q129/random_k2/random_2.md

|     | 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
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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
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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. Towardsun- LeoGao, TomDuprélaTour, HenkTillman, Gabriel
derstandingdistilledreasoningmodels: Arepresenta- Goh, Rajan Troll, Alec Radford, Ilya Sutskever,
tionalapproach. arXivpreprintarXiv:2503.03730. Jan Leike, and Jeffrey Wu. 2024a. Scaling and
|                                                 |     |                             |     |     |     | evaluating        | sparse | autoencoders. |     |     | arXiv | preprint |
| ----------------------------------------------- | --- | --------------------------- | --- | --- | --- | ----------------- | ------ | ------------- | --- | --- | ----- | -------- |
| YonatanBisk,RowanZellers,JianfengGao,YejinChoi, |     |                             |     |     |     | arXiv:2406.04093. |        |               |     |     |       |          |
| and1others.2020.                                |     | PIQA:Reasoningaboutphysical |     |     |     |                   |        |               |     |     |       |          |
commonsenseinnaturallanguage. InProceedings Leo Gao, Jonathan Tow, Baber Abbasi, Stella Bider-
oftheAAAIconferenceonartificialintelligence,vol- man, Sid Black, Anthony DiPofi, Charles Foster,
ume34,pages7432–7439. Laurence Golding, Jeffrey Hsu, Alain Le Noac’h,
|     |     |     |     |     |     | Haonan | Li, Kyle | McDonell, |     | Niklas | Muennighoff, |     |
| --- | --- | --- | --- | --- | --- | ------ | -------- | --------- | --- | ------ | ------------ | --- |
Yupeng Chang, Xu Wang, Jindong Wang, Yuan Wu, ChrisOciepa,JasonPhang,LariaReynolds,Hailey
| Linyi Yang, | Kaijie | Zhu, Hao | Chen, | Xiaoyuan | Yi, |     |     |     |     |     |     |     |
| ----------- | ------ | -------- | ----- | -------- | --- | --- | --- | --- | --- | --- | --- | --- |
Schoelkopf,AviyaSkowron,LintangSutawika,and
CunxiangWang,YidongWang,and1others.2024. 5 others. 2024b. The language model evaluation
| A survey | on evaluation | of  | large | language | models. | harness. |     |     |     |     |     |     |
| -------- | ------------- | --- | ----- | -------- | ------- | -------- | --- | --- | --- | --- | --- | --- |
ACMtransactionsonintelligentsystemsandtechnol-
ogy,15(3):1–45. AaronGrattafiori,AbhimanyuDubey,AbhinavJauhri,
|     |     |     |     |     |     | Abhinav | Pandey, | Abhishek |     | Kadian, | Ahmad | Al- |
| --- | --- | --- | --- | --- | --- | ------- | ------- | -------- | --- | ------- | ----- | --- |
RuizheChen,TianxiangHu,YangFeng,andZuozhu
Dahle,AieshaLetman,AkhilMathur,AlanSchelten,
Liu. 2024. Learnable privacy neurons localization AlexVaughan,and1others.2024. Thellama3herd
inlanguagemodels. InProceedingsofthe62ndAn- ofmodels. arXivpreprintarXiv:2407.21783.
nualMeetingoftheAssociationforComputational
Linguistics,ACL2024-ShortPapers,Bangkok,Thai- Daya Guo, Dejian Yang, Haowei Zhang, Junxiao
land,August11-16,2024,pages256–264.Associa- Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shi-
rongMa,PeiyiWang,XiaoBi,and1others.2025.
tionforComputationalLinguistics.
|     |     |     |     |     |     | Deepseek-r1: |     | Incentivizingreasoningcapabilityin |     |     |     |     |
| --- | --- | --- | --- | --- | --- | ------------ | --- | ---------------------------------- | --- | --- | --- | --- |
TianzheChu,YuexiangZhai,JihanYang,Shengbang LLMs via reinforcement learning. arXiv preprint
| Tong, Saining | Xie, | Dale Schuurmans, |     | Quoc | V Le, | arXiv:2501.12948. |     |     |     |     |     |     |
| ------------- | ---- | ---------------- | --- | ---- | ----- | ----------------- | --- | --- | --- | --- | --- | --- |

ZishanGuo,RenrenJin,ChuangLiu,YufeiHuang,Dan NeginRaoof,EtashKumarGuha,RyanMarten,Jean
Shi,LinhaoYu,YanLiu,JiaxuanLi,BojianXiong, Mercat, Eric Frankel, Sedrick Keh, Hritik Bansal,
and Deyi Xiong. 2023. Evaluating large language GeorgiosSmyrnis,MariannaNezhurina,TrungVu,
models: A comprehensive survey. arXiv preprint ZayneReaSprague,MikeAMerrill,LiangyuChen,
arXiv:2310.19736. CarolineChoi,ZaidKhan,SachinGrover,Benjamin
|     |     |     |     |     |     |     | Feuer, | Ashima | Suvarna, | Shiye | Su, and | 27 others. |
| --- | --- | --- | --- | --- | --- | --- | ------ | ------ | -------- | ----- | ------- | ---------- |
ZhuowenHan,XinweiWu,DanShi,RenrenJin,and 2025. AutomaticevalsforLLMs.
| DeyiXiong.2025. |     | Towardsaunifiedparadigmof |     |     |     |     |     |     |     |     |     |     |
| --------------- | --- | ------------------------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
concepteditinginlargelanguagemodels. InProceed- Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu,
ingsofthe2025ConferenceonEmpiricalMethodsin
JunxiaoSong,XiaoBi,HaoweiZhang,Mingchuan
NaturalLanguageProcessing,pages18445–18461.
|     |     |     |     |     |     |     | Zhang, | YK  | Li, Yang | Wu, and | 1 others. | 2024. |
| --- | --- | --- | --- | --- | --- | --- | ------ | --- | -------- | ------- | --------- | ----- |
AssociationforComputationalLinguistics. DeepSeekMath: Pushingthelimitsofmathematical
|                                                |     |     |     |     |     |     | reasoninginopenlanguagemodels. |     |     |     | arXivpreprint |     |
| ---------------------------------------------- | --- | --- | --- | --- | --- | --- | ------------------------------ | --- | --- | --- | ------------- | --- |
| DanHendrycks,CollinBurns,StevenBasart,AndyZou, |     |     |     |     |     |     | arXiv:2402.03300.              |     |     |     |               |     |
MantasMazeika,DawnSong,andJacobSteinhardt.
2021. Measuringmassivemultitasklanguageunder-
|           |                                     |     |     |     |     |     | Guangming | Sheng, | Chi Zhang, | Zilingfeng |     | Ye, Xibin |
| --------- | ----------------------------------- | --- | --- | --- | --- | --- | --------- | ------ | ---------- | ---------- | --- | --------- |
| standing. | InInternationalConferenceonLearning |     |     |     |     |     |           |        |            |            |     |           |
Wu,WangZhang,RuZhang,YanghuaPeng,Haibin
| Representations. |     |     |     |     |     |     | Lin,andChuanWu.2025.       |     |     | HybridFlow: |                 | Aflexible |
| ---------------- | --- | --- | --- | --- | --- | --- | -------------------------- | --- | --- | ----------- | --------------- | --------- |
|                  |     |     |     |     |     |     | andefficientRLHFframework. |     |     |             | InProceedingsof |           |
Maggie Huan, Yuetai Li, Tuney Zheng, Xiaoyu Xu, the Twentieth European Conference on Computer
SeungoneKim,MinxinDu,RadhaPoovendran,Gra-
Systems,pages1279–1297.
| hamNeubig,andXiangYue.2025. |     |         |                   | Doesmathrea- |        |     |          |        |              |       |         |       |
| --------------------------- | --- | ------- | ----------------- | ------------ | ------ | --- | -------- | ------ | ------------ | ----- | ------- | ----- |
| soning improve              |     | general | LLM capabilities? |              | under- |     |          |        |              |       |         |       |
|                             |     |         |                   |              |        |     | Dan Shi, | Renren | Jin, Tianhao | Shen, | Weilong | Dong, |
arXiv
standing transferability of LLM reasoning. XinweiWu,andDeyiXiong.2024a. IRCAN:Mit-
preprintarXiv:2507.00432. igatingknowledgeconflictsinLLMgenerationvia
identifyingandreweightingcontext-awareneurons.
AaronJaech,AdamKalai,AdamLerer,AdamRichard-
AdvancesinNeuralInformationProcessingSystems,
| son, Ahmed | El-Kishky, |     | Aiden | Low, | Alec Helyar, |     |     |     |     |     |     |     |
| ---------- | ---------- | --- | ----- | ---- | ------------ | --- | --- | --- | --- | --- | --- | --- |
37:4997–5024.
AleksanderMadry,AlexBeutel,AlexCarney,and1
| others.2024. | Openaio1systemcard. |     |     | arXivpreprint |     |     |     |     |     |     |     |     |
| ------------ | ------------------- | --- | --- | ------------- | --- | --- | --- | --- | --- | --- | --- | --- |
DanShi,TianhaoShen,YufeiHuang,ZhigenLi,Yongqi
arXiv:2412.16720.
Leng,RenrenJin,ChuangLiu,XinweiWu,Zishan
|               |          |            |         |          |             |     | Guo,                              | Linhao | Yu, and | 1 others. | 2024b.        | Large lan- |
| ------------- | -------- | ---------- | ------- | -------- | ----------- | --- | --------------------------------- | ------ | ------- | --------- | ------------- | ---------- |
| Jack Lindsey, | Adly     | Templeton, |         | Jonathan | Marcus,     |     |                                   |        |         |           |               |            |
|               |          |            |         |          |             |     | guagemodelsafety:Aholisticsurvey. |        |         |           | arXivpreprint |            |
| Thomas        | Conerly, | Joshua     | Batson, | and      | Christopher |     |                                   |        |         |           |               |            |
arXiv:2412.17686.
| Olah. 2024. | Sparse    | crosscoders |             | for | cross-layer |     |     |     |     |     |     |     |
| ----------- | --------- | ----------- | ----------- | --- | ----------- | --- | --- | --- | --- | --- | --- | --- |
| features    | and model | diffing.    | Transformer |     | Circuits    |     |     |     |     |     |     |     |
DanShi,ChaobinYou,JiantaoHuang,TaihaoLi,and
Thread.
|     |     |     |     |     |     |     | DeyiXiong.2024c. |     | CORECODE:Acommonsense |     |     |     |
| --- | --- | --- | --- | --- | --- | --- | ---------------- | --- | --------------------- | --- | --- | --- |
annotateddialoguedatasetwithbenchmarktasksfor
| Jian Liu, Leyang | Cui, | Hanmeng    | Liu, | Dandan | Huang,  |     |         |       |          |         |                |     |
| ---------------- | ---- | ---------- | ---- | ------ | ------- | --- | ------- | ----- | -------- | ------- | -------------- | --- |
|                  |      |            |      |        |         |     | chinese | large | language | models. | In Proceedings | of  |
| Yile Wang,       | and  | Yue Zhang. |      | 2021.  | LogiQA: | a   |         |       |          |         |                |     |
theAAAIConferenceonArtificialIntelligence,vol-
| challenge | dataset | for machine |     | reading | comprehen- |     |     |     |     |     |     |     |
| --------- | ------- | ----------- | --- | ------- | ---------- | --- | --- | --- | --- | --- | --- | --- |
sion with logical reasoning. In Proceedings of the ume38,pages18952–18960.
Twenty-NinthInternationalConferenceonInterna-
|              |             |     |               |     |               |     | Alon Talmor,         |     | Jonathan Herzig, | Nicholas             | Lourie, | and |
| ------------ | ----------- | --- | ------------- | --- | ------------- | --- | -------------------- | --- | ---------------- | -------------------- | ------- | --- |
| tional Joint | Conferences |     | on Artificial |     | Intelligence, |     |                      |     |                  |                      |         |     |
|              |             |     |               |     |               |     | JonathanBerant.2019. |     |                  | CommonsenseQA:Aques- |         |     |
pages3622–3628.
|     |     |     |     |     |     |     | tion answering |     | challenge | targeting | commonsense |     |
| --- | --- | --- | --- | --- | --- | --- | -------------- | --- | --------- | --------- | ----------- | --- |
InProceedingsofthe2019Conference
| MichaelLuo,SijunTan,JustinWong,XiaoxiangShi, |     |     |     |     |     |     | knowledge. |     |     |     |     |     |
| -------------------------------------------- | --- | --- | --- | --- | --- | --- | ---------- | --- | --- | --- | --- | --- |
WilliamY.Tang,MananRoongta,ColinCai,Jeffrey oftheNorthAmericanChapteroftheAssociationfor
Luo,LiErranLi,RalucaAdaPopa,andIonStoica. ComputationalLinguistics: HumanLanguageTech-
nologies,Volume1(LongandShortPapers),pages
| 2025. DeepScaleR: |     | Surpassing |     | o1-preview | with | a   |     |     |     |     |     |     |
| ----------------- | --- | ---------- | --- | ---------- | ---- | --- | --- | --- | --- | --- | --- | --- |
4149–4158,Minneapolis,Minnesota.Associationfor
| 1.5bmodelbyscalingRL. |     |     | NotionBlog. |     |     |     |     |     |     |     |     |     |
| --------------------- | --- | --- | ----------- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
ComputationalLinguistics.
SamuelMarks,CanRager,EricJMichaud,YonatanBe-
linkov,DavidBau,andAaronMueller.2025. Sparse Kimi Team, Angang Du, Bofei Gao, Bowei Xing,
featurecircuits:Discoveringandeditinginterpretable Changjiu Jiang, Cheng Chen, Cheng Li, Chenjun
|     |     |     |     | InTheThirteenth |     |     | Xiao,ChenzhuangDu,ChonghuaLiao,and1others. |     |     |     |     |     |
| --- | --- | --- | --- | --------------- | --- | --- | ------------------------------------------ | --- | --- | --- | --- | --- |
causalgraphsinlanguagemodels.
|               |            |     |             |     |             |     | 2025.     | Kimi | k1. 5: Scaling                 | reinforcement |     | learning |
| ------------- | ---------- | --- | ----------- | --- | ----------- | --- | --------- | ---- | ------------------------------ | ------------- | --- | -------- |
| International | Conference |     | on Learning |     | Representa- |     |           |      |                                |               |     |          |
| tions.        |            |     |             |     |             |     | withLLMs. |      | arXivpreprintarXiv:2501.12599. |               |     |          |
TodorMihaylov,PeterClark,TusharKhot,andAshish David Vilares and Carlos Gómez-Rodríguez. 2019.
Sabharwal.2018. Canasuitofarmorconductelec- HEAD-QA:Ahealthcaredatasetforcomplexreason-
tricity? a new dataset for open book question an- ing. InProceedingsofthe57thAnnualMeetingof
swering. InProceedingsofthe2018Conferenceon theAssociationforComputationalLinguistics,pages
EmpiricalMethodsinNaturalLanguageProcessing, 960–966,Florence,Italy.AssociationforComputa-
| pages2381–2391. |     |     |     |     |     |     | tionalLinguistics. |     |     |     |     |     |
| --------------- | --- | --- | --- | --- | --- | --- | ------------------ | --- | --- | --- | --- | --- |

JohannesWelbl,NelsonFLiu,andMattGardner.2017.
| Crowdsourcing |     | multiple | choice | science | questions. |
| ------------- | --- | -------- | ------ | ------- | ---------- |
InProceedingsofthe3rdWorkshoponNoisyUser-
generatedText,pages94–106.
JiaqiWeng,HanZheng,HanyuZhang,QinqinHe,Jial-
| ingTao,                           | HuiXue,  | ZhixuanChu, |        | andXitingWang. |            |
| --------------------------------- | -------- | ----------- | ------ | -------------- | ---------- |
| 2025. Safe-SAIL:                  |          | Towards     | a      | fine-grained   | safety     |
| landscape                         | of large | language    | models | via            | sparse au- |
| toencoderinterpretationframework. |          |             |        | arXivpreprint  |            |
arXiv:2509.18127.
XinweiWu,JunzhuoLi,MinghuiXu,WeilongDong,
| ShuangzhiWu, |     | ChaoBian, | andDeyiXiong.2023. |     |     |
| ------------ | --- | --------- | ------------------ | --- | --- |
DEPN:Detectingandeditingprivacyneuronsinpre-
| trainedlanguagemodels. |              |     | InProceedingsofthe2023 |            |      |
| ---------------------- | ------------ | --- | ---------------------- | ---------- | ---- |
| Conference             | on Empirical |     | Methods                | in Natural | Lan- |
guageProcessing,EMNLP2023,Singapore,Decem-
| ber 6-10, | 2023, | pages 2875–2886. |     | Association | for |
| --------- | ----- | ---------------- | --- | ----------- | --- |
ComputationalLinguistics.
AnYang,AnfengLi,BaosongYang,BeichenZhang,
| Binyuan      | Hui,  | Bo Zheng, | Bowen   | Yu,     | Chang     |
| ------------ | ----- | --------- | ------- | ------- | --------- |
| Gao, Chengen |       | Huang,    | Chenxu  | Lv, and | 1 others. |
| 2025.        | Qwen3 | technical | report. | arXiv   | preprint  |
arXiv:2505.09388.
AnYang,BaosongYang,BeichenZhang,BinyuanHui,
BoZheng,BowenYu,ChengyuanLi,DayihengLiu,
FeiHuang,GuantingDong,HaoranWei,HuanLin,
JianYang,JianhongTu,JianweiZhang,JianxinYang,
JiaxinYang,JingrenZhou,JunyangLin,and25oth-
| ers.2024. | Qwen2.5technicalreport. |     |     | arXivpreprint |     |
| --------- | ----------------------- | --- | --- | ------------- | --- |
arXiv:2412.15115.
| Jehyeok Yeon, | Federico                        | Cinus, | Yifan  | Wu,       | and Luca |
| ------------- | ------------------------------- | ------ | ------ | --------- | -------- |
| Luceri.2025.  | GSAE:Graph-regularizedsparseau- |        |        |           |          |
| toencoders    | for robust                      | LLM    | safety | steering. | arXiv    |
preprintarXiv:2512.06655.
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.