key,title,year,mechanism,where_computation_is_adapted,persistent_memory,sparse_local_writes,supervision_for_routing,exact_zero_budget_identity,code_available,license,closest_overlap_with_PRISME,verified_source_url
dehghani2019universal,Universal Transformers,2019,depth-shared block applied recurrently to all positions; ACT-style per-position halting,depth,no,no,ACT,no,yes (tensor2tensor),Apache-2.0,learned per-position halting of a shared block; dense update of every position's state,https://arxiv.org/abs/1807.03819
banino2021pondernet,PonderNet: Learning to Ponder,2021,"probabilistic halting over recurrent steps, geometric prior, expected loss + KL",depth,no,no,ACT (probabilistic),no,no official,n/a,learned stopping distribution; STOP as an action with expected-loss training,https://arxiv.org/abs/2107.05407
hawthorne2022perceiverar,"General-purpose, long-context autoregressive modeling with Perceiver AR",2022,few latents (last positions) cross-attend causally to long input; latents built per forward pass,none (fixed latent count),no,no,none,no,yes,Apache-2.0,small ephemeral latent set initialised from input and cross-attending to a causal source bank (PRISME S0 = e + P h_t; source bank),https://arxiv.org/abs/2202.07765
goyal2019rims,Recurrent Independent Mechanisms,2019,K recurrent modules; top-k activated per step via input attention; sparse communication,slots (which modules update),yes,yes (top-k modules updated),none (attention competition),no,yes,none in repo,only selected modules are written per step; competition for updates,https://arxiv.org/abs/1909.10893
raposo2024mixtureofdepths,Mixture-of-Depths,2024,per-layer top-k token routing with fixed capacity; others skip via residual,tokens,no,no,"none (router trained end-to-end via LM loss, aux causal predictor)",yes (non-routed tokens pass through residual exactly),no official,n/a,budgeted sparse compute allocation per token with exact residual bypass,https://arxiv.org/abs/2404.02258
geiping2025recurrentdepth,Scaling up Test-Time Compute with Latent Reasoning (Huginn),2025,prelude/recurrent core/coda; core iterated r times; random r at training,depth,no,no,none (zero-shot KL-threshold exit),no (one iteration still differs from a non-recurrent model),yes,Apache-2.0,global latent recurrence baseline; per-token adaptive exit without training,https://arxiv.org/abs/2502.05171
bae2025mixtureofrecursions,Mixture-of-Recursions,2025,shared recursive block; routers assign recursion depth per token; recursion-wise KV caching,depth x tokens,no,no,"other (expert-/token-choice router, aux losses)",no,yes,Apache-2.0,token-level routed recurrence; main Pareto-frontier baseline,https://arxiv.org/abs/2507.10524
zhu2025ouro,Scaling Latent Reasoning via Looped Language Models (Ouro),2025,weight-tied stack looped <=4x; per-step exit gate; entropy-regularised objective; Stage II gate fit to loss-improvement labels,depth,no,no,value-like (labels from per-token loss improvement L_{t-1}-L_t) + entropy reg.,no,weights yes; no official training code,"Apache-2.0 (weights, research notice)",learned stopping supervised by observed loss reduction between steps (binary continue/stop),https://arxiv.org/abs/2510.25741
wang2026recurtrace,RecurTrace: Adaptive Latent Reasoning with Loop-Time Memory,2026,Loop Memory Attention over the layer's own earlier-loop states (same position); sequence-level halting head,depth (sequence-level),no (loop-time only),no,oracle-stop (label = 1[min future loss < current loss - delta]),partial (LMA returns zero at loop 1; one loop = plain looped backbone),yes,Apache-2.0,oracle loss-reduction supervision of a stop decision; attention over own trajectory,https://arxiv.org/abs/2609.03379
ladhak2026elastic,One Model to Loop Them All: Elastic Latent Recurrence,2026,gated state update with learned step size; mixed loop counts per update; loop-index/budget conditioning (zero-init),depth (budget chosen externally),no,no,"none (budget-conditioned, not learned stopping)","no (empirical, not structural: one-loop accuracy ~matches baseline after training)",no (not verified),unverified,removing the 'one-loop tax'; gated/zero-init update is the training analogue of PRISME's exact bypass,https://arxiv.org/abs/2610.12582
behrouz2024titans,Titans: Learning to Memorize at Test Time,2024,neural long-term memory updated by surprise gradient at test time; persistent memory tokens,none (memory updated every step),yes,no (dense gradient update),none,no,"no official (unofficial lucidrains, MIT)",n/a,test-time memory writes; contrasts with PRISME's non-persistent slots,https://arxiv.org/abs/2501.00663
elhoushi2024layerskip,LayerSkip,2024,layer dropout + shared early-exit loss; self-speculative decoding,depth (early exit),no,no,other (confidence/early-exit),no (early exit changes output),yes,CC-BY-NC-4.0,depth adaptivity at inference via exits,https://arxiv.org/abs/2404.16710
graves2016act,Adaptive Computation Time for RNNs,2016,sigmoid halting units accumulated to threshold; ponder cost,depth,no,no,ACT,no,no official,n/a,origin of learned stopping with compute penalty (PRISME lambda*c_hat),https://arxiv.org/abs/1603.08983
hao2024coconut,Training LLMs to Reason in a Continuous Latent Space (Coconut),2024,last hidden state fed back as next input for fixed latent steps; CoT curriculum,none (fixed latent steps),no,no,none,no,yes,MIT,continuous latent thoughts before emitting a token,https://arxiv.org/abs/2412.06769
giannou2023looped,Looped Transformers as Programmable Computers,2023,constructive: looped transformer + scratchpad emulates a computer,none,n/a,n/a,none,n/a,no,n/a,expressivity argument for looping,https://arxiv.org/abs/2301.13196
saunshi2025reasoning,Reasoning with Latent Thoughts: On the Power of Looped Transformers,2025,k-layer block looped L times; theory + looping regulariser,depth (fixed),no,no,none,no,no,n/a,depth-via-looping vs parameters trade-off,https://arxiv.org/abs/2502.17416
fan2025loopedlength,Looped Transformers for Length Generalization,2025,loop count tied to problem length,depth,no,no,other (length-based),no,not verified,n/a,adaptive loop count,https://arxiv.org/abs/2409.15647
bae2024relaxed,Relaxed Recursive Transformers,2024,looped layers with per-loop LoRA; depth-wise batching / early exit,depth,no,no,other (early exit),no,not verified,n/a,parameter-shared recursion predecessor of MoR,https://arxiv.org/abs/2410.20672
goyal2023pause,Think before you speak: Pause Tokens,2023,learnable dummy tokens appended before answer; outputs discarded,none (fixed number of pauses),no,no,none,no,not verified,n/a,"ephemeral extra computation per prediction that does not persist (dense, unselected)",https://arxiv.org/abs/2310.02226
sun2025latenttokens,Enhancing Latent Computation in Transformers with Latent Tokens,2025,dummy latent tokens inserted before verbal tokens; loss dropped,none,no,no,none,no,not verified,n/a,ephemeral scratch tokens,https://arxiv.org/abs/2505.12629
zeng2025ponderlm,PonderLM,2025,feed back probability-weighted embedding for extra forward passes per token,none (fixed ponder steps),no,no,none,no,yes,Apache-2.0,per-token extra latent passes before committing,https://arxiv.org/abs/2505.20674
chen2025innerthinking,Inner Thinking Transformer,2025,Adaptive Token Routing selects critical tokens for extra inner iterations; residual thinking connections,tokens x depth,no,no,other (router trained end-to-end),unclear,not verified,n/a,selected tokens get more iterations,https://arxiv.org/abs/2502.13842
koishekenov2025etd,"Encode, Think, Decode",2025,iterate a subset of reasoning layers; adaptive per-token depth explored,depth (per token),no,no,other (threshold on halting value),partial (zero extra iterations = base pass),not verified,n/a,per-token iteration of selected layers,https://arxiv.org/abs/2510.07358
wu2025parallelloop,Parallel Loop Transformer,2025,cross-loop parallelism; first-loop KV sharing; gated sliding window,"depth (fixed, parallelised)",no,no,none,no,not verified,n/a,latency-neutral looping,https://arxiv.org/abs/2510.24824
fu2026thinkathard,Think-at-Hard (TaH),2026,neural decider triggers 2nd latent iteration only at likely-wrong tokens; depth-aware LoRA; duo-causal attention,tokens (binary: iterate or not),no,no,oracle-stop (token-mismatch oracle distilled),partial (skipped tokens keep first-pass output of co-trained backbone),yes,Apache-2.0,selective extra computation at few tokens with oracle supervision; bypass = first pass,https://arxiv.org/abs/2511.08577
you2026tah2,Improving Test-Time Scaling with Adaptive Looped Transformers (TaH2),2026,joint post-training of backbone + per-token iteration decider with lookahead depth supervision,tokens x depth,no,no,value (online labels = loss gain L_m - L_{m+1} from no-gradient lookahead branch; cost-sensitive BCE; no propensities),partial (stop at depth 1 = base pass of co-trained backbone),stated (thu-nics/TaH),Apache-2.0,CLOSEST to C2: counterfactual loss-difference labels from an executed extra branch; binary action only,https://arxiv.org/abs/2609.35748
jeddi2026loopformer,LoopFormer,2026,shortcut-consistency training on variable-length loop trajectories; step-size conditioning,depth (budget-conditioned),no,no,none,no,not verified,n/a,elastic depth,https://arxiv.org/abs/2602.11451
song2026adaponderlm,AdaPonderLM,2026,iteration-specific MLP gates with monotonic halting mask; KV reuse for halted tokens,tokens x depth,no,no,other (self-supervised gates),no,not verified,n/a,token-wise learned early exit in recurrence,https://arxiv.org/abs/2603.01914
noci2026lookahead,Thinking into the Future: Latent Lookahead Training,2026,"at selected positions, recursive latent steps supervised by next tau tokens",tokens (selected positions),no,no,other,no,not verified,n/a,extra latent compute at selected positions,https://arxiv.org/abs/2603.20219
frey2026adaptiveloops,Adaptive Loops and Memory in Transformers,2026,per-layer adaptive looping with learned halting + gated memory banks,depth,yes (memory banks),no,ACT-like (learned halting),no,not verified,n/a,looping + memory combination,https://arxiv.org/abs/2603.08391
park2026loopus,LoopUS,2026,encoder/looped block/decoder recast; selective gate; random deep supervision; confidence head,depth,no,no,other (confidence head),no,not verified,n/a,confidence-based stopping in looped LLMs,https://arxiv.org/abs/2605.11011
huang2026lrt,Latent Recurrent Transformer,2026,previous token's source-layer state reused as recurrent memory; one forward per token,none,yes (cross-token latent),no,none,no,not verified,n/a,cross-token latent recurrence (PRISME's source bank is read-only),https://arxiv.org/abs/2605.26797
li2026later,LaTER,2026,bounded latent exploration then explicit CoT; halting supervision,tokens (latent vs explicit),no,no,oracle-stop (supervised switch),no,yes,Apache-2.0,supervised halting of latent phase,https://arxiv.org/abs/2605.07315
sharma2026readout,Dense Supervision Is Not Enough: The Readout Blind Spot,2026,analysis of per-loop CE through scale-invariant readouts,depth,no,no,n/a,n/a,not verified,n/a,readout design in looped models,https://arxiv.org/abs/2606.24898
zeng2026depthattention,Depth-Attention,2026,query attends over earlier-layer keys at same position inside attention,none,no,no,none,no,not verified,n/a,cross-depth read at same position (cf. PRISME source bank),https://arxiv.org/abs/2606.05014
popescu2026adaptivedepth,Adaptive Depth in Looped Transformers: Diagnosing Learned Halting Gates,2026,diagnostic: gates vs post-hoc confidence readouts on fixed-prior trajectories,depth,no,no,analysis,n/a,not verified,n/a,evidence that jointly trained gates can underperform post-hoc rules,https://arxiv.org/abs/2607.20519
logan2026fixedpoint,Per-Token Fixed-Point Convergence in Depth-Recurrent Transformers,2026,training-free convergence exit per token,tokens x depth,no,no,none (convergence test),no,yes,MIT,training-free exit beats trained router,https://arxiv.org/abs/2607.14427
ye2026reflux,Write Back the Delta (ReFlux),2026,"router selects sparse deep->shallow feedback edges carrying Delta = z_s - z_d, written additively into a frozen backbone","slots (routes; per block, shared across tokens)",no (synchronous) / yes (streaming),yes (sparse selected routes),"other (LM loss + L1/L2, Gumbel-sigmoid; no counterfactual labels)",yes (no active edge => frozen backbone unchanged),yes,MIT,CLOSEST to C1+C3 jointly: sparse selected additive writes of a difference signal with exact bypass; but selection is per block not per token and no value supervision,https://arxiv.org/abs/2609.32457
locatello2020slot,Object-Centric Learning with Slot Attention,2020,K slots sampled per input; competitive cross-attention + GRU updates; all slots updated,none (fixed iterations),no,no (all slots updated),none,no,yes,Apache-2.0,ephemeral per-input slot bank refined by cross-attention,https://arxiv.org/abs/2006.15055
goyal2022workspace,Coordination Among Neural Modules Through a Shared Global Workspace,2022,bandwidth-limited workspace; specialists compete (top-k) to write; broadcast,slots (which specialists write),yes (workspace carried across steps),yes (top-k writers),none (attention competition),no,not verified,n/a,CLOSEST to C1's sparse competitive writes to a small slot workspace; but persistent and unsupervised,https://arxiv.org/abs/2103.01197
jaegle2021perceiver,Perceiver,2021,latent array cross-attends to inputs; latent self-attention; weight sharing,none,no,no,none,no,yes (deepmind-research),Apache-2.0,latent bottleneck cross-attending to a large input,https://arxiv.org/abs/2103.03206
graves2014ntm,Neural Turing Machines,2014,differentiable addressing; soft erase/add writes,none,yes,"no (soft, dense)",none,no,no official,n/a,learned read/write to memory,https://arxiv.org/abs/1410.5401
weston2014memory,Memory Networks,2014,memory with I/G/O/R components,none,yes,no,none,no,no official,n/a,memory-augmented reasoning,https://arxiv.org/abs/1410.3916
rae2016sparse,Scaling Memory-Augmented NNs with Sparse Reads and Writes (SAM),2016,top-k sparse differentiable reads/writes to large memory,slots (sparse addresses),yes,yes,none,no,no official,n/a,sparse writes for efficiency (persistent memory),https://arxiv.org/abs/1610.09027
wu2020memformer,Memformer,2020,"fixed-size memory slots read by cross-attention, written per segment",none,yes,no,none,no,not verified,n/a,slot memory read by cross-attention,https://arxiv.org/abs/2010.06891
bulatov2022rmt,Recurrent Memory Transformer,2022,memory tokens carried across segments,none,yes,no,none,no,yes,none in repo,memory tokens,https://arxiv.org/abs/2207.06881
ryoo2023ttm,Token Turing Machines,2023,token memory read/written by transformer controller via token summarisation,none,yes,no,none,no,yes (scenic),Apache-2.0,transformer as memory controller,https://arxiv.org/abs/2211.09119
berges2024memorylayers,Memory Layers at Scale,2024,sparsely activated product-key memory layers,slots (sparse keys),no (parameters),yes (sparse lookup),none,no,not verified,n/a,sparse memory access,https://arxiv.org/abs/2412.09764
darcet2023registers,Vision Transformers Need Registers,2023,"extra register tokens as scratch, discarded at output",none,no,no,none,no,not verified,n/a,ephemeral scratch tokens,https://arxiv.org/abs/2309.16588
dai2019transformerxl,Transformer-XL,2019,segment-level recurrence with cached states,none,yes (cache),no,none,no,yes,Apache-2.0,read-only cache of past states (PRISME source bank),https://arxiv.org/abs/1901.02860
rae2019compressive,Compressive Transformers,2019,compress old memories,none,yes,no,none,no,not verified,n/a,compressed past-state bank,https://arxiv.org/abs/1911.05507
gu2023mamba,Mamba,2023,selective state space; fixed-size recurrent state,none,yes (state),no,none,no,yes,Apache-2.0,fixed-state recurrence baseline,https://arxiv.org/abs/2312.00752
shazeer2017moe,Sparsely-Gated Mixture-of-Experts,2017,noisy top-k gating over experts,slots (experts),no,yes (sparse experts),none (gate via LM loss + balancing),no,not verified,n/a,discrete sparse routing,https://arxiv.org/abs/1701.06538
fedus2022switch,Switch Transformers,2022,top-1 expert routing per token,slots (experts),no,yes,none,no,not verified,n/a,discrete sparse routing,https://arxiv.org/abs/2101.03961
ernst2005tree,Tree-Based Batch Mode RL (fitted Q iteration),2005,fitted Q from logged transitions,n/a,n/a,n/a,value (fitted Q),n/a,n/a,n/a,value regression for discrete actions from logged data,https://www.jmlr.org/papers/v6/ernst05a.html
mnih2013atari,Playing Atari with Deep RL (DQN),2013,deep Q-network; greedy argmax over action values,n/a,n/a,n/a,value (Q-learning),n/a,n/a,n/a,greedy action selection from predicted action values,https://arxiv.org/abs/1312.5602
dudik2011doublyrobust,Doubly Robust Policy Evaluation and Learning,2011,DR off-policy estimator with logged propensities,n/a,n/a,n/a,other (off-policy evaluation),n/a,n/a,n/a,propensity-logged counterfactual estimation (PRISME label collection),https://arxiv.org/abs/1103.4601
bottou2013counterfactual,Counterfactual Reasoning and Learning Systems,2012,counterfactual estimation from randomised logs,n/a,n/a,n/a,other,n/a,n/a,n/a,counterfactual estimation with logged randomisation,https://arxiv.org/abs/1209.2355
swaminathan2015crm,Counterfactual Risk Minimization,2015,variance-regularised IPS from logged bandit feedback,n/a,n/a,n/a,other (CRM),n/a,n/a,n/a,learning from logged propensities,https://arxiv.org/abs/1502.02362
schuster2022calm,Confident Adaptive Language Modeling (CALM),2022,per-token early exit with calibrated confidence,depth (per token),no,no,other (confidence; consistency calibration),no,not verified,n/a,per-token adaptive depth,https://arxiv.org/abs/2207.07061
leviathan2023speculative,Speculative Decoding,2023,draft + verify sampling,none,no,no,none,n/a,not verified,n/a,compute-quality trade-off at inference,https://arxiv.org/abs/2211.17192
snell2024testtime,Scaling LLM Test-Time Compute Optimally,2024,compute-optimal test-time allocation by difficulty,none (token-level search),no,no,other,n/a,not verified,n/a,difficulty-dependent compute,https://arxiv.org/abs/2408.03314
ye2024physics,Physics of LMs 2.1: Grade-School Math,2024,controlled synthetic study of hidden reasoning; depth matters,none,no,no,none,n/a,not verified,n/a,evidence on depth vs reasoning,https://arxiv.org/abs/2407.20311
bachlechner2020rezero,ReZero,2020,residual branch scaled by zero-initialised scalar,none,no,no,none,yes (at init),not verified,n/a,zero-init exact identity insertion (C3),https://arxiv.org/abs/2003.04887
zhang2023controlnet,ControlNet,2023,zero convolutions on added branch; frozen backbone reproduced,none,no,no,none,yes (at init),yes,unverified,zero-init exact identity insertion (C3),https://arxiv.org/abs/2302.05543
alayrac2022flamingo,Flamingo,2022,tanh-gated cross-attention initialised at zero,none,no,no,none,yes (at init),no official,n/a,zero-init gated insertion (C3),https://arxiv.org/abs/2204.14198
ernst2026dsi,Distributed Sparse Interventions,2026,steer via sparse neuron set chosen iteratively,slots (neurons),no,yes (static sparse edits),other (task objective),yes (no intervention = base model),not verified,n/a,"sparse latent interventions (static, not per-token learned)",https://arxiv.org/abs/2607.07128