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Why Does Reinforcement Learning Generalize? A Feature-Level
Mechanistic Study of Post-Training in Large Language Models
DanShi1,ZhuowenHan1,SimonOstermann2,3,RenrenJin1,
JosefvanGenabith2,3,DeyiXiong1*
1TJUNLPLab,SchoolofComputerScienceandTechnology,TianjinUniversity,China
2GermanResearchCenterforArtificialIntelligence(DFKI),Saarbrücken,Germany
3SaarlandUniversity,Saarbrücken,Germany
{shidan, dyxiong}@tju.edu.cn
--- ------------- --- -------- --- ---------- ------------------- -------------------------- ------------ --- --------------------- ---------- ---
Abstract performance improvements on tasks far beyond
theirtrainingdistribution. Incontrast,supervised
Reinforcement learning (RL)-based post-
6202 rpA 72 ]LC.sc[ 1v11052.4062:viXra
fine-tuning(SFT)isfrequentlyobservedtoinduce
training often improves the reasoning perfor-
--- -------- ----- -------- --- --------- ------- --- --- --- --- --- ---
mance of large language models (LLMs) be- degradation or forgetting of previously acquired
general-purpose capabilities (Huan et al., 2025;
--- ---------------------------------------- ------------ ----------- -------- ----- ---------- --------------- --- ------------ ----- ------- -----
yond the training domain, while supervised
fine-tuning(SFT)frequentlyleadstogeneral Chuetal.,2025).
capabilities forgetting. However, the mecha-
Despitetheseconsistentempiricalfindings,why
nismsunderlyingthiscontrastremainunclear. RL-tuned models can generalize well remains
Tobridgethisgap,wepresentafeature-level
poorlyunderstood. UnlikeSFT,whichdistillsfull
--- ----------------- --- -------- ----------- ---------- -------- ----------------- ------------ --------------------------- --------- ------ ---
mechanistic analysis methodology to probe
reasoning trajectories from a teacher model, RL
RL generalization using a controlled experi-
mentalsetup,whereRL-andSFT-tunedmod- typicallyreliesonlyonoutcome-levelsupervision.
Fromamechanisticperspective,itisunclearhow
els are trained from the same base model on
--- ------- ------- ---- -------- ---- -------- --- --- --- --- --- ---
identical data. Leveraging our interpretabil- suchweakandindirectsignalsyieldbroad,trans-
ity framework, we align internal activations
--- -------------- --- --- ----- -------- ----------- --- --- --- --- --- ---
ferableimprovementsacrossdiversetasks.
across models within a shared feature space In this work, we address this gap through a
andanalyzehowfeaturesevolveduringpost-
feature-levelinterpretabilityframeworkdesigned
training. WefindthatSFTrapidlyintroduces
--- --------- ------------------------------ ----------- --- -------- ----------- -------------- --- --- --------------------- --- ---
to investigate how SFT and RL differentially re-
many highly specialized features that stabi-
lize early in training, whereas RL induces shape internal representations. We first employ
SparseCrosscodertoaligntheinternalactivations
morerestrainedandcontinuallyevolvingfea-
turechangesthatlargelypreservebasemodels’ of the base model with those of its RL- and SFT-
representations. Focusing on samples where tuned counterparts within a shared, interpretable
RLsucceedsbutthebasemodelfails,weiden- feature space. This alignment allows us to sys-
tify a compact, task-agnostic set of features
--- ------ -------- ------------- --- --- ----------- --- --- --- --- --- ---
tematicallycompareinternalrepresentationsacross
thatdirectlymediategeneralizationacrossdi-
modelsandtotrackhowindividualfeaturesemerge,
verse tasks. Feature-level interventions con-
--- ----- ------ ------------- --- ------------- ---- --- --- --- --- --- ---
evolve,anddivergeduringpost-training.
firm their causal role: disabling these fea-
--- ---- ------------ --- --------------- --- ---------- --- --- --- --- --- ---
However,pairwisecomparisonsaloneareinsuf-
turessignificantlydegradesRLmodels’gener-
alizationperformance,whileamplifyingthem ficientforfullycharacterizingtherelationshipbe-
improves base models’ performance. The tweenSFTandRLrepresentations. Toovercome
code is available at https://github.com/ this limitation, we then propose a three-model
danshi777/RL-generalization.
SparseCrosscoderthatjointlyalignsthebase,SFT-
1 Introduction trained, and RL-trained models within a single
sparsefeaturespace,andanovelModelAttribution
Reinforcement learning (RL) has emerged as a Score(MAS)tomeasurefeaturespecificity. This
powerful paradigm for enhancing the reasoning
-------- --- -------- --- --------- --- ------------- --- --- --- --- --- ---
unifiedrepresentationenablesdirectattributionof
capabilitiesoflargelanguagemodels(LLMs),par-
eachfeaturetoaspecifictrainingparadigm.
ticularlyinsolvingcomplexlogicaltasksinvolving Usingthisframework,weconductasystematic
mathematicsandprogramming(Guoetal.,2025;
analysis of feature dynamics throughout training.
----- --- ---------- ---- --- ----------- -------- -------- ---------- -------- ---------- --------- ---
Jaech et al., 2024; Team et al., 2025). Notably,
Ourresultsrevealaclearandconsistentdistinction
modelsoptimizedviaRLonnarrowlydefinedrea- between the two paradigms. SFT rapidly intro-
soning objectives often demonstrate substantial
------ ---------- --- ----- ----------- --- ----------- --- --- --- --- --- ---
ducesalargenumberofhighlyspecializedfeatures
*Correspondingauthor thatstabilizeearlyintraining,whereasRLinduces

morerestrainedandcontinuouslyevolvingfeature asaprominentdirection(Daietal.,2022;Shietal., changes,largelypreservingthebasemodel’srep- 2024a;Chenetal.,2024;Wuetal.,2023;Shietal., resentational structure. This difference provides 2024b). Recent work has explored feature-level aninitialrepresentationalexplanationforwhySFT interpretability in LLMs, often using Sparse Au- tendstomemorizetask-specificpatterns,whileRL toencoders(SAEs,Cunninghametal.,2023;Gao maintainsbroadercapabilities. etal.,2024a;Marksetal.,2025)toidentifyinternal Beyond descriptive analysis, our framework features associated with specific functions, such enables direct mechanistic investigation of RL- as emotions (Han et al., 2025), safety behaviors inducedgeneralization. Weidentifyacompactset (Weng et al., 2025; Yeon et al., 2025), language- ofinternalfeaturesthatactivelycontrolcross-task specific representations (Deng et al., 2025), and transfer by focusing on samples where general- reasoningprocesses(Galichinetal.,2025). Sparse ization explicitly occurs, cases in which the RL- Crosscoders extend SAEs, have further enabled tunedmodelsucceedswhilethebasemodelfails, comparisons between fine-tuned and base mod- andmeasuringfeature-levelactivationdifferences els,revealingfeaturesintroducedbySFT(Lindsey withinthealignedfeaturespace. etal.,2024;BaekandTegmark,2025). Incontrast, Throughtargetedfeatureinterventions,wefur- ourworkcomparesbothSFT-andRL-trainedmod- ther demonstrate that these features are causally elsagainstthesamebasemodelandintroducesa responsible for generalization: disabling them in three-model sparse crosscoder to jointly analyze RL-tunedmodelsleadstosignificantperformance theirfeaturedifferences. degradation,whileamplifyingtheminbasemodels Generalization Comparison of SFT and RL. induces substantial gains, even on unseen tasks. Severalstudieshavecomparedthegeneralization These results indicate that RL does not merely of SFT- and RL-tuned models at the behavioral improve task-specific performance, but instead level,documentingperformancegainsandlosses strengthensacompact,task-agnosticsetoffeatures acrossdiversetasks. Theseworksconsistentlyre- thatgovernsgeneralizationbehavior. portthatRL-tunedmodelsgeneralizemorerobustly Insummary,ourcontributionsareasfollows: across domains, while SFT often leads to forget- • We propose a feature-level interpretability tingofgeneralcapabilities(Huanetal.,2025;Chu frameworkformechanisticallyanalyzinghow et al., 2025). However, the internal mechanisms differentpost-trainingparadigmsreshapein- underlyingthiscontrastremainlargelyunexplored. ternalrepresentationsandgiverisetoRLgen- Although Huan et al. (2025) attempt to explain eralization. this difference by relating it to larger representa- tion or output distribution drift induced by SFT, • Wepresentathree-modelSparseCrosscoder theiranalysisremainsatthelevelofglobalrepre- andaModelAttributionScore(MAS)thaten- sentationsanddoesnotidentifythespecificinter- ableunifiedfeaturealignmentandattribution nalmechanismsthatcausallydrivegeneralization. acrossbase,SFT,andRLmodels. Ourworkaddressesthisgapbyprovidingafeature- level,causallyvalidatedexplanationofRL-induced • We reveal a fundamental distinction be- generalization. tweenpost-trainingparadigms: SFTinduces early-stabilized, highly specialized features, 3 InterpretabilityMethodology whereasRLyieldsmorerestrainedandcontin- uouslyevolvingfeaturechanges,andweiden- To systematically analyze how different post- tifyasmallsetofgeneralization-controlling trainingparadigmsreshapeinternalrepresentations, featuresthatprovideadirectmechanisticex- we introduce a unified feature-level interpretabil- planationforRLgeneralization. ityframework. Theframeworkisguidedbythree core principles. First, the models under compari- 2 RelatedWork sonmustbestrictlycomparable,suchthatobserved Feature-Level Interpretability in LLMs. As representationaldifferencescanbeattributedsolely LLMscontinuetoexhibitdiverseandsophisticated to the training paradigm. Second, internal repre- capabilities(Guoetal.,2023;Changetal.,2024; sentationsfromdifferentmodelsmustbealigned Shietal.,2024c),understandingtheinternalmecha- into a shared feature space to enable direct, fine- nismsthatgiverisetothesebehaviorshasemerged grainedcomparisonoffeatures. Third,theframe-

workshouldnotonlysupportdescriptiveanalysis sparsityregularizationL : sparsity offeaturedifferences,butalsoprovidedirectevi- L = L +βL , denceforthegeneralizationcapacityofRL. recon sparsity Tosatisfytheseprinciples,wedesignthreekey L = (cid:88) (cid:13) (cid:13)a(i)−aˆ(i) (cid:13) (cid:13) 2 , recon (cid:13) (cid:13) componentsinourinterpretabilityframework: (i) (3) i=O,T sparsecrosscodersforfeature-levelalignmentand L = (cid:88) f (x ) (cid:88) (cid:13) (cid:13)W (i) (cid:13) (cid:13). attributionbetweenthebasemodelandtunedmod- sparsity k j (cid:13) dec,k(cid:13) els,(ii)athree-modelextensionthatenablesjoint k i=O,T comparison across base, SFT, and RL models, Thisobjectiveforcesthemodeltolearnasmallset and (iii) a method for identifying generalization- of interpretable features that capture the distinct controllingfeatures. Weintroduceeachcomponent properties of the activations. Within our frame- inturnbelow. work,thistwo-modelsparsecrosscoderservesas thebasicbuildingblockforpairwisecomparison 3.1 Feature-LevelAlignmentandAttribution betweenatunedmodelanditsbasecounterpart. viaSparseCrosscoders IdentifyingModel-SpecificFeatureswithNRN Acentralchallengeincomparinginternalrepresen- Toquantifyhowstronglyeachfeatureisuniqueto tationsacrossindependentlytrainedmodelsisthat eachmodel,wefollowBaekandTegmark(2025) theiractivationspacesarenotdirectlyaligned. To usingtheNormalizedRelativeNorm(NRN)metric address this challenge, we employ Sparse Cross- to analyze the features. NRN is computed as the coders (Lindsey et al., 2024) to align activations ratio between the L1 norm of the decoder vector fromthedifferentmodelsintoasharedsparsefea- foreachmodel: turespace,enablingdirect,meaningfulcomparison (cid:13) (cid:13) ofrepresentationalchangesinducedbytuning. (cid:13)W (T) (cid:13) (cid:13) dec,k(cid:13) NRN = (cid:13) (cid:13) (cid:13) 1 (cid:13) , (4) (cid:13)W (O) (cid:13) +(cid:13)W (T) (cid:13) Two-Model Sparse Crosscoder for Compari- (cid:13) dec,k(cid:13) (cid:13) dec,k(cid:13) 1 1 sonofTunedModelsandBaseModel. Sparse where O denotes the original base model, T rep- CrosscodersextendSAEsbyjointlyencodingac- (·) resents the tuned model (SFT or RL), and W tivationsfromdifferentsources,suchasdifferent dec denotes the corresponding crosscoder’s decoder. models, layers, or positions, into a shared sparse Intuitively,ifafeaturecontributesmoretorecon- feature space. This formulation enables a fine- structingthetunedmodel’sactivations,thedecoder grained comparison of representational changes inducedbytuning. assignsitalargernorminW ( d T ec ) ,yieldingNRN→

  1. Inthiscase,NRN→1correspondstofeatures Formally,theencodercomputesfeatureactiva- thatareuniquetothetunedmodel,NRN→0cor- tionsas: respondstofeaturesuniquetotheoriginalmodel,   whileNRN=0.5correspondstosharedfeatures. (cid:88) f(x j ) = ReLU W( e i n ) c a(i)(x j )+b enc, Three-Model Sparse Crosscoder for Joint i∈O,T Representation Comparison. The two-model (1) Sparse Crosscoder enables fine-grained compar- and the decoder reconstructs the activations for isonsbetweenatunedmodelanditsbasecounter- eachmodel: part. However, such pairwise analyses are inher- entlylimitedwhenmultipletrainingparadigmsare aˆ(i)(x ) = W (i) f(x )+b (i) . (2) j dec j dec involved. In particular, when comparing an SFT- tuned model and an RL-tuned model against the Here, O denotes the original base model and T samebasemodel,pairwisecrosscoderscannotdis- represents the tuned model (either SFT or RL). entanglewhetherafeatureissharedbyallmodels, a(i)(x j ) ∈ Rd model is the residual-stream activa- specifictoonetunedmodel,orsharedbythetwo tion of model i at token x j , f(x j ) ∈ Rdsparse is tunedmodelsbutabsentinbasemodel. the sparse feature activations, and aˆ(i)(x ) is the Moreimportantly,featuresidentifiedindifferent j reconstructedactivation. Thecrosscoderistrained pairwisecrosscodersarenotdirectlycomparable. by minimizing a reconstruction loss L with For example, a feature with a given index (e.g., recon

(cid:13) (cid:13) feature #2026) in the SFT-Base crosscoder does (cid:13)W(S) (cid:13) MAS = (cid:13) dec,k(cid:13) 1 , (9) notnecessarilycorrespondtothefeaturewiththe S (cid:13) (cid:13)W(O) (cid:13) (cid:13) + (cid:13) (cid:13)W(S) (cid:13) (cid:13) + (cid:13) (cid:13)W(R) (cid:13) (cid:13) same index in the RL-Base crosscoder, since the (cid:13) dec,k(cid:13) 1 (cid:13) dec,k(cid:13) 1 (cid:13) dec,k(cid:13) 1 (cid:13) (cid:13) twocrosscodersaretrainedindependentlyandmay MAS = (cid:13) (cid:13) W( d R ec ) ,k (cid:13) (cid:13) 1 . learnentirelydifferentsparsebases. R (cid:13) (cid:13)W(O) (cid:13) (cid:13) + (cid:13) (cid:13)W(S) (cid:13) (cid:13) + (cid:13) (cid:13)W(R) (cid:13) (cid:13) (cid:13) dec,k(cid:13) 1 (cid:13) dec,k(cid:13) 1 (cid:13) dec,k(cid:13) 1 Toaddressthislimitation,weintroduceathree- (10) modelSparseCrosscoder,whichjointlyalignsthe Here,O,S,andRdenotetheoriginalbasemodel, base,SFT-tuned,andRL-tunedmodelswithinasin- the SFT-tuned model, and the RL-tuned model, glesparsefeaturespace. Byunifyingallthreemod- respectively. By construction, MAS , MAS , O S els within a single sparse basis, the three-model MAS ∈ [0,1], MAS +MAS +MAS = 1. R O S R sparsecrosscoderconstitutesakeycomponentof ThemodelwiththelargestMASvalueistheoneto ourinterpretabilityframework,enablingdirect,si- whichthefeatureismoststronglyattributed. For multaneouscomparisonoffeaturesharingandspe- example, a feature with MAS → 1 is an SFT- S cializationacrosspost-trainingparadigms. specificfeature. Specifically,givenatokenx ,wejointlyencode j 3.2 IdentifyingGeneralization-Controlling theresidual-streamactivationsfromthethreemod- Features elsintoasharedsparsefeaturerepresentation:   Thefinalcomponentofourinterpretabilityframe- (cid:88) workaimstomovebeyonddescriptivecomparison f(x j ) = ReLU W( e i n ) c a(i)(x j )+b enc, andtoidentifyinternalfeaturesthatcausallycon- i=O,S,R trolgeneralizationbehavior. Therefore,wehypoth- (5) esize that RL selectively strengthens a subset of whereO,S,andRdenotetheoriginalbasemodel, featuresthatplayacausalroleinenablinggeneral- theSFT-tunedmodel,andtheRL-tunedmodel,re- spectively. a(i)(x ) represents the activation of izationacrosstasks. j Prior work has attempted to localize function- modeli,andf(x )isthesharedsparsefeaturevec- j ally meaningful features by analyzing which fea- tor. Then,thedecoderreconstructstheactivations tures are frequently activated on specific lexical foreachmodel: cues, such as identifying self-reflection features aˆ(i)(x j ) = W ( d i e ) c f(x j )+b ( d i e ) c . (6) via activations on tokens like “Wait”, or con- trastive features via “But” and “However” (Baek Thetrainingobjectiveminimizesacombination andTegmark,2025;Galichinetal.,2025). While ofreconstructionlossandsparsityregularization: such approaches are useful for interpretability, L = (cid:88) (cid:13) (cid:13)aˆ(i)−a(i) (cid:13) (cid:13) 2 theyimplicitlyassumethatfunctionalfeaturesare (cid:13) (cid:13) tightly coupled to surface-level tokens. In con- i=O,S,R (7)

  • (cid:88) f (x ) (cid:88) (cid:13) (cid:13)W (i) (cid:13) (cid:13). trast,wethinkthatfeaturescontrollinggeneral- k j (cid:13) dec,k(cid:13) izationshouldnotdependonspecificwordsor k i=O,S,R task-specific lexical patterns. Instead, such fea- Thisobjectiveencouragesthemodeltodiscover turesshouldbeidentifiablethroughtheirfunctional acompactsetofsparsefeaturesthatjointlyexplain role,namely,whethertheysystematicallyalterthe theactivationsofallthreemodels,whileallowing model’sdecision-makingbehavioracrosstasksin each feature to contribute unequally to different situationswheregeneralizationactuallyoccurs. models. We propose to localize generalization-related featuresbyfocusingonsamplesthatexplicitlyin- MeasuringFeatureSpecificitywithMAS. To stantiate generalization behavior. For each task, quantifyhowstronglyeachfeatureisattributedto we construct a subset of samples on which the a particular model within the shared crosscoder basemodelfailsbuttheRL-tunedmodelsucceeds. space,wedefineathree-waynormalization,which Thesesamplesrepresenttheminimalevidenceof werefertoastheModelAttributionScore(MAS). generalizationandaretheonlyinstanceswheregen- For each feature k, the formula for calculating eralization can be unambiguously observed. We MASisasfollows: refertothemasgeneralization-criticalsamples. (cid:13) (cid:13) MAS = (cid:13) (cid:13) W( d O ec ) ,k (cid:13) (cid:13) 1 , (8) Foreachgeneralization-criticalsample,weex- O (cid:13) (cid:13)W(O) (cid:13) (cid:13) + (cid:13) (cid:13)W(S) (cid:13) (cid:13) + (cid:13) (cid:13)W(R) (cid:13) (cid:13) tractthe residual-streamactivation atthe finalto- (cid:13) dec,k(cid:13) 1 (cid:13) dec,k(cid:13) 1 (cid:13) dec,k(cid:13) 1
MathReasoningTasks GeneralTasks
Model
MATH500 AIME24 AIME25 OpenBookQA CommonsenseQA HeadQA SciQ ARC-Challenge
Qwen3-4B-Base 26.0 13.3 0.0 23.6 20.1 31.7 78.5 36.0
-------------- --- --- ---- ---- ---- --- ---- ---- --- ---- ---- ---- ---
Qwen3-4B-SFT 68.4 13.3 13.3 25.8 19.6 31.2 51.8 34.4
Qwen3-4B-RL 77.0 26.7 20.0 27.2 50.5 32.7 89.5 39.3
∆(RL-SFT) 8.6 13.4 6.7 1.4 31.0 1.5 37.7 4.9
Qwen2.5-7B 40.0 10.0 3.3 28.4 77.6 33.7 86.9 41.9
Qwen2.5-7B-SFT 69.2 13.3 10.0 26.4 30.1 31.2 79.4 37.0
Qwen2.5-7B-RL 71.4 20.0 13.3 32.8 76.1 36.1 90.7 42.5
∆(RL-SFT) 2.2 6.7 3.3 6.4 46.0 5.0 11.3 5.5
Table1: PerformancecomparisonofSFT-andRL-tunedmodelsonmathreasoningtasksandothertasks.
kenpositionfromthebasemodelandtheRL-tuned 2025) and Qwen2.5-7B (Yang et al., 2024) mod-
model, respectively. Then we encode them sep- els, respectively. Details about training datasets,
arately using the model-specific branches of the implementationspecifics,andhyperparametersare
trainedSparseCrosscoderencoder,yieldingfeature providedinAppendixA.2.
vectorsf(RL)(x)andf(Base)(x),respectively.
EvaluationBenchmarks. WeevaluatedtheSFT-
--- --------- --- ----- ---------- -------------- --- --------------------- --- --- --- ------------------ --- ---
For a feature k, we define its generalization
andRL-tunedmodelsonadiversesuiteofbench-
scoreonagiventaskastheaverageactivationdif-
marks,spanningbothmathematicalreasoningand
ferencebetweentheRLmodelandthebasemodel
other general tasks. Specifically, the mathemat-
--- --- --- --- --- --- --- ----- ------- ------ ------------- --- ------------- ---
acrossallgeneralization-criticalsamples:
ical reasoning benchmarks include MATH500
----- --- --- --------- ----- ------ --------- --------------------------------------- ------- ---------- ------------- ---------- ------- -------
(cid:104) (cid:105)
E (RL) (Base) (Hendrycksetal.,2021),AIME24,andAIME25,
Score = f (x)−f (x) , (11)
k x∈G k k
while other tasks comprise OpenBookQA (Mi-
haylov et al., 2018), CommonsenseQA (Talmor
whereG denotesthesetofgeneralization-critical
(·) et al., 2019), HeadQA (Vilares and Gómez-
----------------------- --- --- --- ------------------ --- --- ------- ------ ------ --- -------- --- ------
samplesforthattask,andf (x)istheactivation
k
Rodríguez, 2019), SciQ (Welbl et al., 2017), and
------------------------------------- --- ----- -------- -------- ----- --------- ------------------------------- --- ---------- ----------- -------------- -------------- -------
of feature k for input x. For each task, we retain
ARC-Challenge(Clarketal.,2018). Detailedde-
featureswhosescoresexceedathresholdt. These
scriptions of benchmarks and evaluation metrics
featuresaretreatedastask-relevantgeneralization
canbefoundinAppendixA.4.
features. Finally, we take the intersection of the
--------- --- -------- ------- ---------------- --- ------ --- --- --- --- --- --- ---
selectedfeaturesetsacrossalltasks,yieldingaset
Results. As shown in Table 1, we observe that
--- --- --- --- --- --- --- -------- --- ----- -------- --- ---------- ----
offeaturesthatconsistentlycontributetosuccessful
RL-tuned models exhibit strong generalization
--- --- --- --- --- --- --- -------- ------ --- ------- ------ -------------- ---
generalizationregardlessoftaskdomain. acrossdiversedomains,whereasSFT-tunedmodels
In summary, the features we identify are those sometimessufferfromgeneralcapabilitiesforget-
that(i)systematicallydifferentiatetheRLmodel
ting,consistentwithobservationsreportedinprior
from the base model on generalization-critical work(Huanetal.,2025).
samples, (ii) influence model behavior in a task-
-------- --- -------------- --- -------------- --- ---------- --- --- --- --- --- --- ---
agnostic manner, and (iii) do not rely on explicit 5 Experiments: ComparingSFTandRL
taskknowledgeorlexicaltriggers. ModelsviaTwo-ModelSparse
------------------------------- --- --- --- --- --- --- ------------------------ --- --- --- --- --- ---
Crosscoders
4 Phenomena: Performance
--- ---------- --- ----------- --- --- --- --- --- --- --- --- --- ---
DiscrepanciesofReasoningModels ToanalyzehowSFTandRLaltertheinternalrep-
resentationsofthebasemodel,weindependently
To ensure that differences between the resulting trainedtwoSparseCrosscoders: onebetweenthe
reasoning models can be attributed solely to the
--------- --- ------ ------ ---------- ------ ------ --- --- --- --- --- --- ---
SFT-tunedmodelandthebasemodel,andanother
trainingparadigmratherthanconfoundingfactors betweentheRL-tunedmodelandthebasemodel.
such as data composition, we deliberately avoid Implementation and training details are provided
using existing off-the-shelf distilled or RL-tuned inAppendixA.1.
----- -------- ------------- --- --------- --- -------- -------------- --- --- --- --- --- ---
models. Instead,wetrainedboththeSFTandRL
5.1 FeatureDiscrepanciesBetweenRLand
modelsfromthesamebasemodelonanidentical
SFT
datasetusingfull-parametertuning,ensuringthat
any observed differences can be attributed solely Using the trained crosscoders, we computed the
tothetrainingparadigms. Weperformedthiscon- NRNs for both the SFT- and the RL-tuned mod-
trolledtuningontheQwen-3-4B-Base(Yangetal., elsrelativetotheoriginalbasemodel,denotedas
Qwen3-4B-SFT Qwen3-4B-RL Qwen2.5-7B-SFT Qwen2.5-7B-RL
104 104 104 104
103 103 103 103
tnuoC tnuoC tnuoC tnuoC
102 102 102 102
101 101 101 101
100 100 100 100
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
Normalized Relative Norm Normalized Relative Norm Normalized Relative Norm Normalized Relative Norm
Figure1: DistributionofNormalizedRelativeNormsacrossdifferenttrainingmethodsanddifferentmodelscales.
NRN SFT andNRN RL ,respectively. Theresulting largelypreservestheoriginalmodel’srepresenta-
NRNdistributionsarevisualizedinFigure1. tional structure. This pattern can be attributed to
Acrossbothtrainingparadigms,themajorityof thenatureofRLsupervision. UnlikeSFT,which
featuresclusteraroundNRN≈ 0.5,indicatingthat directlyconstrainstheentirereasoningtrajectory,
most features are shared between the fine-tuned RL only provides outcome-level feedback based
modelsandthebasemodel. Moreover,thenumber onfinalanswercorrectness. Asaresult,RLdoes
offeaturesdecaysapproximatelyexponentiallyto- not force the model to adopt a particular reason-
wardbothextremesofthedistribution,suggesting ing style or surface form. Instead, it selectively
that highly model-specific features are relatively reinforcesinternalcomputationsthatcontributeto
rare. However, thetailsofthedistribution, corre- correctdecisions,whileleavingmuchofthebase
spondingtomodel-specificfeatures,exhibitstrik- model’srepresentationalstructureintact.
inglydifferentbehaviorsforSFTandRL. Overall, these results suggest a fundamental
contrast in post-training dynamics: SFT drives
--- ------- ------- ------ --------- --- ---- ----------- ---------------- --- --------- ---------- --- ------
SFT Induces a Large Number of Unique Fea-
substantial feature turnover, generating many
tures. FortheSFT-tunedmodel,theNRNdistri-
highly model-specific features while erasing oth-
--- --- --- --- --- --- --- ------ -------------- --- -------- ----- ------- ----
butionexhibitsapronouncedrighttail,withasub- ers, whereas RL induces restrained and targeted
stantialnumberoffeaturesachievingNRN >
------------------------------------ ---- ---------------- --- --- --- ---- --------------------------------------------- --- --- --- --- --- ---
SFT adjustmentsthatlargelypreservetheoriginalfea-
0.8, and some even approaching NRN = 1.
SFT turespace.
Thesefeaturescorrespondtorepresentationsthat
are almost entirely unique to the SFT model. At 5.2 FeatureFormationandEvolutionDuring
the same time, we also observe a non-negligible Training
-------- ----- ------- ------- ---------------- --- --- --- -------- --- --- --- --- ---
numberoffeatureswithNRN → 0,indicating TofurtherunderstandhowSFTandRLalterthein-
SFT
featuresthatareeffectivelyexclusivetotheorigi- ternalrepresentationsofthebasemodelovertime,
nalmodel. ThesetwoextremessuggestthatSFT
--------- --- ------------------------------ --- --- --- --- --- --- --- --- --- --- ---
weanalyzedthetemporalevolutionoffeaturesdur-
inducesapronouncedrepresentationalshift: while ingtraining. Ratherthanfocusingsolelyonthefi-
introducingmanynew,highlyspecializedfeatures, naltunedmodels,weexaminedhowmodel-specific
italsosuppressesorabandonsaconsiderablepor-
featuresemerge,persist,andchangeacrosstraining
tionofthebasemodel’sfeaturerepertoire.
checkpoints.
Furthermore, the Qwen2.5-7B crosscoders ex-
------------ -------- -------------- ------------- ----------- -------- --- ------------ ------ --------- ----------- ------------ ---- --------
Experimental Setup. For each training
hibit a larger number of features with extreme
paradigm, we saved checkpoints at regular
NRN values than the Qwen3-4B-Base counter-
intervals (every one-fifth of an epoch) and pair
parts,implyingthatlargermodelstendtodevelop
each checkpoint with the base model to train a
-------- --- -------------- -------- -------- ------ --- ------ ----------- ---- -------- ---------- ----------- ----------
a richer set of distinctive internal features during
Sparse Crosscoder, yielding five crosscoders per
post-training.
paradigm. Thissetupenablesstage-wisecompar-
--- --- --- --- --- --- --- --------- --------------------------------- --- --- --- --- ---
RLPreservesCoreRepresentationsWhileIntro- isonsbetweenthebasemodelandpartiallytrained
ducing Fewer, Milder Deviations. In contrast, models. Using these crosscoders, we conducted
theRL-tunedmodelexhibitsamarkedlydifferent twocomplementaryanalyses: (1)featureoverlap
NRN profile. Only a small number of features across checkpoints, and (2) feature rank shifts
exhibit extreme NRN RL values (close to either 0 betweenconsecutivecheckpoints. Theseanalyses
or 1), with very few approaching either end of allow us to quantify both the stability of learned
the spectrum. This indicates that RL introduces featuresandtheextenttowhichtheinternalfeature
relatively few novel, model-specific features and spaceisreorganizedduringtraining.

Qwen3-4B-SFT Qwen3-4B-RL Qwen2.5-7B-SFT Qwen2.5-7B-RL 1.0 1.0 1.0 1.0 ckpt-1 1.00 0.28 0.22 0.30 0.25 ckpt-1 1.00 0.06 0.06 0.06 0.08 ckpt-1 1.00 0.28 0.20 0.30 0.23 ckpt-1 1.00 0.04 0.05 0.03 0.05 0.8 0.8 0.8 0.8 ckpt-2 0.28 1.00 0.37 0.33 0.32 ckpt-2 0.06 1.00 0.12 0.10 0.08 ckpt-2 0.28 1.00 0.19 0.19 0.18 ckpt-2 0.04 1.00 0.15 0.33 0.18 0.6 0.6 0.6 0.6 ckpt-3 0.22 0.37 1.00 0.43 0.35 ckpt-3 0.06 0.12 1.00 0.10 0.08 ckpt-3 0.20 0.19 1.00 0.35 0.28 ckpt-3 0.05 0.15 1.00 0.19 0.32 0.4 0.4 0.4 0.4 ckpt-4 0.30 0.33 0.43 1.00 0.47 ckpt-4 0.06 0.10 0.10 1.00 0.08 ckpt-4 0.30 0.19 0.35 1.00 0.39 ckpt-4 0.03 0.33 0.19 1.00 0.23 0.2 0.2 0.2 0.2 ckpt-5 0.25 0.32 0.35 0.47 1.00 ckpt-5 0.08 0.08 0.08 0.08 1.00 ckpt-5 0.23 0.18 0.28 0.39 1.00 ckpt-5 0.05 0.18 0.32 0.23 1.00 0.0 0.0 0.0 0.0 ckpt-1ckpt-2ckpt-3ckpt-4ckpt-5 ckpt-1ckpt-2ckpt-3ckpt-4ckpt-5 ckpt-1ckpt-2ckpt-3ckpt-4ckpt-5 ckpt-1ckpt-2ckpt-3ckpt-4ckpt-5 Figure2: Featureoverlapheatmapsacrosstrainingcheckpointsunderdifferenttrainingparadigms. 104 103 102 101 100 0.0 0.2 0.4 0.6 0.8 1.0 Model Attribution Score tnuoC Qwen3-4B-Base 104 103 102 101 100 0.0 0.2 0.4 0.6 0.8 1.0 Model Attribution Score tnuoC Qwen3-4B-SFT 104 103 102 101 100 0.0 0.2 0.4 0.6 0.8 1.0 Model Attribution Score tnuoC Qwen3-4B-RL Figure3: DistributionofModelAttributionScoresacrossdifferenttrainingmethodsonQwen3-4B-Base. SFTQuicklyEstablishesaRelativelyFixedSet servethatSFTrapidlyformsacomparativelysta- of Internal Features, While RL Promotes a blehierarchyofmodel-specificfeatures,withlater Slower and More Incremental Process of Fea- trainingprimarilyrefiningtheirrelativeimportance. tureFormation. Foreachcheckpoint,weranked In contrast, RL induces features more gradually, featuresbydescendingNRNandretainthetop50 withtrainingpersistentlyreshapingwhichinternal as the most distinctive (i.e., model-specific) fea- featuresaremostsalientforgeneratingcorrectout- tures at that stage. We then computed the over- comes. Visualizationresultsanddetailedanalyses lap of these top-ranked features across different areprovidedinAppendixB.1. checkpoints. AsshowninFigure2,theSFT-tuned Toassesswhetherourfindingsgeneralizeacross model exhibits a high degree of feature overlap model families, we further conduct controlled across checkpoints. A substantial portion of the post-training and feature-level analysis on a dif- top-rankedSFT-specificfeaturesidentifiedatearly ferentarchitecture,namelyLlama3.1-8B-Instruct checkpointspersiststhroughoutlaterstagesoftrain- (Grattafiori et al., 2024). The corresponding re- ing. Thisindicatesthatmanyofthefeaturesintro- sultsarepresentedinAppendixB.2. Weobserve ducedbySFTemergeearlyandremainconsistently consistentpatternswiththosefoundintheQwen dominantduringsubsequentoptimization. family,indicatingthattherepresentationaldistinc- In contrast, the RL-tuned model displays neg- tionsbetweenSFTandRLarenotmodel-specific ligible overlap between the top-ranked feature butbroadlyapplicableacrossarchitectures. sets of adjacent checkpoints. Features that are Inconclusion,thecontrastbetweenSFTandRL highlyrankedatanearliercheckpointrarelyremain featuresrevealstwofundamentallydifferentmodes among the top features at the subsequent check- ofrepresentationchange: point. Only toward the end of training does the overlapincrease,suggestingthatRLdelaysfeature • SFT rapidly introduces a large number of consolidationandinsteadexploresabroadersetof model-specificfeaturesthatcloselyreplicate candidatefeaturesbeforegraduallystabilizingits the teacher’s reasoning traces, while simul- featurecomposition. taneously discarding many pre-existing fea- SFT Primarily Refines Feature Strengths Af- tures. Aftertheformation,theoverallfeature ter Early Formation, While RL Continuously composition remains largely stable. Subse- ReordersFeatureImportance Beyondfeature quent optimization primarily adjusts the rel- persistence,wefurtherexaminedhowtherelative ativestrengthsofthesefeatures. Thisyields importanceoffeaturesevolvesbyanalyzingrank a rigid and specialized feature space tightly shifts between consecutive checkpoints. We ob- alignedwiththetrainingdistribution.

1.0 1.0 Com O m p o e n n s B e o n o se kQ Q A A 1 0 . . 0 6 0 8 0 1 . . 6 0 8 0 0 0 . . 5 5 0 4 0 0 . . 4 5 9 7 0 0 . . 6 7 8 4 0 0 . . 6 8 Com O m p o e n n s B e o n o se kQ Q A A 1 0 . . 0 8 0 4 0 1 . . 8 0 4 0 0 0 . . 4 5 6 3 0 0 . . 6 7 2 4 0 0 . . 6 8 9 2 0 0 . . 6 8 SciQ 0.50 0.54 1.00 0.51 0.57 SciQ 0.46 0.53 1.00 0.57 0.56 0.4 0.4 HeadQA 0.49 0.57 0.51 1.00 0.62 0.2 HeadQA 0.62 0.74 0.57 1.00 0.74 0.2 ARC C -C om ha m lle o n n g se e nse O Q 0 p A . e 6 nB 8 ookQ 0 A .74 Sc 0 iQ .5 H 7 ea A d R Q 0 C A - . C 6 h 2 alleng 1 e .00 0.0 ARC C -C om ha m lle o n n g se e nse O Q 0 p A . e 6 nB 9 ookQ 0 A .82 Sc 0 iQ .5 H 6 ea A d R Q 0 C A - . C 7 h 4 alleng 1 e .00 0.0 Figure4: Overlapofidentifiedgeneralization-controllingfeaturesacrosstasks. Left: Qwen3-4B-RLvs.Qwen3-4B- Base. Right: Qwen2.5-7B-RLvs.Qwen2.5-7B. • RLintroducesfeaturedeviationsinagradual theinternalfeaturelandscapeinfundamentallydif- andrestrainedmanner,yieldingrelativelyfew ferent ways. SFT introduces a large number of andlessexclusivefeatures. Ratherthansub- strongly model-specific features, while RL pre- stantiallyreplacingthebasemodel’sinternal dominantlypreservesandreweightssharedfeatures representationalstructure,RLinduceslimited within the existing representational space. More featureinnovationwhileexhibitingsustained importantly, it enables downstream mechanistic featureturnoverthroughouttraining. analysis: itservesasthefoundationforidentifying featuresassociatedwithcross-taskgeneralization These findings indicate that SFT and RL dif- inthenextsection. fernotonlyinthefinalfeaturestheyproduce,but alsointhetemporaldynamicsoffeatureformation. 7 MechanisticExplanationforthe Importantly,theprolongedfeaturereconfiguration GeneralizationAbilityofRL observedinRLsuggestsatrainingprocessthatre- RL-tuned models are optimized solely on math- mainssensitivetoperformancefeedbackthrough- ematical reasoning tasks, yet they achieve sub- out optimization, a property that may be closely stantialgainsnotonlyonin-domainmathematics relatedtothestrongercross-taskgeneralizationbe- benchmarks but also on disparate tasks such as havioranalyzedinthenextsection. commonsense and scientific knowledge question 6 Experiments: JointComparisonwith answering. Thiscross-taskgeneralizationcannot Three-ModelSparseCrosscoders beexplainedbydataoverlaportasksimilarity,and thereforecallsforamechanisticexplanation. Usingthetrainedthree-modelSparseCrosscoder, Ourprioranalysesprovideaninitialexplanation: wecomputedtheMASsforeachfeature,measur- RLinducesrestrained,incrementalfeaturechanges, inghowstronglythefeatureisattributedtothebase, whereasSFTintroducesaggressivefeaturerecon- SFT-tuned,orRL-tunedmodelwithinasharedfea- figuration that may lead to over-specialization. ture space. Figure 3 illustrates the MAS distri- However, this explanation remains indirect. To butions for Qwen3-4B-Base across the different establishamoreconcretemechanisticaccount,we training conditions. The MAS distributions for seek direct evidence linking specific internal fea- theSFT-tunedmodelsexhibitapronouncedright turestotheobservedgeneralizationbehavior. tail. A substantial number of features attain high attributionscores. ThispatternsuggeststhatSFT Experimental Setup. We performed feature introduces a large set of strongly model-specific identification using the method proposed in Sec- features. ComparedtoSFT,RLproducesfarfewer tion 3.2 on all five evaluation tasks introduced in features that are strongly attributed to itself. The Section4. Foreachtask,wesetthethresholdtas sameobservationscanbefoundonQwen2.5-7B, 20%ofthemaximumscoreobservedforthattask. asshowninFigure5inAppendixB.3. Whenexaminingthegeneralizationfeaturesiden- Thethree-modelSparseCrosscoderprovidesdi- tified for each task, we observe a striking degree rectempiricalevidencethatSFTandRLreshape of consistency across tasks. To further substan-

Model OpenBookQA CommonsenseQA HeadQA SciQ ARC-Challenge
Qwen3-4B-RL -46.2 -43.9 -21.2 -14.0 -33.3
Qwen2.5-7B-RL -21.9 -24.4 -23.8 -44.4 -20.0
Table2: Performancedegradationinducedbytheremovalofgeneralization-relatedfeaturesinRL–tunedmodels.
Model OpenBookQA CommonsenseQA HeadQA SciQ ARC-Challenge
--- ------------- --- --- ---------- --- ------------- --- ------ --- ----- ------------- ----- ---
Qwen3-4B-Base +36.3 +36.0 +21.2 +38.0 +33.3
Qwen2.5-7B +12.5 +24.4 +14.3 +55.6 +40.0
Table3: Performanceimprovementachievedbyamplifyinggeneralization-relatedfeaturesinthebasemodel.
tiate this observation, we quantified the overlap Qwen2.5-7Btocorrectlyanswer56%ofsamples
amongtheidentifiedfeaturesacrossdifferenttasks, thatitpreviouslyansweredincorrectly.
asillustratedinFigure4. Theresultsrevealasub- Thisfindingsuggeststhatthebasemodeldoes
stantial level of feature overlap, even over 80%.
-------- ----- ---------- --- -------- --------- ---- ----------------------------- --- --- --- --- ---------------- ---
notlackthenecessaryknowledge. Instead,therele-
Despite the diversity of these benchmarks, many vantupstreamcircuitryispresentbutnotnaturally
featuresconsistentlyappearacrosstasks,strongly activated. Onceacontrolsignalisforciblyinjected,
suggestingtheexistenceoftask-agnosticfeatures generalizedbehaviorsemergeprominently.
thatsupportgeneralization.
Generalization to Unseen Tasks. We further
--- -------- ----------------- --- ---------- -------------- -------- -------------- --- ------- -------------- ------ -------------- ----------
The final intersection across all tasks contains
evaluated whether the identified generalization
50 features for Qwen3-4B-Base and 16 features
for Qwen2.5-7B, which we refer to as the final features transfer beyond the tasks used for fea-
ture identification. Specifically, we tested them
--- --- --- --- --- --- --- ---- --------------- --- ------------- --- --------- ----
generalization-controllingfeatures.
on two unseen benchmarks, LogiQA (Liu et al.,
--- --- --- --- --- --- --- ------ ------ ----------- --- ------ --- ------------
7.1 CausalValidationviaFeature 2021) and PIQA (Bisk et al., 2020). We observe
Interventions consistentperformancedegradationwhenzeroing
--- ------------- -------------- --- ---------- -------- ---- ------------------------------------------- -------- ------------- --- ------- --- ----------
these features in RL-trained models, and corre-
To verify the functional importance of these fea-
spondingperformanceimprovementswhenampli-
tures,weconductedtwocomplementaryinterven-
fying them in base models. This provides addi-
--- --- --- --- --- --- --- ----- ---- ------- ------- ---- -------- -----
tionexperiments.
tionalevidencethattheidentifiedfeaturescapturea
ZeroingGeneralizationFeaturesintheRLMod- general-purposegeneralizationmechanism,rather
els. Wefirstconductedablationexperimentsby thantask-specificheuristics. Detailedexperimental
zeroingouttheidentifiedfeaturesintheRLmodel
setupandresultsareprovidedinAppendixB.4.
andevaluatingperformanceonthecorresponding
generalization-critical samples. As shown in Ta- 8 Conclusion
----------------------- ------- ------------ -------- -------------- ----------- ------ ---- ---------- ---------------- --- --- -------- ----
ble 2, this intervention leads to substantial per-
This work has investigated why RL-tuned LLMs
formance degradation. In particular, for Open-
generalizebeyondtheirtrainingdistribution,while
BookQAandCommonsenseQA,zeroingthesefea-
SFToftenleadstothelossofgeneralcapabilities.
tures causes the Qwen3-4B-RL model to answer
----- ------ --------------- --- --- -------- ------ --- --- --- --- --- --- ---
Usingacontrolledexperimentalsetupandafeature-
over40%ofpreviouslycorrectsamplesincorrectly.
levelinterpretabilityframework,wehavecompared
These results indicate that the identified features
----- ------- -------- ---- -------------- --- -------- --- --- --- --- --- --- ---
howRLandSFTreshapeinternalrepresentations
arenecessaryforsuccessfulgeneralization.
during post-training. We have shown that SFT
--- --- --- --- --- --- --- ------ -------------- --- --- ---- ----- --------
AmplifyingGeneralizationFeaturesintheBase rapidlyintroduceshighlyspecializedfeaturesthat
Models. Conversely,weamplifiedthesameset stabilize early in training, whereas RL induces
offeaturesinthebasemodelbysettingtheiracti- more restrained and continually evolving feature
vations to a fixed large value (we set to 3.0), fol- changesthatlargelypreservethebasemodel’srep-
lowing standard feature intervention practices in resentations. Buildingonthisdistinction,wehave
SAE-basedanalyses(Zhangetal.,2025;Hanetal., identified a compact set of internal features that
2025). TheresultsareshowninTable3. Acrossall causallycontrolcross-taskgeneralization. Feature-
tasks,performanceimprovessubstantially. Inpar- levelinterventionshaveconfirmedtheirrole: dis-
ticular,forSciQ,amplifyingthesefeaturesenables abling these features degrades RL performance,

whileamplifyingthemtransfersgeneralizationbe- haviortobasemodels,includingonunseentasks.

Overall, our results have provided a mechanistic
explanation for why RL generalizes while SFT
memorizes, and have demonstrated the value of
feature-levelinterpretabilityforunderstandingpost-
trainingdynamicsinLLMs.

Limitations

Sergey Levine, and Yi Ma. 2025. SFT mem-
orizes, RL generalizes: A comparative study of
First, our feature-level analysis relies on Sparse foundation model post-training. arXiv preprint
arXiv:2501.17161.
Crosscoders as the underlying alignment mecha-
----------- ------ ---------- --------- --- ------ --- --- --- --- --- --- ---
nism. Althoughthisapproachenablesinterpretable
PeterClark,IsaacCowhey,OrenEtzioni,TusharKhot,
andcomparablefeaturerepresentations,thelearned
AshishSabharwal,CarissaSchoenick,andOyvind
featurespaceisnotguaranteedtocaptureallfunc- Tafjord.2018. Thinkyouhavesolvedquestionan-
swering? try ARC, the AI2 reasoning challenge.
----------------- -------- ----------- --- ----- ------ -------- --- ---- ------- --------- --- ----------
tionally relevant internal structures. Other inter-
CoRR,abs/1803.05457.
pretabilitymethodsoralignmentschemesmayre-
vealcomplementarymechanismsthatarenotcap- HoagyCunningham,AidanEwart,LoganRiggs,Robert
tured by sparse feature decomposition. Second, Huben,andLeeSharkey.2023. Sparseautoencoders
whileourinference-timefeatureinterventionses- findhighlyinterpretablefeaturesinlanguagemodels.
arXivpreprintarXiv:2309.08600.
tablishcausallinkstomodelbehavior,theydonot
directly inform how to design training objectives DamaiDai,LiDong,YaruHao,ZhifangSui,Baobao
Chang, and Furu Wei. 2022. Knowledge neurons
--- --- --- --- --- --- ------ -------- ---- ----- --------- --- -------
thatexplicitlyencouragegeneralization-controlling
features. Weleavethedevelopmentofsuchtraining in pretrained transformers. In Proceedings of the
60thAnnualMeetingoftheAssociationforCompu-
strategiestofuturework.
tationalLinguistics(Volume1: LongPapers),ACL
--- --- --- --- --- --- ---------------------------- --- --- --- --------------- --- ---
2022,Dublin,Ireland,May22-27,2022,pages8493–
Acknowledgements 8502.AssociationforComputationalLinguistics.
The present research was supported by the Na- BoyiDeng,YuWan,BaosongYang,YidanZhang,and
tional Key Research and Development Program Fuli Feng. 2025. Unveiling language-specific fea-
tures in large language models via sparse autoen-
-------- ---------- --------------- --- --- --- -------- ----- -------- ------ --- ------ -------
of China (Grant No. 2024YFE0203000) and
coders. InProceedingsofthe63rdAnnualMeeting
the International Cooperation Program for Inno-
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oftheAssociationforComputationalLinguistics(Vol-
vative Talents Development of CSC (Grant No. ume1: LongPapers),pages4563–4608.
CXXM2310203712). We would like to thank
---------------- --- --- ----- ---- -------- --- --- --- --- --- --- ---
AndreyGalichin,AlexeyDontsov,PolinaDruzhinina,
theanonymousreviewersfortheirinsightfulcom-
AntonRazzhigaev,OlegYRogov,ElenaTutubalina,
ments.
and Ivan Oseledets. 2025. I have covered all the
---------- --- --- --- --- --- ------------------------- ------------------------------------ ----- ------ ------------- ------- -------
baseshere: Interpretingreasoningfeaturesinlarge
language models via sparse autoencoders. arXiv
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A ExperimentalSettings

et al., 2025), and we retain only those responses
thatleadtocorrectfinalanswers.
Inthissection,weprovidemoredetailsaboutthe
experimentalsettings. A.3 TrainingDetails
--------------------- --- --- --- --- --- --- ------------------- --- -------- --- ---- --- --------
Reinforcement Learning (RL) has recently
A.1 TrainingDetailsofCrosscoders
demonstrated notable success in enhancing the
--- --- --- --- --- --- --- ------------ --- ------- ------- --- --------- ---
Following Baek and Tegmark (2025), we train complex, multi-step reasoning capabilities of
each crosscoder with d sparse = 32,768 LLMs by optimizing policies with scalar reward
features on 200 million tokens from open-
-------- --- --- ------- ------ ---- ----- --- --- --- --- --- --- ---
signals. Inourstudy,weadopttheverlframework
thoughts/OpenThoughts-114k1 and another 200 (Shengetal.,2025)andimplementGRPO(Shao
milliontokensfromtogethercomputer/RedPajama- etal.,2024)ontheQwen-3-4B-BaseandQwen2.5-
Data-1T-Sample2 dataset. The former includes
--------------- --- -------- --- --- ------ -------- --------- -------------------------------- --- --- --- --- ---
7Bmodels. Trainingisperformedwithanoverall
math, science, and code reasoning traces gener- batchsizeof128andalearningrateof1×10−6.
atedbyDeepSeek-R1,whereasthelattercontains Wesetthegenerationsequencelengthupto16kto-
general-domaintexts. Toavoiddistributionalbias, kens,andperform8rolloutsperprompt,updating
thetwodatasetsaremergedandjointlyshuffledbe-
themodelinmini-batchesof64samples. Clipping
--- --- --- --- --- --- --- ---------------------------------- --- --- --- --- -------- ---
foretraining,ratherthanbeingtrainedsequentially. thresholdsaresetbetween0.22and0.28toensure
Thismixedcorpusallowsthecrosscodertocapture stable policy updates, while both KL-divergence
both reasoning-related and general linguistic fea-
---------------------- --- --- --- ------- ---------- ---- --- --- --- --- --- --- ---
andentropypenaltiesareturnedoff(coefficientsset
tures. Allcrosscodersaretrainedtoreconstructthe
tozero). Themodelistrainedforoneepoch,and
--- --- --- --- --- --- --- -------- -------------------------------- --- --- --- --- ---
residualstreamofthemiddlelayerofeachmodel. thecheckpointfromthefinaliterationispreserved
Trainingisconductedwithabatchsizeof1024and forsubsequentevaluation.
alearningrateof1×10−4. Theβ,whichcontrols
---------------------- --- --- --- ------------------ --- --- ---------- --- ----------- --- ----- --- -------
Supervised Fine-Tuning (SFT) remains
thesparsityregularizationstrength,issetto2.
a widely adopted approach for transferring
--- --- --- --- --- --- --- -------- ------- --- -------- --- ---------------- ---
A.2 TrainingSetupforSFTandRL knowledge and desired behaviors from large
pre-trained language models to task-adapted or
--- --- --- --- --- --- --- ----------- -------- --- ------ --- ------------ ---
Thissubsectiondetailsthetrainingsetupusedfor
resource-constrained models. In particular, SFT
--- --- --- --- --- --- --- -------------------- --- --- ------- --- ----------- ---
SFTandRL,includingthedatasets,optimization
has recently been extensively used as a form of
--- --- --- --- --- --- --- ------------ --- ---------------- --- ---- ---- -------
objectives,implementationdetails,andtraininghy-
reasoning distillation, where the intermediate
--- --- --- --- --- --- --- --------- ------------- --- ----- --- ------------ ---
perparametersforbothparadigms.
reasoning processes of a stronger teacher model
--- --- --- --- --- --- --- --------- --------- --- ------------- --- ------- -----
aredistilledintoasmallerstudentmodelthrough
TrainingDatasets Totrainourmodels,weadopt
---------------- --- --- ------------------------ --- --- --- ------------- --- ----------------- --- --- ---------------- ---
high-quality, teacher-generated chain-of-thought
thehigh-qualitymathematicsdatasetconstructed
byHuanetal.(2025),whichconsistsof47Khigh- annotations(Guoetal.,2025). Byminimizingthe
cross-entropylossoncurateddatasets,SFTallows
qualitymathematicsproblemsderivedfromMATH
the model to internalize desired behaviors and
--- --- --- --- --- --- --- --------- --- ----------- --- ------- --------- ---
(Hendrycksetal.,2021)andDeepScaler(Luoetal.,
2025). Bothtrainingparadigmsareappliedtothe reasoningpatternsinafullysupervisedmanner. In
our experiments, we employ the LLaMA-Factory
-------------- --- ------------- --- --------- ----- -------- ---------------- ------ --- ------- ----- ------------- ---
same backbone, Qwen3-4B-Base and Qwen2.5-
framework (Zheng et al., 2024) to fine-tune the
7B. For RL, the model is optimized using stan-
dardGroupRelativePolicyOptimization(GRPO, twomodelsonteacher-providedchain-of-thought
5×10−5
Shaoetal.,2024),whererewardsarecomputedby traces. The learning rate is set to with
a batch size of 128. For consistency with the RL
------------ --- -------- ----- ------------ ------- ----- -------- -------- ------- --------------- --- ------- ------
comparing the model’s final answers against the
setting, training is also performed for one epoch,
gold answers provided in the dataset. This setup
strictlysupervisesoutcomecorrectnesswithoutex- andthefinalcheckpointisretainedfordownstream
evaluation.
posingintermediatereasoningtracestothemodel.
AlltrainingrunswereconductedonH200and
For SFT, the training targets are complete chain-
------------------------------------------ --- -------- ------- --- -------- ------ --------- --- --- --- --- --- ---
of-thought(CoT)reasoningtracesgeneratedbya H100GPUs.
strongteachermodel,Qwen3-32B-Instruct(Yang
A.4 DetailedDescriptionoftheBenchmarks
andEvaluationMetrics
1https://huggingface.co/datasets/open-
thoughts/OpenThoughts-114k
In the experiment, we evaluated our models
--- --- --- --- --- --- --- ------ ----------- --- --- --------- --- ------
2https://ai.gitee.com/hf-datasets/togethercomputer/RedPajama-
Data-1T-Sample on a broad range of benchmarks designed to
-------------- --- --- --- --- --- --- ---------- --- ----- ------------- --- -------- ---

probe different aspects of reasoning and gener- • ARC-Challenge (Clark et al., 2018): The alization. These benchmarks can be broadly more difficult subset of the AI2 Reasoning groupedintomathematicalreasoningtasksandnon- Challenge, containing grade-school science mathematicaltasks,whichvaryindomainknowl- questionsthattypicallyrequiremulti-hoprea- edgeandreasoningrequirements. soning and background knowledge integra- tion.

Math reasoning tasks The following bench-
marksprimarilyevaluateamodel’sabilitytoper-
Collectively, these benchmarks span a wide
--------------- ---------- -------- ------------ --- ---------- ------ ------------- ------- ----- ---------- ------ ----- ----
form explicit multi-step mathematical reasoning,
range of domains and reasoning types. Their di-
often requiring symbolic manipulation and struc-
versityallowsustoprobewhetherimprovements
turedproblemsolving.
inducedbyRLtrainingreflecttask-specificadapta-
• MATH500(Hendrycksetal.,2021): Asub- tionsorgeneral-purposereasoningcapabilitiesthat
setof500problemssampledfromtheMATH transferacrossdomains.
---------------------------------- --- --- --- --- --- --- ---------------------- --- --- --- --- --- ---
dataset,coveringalgebra,geometry,number WeusedLLM-Evaluation-Harness(Gaoetal.,
theory,andcombinatorics. Eachproblemtyp-
------------------------ --- --- --- --------------- --- --- --------- -------- --- ------- ----------- --- ---
2024b) to evaluate the models’ performance on
icallyrequiresmulti-stepderivationsandpre- OpenBookQA,CommonsenseQA,HeadQA,SciQ,
cisenumericalorsymbolicanswers. andARC-Challenge,andusedEval-Chemy(Raoof
et al., 2025) to evaluate the performance on
-------- --- -------- -------- --- ------ ----- ------------------------- --- ----------- --- ----------- ----------- ---
• AIME24 / AIME25: Problems drawn from
MATH500,AIME24,andAIME25. Inourexper-
the 2024 and 2025 editions of the Amer-
iments,weadoptedexact-matchaccuracytoeval-
ican Invitational Mathematics Examination
---- ------------ --- ----------- --- ----------- --- --- --- --- --- --- --- ---
uatethemodels’performanceonmathreasoning
(AIME).Eachbenchmarkconsistsof30chal-
tasks. Specifically,forAIME24andAIME25,we
--- --- --- --- --- --- --- ----------------------------------------- --- --- --- --- --- ---
lengingshort-answerquestionsthatdemand
averaged accuracy on 10 repetitions. For MATH
--- --- --- --- --- --- --- -------- -------- --- --------------- --- -------- ---
carefulreasoningandmathematicalinsight.
500,ourscoreistheaverageaccuracyover3repe-
Other tasks The following benchmarks assess
----------- ------------- --------- --- ---------- --- ------ -------------------------------------------- --- --- --- --- --- ---
titions. Forotherbenchmarks,wereportaccuracy
reasoning and knowledge use outside the mathe-
followingstandardevaluationprotocols.
maticaldomain,makingthemparticularlysuitable
forevaluatinggeneralization. B MoreExperimentalResults
---------------------------- --- --------- --- --------- ----------- ------ ------------------------- --- ---------- ---------- --- ---------- ---
• OpenBookQA (Mihaylov et al., 2018): A
In this section, we present additional experimen-
multiple-choice question answering bench-
talresultsthatcomplementthemainfindingsdis-
mark focused on elementary science knowl-
---- ------- --- ---------- --- ------- ------ --- --- --- --- --- --- ---
cussedinthemainpaper.
edge. Each question is associated with a set
------- ------ -------- --------- ---------- ------ ----- --------------------------------------- --- --- --- --- --- ---
of core facts, and the model must select the
B.1 FeatureRankShiftsBetweenConsecutive
correctanswerfromfouroptions.
Checkpoints
• CommonsenseQA (Talmor et al., 2019): A To further examine the dynamics of feature evo-
multiple-choice benchmark designed to test lution during training, for each pair of adjacent
generalcommonsenseknowledge. Questions checkpoints,wecomputehowmucheachfeature’s
are constructed around concepts from struc- rank(basedonNRN)changesfromonecheckpoint
turedknowledgebases,withdistractoroptions tothenext.
----------------------------------------- --- --- --- --- --- --- ---------- --- --- --- --- --- ---
chosentobesemanticallyplausible. Theresults,visualizedinFigure8to11,reveal
distinctpatternsforSFTandRL.IntheSFT-tuned
• HeadQA (Vilares and Gómez-Rodríguez,
-------- ------------------------------- -------- --- ---------------- --- --- ------------------------------------------ --------- ------ ------ --- ------ ---
model, rankchangesbetweenconsecutivecheck-
2019): Amedicalquestionansweringbench-
points are generally small. First, the number of
markcomposedofmultiple-choicequestions
blank features is limited, where a blank feature
------- ---- ---------- --- -------------- --- --- -------------- --- ----------- ----- ------- --- -------
derived from healthcare specialization ex-
denotesonethatappearsinthetop50atonecheck-
ams, including questions across pharmacol-
---- --------- --------- --- ------ ---------- --- --------- ----- ------- ------- ----- ------------ ---
point but falls outside the top 50 at the adjacent
ogy,chemistry,nursing,psychology,biology,
checkpoint. Second, most features exhibit rela-
--- --- --- --- --- --- --- ----------- ------- --- ------------- --- ------- -----
andmedicine.
tivelysmallrankshifts,asreflectedbylightercol-
• SciQ(Welbletal.,2017): Asciencequestion orsinthevisualization. Moreover,somefeatures
answering dataset focusing on elementary- consistentlyappearinthetop50acrossallcheck-
levelscientificconcepts. points,indicatingthatcertainSFT-inducedfeatures
Qwen2.5-7B Qwen2.5-7B-SFT Qwen2.5-7B-RL
104 104 104
103 103 103
tnuoC tnuoC tnuoC
102 102 102
101 101 101
100 100 100
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
Model Attribution Score Model Attribution Score Model Attribution Score
Figure5: DistributionofModelAttributionScoresacrossdifferenttrainingmethodsonQwen2.5-7B.
Llama3.1-8b-Instruct-SFT Llama3.1-8b-Instruct-RL Llama3.1-8b-Instruct-SFT Llama3.1-8b-Instruct-RL
1.0 1.0
----- --- --- --- ----- --- --- --- ----------- --------- --------- ------ -------------- ---------
104 104
ckpt-1 1.00 0.32 0.28 0.33 0.33 ckpt-1 1.00 0.09 0.08 0.08 0.06
0.8 0.8
103 103 0.32 1.00 0.45 0.45 0.45 0.09 1.00 0.30 0.22 0.15
tnuoC tnuoC ckpt-2 ckpt-2
0.6 0.6
102 102 ckpt-3 0.28 0.45 1.00 0.56 0.54 ckpt-3 0.08 0.30 1.00 0.32 0.22
101 101 0.4 0.4
--- --- --- --- --- --- --- --- ----------- --------- --------- ------ -------------- ---------
ckpt-4 0.33 0.45 0.56 1.00 0.72 ckpt-4 0.08 0.22 0.32 1.00 0.28
100 100 0.2 0.2
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 ckpt-5 0.33 0.45 0.54 0.72 1.00 ckpt-5 0.06 0.15 0.22 0.28 1.00
Normalized Relative Norm Normalized Relative Norm
-------- ------------------------ ------------------------------------- -------- ------- ------------------------ ------------ --- ------------------------------ ------- --------- -------- ------------------------------ --------
ckpt-1ckpt-2ckpt-3ckpt-4ckpt-5 0.0 ckpt-1ckpt-2ckpt-3ckpt-4ckpt-5 0.0
Figure 7: Feature overlap heatmaps across training
Figure6: DistributionofNormalizedRelativeNorms
checkpoints under different training paradigms on
across different training methods on Llama3.1-8B-
Llama3.1-8B-Instruct.
Instruct.
model-specific features, while RL preserves the
--- --- --- --- --- --- --- --- -------------- --- --------- ----- ------------ ---
areestablishedearlyandpersistthroughouttrain-
baserepresentationsandinducesmorerestrained
ing. Together,theseobservationssuggestthatSFT
feature changes. In addition, Figure 7, 12, and
--- --- --- --- --- --- --- --- ------- -------- --- --------- ------ ----------
quicklyestablishesarelativelystablehierarchyof
13 show that SFT features stabilize early during
--- --- --- --- --- --- --- --- ------- ---- ------------ --- --------------- ------
model-specificfeatures,withlatertrainingprimar-
training,whereasRLexhibitsmoregradualfeature
ilyrefiningtheirrelativeimportance.
evolution.
By contrast, the RL-tuned model exhibits sub-
-------------------------------------------- ------------ --- ------------ --- ----- -------- ---- ------------------------------------- --- --- --- --- ---
stantiallylargerrankshiftsacrosscheckpoints. A
B.3 AdditionalMASResultsforQwen2.5-7B
large number of features are blank between ad-
Figure5providesadditionalMASdistributionson
jacent checkpoints, indicating frequent turnover
------ ------------ --- ---------- --- -------- --- -------- --- --- --- --- --- ---
Qwen2.5-7B.Thesamequalitativetrendspersist:
among top-ranked features. Features frequently
----- ---------- --- --------- --- -------- ---------- --- --- --- --- --- --- ---
SFTinducesaheavilyright-skewedMASdistribu-
undergo significant reordering, with previously
------- --- ----------- --- ----------- ---- ---------- --- --- --- --- --- --- ---
tionwithmanyhighlyattributedfeatures,whereas
prominentfeaturesdiminishinginimportanceand
RLresultsinasignificantlyflatterdistributionwith
new features rising to prominence at later stages.
--- -------- ------ --- ---------- --- -------- ------- --- --- --- --- --- ---
fewerstronglymodel-specificfeatures.
ThispatternsuggeststhatRL-inducedfeaturesare
formedgraduallyandslowly,withtrainingcontin-
B.4 GeneralizationtoUnseenTasks.
--- --- --- --- --- --- --- --- -------------------------------- --- --- --- --- ---
uouslyadjustingwhichinternalfeaturesaremost
Tofurtherevaluatewhethertheidentifiedgeneral-
relevantforproducingcorrectoutcomes.
ization features extend beyond the tasks used for
--- --- --- --- --- --- --- --- ---------------- --- ------ ------ --------- --------
featureidentification,weconductadditionalexper-
B.2 ResultsonLlama3.1-8B-Instruct
imentsontwounseenbenchmarks: LogiQA(Liu
--- --- --- --- --- --- --- --- ---------------------------- --- --- --- ---------- ---
To evaluate the robustness and generality of our etal., 2021), alogical reasoningbenchmark, and
findingsacrossmodelfamilies,weextendouranal- PIQA(Bisketal.,2020),aphysicalcommonsense
ysistoLlama3.1-8B-Instruct. Followingthesame
--------------------------- --- --- --- --- ---------------- --- --- -------- --------- ---------- --- ----- ----------
question answering benchmark. These tasks dif-
controlledexperimentalsetupdescribedinSection fersubstantiallyfromtheoriginalevaluationsetin
4,wetrainbothSFT-andRL-tunedmodelsfrom domain and question structure, and are not used
thesamebasemodelusingidenticaldata.
duringfeatureselection.
The results show consistent trends with those Weperformthesamefeature-levelinterventions
observed in the Qwen models. As shown in Fig- asinthemainexperiments. Specifically,we(i)set
ure 6, SFT introduces a larger number of highly theidentifiedgeneralizationfeaturestozerointhe
Model LogiQA PIQA
Qwen3-4B-RL -24.5 -17.6
Qwen2.5-7B-RL -24.0 -11.8
Table4: Performancedegradationonunseentasksby
zeroinggeneralizationfeaturesintheRL-tunedmodel.
Model LogiQA PIQA
------------- --- --- ------ -----
Qwen3-4B-Base +23.3 +28.2
Qwen2.5-7B +24.0 +32.9
Table5: Performanceimprovementsonunseentasksby
amplifyinggeneralizationfeaturesinthebasemodel.
RL-trainedmodels,and(ii)amplifythesamefea-
turesinthebasemodels,andevaluateperformance
ongeneralization-criticalsamples.
Table 4 shows that zeroing the generalization
-------- ------------- ---- ------------ --------------
features in RL-trained models leads to clear per-
formancedegradationonbothLogiQAandPIQA.
Conversely,asshowninTable5,amplifyingthese
featuresinthebasemodelsconsistentlyimproves
performanceontheunseentasks. Theseresultsfur-
---------------------------- --- --- --- ----------------
thersupportthattheidentifiedfeaturesimplement
ageneral-purposegeneralizationmechanismrather
thantask-specificheuristics.

Qwen3-4B-SFT 50

64 64 396 64
255 255 525 255
396
396 2513 396
---- ------- ------- ------- ---
995 995 2618 525
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8271
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---- ------- ------- ---- ---
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9116 9286 7746
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9 5 4 5 9 4 0 2
9286 9 5 4 5 7978 20
9545 9 8 4 5 8271
10380 9845 )regnorts = evitagen ,rekaew = evitisop( tfihS knaR
9845 10406 10380 8520
----- ----- ----- ---- ---
10380 8555
10406 10843 10406
11410 11410 8578
10843
11410 11928 11846 8865
----- ----- ----- ---- ---
11846 11997 11928 9116
10
11928 12734 11997 9281
---------------- ----- ----- ----- ---
11997 12788 9286
12734 12734
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13288 14080 14080
DI erutaeF 13744 14352 10406
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23547 24368 22629
24481
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----- --------- --------- --------- ---
24804 24481 24481
25087 25291
25087 25555 25087
25310 25291 25555
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50
ckpt-2-to-ckpt-1 Rank Shift ckpt-3-to-ckpt-2 Rank Shift ckpt-4-to-ckpt-3 Rank Shift ckpt-5-to-ckpt-4 Rank Shift
Figure8: FeaturerankshiftacrossadjacentcheckpointsduringSFTonQwen3-4B-Base.

Qwen3-4B-RL 50

254 254 86 86
1520 1171 158 158
1742 1308 254 254
1868 1520 805 645
2117 1742 1171 805
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7878 6 8 9 5 7 5 2 4 )regnorts = evitagen ,rekaew = evitisop( tfihS knaR
8080 6 9 3 2 7 5 3 2 7 7 2 6
---------------- --------- --------- --------- ---
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50
ckpt-2-to-ckpt-1 Rank Shift ckpt-3-to-ckpt-2 Rank Shift ckpt-4-to-ckpt-3 Rank Shift ckpt-5-to-ckpt-4 Rank Shift
Figure9: FeaturerankshiftacrossadjacentcheckpointsduringRLonQwen3-4B-Base.

Qwen2.5-7B-SFT 50

15 440 440 15
440 659 1097 440
646 1097
1 2 2 1 1221 1097
659 1542 1221
1097 1 8 9 5 1895
1221 1962 1542
2241 1962 1962
1962 2332 2241 2241
2241
2842 2689 2332 2332 40
---------------- --------- --------- --------- ---------------------------------------------------
2842 2613 2613
3203 3 2 0 3
5331 5 3 5 8 2 6 8 9 2 6 8 9
2 8 4 2 3 2 0 3
5660 5 5 9 9 3203
5824 5660 5797
6184 5797 5358 6184
6184 5599
6323 6437
7213 6323 5797 7213 30
8117 6974 6184
7213 7542
8509 8509 6974 7898
8642 7213
9534 8642 7542 8117
9534 8509
10583 10583 8117
10893 8509 9761
11186 10893 10583
10934 9761
12220 11186 10893 10893 20
12502 12220 11525
10934 11674 )regnorts = evitagen ,rekaew = evitisop( tfihS knaR
12698 13717 11674
13744 13744 12698 12698
13748 1 3 7 4 8 1 3 6 0 5
1 3 9 9 1 1 3 7 1 7
14301 1 3 9 9 1 1 3 7 1 7
14697 1 4 3 0 1 14906
14906 14697 14906
15353 14914 14914 10
15258 15455 15258
15353 15258
15455 15757 15353 15353
16099 16099 16099
15757 1 6 1 5 1
16008 1 6 2 7 3 16151 16715
DI erutaeF 16273 16361 16991
16361
16715 16715 16715 17819
----- ----- ----- ----- ---
17073 16991 16991 18508
17819 17819 0
17819 19264
18403 18508 18508 19340
18700 18700 18719 19998
1 8 7 1 9
18719 1 9 2 6 4 19264 20148
----- --------- --------- --------- ---
19264 19340 20637
19340 19340
19998 19998 20642
19998 20070 20148 20821
20070 10
20146 20146 20510 21823
20148 20637 22681
20148 2 0 2 7 4 2 0 6 4 2
20274 2 0 5 1 0 2 2 8 7 4
21359 2 0 8 2 1 2 3 2 3 1
2 2 1 2 8 21823
22128 22173 23472
22880 22880 22173 23515
23221 23231 22681
23920
23231 23472 22874 24699 20
----- ----- ----- ----- ---
23472 23637 23231
24299 23637 25727
25339 24418 26051
25727 23920
25787 25727 24299 26279
26051 26506
26051 26613 24418 26613
26385 27227 24699
26613 27550
27738 25727 27678
27738 27778 26051 30
27778 28651 27227 27778
28651 28732 28937
27550
28791 29009 27778 29009
----- --------- --------- --------- ---
28937 2 9 2 7 6 2 9 4 0 7
29448 2 9 4 0 7 2 8 7 3 2
2 9 4 4 8 2 9 0 0 9 2 9 6 3 3
29660 30264
29835 29633 29276
29660 29407 30659 40
30264 29835 29448 31036
30613
30659 30264 29633 31931
----- --------- ----- ----- ---
30659 30264 31945
30984 3 0 9 8 4
31723 3 1 1 3 4 30659 32061
31945 31134 32113
31723 32232
32232 32232 31931
32521 32521 31945 32735
50
ckpt-2-to-ckpt-1 Rank Shift ckpt-3-to-ckpt-2 Rank Shift ckpt-4-to-ckpt-3 Rank Shift ckpt-5-to-ckpt-4 Rank Shift
Figure10: FeaturerankshiftacrossadjacentcheckpointsduringSFTonQwen2.5-7B.

Qwen2.5-7B-RL 50

521 459 267 267
710 521 459 710
1175 710 710 845
1202 1175 845
1307 1202 864
1802 1030 1030
2277 2514 1175 1175
2514 2613 2558 2277
2613 3 5 8 7 2 6 1 3
3587 3 6 2 7 2 5 5 8
3 6 5 0 3 5 8 7 2 5 7 8 40
3650 3 6 2 7 2 6 1 3
3676 3 6 7 6 3 6 5 0
3683 3 6 8 3 3 6 7 6 3 2 0 3
5393 3 7 9 4 3 5 8 7
5960 5 4 2 3 3 6 8 3 3 6 5 0
6062 3 7 9 4
6153 6062 5 4 2 3 3676
6267 6 1 5 3 6 0 6 2 3 6 8 3
6836 6 2 6 7 4 3 9 3
7039 6 9 2 5 6 1 5 3 5 3 5 8 30
7 2 7 9 6 1 7 7
7193 6 9 2 5 5 4 2 3
7368 7 3 6 8 7 2 7 9 5 4 6 4
7427 7 4 2 7 6 0 6 2
7675 7 4 4 1 7 4 2 7
7778 9005 7441 6153
7788 8385 6177
7926 9375 6925
8706 10688 9005
8752 10774 10688 7246
9375 10875 10774 7279 20
10908 11049 7427
9552 )regnorts = evitagen ,rekaew = evitisop( tfihS knaR
9703 11327 11327 7441
9961 11496 11496 8385
10167 11570 11570 8533
10610 11580 11580 10688
10875 11892
10908 11671 10788
11496 12020 11892 11049
11570 12400 12400 11671 10
11892 12702 12702
1 3 3 4 6 11892
12020 1 3 0 6 9 1 2 7 0 2
12702 1 3 3 7 1 1 3 3 4 6 1 3 0 6 9
12882 1 3 7 9 1 1 3 3 7 1
13371 1 3 8 1 7 1 3 8 1 7 1 3 3 4 6
DI erutaeF 13791 1 5 0 0 7 1 3 3 7 1
15007 1 5 4 6 7 1 5 4 6 7 1 4 0 3 3
15345 1 5 4 7 0
15470 1 5 4 7 0 1 5 6 8 9 1 4 9 8 3
15680 15680 1 5 9 3 1 15467 0
15931 1 5 6 8 9 1 5 4 7 0
1 5 9 3 1 1 6 0 0 2 1 5 9 3 1
16099 1 6 0 9 9 1 6 0 9 9
16353 1 6 3 5 3 1 5 9 4 7
16537 1 6 3 5 3 1 7 2 6 6 1 6 0 0 2
17464 1 6 5 3 7 1 6 0 9 9
17472 1 7 2 6 6 1 7 4 5 9
18289 1 7 4 5 9 1 7 4 7 2 1 6 3 5 3
18372 18189 17266
18785 17472 17472 10
18937 18189 18372
19623 18372 18785 18189
18785 20784 18289
19676 20784 20937 18372
21258 18785
21547 20937 21022
22441 21258 21072 20937
22489 22154 21258 21022
22830 22277 21596 21072
22953 22441
23117 21961 21258 20
23640 22743 22014 21596
23652 23117 22154 21961
23502 22173
23797 23652 22014
24032 22277 22173
24447 2 3 7 9 7 2 2 7 4 3 2 3 1 1 7
24506 2 4 8 8 2 2 3 1 1 7
24882 2 5 5 3 9 2 3 5 0 2 2 3 6 4 8
24988 2 5 5 7 1 2 3 6 5 2
25079 2 5 8 3 9 2 3 6 4 8 2 4 8 8 2
25155 2 3 6 5 2 2 5 8 3 9 30
25839 2 6 0 5 1 2 4 8 8 2
2 6 6 2 1 2 5 5 3 9 2 5 9 2 0
26393 26760 26051
26453 2 7 0 3 5 2 5 5 7 1 2 6 2 2 4
26621 2 7 0 5 7 2 5 8 3 9
26760 2 5 9 2 0 2 6 3 2 4
27057 2 7 2 8 5 2 6 0 5 1 2 6 8 7 3
28734 2 9 1 6 8 2 7 0 5 7
28964 2 9 3 0 2 2 6 2 2 4
29006 2 9 5 3 8 2 7 0 3 5 2 7 1 3 9 40
29168 2 7 0 5 7 2 8 1 5 1
29302 2 9 9 2 4 29039
30109 27285
29538 30419 29168 29168
30109 30615 29302 29302
30615 30902 29924 30123
30902 30574
30992 31384 30419
31384 31423 30574 30661
31423 31896 31896 32311
50
ckpt-2-to-ckpt-1 Rank Shift ckpt-3-to-ckpt-2 Rank Shift ckpt-4-to-ckpt-3 Rank Shift ckpt-5-to-ckpt-4 Rank Shift
Figure11: FeaturerankshiftacrossadjacentcheckpointsduringRLonQwen2.5-7B.

Llama3.1-8b-Instruct-SFT 50

279 279 567 567
1000 567 779
1097 1000
779 1000
1621 1 0 0 0 1097
1741 1 0 9 7 1103
1 1 0 3 1 1 0 3
1923 1621 1621
2190 1621
2691 2190 2190
2447 2190 40
3242 2447 2691
5351 3468
2691 2856
6202 5351 3009
6531 6202 3009
6612 3468 3468
6612
6869 6869 6202 6202
---- ---- ---- ---- ---
7682
7682 6612 6612 30
----- ---- ---- ---- ---
7838 7838 6869
8523 6869
9123 8523 6973
9123 6973
9671 7682 8445
10434 9309 9123
10456 9671 9123
9309
10613 9787 9309
----- ----- ---- ---- ---
10759 10434 9671
9787 9671 20
11288 10759
11442 11288 9904 9904 )regnorts = evitagen ,rekaew = evitisop( tfihS knaR
11879 10434
----- ----- ----- ----- ---
11442 10434
11955 11952 10759 11288
12133
12145 11288 12145
----- ----- ----- ----- ---
12145 11952
12225 12225 12849
12697 12697 12145 10
13184
12849 12849 12849
----- ----- ----- ----- ---
13086 13184 13184 13418
14114
13184 13418 13418
---------------- ----- ----- ----- ---
13418 13759 14665
DI erutaeF 13759 14114
14114 14665 15079
14114 14255
14255 15079 15467
14665 0
14406 15079 15467 15655
14665 15655
15079 15655 16296
16296 16296 17043
15253
15655 17309 17043 17309
----- ----- ----- ----- ---
16296 17425 17309
17425
17205 17459 17425
----- ----- ----- ----- ---
17309 17947 10
18341 17459
17411 18567 17947 18341
17425 18567
18341 18992 18567
19299 19071
18439 18992
18496 19499 19071 19299
19821
18567 19299 19499
----- ----- ----- ----- ---
19299 21141 19499
19499 21365 19821 20
20918
19821 21720 20918
----- ----- ----- ----- ---
21365 21945 21141 21141
21365
21945 22513 21365
----- ----- ----- ----- ---
22513 22754 21720
22754 21720
23231 21945
23396 23396 22513 21945
24038
23408 22754 22513 30
--- ----- ----- ----- ---
25051
25511 25051 23231 22754
----- --------- --------- ----- ---
26064 25511 23396 23396
26389 26064 23408 25511
29460 26389
29627 25511 26064
29501 26064
29728 29627 26389
29989 26389 40
29728 26978
30060 29989 26978 27663
30151 2 9 5 0 1
30216 3 0 0 6 0 27982
3 0 1 5 1 2 9 6 2 7
30518 29627
31003 30216 29728
30518 30151 29728
31774
32628 31003 31003 30151
----- ----- ----- ----- ---
50
ckpt-2-to-ckpt-1 Rank Shift ckpt-3-to-ckpt-2 Rank Shift ckpt-4-to-ckpt-3 Rank Shift ckpt-5-to-ckpt-4 Rank Shift
Figure12: FeaturerankshiftacrossadjacentcheckpointsduringSFTonLlama3.1-8B-Instruct.

Llama3.1-8b-Instruct-RL 50

7 3 1 1
8 8 3 5
15 9 5 7
17
18 15 7 8
--- --- --- --- ---
21 17 8 16
22 18
18 9
23 21 16 21
28 22 17 22
30 23 40
31 23 22
32 24 23 24
34 28 31
35 24
30 30 32
38 31 31 33
45 32 34
54 32
55 34 33 35
58 35 37 30
63 34 38
37 35
67 38 37 39
71 54 42
74 38 45
86 55 39
88 57 45 49
97 5 8 5 2
100 4 9 5 3
6 3 5 5
101 6 8 5 4 2 0
106 5 7 5 5
107 6 9 6 2 )regnorts = evitagen ,rekaew = evitisop( tfihS knaR
108 7 1 6 3 5 7
-------------- ----- ----- ------ ---
113 7 3 5 8
120 6 8 6 2
123 7 4 6 9
8 5 6 3
128 8 6 7 0 6 6
129 7 1 6 8
133 8 7 7 3 1 0
134 8 8 7 0
136 7 4 7 3
138 9 1 8 2 7 4
145 9 7
100 85 81
148 86 82
DI erutaeF 150 106 87 84
162 113
179 114 88 85
180 91 86
182 115 87 0
116 97
199 100 88
200 120 105 90
203 123
207 125 106 91
211 108 93
214 1 2 8 1 1 3 9 7
217 1 2 9
1 3 3 1 1 4 1 0 2
219 1 1 5 1 0 5 1 0
221 1 3 4 1 0 6
236 1 3 6 1 1 6
238 1 2 0 1 0 8
248 1 3 8 1 2 3 1 1 3
254 1 4 5 1 1 4
270 1 4 7 1 2 5
1 2 9 1 1 5
281 1 4 8 1 1 6
287 1 5 5 1 3 3 1 2 0
298 1 6 2 1 3 4
323 1 3 6 1 2 3 2 0
346 1 7 9 1 2 5
350 1 8 0 1 4 5
147 16 1 0
353 182 1988
374 200 148 2691
379 203 155
382 162 3029
394 211 4727
400 214 179 6973
408 219 1610
8063 30
415 221 1988 10930
420 236 2050 12982
423 3029
425 238 13600
432 248 4511 14665
433 254 6973 15248
445 8063
1610 20405
446 1988 9962 21376
447 2050 10930 40
454 25051
456 4511 12982 25831
464 6973 14665 26510
486 18247
9962 26761
501 10930 21376 27913
505 18247 27913 30507
6973
30591 30591 30591 30591
----- ----- ----- ----- ---
32100 32100 32100 32100
50
ckpt-2-to-ckpt-1 Rank Shift ckpt-3-to-ckpt-2 Rank Shift ckpt-4-to-ckpt-3 Rank Shift ckpt-5-to-ckpt-4 Rank Shift
Figure13: FeaturerankshiftacrossadjacentcheckpointsduringRLonLlama3.1-8B-Instruct.