| | 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- | | | | | | | | | ----------------- | ----------- | --- | ------- | --- | --------- | --- | --- | --- | --- | --- | --- | --- | 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 | | References | | | | | | preprintarXiv:2503.18878. | | | | | | | DavidDBaekandMaxTegmark.2025. 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KaichenZhang,YifeiShen,BoLi,andZiweiLiu.2025. Largemulti-modalmodelscaninterpretfeaturesin | large multi-modal | | models. | In | Proceedings | of the | | ----------------- | ------------- | ------- | ---------- | ----------- | -------- | | IEEE/CVF | International | | Conference | on | Computer | Vision,pages3650–3661. | Yaowei Zheng, | Richong | Zhang, | | Junhao Zhang, | Yan- | | ------------- | ------- | ------ | --- | ------------- | ---- | hanYe,ZheyanLuo,ZhangchiFeng,andYongqiang | Ma. 2024. | Llamafactory: | | Unified | efficient | fine- | | --------- | ------------- | -------- | ------- | --------- | -------- | | tuning of | 100+ | language | models. | arXiv | preprint | arXiv:2403.13372. 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 | | | 1546 | 1546 | | | | | 2513 | | 2685 | 2139 | | | | 2513 | 2955 | | | | 2618 | 2 6 1 8 | | 2513 | | | 2955 | | 3 1 5 2 | 2 6 1 8 | | | 3152 | 2 9 5 5 | 3 5 9 9 | | 40 | | | 3 1 5 2 | | 2 6 8 5 | | | 3290 | | 4 0 5 5 | 2 9 5 5 | | | 3819 | 3 8 1 9 | 4 3 3 7 | | | | | 4 0 5 5 | | 3 1 5 2 | | | 5976 | | 5976 | 3291 | | | 6132 | 4337 | 6857 | | | | 6663 | 6857 | | 3469 | | | | | 7460 | 3599 | | | 6857 | 7460 | 7746 | | | | 7460 | 8271 | | 4337 | 30 | | 7857 | 8865 | 7978 | 5505 | | 8271 | 8520 | 8997 | | 5976 | | | ---- | ------- | ------- | ---- | --- | | 8578 | 9116 | 8865 | | | | 8865 | | 9116 | 6333 | | | | 9281 | | 6857 | | | 8997 | 9286 | 9281 | | | | 9116 | | 9286 | 7746 | | | 9281 | 9402 | | 7883 | | | | 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 | | | | | 13288 | 13744 | 9545 | | | 12788 | 13744 | | 10380 | | | 13288 | 14080 | 14080 | | | | DI erutaeF 13744 | | 14352 | 10406 | | | | 14352 | | 11410 | | | 13933 | 14381 | 14381 | | | | 14080 | | 14392 | 11846 | | | 14111 | 14392 | | | 0 | | | 14458 | 14458 | 12734 | | | 14336 | | 14545 | 13488 | | | 14392 | 14545 | | | | | | 14688 | 15151 | 13744 | | | 14458 | | 18362 | 14336 | | | 14545 | 15151 | | | | | 14688 | 15762 | 18403 | 14352 | | | | | 18686 | 14392 | | | 15762 | 18299 | | | | | 16834 | 18362 | 18802 | 14458 | 10 | | 18299 | 18403 | 19164 | 14545 | | | 18362 | 18686 | 19325 | 14756 | | | 20826 | 19325 | 19583 | | | | 21495 | | | 18362 | | | | 19583 | 19979 | 18403 | | | 21594 | 19979 | 21495 | | | | 21608 | | | 18686 | | | 21853 | 20826 | 21594 | 18802 | | | | 21495 | 21608 | | | | 21906 | | | 19164 | 20 | | 22103 | 21608 | 21906 | 19325 | | | | 21906 | 22103 | | | | 22152 | 22103 | | 19979 | | | 22629 | | 22152 | 21594 | | | 22773 | 22152 | 22629 | | | | | 22629 | | 21608 | | | 23294 | | 23080 | | | | 23474 | 23474 | 24451 | 22152 | | | 23547 | 24368 | | 22629 | | 24481 | 24368 | 24451 | 25087 | 23080 | 30 | | ----- | --------- | --------- | --------- | --- | | 24804 | 24481 | | 24481 | | | 25087 | | 25291 | | | | | 25087 | 25555 | 25087 | | | 25310 | 25291 | | 25555 | | | 25555 | 2 5 5 5 5 | 26120 | | | | 26101 | | 2 7 1 0 1 | 2 6 1 2 0 | | | | 2 6 1 0 1 | | 2 6 9 2 9 | | | 27101 | 2 6 1 2 0 | 2 7 6 8 1 | | | | 28805 | | 2 7 9 5 4 | 2 7 1 0 1 | | | | 2 7 9 5 4 | | | 40 | | 29122 | 2 8 8 0 5 | 2 8 8 0 5 | 2 7 5 2 0 | | | 29214 | | 29214 | 27681 | | | 29719 | 29122 | | | | | | 29214 | 29485 | 28805 | | | 29721 | | 29719 | 29214 | | | 29792 | 29719 | | | | | 30253 | 29721 | 29721 | 29485 | | | | | 30381 | 29721 | | | 30333 | 30381 | | | | | 32267 | 32507 | 32507 | 30381 | | 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 | | | 2357 | 1868 | 1308 | 946 | | | 2537 | | | 1523 | | | 2712 | 1929 | 1929 | 1883 | | | | 2117 | 2357 | | | | 2756 | 2 3 5 7 | 2 4 7 0 | 2 3 5 7 | | | 2792 | 2 4 7 0 | 2 4 9 9 | 2 4 9 9 | 40 | | 3289 | 2537 | 2712 | 2601 | | | 3585 | | 2 7 5 6 | 2 7 1 2 | | | 3609 | 2 7 1 2 | 3 0 0 9 | 2 7 5 6 | | | 4088 | 2 7 5 6 | | 3 0 0 9 | | | 4430 | 3 0 0 9 | 3 0 2 5 | 3 0 2 5 | | | 4967 | 4 0 8 8 | 3 2 1 5 | | | | | 4 4 3 0 | 4 4 3 0 | 3 2 1 5 | | | 4998 | | 4 5 4 7 | 4 4 3 0 | | | 5001 | 4 9 9 8 | 4 9 9 8 | 4 5 4 7 | | | 5120 | 5 0 0 1 | 5 3 3 1 | 4 7 7 4 | 3 0 | | 5286 | 5 2 8 6 | | 5 4 1 0 | | | 5648 | 5 3 3 1 | 5 4 1 0 | 5 5 8 7 | | | 5938 | 5 4 1 0 | 5 5 8 7 | 6 0 6 3 | | | 6000 | 5 6 4 8 | 5 7 3 5 | | | | 6292 | | 6 0 0 0 | 6 2 6 5 | | | | 5 7 3 5 | 6 1 1 5 | 6 4 1 2 | | | 6348 | 5 9 3 8 | 6 2 6 5 | 6 5 1 1 | | | 6663 | 6 0 0 0 | | 6 8 1 6 | | | 6932 | 6 1 1 5 | 6 3 4 8 | 7 1 9 0 | | | 7027 | 6 3 4 8 | 6 8 9 5 | 7 2 8 8 | | | 7038 | | 6 9 6 1 | 7 3 4 9 | 2 0 | | 7524 | 6 6 6 3 | 7 4 9 7 | 7 4 9 7 | | 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 | | | ---------------- | --------- | --------- | --------- | --- | | | 6 9 6 1 | | 8 9 9 9 | | | 8183 | 7 0 3 8 | 7 6 9 5 | 9 2 5 9 | | | 8329 | | 7 7 2 6 | 9 2 8 6 | | | 9253 | 7 5 2 4 | 8 4 3 6 | 9 6 3 6 | | | 9286 | 7 5 3 2 | 8 7 3 3 | 10 0 3 8 | | | 9372 | 7695 | 9259 | 10471 | | | 10558 | 7878 | 9286 | | 10 | | 10684 | 8080 | | 10737 | | | 10737 | | 10471 | 11007 | | | | 8183 | 10695 | 11262 | | | 11007 | 8436 | 10737 | 12086 | | | 11766 | 8733 | 10803 | 13220 | | | 12146 | 9286 | 11262 | 13931 | | | DI erutaeF 12296 | 10558 | 12086 | 14540 | | | 12583 | 10684 | 13220 | | | | 13422 | | | 14798 | | | 13568 | 10695 | 13931 | 15448 | | | 14101 | 10803 | 14563 | 15656 | 0 | | | 11262 | 15448 | 15755 | | | 14449 | 12086 | 15656 | 15840 | | | 14609 | 12296 | 15755 | 16458 | | | 14798 | | 15840 | 16814 | | | 15448 | 13568 | | | | | 15840 | 14449 | 16458 | 17012 | | | 16655 | 14563 | 17315 | 17315 | | | 16847 | 15448 | 17703 | 17881 | | | 17061 | 15755 | 17821 | 18729 | | | | | 17881 | 18766 | 10 | | 17276 | 15840 | 18729 | 19527 | | | 17315 | 16655 | | 1 9 8 1 5 | | | 17317 | 1 7 3 1 5 | 1 8 7 6 6 | 2 1 2 2 6 | | | 17480 | 1 7 4 8 0 | 1 9 5 2 7 | | | | 17703 | 1 7 7 0 3 | 1 9 5 8 3 | 2 1 2 8 7 | | | 17881 | 1 7 8 2 1 | 2 0 8 1 9 | 2 1 4 2 2 | | | 18415 | | 2 1 2 2 6 | 2 1 5 1 3 | | | 18575 | 1 8 8 1 1 | 2 1 4 2 2 | 2 1 5 1 4 | | | | 1 9 5 8 3 | | 2 1 7 0 2 | | | 18721 | 1 9 8 1 5 | 2 1 4 8 8 | 2 1 7 5 5 | | | 18811 | 2 0 6 7 6 | 2 1 6 2 7 | 2 1 9 4 5 | 2 0 | | 19072 | 2 0 8 1 9 | 2 1 6 6 1 | | | | 19527 | | 2 1 7 0 2 | 2 2 0 8 3 | | | 19815 | 2 1 2 8 7 | 2 2 0 8 3 | 2 2 7 4 6 | | | 19966 | 2 1 4 2 2 | 2 2 9 1 9 | 2 3 0 1 1 | | | 20676 | 2 1 4 8 8 | | 2 3 0 6 9 | | | 20910 | 2 1 6 2 7 | 2 3 0 1 1 | 2 3 1 9 2 | | | | 2 1 6 6 1 | 2 3 0 6 9 | 2 3 8 2 4 | | | 21287 | | 2 3 1 9 2 | 2 3 8 7 2 | | | 21661 | 2 1 7 0 2 | 2 3 9 5 6 | | | | 21702 | 2 2 9 1 9 | 2 4 3 4 1 | 2 3 9 5 6 | | | 22919 | 2 3 0 6 9 | 2 4 3 6 8 | 2 4 3 6 8 | 3 0 | | 23192 | 2 3 1 9 2 | | 2 4 4 7 4 | | | 23220 | 2 3 9 5 6 | 2 4 4 1 5 | 2 4 9 9 8 | | | 23956 | 2 4 3 4 1 | 2 4 9 9 8 | 2 5 0 0 9 | | | 24243 | | 2 5 0 0 9 | 2 5 4 1 4 | | | | 2 4 3 9 8 | 2 5 4 1 4 | 2 6 0 8 0 | | | 24341 | 2 4 4 1 5 | 2 6 0 8 0 | 2 6 1 5 1 | | | 24398 | 2 4 9 9 8 | 2 6 2 1 3 | | | | 24931 | 25049 | 26891 | 2 6 8 9 1 | | | 25049 | 2 5 5 5 4 | | 27486 | | | 25554 | | 2 7 4 8 6 | 2 7 5 4 9 | 40 | | 27347 | 2 6 0 8 0 | 2 7 5 4 9 | 2 8 6 1 3 | | | 27468 | 26213 | 27704 | 28854 | | | 27486 | 27486 | 28613 | 29081 | | | 27505 | 27505 | 29081 | 29147 | | | | 27704 | 29147 | | | | 28613 | | | 30542 | | | 28699 | 29081 | 29155 | 31350 | | | 29146 | 29155 | 30803 | 31817 | | | 30400 | 30400 | 31817 | 31903 | | | 30542 | 30803 | 31903 | 32219 | | 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.