Repeat parts of the model or keep intermediate information in memory while working through a problem. Some methods also learn how many passes to run.
For example: A model runs the same layers several times, updating the information it keeps between passes. If it has learned a stopping rule, it can decide when to produce its answer.
Recurrent depth and fixed-point models repeat computation in different ways. Geiping and colleagues reuse a transformer block, allowing the number of passes to change at inference. The implicit state-space models studied by Schöne and colleagues instead iterate toward a fixed point, with experiments testing when approximate convergence is sufficient. Both add computation without adding a written reasoning trace, but their stopping rules and training costs differ.
Sources: Recurrent-depth paper · Implicit state-space paper
Paper details: Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach · Implicit Language Models are RNNs: Balancing Parallelization and Expressivity
Dates usually refer to the first arXiv submission. Search or filter these papers →
Runs shared transformer blocks repeatedly, keeping earlier passes available to attention. A learned router chooses how many passes each token receives.
Pretrains a depth-recurrent language model whose computation can be extended at inference time, separating test-time compute from generated token length.
Connects implicit language models to recurrent computation and analyzes the trade-off between parallel training and expressive sequential depth.
Routes selected tokens through extra computation while reusing model parameters. Marks successive thinking steps so the model can distinguish one pass from the next.
Analyzes the expressive power of transformers that repeatedly apply shared layers, treating recurrent depth as a form of internal reasoning.
Adds hidden decoding tokens during pretraining, then discards their key/value cache entries after use. Keeps the original tokens' entries to preserve longer-range context.
Skips layers and compares shallow and deep models to examine what extra layers compute. In the models studied, later layers mostly make smaller refinements rather than adding new reasoning steps.
Formally compares explicit chain-of-thought computation with repeated internal transformations in looped transformer architectures.
Pretrains language models with repeated continuous-space pondering steps before token prediction.
Uses coupled recurrent modules operating at different timescales to perform iterative internal computation on difficult reasoning tasks.
Probes a depth-recurrent transformer to test what its repeated hidden-state computation represents and whether it behaves like a latent chain of thought.
Adapts the depth of pretrained language models at test time by selectively skipping or repeating layers.
Learns token-level routing across recursive depths so different positions can receive different amounts of internal computation.
Scales looped language models that reuse layers across recurrent depth and studies how performance changes with additional internal computation.
Adds recurrent depth to pretrained language models and trains them to use repeated internal computation without pretraining from scratch.
Uses dynamic looping to vary internal depth with problem difficulty and studies the resulting reasoning and efficiency trade-offs.
Uses differentiable masks to allocate a variable number of recurrent pondering steps to different token positions.
Trains switchable hidden-state recurrence with on-policy reinforcement learning and analyzes how the internal loop contributes to reasoning.
Stabilizes repeated transformer layers and stops looping when the hidden state converges, allowing the model to spend different amounts of computation on different problems.
Feeds both token embeddings and hidden states back through repeated transformer layers to connect successive steps of multi-hop reasoning.
Carries a cached middle-layer state from one token position into an earlier layer at the next position, providing localized temporal recurrence that can also be retrofitted into pretrained transformers.
Trains each transformer loop to anticipate a different future token, using token embeddings to guide its hidden state.
Studies when extra transformer loops improve an answer or make it worse. Gives a condition under which further loops cannot change the answer, and trains models toward this stable behavior.
Studies which transformer components should recur and introduces MixerLoop, which repeats the sequence mixer while applying the dense feed-forward component once.
Uses state interventions, probes, and feature ablations to study how hierarchical recurrent models solve Sudoku, mazes, and ARC tasks. Compares hierarchical and single-state recurrence, and distinguishes information that can be read from a state from information that causally affects an answer.
Tests when a hierarchical reasoner should revise the internal plan guiding its lower-level computation. Compares learned revision schedules with fixed schedules, separating whether a controller responds to its state from whether that response improves decisions.
Uses a task-specific proposer and small recurrent auxiliary network to iteratively refine continuous thoughts that a frozen language model then decodes.
Loops the middle half of a mixture-of-experts transformer twice while matching an unlooped baseline on computation, parameter count, and KV-cache size. Studies how the comparison changes with model scale and examines the attention patterns produced by revisiting layers.
Turns a diffusion denoiser into a recurrent puzzle solver by adding a persistent hidden state and removing timestep conditioning. Separates the role of denoising during training from the role of repeated updates and noise at inference.
Tracks information that can be decoded from, and altered within, repeated transformer layers. Finds that Ouro reconstructs this information each loop, while Huginn carries it forward.
Lets looped layers attend to their own earlier iteration states and learns a halting head that allocates recurrent depth per input.
Studies recurrent reasoning trajectories as dynamical systems on puzzles and mathematical logic. Links long solution times in the tested models to transient trapping near unstable states associated with nearly correct solutions.
Trains recurrent reasoners against a distribution of targets near each correct solution, using an adversarial objective instead of a single point target. Evaluates generalization and stability on maze, chess, and Sudoku tasks.
Learns a router that chooses how many recurrent passes each token receives, and keeps separate key/value caches for each pass.
Studies updates that initially increase support for a reference answer but overshoot when applied in full. Uses curvature along each update to explain failures and identify smaller useful steps.
Drafts future tokens from early loops while later loops verify current tokens, overlapping the work without training an extra model. Final verification preserves the full model's decoding behavior.
Studies how growing a model during training, reusing layers, and modifying the connections between repeated blocks affect language-model scaling. Compares shared and unshared weights and operators that normalize or reintroduce earlier representations.
Adds a small gated memory to a looped transformer and compares it with storing the full history of recurrent states. Uses a cellular-automaton task and language modeling to test whether memory remains useful as computation grows.
Inserts a hidden-state refinement step between consecutive text tokens in a recurrent transformer. Compares this extra thinking time with adding physical layers or transformer loops under matched computation budgets.
Uses intermediate loop depths to propose tokens that later loops verify. Arranges speculation across recurrent depths so that more of the draft and verification work can run together.
Uses differences between early- and late-loop predictions to adjust token sampling at inference time, without retraining the model.
Studies when a recurrent language model settles on which context tokens to attend to. Reuses that selected working set in later loops while still recomputing attention weights and hidden-state updates.
Compares how two looped-transformer training schemes solve multi-step tasks beyond their training length. Uses hidden-state interventions to identify how intermediate information moves through each model and where that process breaks down.
Combines a recurrent reasoner with sparse, compositional task embeddings for ARC puzzles. Studies how task-memory size, recurrent depth, and training horizon affect performance.
Regularizes fine-tuning of looped language models by randomly masking adapter updates at selected loops. The shared backbone still runs at every loop; the method targets adapter updates that otherwise become concentrated at particular depths.
Post-trains a looped reinforcement-learning policy to make useful decisions at several recurrent depths. Combines its original objective with distillation between neighboring depths, then uses agreement across depths to decide when to stop.
Uses shallower-loop queries with values from deeper loops to improve draft-token predictions in a looped language model. Studies the different rates at which queries, keys, and values develop, and uses that difference for self-speculative decoding.
Trains an iteration controller to give extra transformer loops only to tokens whose predictions benefit from them. Compares reasoning accuracy as both output length and internal computation increase.
Builds a looped mixture-of-experts model by pooling experts across layers and revisiting them. Shares experts and routing across passes while giving each pass its own attention parameters.
Compares loop layouts and ways of passing information between loops in language models. Examines when recurrence helps reasoning and when it helps less on knowledge-dependent tasks.
Adjusts the size of each hidden-state update based on whether recent updates make consistent progress or fluctuate. Tests the resulting scheduler with and without additional training.
Separates hidden-state updates into attracting and rotating components to reduce errors from running a recurrent reasoner for more steps. Tests a tensor-based implementation on logical and multi-hop reasoning tasks.
Treats each recurrent hidden-state update as an optimization step and derives loop designs from this view. Introduces OperLoop, combining adaptive step sizes and weight decay.
Uses a shared transformer block to refine a reinforcement-learning policy's internal state before choosing an action. Learns to vary the number of loops with the current state, and studies adaptive computation in puzzles and robotic-control tasks.
Extends shared-module and whole-model looping to vision-language models, repeatedly updating a joint visual-language state. Trains from scratch through language and multimodal stages and evaluates visual understanding and reasoning.
Learns when to perform another internal reasoning step, recall stored evidence or intermediate states, or emit a token. Trains these choices by branching over alternative actions and measuring their effects on the next emitted token.
Uses graph-walk tasks to study how a looped transformer performs different computations with the same weights. Tests whether changing the state entering a loop can select its computation, using steering and activation-patching experiments.
Compares recursive reasoning models under a common training and evaluation setup. Isolates the effects of gradient propagation, batch size, state updates, and hierarchical structure on algorithmic tasks and generalization.
Fits scaling laws that jointly account for recurrent depth, expert sparsity, model size, and training data in looped mixture-of-experts models. Uses them to study how to allocate resources under compute and memory constraints.
Gives training recipes for looped language models both from scratch and by converting pretrained models. Uses controlled data and compute comparisons to separate the benefit of recurrence from the training setup.
Splits the recurrent residual into groups and rotates each group separately, aiming to preserve information across repeated transformer loops. Evaluates state tracking and language modeling.
Studies how to train mixture-of-experts transformers with more than two recurrent passes. Combines stabilized residual updates, reintroduced input information, and loop-specific routing to support deeper reuse of the shared model.
Compares a looped model's final prediction with predictions from earlier loops to improve decoding without additional training. Tests contrastive variants using either output logits or hidden states on mathematical reasoning and code generation.
Shares a long-context KV memory written by the first loop across later loops, which also keep a short local memory. Studies this architecture during pretraining and examines how shared memory changes representations and gradient flow.
Tests how recurrent depth affects the ability to monitor a language model through its written chain of thought. Finds task-dependent changes under stress tests, while matched comparisons do not show a general monitorability disadvantage for looped architectures.
Adds a shared recurrent block between an audio encoder and language model. A question-conditioned halting mechanism chooses how many refinement passes to apply, with deeper computation learned for tasks requiring finer acoustic distinctions.
Processes selected video clips sequentially while persistent think tokens accumulate evidence for a fixed-size retrieval embedding. Intermediate retrieval supervision and self-distillation train partial-video readouts; the output is an embedding rather than a generated reasoning trace.
Uses near-fixed-point recurrent states to reduce the cost of training, key/value caching, and prefill. Learns how to sample loop depths and changes how the input is reintroduced on each loop.
Passes each token's final decoder state to the next token, alongside a causal encoder representation. Tests whether this growing computation path supports state tracking on sequences longer than those seen during training.
Refines an internal state across loops to choose among typed answer options without generating a written reasoning trace. Supervises decisions at multiple depths and evaluates how prediction quality changes with the available computation budget.
Keeps separate short- and long-term matrix memories and lets a transformer update both through bidirectional reads and writes. Tests this recurrent architecture on algorithmic, in-context learning, and reasoning tasks.
PaTh uses a small recursive network to refine learned image-state tokens inside each denoising step and steer a frozen diffusion model through adapters. It learns visual puzzles from reconstruction targets without symbolic solutions or an external verifier.
Trains an intermediate loop using a deeper loop of the same language model as its teacher on student-generated outputs. A dynamic variant refreshes the teacher during training, turning additional recurrent computation into a source of supervision.
Evaluates harmful-query and jailbreak behavior at different recurrent depths of looped language models. Proposes depth-specific control, state sharing, and joint supervision to align safety behavior across depths.
Predicts by averaging over the long-run distribution of recurrent hidden states instead of reading a single final state. This lets the model use changing hidden states without requiring them to settle at one fixed point.
Adds a learned running summary of previous recurrent states so that each update can retain useful earlier work. Uses content-based weighting and temporal decay with constant aggregation memory, and tests whether puzzle-solving improves over much longer inference runs.
Trains one language model to operate at different loop counts by mixing depths during training and conditioning each pass on its index and budget. A learned gate controls each recurrent update.
Trains a looped language model at a fixed depth first, then introduces varying depths only near the end of training. Compares the resulting training cost and performance across inference depths with varying depth throughout training.
Analyzes how many extra loops a model trained on graph connectivity can safely run. Derives a finite range where added depth solves harder graphs before further loops create false connections.
Evaluates a depth-recurrent model on Sudoku-like worlds with different rule combinations. Compares symbolic rule descriptions with solved examples when the test world contains new puzzles, new combinations, or unfamiliar rule instances.
Studies how reducing recurrent depth changes refusal behavior in two looped language-model families. Uses probes and interventions to distinguish recognizing a harmful request from refusing it, and tests safety training across randomly selected depths.
Separately perturbs the answer state and the reasoning state of a recursive puzzle solver to study where extra search is useful. Uses the model's halting prediction to trigger restarts that resample the answer state.
Inspects eight looped language models for state convergence, token decisions, readout quality, attention behavior, and sensitivity to injected noise. Finds important differences between models that receive the prompt once and those that reintroduce it at each loop.
Searches for layers to repeat to make a stronger teacher from the current model, then distills its predictions into the original student. Repeats search and distillation as the student improves.
Studies how oscillations can slow convergence in recurrent reasoning models. Proposes an architecture whose rotational state changes are separated from the representation used for reasoning, and tests convergence on puzzle-solving tasks.
Searches over input conditions to change a recursive reasoner's update rule without retraining it. Tests whether these alternative updates can redirect a trajectory away from an incorrect solution, rather than only adding more steps or perturbing its state.
Analyzes the Continuous Thought Machine's repeated updates during image classification. Finds that its hidden states follow moving fixed points and that much of its attention schedule is shared across images.
Separates computing an answer, preserving it through additional loops, and keeping its hidden state usable for later steps. On state-machine and maze tasks, shows that training can improve one ability without securing the others.
Trains a small drafter to predict several future tokens from early-loop hidden states. Later loops decide which speculative branches to continue, and full-depth verification determines the final output.