average Score 14436 #30 of 57 Archive leaderboard report
Atari Games Atari 2600 Q*Bert Recurrent Rational DQN Average Score 14080 #34 of 57 Archive leaderboard report
Atari Games Atari 2600 Seaquest Recurrent Rational DQN Average Score 7460 #27 of 57 Archive leaderboard report
Atari Games Atari 2600 Seaquest Rational DQN Average Score 6603 #29 of 57 Archive leaderboard report
Atari Games Atari 2600 Skiing Recurrent Rational DQN Average Score -23582 #16 of 23 Archive leaderboard report
Atari Games Atari 2600 Skiing Rational DQN Average Score -23487 #17 of 23 Archive leaderboard report
Atari Games Atari 2600 Space Invaders Recurrent Rational DQN Average Score 1395 #40 of 55 Archive leaderboard report
Atari Games Atari 2600 Space Invaders Rational DQN Average Score 650 #51 of 55 Archive leaderboard report
Atari Games Atari 2600 Tennis Recurrent Rational DQN Average Score 20.6 #10 of 43 Archive leaderboard report
Atari Games Atari 2600 Tennis Rational DQN Average Score 20.5 #11 of 43 Archive leaderboard report
Atari Games Atari 2600 Time Pilot Rational DQN Average Score 17632 #13 of 44 Archive leaderboard report
Atari Games Atari 2600 Time Pilot Recurrent Rational DQN Average Score 13261 #15 of 44 Archive leaderboard report
Atari Games Atari 2600 Tutankham Recurrent Rational DQN Average Score 184 #27 of 44 Archive leaderboard report
Atari Games Atari 2600 Tutankham Rational DQN Average Score 179 #29 of 44 Archive leaderboard report
Atari Games Atari 2600 Video Pinball Rational DQN Average Score 149712 #30 of 42 Archive leaderboard report
Atari Games Atari 2600 Video Pinball Recurrent Rational DQN Average Score 86942 #34 of 42 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Methods

1x1 ConvolutionAverage PoolingBatch NormalizationBottleneck Residual BlockConvolutionDQNDense ConnectionsDouble DQNDouble Q-learningExperience ReplayGlobal Average PoolingKaiming InitializationMax PoolingPELUQ-LearningRational Activation functionReLUResidual BlockResidual ConnectionTanh Activation

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections