Can Models Learn Skill Composition from Examples?
Authors: Haoyu Zhao
Simran Kaur
Dingli Yu
Anirudh Goyal
Sanjeev Arora
Venue: NeurIPS 2024 poster (2024)
Keywords: Skill Composition
Large Language Model
Primary area: generative_models

Abstract: As large language models (LLMs) become increasingly advanced, their ability to exhibit compositional generalization---the capacity to combine learned skills in novel ways not encountered during training---has garnered significant attention. This type of generalization, particularly in scenarios beyond training data, is also of great interest in the study of AI safety and alignment. A recent study introduced the Skill-Mix evaluation, where models are tasked with composing a short paragraph demonstrating the use of a specified $k$-tuple of language skills. While small models struggled with composing even with $k=3$, larger models like GPT-4 performed reasonably well with $k=5$ and $6$.

In this paper, we employ a setup akin to Skill-Mix to evaluate the capacity of smaller models to learn compositional generalization from examples. Utilizing a diverse set of language skills---including rhetorical, literary, reasoning, theory of mind, and common sense---GPT was used to generate text samples that exhibit random subsets of $k$ skills. Subsequent fine-tuning of 7B and 13B parameter models on these combined skill texts, for increasing values of $k$, revealed the following findings: (1) Training on combinations of $k=2$ and $3$ skills results in noticeable improvements in the ability to compose texts with $k=4$ and $5$ skills, despite models never having seen such examples during training. (2) When skill categories are split into training and held-out groups, models significantly improve at composing texts with held-out skills during testing despite having only seen training skills during fine-tuning, illustrating the efficacy of the training approach even with previously unseen skills.

This study also suggests that incorporating skill-rich (potentially synthetic) text into training can substantially enhance the compositional capabilities of models.

Can Models Learn Skill Composition from Examples?
Haoyu Zh 1.2
Simran Kaur
Dingli Yu! Anirudh Goyal Sanjeev Arora 1,2
Department of Computer Science, Princeton University
Princeton Language and Intelligence (PL.), Princeton University
Meta
www.raaaec..i.anettoo..o. princeton. edu
Abstract
As large language models (LLMs) become increasingly advanced, their ability to exhibit compositional generalization- the capacity combine learned skills in novel ways not encountered during training-has garnered significant attention. This type of generalization, particularly in scenarios beyond training data, also of great interest in the study of AI safety and alignment.
A recent study introduced the SKILL-MIX (33) evaluation, where models are tasked with composing a short paragraph demonstrating the use of a specified k-tuple language skills. While small models struggled with composing even with k 3, larger models like GPT-4 performed reasonably well with k = 5 and 6.
In this paper, we employ setup akin to SKILL-MIX to evaluate the capacity of smaller models to learn compositional generalization from examples. Utilizing a diverse set of language skills inclluiinn rhetorical, literary, reasoning, theory of mind, and common sense- GPT-4 was used to generate text samples that exhibit random subsets of l skills. Subsequent fine-tuning of 7B and 13B parameter models on these combined skill texts, for increasing values of k. revealed the following findings:
Training on combinations of k = 2 and 3 skills results in noticeable improve- ments in the ability to compose texts with A: and skills, despite models never having seen such examples during training.
When skill categories significantly improve at composing texts with held-out skills during testing despite having only seen training skills during fine-tuning, illustrating the efficacy of the training approach even with previously unseen skills.
split into training and held-out groups, models
This study also suggests that incorporating skill-rich (potentially synthetic) text into training can substantially enhance the compositional capabilities of models.
Introduction
Today's 's large language models (LLMs) exhibit many impressive skills but remain imperfect in key areas. Arguably, one significant limitation stems from their difficulty in combining or composing skills they have already learned. For example, solving math problem on a specific topic may require certain set of skills, while solving combinations of more skills as compared to a simple question. Understanding how well models can leam to compose skills with limited training examples is therefore a crucial area of investigation.
challenging question may require applying broader
Let us note why this is nontrivial challenge. If model has learned N base skills, and we want be able to compose any subset of skills, there are (M) possible combinations of interest. Since N scales roughly with the k-th power of N, even reasonable-sized training datasets will likely omit k
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Skill Set traiin held
Topic Set
train & held
(1) Data Generation
(3) Evaluation
Train Skilss
Train Topica
Heid-out Skills
Hwid-out Topics
train
T train
he'd out
held out
Selectrandon and topic
Select
1,2,3)
1.2.3.4.5)
Query GPT-4: Generate short test about the Aeelacted topic that exhibits all the selected skills
Query Fine-tuned -ene-tteedd Model: Generate short text about the selected topic that exhibits all the selected skills
Fine-tune Llamm-2-13B-Ohee Mistral-7B-instruut-00..
Grade by GPT-4 Filter
Graded by GPT-4/Claude-3 and Report Metric
Training Data
Figure 1: Pipeline for evaluating the generalization capability to combine skills. We split the language skill set S from 33 into training skills Suain and held-out skills Sheld and the topic set 7 into
training topics Tiaain and held-out topics out The pipeline consists of three steps: (1) generate data by prompting GPT-4. The training texts contain only training skills Suain and training topics Tirain- and each text exhibits at most 3 skills; (2) fine-tune LLaMM-22 2-----2-11- 1----BBBhh and Bestral-7B-Instruct-- using the generated data; (3) evaluate the fine-tuned models on held-out skills Sheld-out and held-out top- ics Theld-out with the number of requested skills being large 5, See our detailed setups in Section 3
examples of many skill combinations. As result, the model must be capable of generalizing to unseen combinations of skills.
This issue was highlighted in [1. which introduced a simple mathematical framework to demonstrate that current L.M scaling laws [3 suggest scaling up models can enhance their ability to combine shills-though the ability increases only gradually with model size. This prediction was validated through the SKILL-MIX evaluation [33], which directly tested models' capability to combine language skills that were listed in the model's prompt (see Section 2 for details). The evaluation revealed that top-tier models like GPT-4 could successfully combine 5 or 6 language skills when composing short piece of text, whereas smaller models like 2- Bhat struggled to combine even 3 skills.
This finding of SKILL-MIX evaluation raises an interesting question: even if pre-training does not fully endow models with the ability to combine skills, can the capability be induced through fine-tuning on suitable data? The current paper investigates this question within the context of the language skills explored in the SKI evaluation (33]
1.1 Our contributions
We address the question posed above by fine-tuning smaller models, including LLaMA-2-13B-CT and 1aadd--7-I-nsttuttt222222 using a small yet high-quality dataset generated by GPT-4. This dataset consists of 13,957 text pieces, each composed of randomly selected & skills with A: 1, 3. We evaluate the capability of the fine-tuned models to combine an another set of held-out skills with potentially higher k. In particular, set and a held-out set, based on skill categories, to minimize correlations between the two groups This ensures clearer evaluation of the models' ability to generalize unseen skills. [ Section 3 detail the full pipeline of our data generation and evaluation process. Our experimental
divide the original SKILL- MIX [33] skill set into training
results demonstrate the following findings (Section 4
Finding 1: Fine-tuning on texts that compose training skills improves capabilities of composing held-out skills. Figure 2 shows the success rate of various models of combining held-out skills. Before fine-tuning, LLaMA-2-1333 13B-Chatt and Mistral-7B B- perform significantly worse than GPT-4, especially when l: > 2. Both models improve remarkably after fine-tuning on our small dataset. For example, with k = 3, the success rate of LLaMA 2- 13B-BBaB increases from 4% to 37%, and the success rate of Mistral-7B-Instrueet.
increases from 8% to 49%. Note in the original SKILL-MIX, model except GPT-4 could reach 15% success rate for k = 3 (see Table 3, (33).

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LLaMA 13B Chat
Mistral 7B Instruct
80
Fine-tuned LLaMA 13B Chat
Ratio of Full Marks
Fine-tuned Mistral 7B Instruct
60
GPT-4
20
0
Figure 2: The success rate of different models to compose held-out skills in a short paragraph. (See the detailed definition of "Ratio of Full Marks" in Section B.3) The strongest model like GPT-4 can compose skills short paragraph reasonably well, while smaller models struggle to compose even 3 skills. After fine-tuning, the models' ability to compose skills improves significantly.
This phenomenon of compositional generalization from training skills to held-out skills suggests that the models are not merely learning to compose each individual combination skills. Instead, they are acquiring a higher-order meta-skil skill that allows them to generalize and apply to combine unseen skills.
Finding 2: Fine-tuning on lexts that compose a smaller number of skills leads improvement of composing larger number of skills. Figure 2 demonstrates that fine-tuning on our small dataset, which includes
composed of k 1.2 2 3 training skills, leads enhanced capability on composing k 4 and held-out skills, even though the models have never trained on such text. In Section
4 we present similar findings: (1) the ability to compose training skills is also improved for l = 4 and after fine-tuning; and (2) if models are fine-tuned exclusively with texts composed of no more than 2 training skills, they also show improved composition ability for 3 and skills.
Note Finding and Finding 2 are beyond the scope of the theory presented in Arora and Goyal 1. which studies the composition ability for skills that appear in the training data.
Finding 3: Fine-tuming on texts that compose more skills (i.e., with larger k) more data data-efficient for learning skill compositions. We design control experiments in Section 4.3 that fine-tune LLaMA- 2-13B-Chat on two datasets: (a) one dataset contains around 10,000 text pieces with only or skills; and (b) another dataset contains 8,000 text pieces, consisting of random subset of the first dataset and around 2,000 text pieces that compose 3 skills. Table 4 shows that LLaMA-2 fine-tuned on the dataset with richer skill composition performs significantly better than the other for all l 2, 2,3, 4,
We discuss our main findings thoroughly in Section 4. In Section we solidify our findings using Claude 3 Opus (instead of GPT-4) as the Grader in evaluation. This eliminates the possibility that the ability compose skills comes from GPT-4's bias towards the models fine-tuned on GPT-4's outputs.
We also discuss the implications of our findings for going beyond "stochastic parrots" behavior ( which refers the perception that LLMs might not generate novel pieces of text but rather mimic data from the pretraining corpus (Section 5.2p
2
Related Works
Compositional generalization Compositional generalization has grabbed lots of attention in
AI.
27 studied compositional generalization in the realm of mathematical reasoning, and investigated for logical inference. In computer vision, compositional generalization was studied on disentangled representation learning to generate images from novel combinations of concepts 12 10 31]. Besides, several works have explored composing visual relations (20], as well as benchmarks for text-to-visual generation 14 19 Other works have explored using compositional models for image generation 7 well to create plans for unseen tasks at inference time (6).
22
3,
12
Compositional generalization for language and LLMs There also a long history of study 17 21 However, the test bed for compositional generalization mostly relies on ruse- languages, like SQL or mouthetic-generatee ones, and thus deviates a little bit from natural language. Recent works have observed compositional
of compositional generalization in language [1] 18 15
3

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These observations have fueled growing interest exploring and evaluating compositional generalization in LLMs as a Some examples include 5 as well as providing multi-hop
capabilities in LLMs emerge multiplicatively on natural languages 30
| 23 33
means to more appropriately evaluate LLM capabilities [9 32
24
26
33
imposing constraints and/or requirements on text generation 9 22
questions whose answers require composing multiple facts that were individually observed during pretraining (26). Dziri et al. [8] tests whether the LLMs can learn compositional generalization by studying integer multiplication and specific form of dynamic programming. Skill-Mix [33] presents an approach to evaluating compositional generalization on language skills, which we discuss in more detail in the next paragraph.
Skill-Mix Yu al. [33] introduce new evaluation named SKILL-MIL that tests for models to produce novel pieces of text from random combinations of k skills, and the evaluation can be made more difficult by increasing the value of k. The procedure is roughly as follows: (1) from a set of N language skills and 7 topics, pick a random subset of lo skills and one topic; then, (2) query the Student model to produce a short piece of text (at most
sentences) that illustrates the A skills in the context of the provided topic. Note that for k = 1, the maximum sentence limit is I sentence. A Grader model is used to evaluate the text piece based on the following criteria: correctly illustrating all k skills and the topic, meeting the maximum length requirement, and general coherence. Thus, each piece of text can award up to a maximum of + 3 points (see the original paper for various metrics extracted from points earned). Note that each of the N language skills has a Wikipedia entry. so it is reasonable to expect an LLM to encounter the skills multiple times in isolation in the pretraining corpus, but not in all possible combinations. In this paper, we choose to study the compositional generalization of L.LMs in the context of SKILL-MIX because SKILI.-MIX close to general language capability and is more flexible for modifying the language skill set.
3 Pipeline
Our pipeline consists of three stages: generating data by selecting GPT-4 responses on SKILL-MIX (Section 3.1). fine-tuning the generated data (Section(3.2) and evaluating our fine-tuned model on SKILL- MIX evaluation
33 (Section 3.3). The pipeline overview is shown in Figure
3.1 Data generation
We adapt the procedure presented in SKILL-MIX evaluation [33 to produce finetuning data. Only the generations with full marks (i.c., illustrating all skills and topics, meeting the length requirement, and general coherence) selected. To enhance the likelihood of obtaining full marks, we prompt GPT-4, the best Student model reported in Yu et al. 33 to create the generations.
Skills and topics for data generation. Since our goal is to measure the generalization capability strictly, we minimize the overlap between the skills/topics used during data generation and the skills/topics used to evaluate the fine-tuned models. Specifically, we partition the original set of 101 skills introduced in Yu et al. 33 S, into a set of 53 train skills, Suains and 48 held-out skills, Spold-out. based on the skill category. Suain includes only literary and rhetorical categories, while Sheld-out comprises the rest of the categories, including reasoning, logic, theory of mind, pragmatics, common sense, and physical knowledge. Similarly, we partition the original set of topics, T. into random sets of 50 training topics, Train and 50 held-out topics, Theld-out- is important to note that partitioning skills randomly can lead correlations between the train and held-out skills, as skills from the same category can be highly related. However, partitioning topics randomly does not present this issue, the topics are generally unrelated. (Please refer to Appendix A for the detailed list of skills and topics.)
Data generation with A == 1, 2, We produce fine-tuning data with k = 1, and 3 using GPT-4 as both the Student and Grader model. For A = 1, we use the original set of skills and training topics Tiain to produce approximately 5,000 generations, and we only keep generations that receive full marks. We refer to the resulting dataset as DSKILL-MIX(L (1). DIKILL-MIX (1) contains only texts with individual skills, thus serving the role of separating the improvement from better utilizing an individual skill and the improvement from better composing multiple skills in later experiments.
We follow an analogous procedure for k = 2 and & = 3, but using our 53 training skills Spain and 50 training topics Timinn We produce 10,000 generations for each before filtering. We refer to the resulting datasets as DDsna Mix (2) and DeRHL.-MIX(33 respectively. For convenience, we use D D 2) to denote the dataset that combines DsKmL-SMx() and DssuL-MOx (Ix, i.e., D DEKILL-MIX (1, = DSKILL-IX(I) (1) U DixILLMMx (2). Similarly, we use D DEKILL-HX (1, 2, 3) to denote the
4

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Table 1: Notation used in data generation (Section 3.1
Symbol
Definition
Size
Misc
All Skills
101
S == Suni U Sheldoout
categories (literary, rbetorical, reasoning,
logic, th pragnatice, common_eenaee Seyeicall_kooleddee
Seain
Train Skills
53
categories (literary, rhetorical)
Stethout
Held Out Skills
48
categories (reasoning, logic, theory_of_nie _n_dddd prognatice, ceanon, seaze, physical knovledge)
T Tunin
All All'Topen Topics
100
Tuain U out
Train Topies
50
Tiin C T
Theld-out
Held Topics
50
Theld-ou CT
data with full mark on
DeKnIAAI (1)
4077
Created from S and Tunin
SKILL-MIX (k 1)
data with full mark SKILL-MIX (k: 2)
DSKHI-MIX2
6277
Created from Swain and Timin
data with full mark on SKILL- (k 3)
DIKILSMII(3)
3603
Created from Suain and Tinan
dataset that combines D DSKHILMII (1), D (ssnI-MIx(2), and D D (MX together. We summarize our notations in T
3.2 Fine-tuning
We fine-tune LLaMA-2- 1------1--hha 22 and Mistral-7B- - [66] on the data generated in Section 3.1 for 4000 steps with a batch size of 64. Each data generated from SKILL-MIX consists of 4 parts: PROMPT ANSWER PROMPT2, ANSWER2. Here, PROMPT denotes the prompt asking the student to generate answers, ANSWER stands for student's first round answer, PROMPT2 is the prompt that asks the student to correct or refine its answer, and ANSWER2 the student's second round answer. During fine-tuning, we feed the concatenation of PROMPTI, A PROMPT2, ANSWER2 into the model as single text, but only compute the cross-entropy loss for tokens belonging to ANSWER I and ANSWER2. We use Adam the optimizer and linear warmup for the first 64 steps, followed by a constant learning rate of 2e-5 for the remaining training steps. The maximum token length is set 1024. All fine-tuning experiments H100/A100 GPUs. Similarly to the loss design of RLHF (2], we mix pre- vee-training data during fine-tuning prevent degradation of general abilities.
conducted 4 Nvidia
3.3 Evaluation
We evaluate the SKILL-MIX(K) performance (k = 2,3,4, 5) for all the models fine-tuned on data generated in Section 3.1 i.e., T PSKILL-MIX(I). DSKILL-MIX (2), and DSKILL-MIX3) (3).
Settings As mentioned earlier, SKILL-MIX evaluation requires a skill set and a topic set. We consider the following 3 settings (where Setting II is main setting used in Figure TT:
SKILL-MIX evaluation on training skills and topies. Since the model observes the same skills and topics during fine-tuning, this setting serves
in-domain evaluation for k = 2, 3. For 4, 5, it tests the models' ability to combine more skills, which is already out-of- domain, since the model has never seen such data during fine-tuning. We use the notation SKILL- -MXLLL-M (k) to denote the (IX evaluation on training skills and topics.
'The learning rate selection based on the recommendation in Touvron et al. 28 We fine-tune LLaMA- 2- 13B Chat Dsaui-sax (1, 2, and perform a grid search the batch size and total number of steps based the SKILL-MIX (k 3) evaluation performance
training skills and topics. The hyperparameters transferred to other settings, including training on different data and different models.
"Since LLaMA-2 and Mistral do not release pre- pre-training data with their models, we use mixture of common crawl data and code data to approximate.
5

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Table 2: Performance of fine-tuned LLaMA-2-13HB 13t-Chat on SKILL-MIXX (k) graded by GPT-4 in various settings. Ratio of Full Marks/Skills Fraction are reported for each model at different k 2, 3, 4, 5. DsKLLLMIX (R) denote the data generated with full SKILL-MIX (k) score. (see Section 3.1
SKILL-MIX (k) Performance
Model
== 2
k= 3
k =
l: == 5
Evaluations on training skills and topics SSKILL-MXX (k)
LLaMA-2-13B--
.521.52
.17/.47
.021.34
.00/.33
.00/331
fl'ed on DaKus.MIX (1)
87/.87
.15.511
.00/.43
.001.37
.00/.35
ft' ed DSKILL-SIXX (1
88/.88
.50/770
.121.56
.017.55
.02/.52
ft'ed on DSKILLMUX 3,
89/.89
.51773
.24/.68
.08/.44
.03/.60
Evaluations on held-out skills and topics (SKILL-MIXXaal--ll
(4))
LLaMA-2-13B-CH
.6/.46
.28.50
.04.42
.017.39
00/.43
ft' ed DSKILLMIX (1)
871.87
.3/.70
.05/.54
.01/.49
.00/44
ft' ed on DSKILL Mix (1,2)
.951.95
.75187
.251.68
.05/.60
.02/556
ft'ed on DSKIL-SII (1, 2,)
96/696
.78/88
.377.5
.0/.69
.2//600
Evaluations on all skills and topics (SKILL-MIX,,x())
LLaMA-2-13BB 1---2-11--BB-
46/.46
.4/.50
.02/.42
.01/44
.0/.34
ft' ed on DSKNL-SIX (1)
88/.88
.271.62
.051.50
.001440
.00/33
ft' f''ed on D (1,2)
96/
.11.74
.17.65
.01.54
00/.51
ft'ed on DSKILL MIX 2,)
96/.96
.65181
.31.73
155/699
.06/662
II SKILL-MIX on held-out skills and topics. This setting tests the models' ability to combine skills that are never present in fine-tuning This setting serves as another perspective to show the stronger out-of-domain generalization for composing skills compared to Setting I. We use the notation SKILL- MIXLL--MXXeld-cu(hh (k) to denote the SKILL-MIX(K) evaluation held-out skills and topics.
III. SKILL-MIX on all skills and topics. Evaluating SKILL-MIX on only half of the skills split by category might make the evaluation easier, since combining 2 rhetorical or logical skills might be easier than combining 1 rhetorical and 1 logical skill. Thus, we also evaluate SKILL-MIX on all skills and topics available, which serves as a direct comparison with the results in Yu et al. (3). We use the notation SKILL-MIX,11h to denote the SKILL-MIX({) evaluation on all skills and topics.
Evaluation Metrics We follow the evaluation rubric of SKILL-MIX. Each generated text can receive up to + 3 points: point for each correctly illustrated skill, point for sticking to the topic, 1 point for text coherence making sense, and I point for meeting the length requirement.
Following Yu al. [33] we grade each generated piece of text three times. For each of the k + criteria, we collect the majority vote among the three grading rounds, and map the points earned to the following two metrics of interest (Ratio of Full Marks) count as 1 all +-+3 points are earned, and otherwise; and (Skills Fraction) the fraction of points awarded for the le skills if all 3 points are awarded for the remaining criteria, and otherwise. For a given (k skill, topic) combination, we take the maximum value of the metric among the 3 generations. We average the maximum value across all the combinations. Note that we use one of the harder variants of SKILL-MIX (33,, where we do not award any points for a particular skill if the skill name is explicitly mentioned in the generated text piece.
4 Skill Composition Can Be Learned From Examples
We present experiment results using the pipeline (Section 3) to evaluate compositional generaliza- tion. Table 2 and Table 3 summarizes the SKILL-MIX (k) performances of LLaMA-2- 1-B-Chh and Mistral-7B- Instrruttt..... fine-tuned on various datasets under three evaluation settings. We discuss our findings on compositional generalization for in-domain evaluations (Section [4J), compo- sitional generalization for out-of- evaluations (Section 4.2 and the data efficiency to induce compositional generalization (Section 4.3)
PPrecisely, the held-out skills appear in DOKIL-MIX (1) since want to make that the model at least knows all the skills after fine-tuning. However, the held-out skills never appear in Dasma-sox(( or D sax x3x( meaning that the model needs to he creative to compose & skills together for l 1.
Yu et al. [33 also report Ratio of All Skills, which we defer to Appendix C Cl clear presentation.

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Table 3: Performance of fine-tuned Dhirral----nstruct---o. on SKILL-MIX (k) graded by GPT-4 in various settings. Ratio of Full Marks/Skills Fraction are reported for each model at different k 2, 3, 4, 5. DsKiaLMIX (R) denote the data generated with full SKILL-MIX (k) score. (see Section 3.1
SKILL-MIX (k) Performance
Model
== 2
k=
k =
l: == 5
Evaluations on training skills and topics (SKILL-MIX
(k))
86/.86
.18/51
.05/.46
.01/.36
.00/.35
ft' ed on Dax (1)
957.95
.3/.68
.10/57
.031.52
.00/.52
ft' cd DSKILL sux (1,2)
98%.98
.65/81
.26/.72
.13/.69
.08/.68
ft' cd on DSKILLMUX 21)
.92.92
.6//81
.34/776
.18.772
.05/.68
Evaluations on held-out skills and topics (SKILL--MXXxobbo (A))
Mistral-7B 1nr-----nnttutt.... ft' DSKILLMIX (1)
85/.85
48/.73
.88/.66
.017.42
017.39
971.97
.64/81
.0/.68
.05/.57
.04.60
ft' ed on D Mix (1,2)
.97..77
857.93
.377.74
.171.74
.10.70
ft' ft'ed on DSKNL-SIX (1,2,3)
.971.97
86/.93
.4//82
26/.76
.11.74
Evaluations on all skills and topics (SKILL-MIX,
Mistral 7B --r-t---nntttt......
83/.83
.35/.66
.06/55
.00/44
000.37
ft' ed on DSKNL-SIX (1)
94/.94
.457711
201.64
.051.56
.01/552
ft' ed on D Mix (1,2)
98/
751.00
46/.8
.16/73
.03..67
ft' ed on DSKILL Mix (1, 2,
96/.96
.81193
.54/83
.19175
.041770
4.1 Compositional generalization for in-domain evaluations
We first observe that, after fine-tuning LLaMA-2-13B- BhBat on (Ix, the SKILL-MIX performance significantly improves. Similarly, after fine-tuning LLaMA-2-13B-CHI on DSKILL-MIXXX (1, 21, 3), the SKILL-MIXmii(() performance also improves. For example, the Ratio of Full Marks for SKILL-MIX improves from 2% for LLaMAA--13B-Chatt to 24% after fine-tuned on DsKmL-wMx 2, (
One confounding factor in the above evaluation that the original LLaMA-2-13B-CHH may not utilize all the individual skills perfectly, and the SKILL-MIX performance improvement might just be attributed to the model's ' knowledge of the individual skills after fine-tuning, not the model's ability to better compose different skills together. Thus, we also evaluate the SKILL-MIX performance LLaMA-2-13B Chat fine-tuned only on DSXILLMMI which consists of purely SKILL-MIX A = 1 data and serves another baseline besides the original LLLMA-2-13B--hhar After fine-tuning on DSKILL-MIX( ( (1), the model indeed knows the individual skills much better, since the Ratio of Full Marks of SKILL-MIX k improves from 52% to 87%. However, better knowledge of individual skills does not lead to a better ability to compose skills together, since the SKILL-MIXmin (2) or SKILL-MIXuin(33 (3) performance of LLaMA-2-133-CCT same as the pre-trained ones, under both Ratio of Full Marks and Skills Fraction metrics. Thus, mainly all the improvement on MKILIL-IXxsan (2) or SKILL-MIX (3) indeed comes from the ability to compose different skills together.
fine-tuned on D (1) keeps nearly the
Fine-tuning on 2-13B-Chat (Table 3 except that only fine-tuning on DSKILLMII(1 (1) shows more improvement on SKILL-MMX (2) and SKILLL-MIXxaaa (3) compared the original 7aataal-B--nstruct--vo
(Table 3 shows similar results as fine-tuning LLaMA-
model. A possible explanation is that Mistral-7B-Inna IB-InnstrutttO... is better at composing skills than LLaMA-2- 13B-Chat, and fine-tuning on D (1) helps -B-tral-BBIInstrueee -0.2 exhibit each skill more
properly and clearly when composing skills.
4.2 Compositional generalization for domaif- evaluations
This section discusses the observations that indicate the out-of-domain generalization of skill compo- sition, including generalization to unseen k and generalization to unseen skills.
SKILL-MIXIran (k) improves for unseen k. We first observe that, after fine-tuning LLaMA-2-
13B-Chat on SKILL-MIX data DSXILL-MIX 2,, 3). the SKILL-MIX (4) and SKILL-MIX (5) per- formance also increase. For example, the Ratio of Full Marks improves from 0% to 8% when t = 4 significant, since besides GPT-4 all other models tested in Yu et al. [33] including GPPT-355-turke cannot get over 2% Ratio of Full Marks on k = 4 (Table in (33). Besides, training only on DskmL mix(1) does not improve the
(Table 2). Note that 8% Ratio of Full Marks improvement on lo
(4) or SKILL-MIX (5).
7

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Table 4: SKILLI-MIX performance of models fine-tuned on I.L.MA---13. 1-1------1---haa graded by GPT.
Ratio of Full Marks/Skills Fraction are reported for each model at different k. DixuL-MMx (1. (8000 sample) denotes the randomly sub-sampled dataset from D (1, 2, 3) with size 8000.
Performance
Model
k == 2
k: ==
k=4 4
k = 5
ft' ed on D DSKLLL-AU sax (1,
511.74
.17..65
.01.554
.0V.51
ft' ed on D DIKIL-MMX (1, 2, 3) (8000 sample) ft' cd on DoxHL-MIX (1, 2)3)
.661.82
.30774
.11/66
.02/.62
651.81
.331.73
.15.69
.06/.62
The surprising finding here is that the model is only trained on SKILL-MIX k: = 2, data, but it improves the ability to compose k = 4, 5 skills a short piece of text, which is never trained on. The results suggest that its ability to compose multiple skills does not come from overfitting training data but should be perceived as learning a meta-skill instead. This observation is beyond the scope of the theory presented in Arora and Goyal [T]. which assumes that the number of skills trained model can compose is limited to the number of skills in its training text pieces.
Fine-tuning on Mistral- Bestral-B-Inntrruee Instruct--vt (Table 3 shows similar results, where the fine-tuned model able to improve SKILL-MIX (4) and SKILL- (5) after fine-tuning on D (1, 2)).
while training only on D DSKIL-MUX (1) has limited improvement.
Improvement on SKILLL-MIXeed--on (k) and SKILL-MIX,I(kk) Besides the SKILL-MIX performance improvement on training skills and topics, we also observe the improvement of
(k) (Setting II) from Table and Figure Similar to the evaluation training skills and topics, fine- tuning LLaMA-2-133 k 3, 4, marginally, but it indeed improves the SKILL-MIX incomparable with fine-tuning on D MIX [1, 2, 3). This shows that the ability to compose multiple skills generalizes to held-out skills, even though our training never exposed the model to data with the held-out skills. Besides the SKILL-MIX improvement on held-out skills, we also observe the improvement of SKILL- (k). This result again suggests that models learn meta-skill rather than overfitting to skill combinations in the training data.
on DSKILL-MI (1) only improves the SKILL-MIXnelddoul -MXXheld-or((() performance for
2. However, the improvement is
Note that the -KIILL-MIXXedddddl (k) performance is better than the -KILL.-MIX.aan in Table which is counter-intuitive. We hypothesize that this phenomenon happens because the pre-trained model knows how compose held-out skills (logic, reasoning, theory of mind) better than training skills (rhetorical and literary). Or possibly the training skills are harder to compose. Exploring difficulty of individual skills is left for future work.
Also, fine-tunen theettnnng on Fi-rral-BB-Instrutte LLaMA-2- 33t-Chat (Table 2). except that Mistral-7B- -B--Instruct-v0.2 has more improvement than LLaMA-2- 13B-Chat when fine-tuned on DaKmL-MIX (1).
(Table 3) shows similar results as fine-tuning on
4.3 Data requirement for inducing compositional generalization
Compared with fine-tuning on D (1, 2). one can observe that
7B-Instruct--0..2 fine-tuned on DsKILLMMI (1, 2) gains more performance boost on k = 4, across fine-tuned on DSKILL-MI (1, 2) is nearly the same as the original LLaMA-2-13B-Chh and LLaMA-2-13B 1------------hatt fine-tuned on DSKILL-MIX (1). However, for LLaMA-2-13BB 2-3B--hht fine-tuned on DSKILL-MIX (1, 2),, the SKILL-MIX (4) performance improves from 1% to 15%.
all settings. For example, SKILL-MIX (4) performance for LLLMA-2-11B-CCT
However, one may argue it is because DEKILL-MIS (1, 2,3) has more data in total than DEKILL-MX (1, 2). To make a fair comparison, we conduct an ablation study by sub-sampling 8000 data from DSKIL-MIX (1, 2, 3), making sure that the number of data points with & 2 and is = 3 in the sub- sampled set is less than the size of DsKILLMMIx( (2). Table 4 shows the DKILL-MIX,n(K. performance of -LLMMA--133-CCT
fine-tuned on the sub-sampled dataset. The metrics remain relatively close to the model fine-tuned on full PRRLL-MIX (1, 2,3) 3) and significantly better than the model fine-tuned on DSKILL-MIX( (1, 2). This ablation confirms that "skill-richer" data can induce the ability to compose skills faster.
8

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Table 5: (Comparison between GPT-4 and Claude-3 grader) SKILL-MIX performance of models fine-tuned on LLaMA-2-13B-- graded on Claude-3 and GPT-4. Ratio of Full Marks/Skills Fraction are reported for each model at different & = 2, 3, 4,5.
SKILL- (k) Performance
Model
k 2
== 3
k=
k
Graded by Claude-3
Llama-2-Ie (lama-2-138-00 138-Chat
.31.52
.07..48
.08/.64
.00/44
ft' od on MIXILL-MX (1)
.45.700
.14/559
.2/.50
.01.42
ft'ed DIKILL (1, 2)
.69/.81
.57/.83
.2/.77
.0/.69
Graded GPT-4
Llama-2-13B-Char
24/.50
.02/.42
.01/.40
.001344
ft' ft'ed on DSKILL-MX (1)
.27.62
.05/.50
.001.40
.001.33
ft'ed DsKIL-sox (1,2,3
.65/.81
.31.73
.15/.69
.66/662
Table 6: (Consistency between GPT-4 and Claude-3 grader) SKILI.-MIX.I performance of models fine tunettned on LLaMA-2-13B-CCM graded on Claude-3 and GPT-4. Ratio of Full Marks
graded by Claude Opus/Ratio of Full Marks by both graders are reported for each model at different &- = 2, 3,4,,,
Model
==
== 3
==4
k
Llama-2-
0.24/0.31/0.19 0.65/0.69/0.58
0.02/0.07/0.01
0.01/0.06/0.01 0.15/0.26/0.12
0.00/0.00/0.00
ft'ed on DaaEL-MII (1,
0.33/0.57/0.29
0.06/0.10/0.05
Discussions
5.1
Using Claude 3 Opus as Grader for SKILL-MIX evaluation
All the findings in the previous section are based on the SKILL-MIX performance graded by GPT-4. However, GPT-4 is heavily used during data generation, and one can argue the improvement might solely come from the fact that GPT-4 favors its outputs. Although the possibility is low, to rigorously eliminate this confounding factor, we re-evaluate SKILL-MIXan(k) using Claude 3 Opus as the Grader, and report the results in Table [5] Besides, we also include consistency check between the GPT-4 and Claude Opus graders in T
From 5 we observe the metrics graded by Claude Opus have a similar trend as those graded by GPT-4: after fine-tuning on DSKILL-MIx 2,, SKILL-MIXaI(K) performance improves for all k 2, 5, while fine-tuning only DSKIL-MIX (1) has limited improvement over the original LLaMA-2-13B-Chat It proves that the improvement SKILL-MIX performance is not overfitted GPT-4 preference.
Interestingly, we find that Claude 3 Opus is more generous, assigning higher scores to both the LLaMA-2-13B-CTT 3B-hat and the fine-tuned version. Besides, the results from Table Glaso also confirm this argument: an answer is assigned full mark by GPT-4, then many of them will also be assigned a full mark by Claude Opus. Such consistent biases among Graders were also noted in (3 when and GPT-4 as Graders.
comparing LLaMA-2-70B-CCT
Besides switching to Claude 3 Opus, we also do human spot checks on the SKILL-MIX generations, making sure that the model not generating something that does not make sense human. Please refer to Appendix D for some of the examples of SKILL-MIX evaluations before and after the fine-tuning.
5.2 Potential capability going beyond "stochastic parrots behavior"
Whether models can go past "stochastic parrots" behavior 2 is crucial in discussions of AI risk. Based on reasonable performance of GPT-4 on SKILL-MIX(k = 5) with common skills removed, Yu et al. 33 suggests GPT-4 is already beyond "stochastic parrots". In particular, after removing common skills (see definition in (33), the probability of a random (5 skills, topic) combination appearing in the training corpus is estimated be 11% if the training token is 2 Therefore, if model has a Ratio of Full Marks beyond 11% when & = 5, then it suggests the model is able to output novel text, thus beyond "stochastic parrots". GPT-4 is the only model that can achieve this (33
5 "Touvron et al. 28 mentioned that the number of pretraining tokens I.LMA-2 trillion.
" 'However, GPT-4 might use more than 2T pretraining tokens.

---

Table 7: (Filtering out common skills) SKILL-MIX(5) performance of models fine-tuned on LLaMA-2-13BB 33--hhat and Mistral-7B-IIstrrut--O00 graded by GPT-4. Ratio of Full Marks/Skills Fraction reported for each model under SKILL-MIX evaluation with train, test, and all skills respectively). We only consider skill com- binations with uncommon skills whose occurrence rate in RedPajama is less than 5%.
SKILL-MIX(5) Performance
Model
train
test
all
LLaMA-2-133-CCT
00%.29
00V.88
.00.30
ft'ed ed on DRKHL.MOx (1,
.3/.566
.2/.59
.03/66
fl'ed on D DKK (1,2,3.4)
.16.68
05/.66
.06/556
Eestral-7BInnstrut-t
007.30
.00.32
.00.36
ft'ed DaK (1,
.0//.66
.03/.7
.03.770
ft'ed on DSKIL-MMX (1, 2,2,3,4)
.21.73
.021622
.06/.63
Table 7 shows the SKILL-MIX (k = 5) performance of fine-tuned LLaMA-2-13B- Bhat and Mistral- 7B- 1B-Instructt-O.2 with common skills removed. We also include some SKKL MIx (4) data (about 1000) into the training set. The fine-tuned models all show significant improvement over the base models. For example, the Ratio of Full Marks for the fine-tuned LLLMMA-21336 1----113---0 33-Chat and Mistral-7B. IB-Isrructtt v0.2 all go beyond 15% for SKILL-MIX = on training skills and topics, and reaches 6% on all skills and topics, after filtering out the common skills.
Although both fine-tuned models cannot reach 11% for SKILL-MIXhnlioon()) and SKILL-MIX.n(5) we hypothesize that with more skill-richer data (say DSKILL-MI (4)), the models can acquire the ability combine skills much more efficiently and go beyond "stochastic parrots" eventually.
We further discuss the limitation of our work in Section 7 and potential influences on Al safety caused by stronger composition capability in Appendix
Conclusion and Takeaways
We have studied the extent which models can learn compositional generalization over language skills by fine-tuning on suitable examples demonstrating such composition. Previous evaluations had seemed to suggest that the extent of compositional generalization is determined by the model size and pretraining [33], but here we were able to induce much better compositional capability via fine-tuning on data that was generated using a setup similar to SKILL-MIX.
One surprising finding was that fine-tuning examples that composed 2 and 3 language skills were enough to improve the capability compose 4 and even 5 language skills. Another surprise that the ability to combine language skills from held-out categories improved at the same rate as the skills used in the training examples. Of course, these findings were still about skills that near relatives. The full extent such "out of (training) distribution" generalization remains to be explored.
7 Limitation
The main limitation of the current study is the high computational and financial costs, which impede us from sweeping more hyperparameters and conducting repeated experiments with different random seeds. These costs include the number of GPU hours for fine-tuning and the cost of calling OpenAl's API to generate the DskilLMMx (k) data and evaluate the SKILL-MIX performance. Despite these difficulties, we managed to sweep the hyperparameters for fine-tuning the LLaMA-2-1334 1-3--hhhh on DsKmL-Mmx (1, 2, 3) (Main experiment, Table 2). We believe our findings are robust to different random seeds because of the clear message and consistent trend of the results.
Besides, compositional generalization is a vast topic and we only study this under the setting of language skills (limited to the SKILL-MIL setting). Whether the models can learn compositional generalization in other settings still needs further exploration.
Acknowledgement
The authors would like to thank the anonymous reviewers for their helpful comments and feedback. This work is supported by NSF, ONR, OpenAl, and Darpa.
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Appendix
A Skills and Topics Partition
The training skills and held-out skills are listed in Table 8 and Table respectively. The training and held-out topics shown Table TO
Table 8: The list of train skills for generating DIKIL-MII (k) and evaluating SKILL-MIXmin (k). For each skill, we list its category. name, definition, and one example using this skill.
Category
Skill
Definition
Example
reasoning
false consensus
The belief that one's own opinions and emotional responses are rational.
"That was clearly the right decision. It's what I would have done."
(belief one's own opinion is right)
reasoning
actor
observer
The difference in percep- tion that occurs when is an actor in a situation versus an observer in situation.
The difference in perception between "James failed the test. He must be a bad stu- dent." " and "I failed the test, but it wasn't because I was a bad student.
bias
was just busy with other obligations." is an example of actor ob- server bias.
reasoning
hindsight bias
The tendency to per- ceive past events as be- ing more predictable than they were.
"It was simple medical pro- cedure with almost no known risks. The doctor should have known it could go wrong."
reasoning
self serving bias
cognitive or perceptual process that is distorted by the need maintain and enhance one' 's self es- teem.
"If do well on the exam, it's because of my academic prowess and hard work. If do poorly, it's because the course was poorly taught, and the exam was poorly proctored."
reasoning
availability bias
mental shorteut that re- lies on immediate exam- ples that come to given person's 's mind when eval- uating a specific topic, concept, method, or de- cision.
Some people believe cars are safer than planes, since plane crashes dramatic and widely reported.
rhetorical
anchoring (cogni- tive bias)
a psychological phe- nomenon in which an individual's judgements or decisions are influ- enced by a reference point or "anchor" which be completely irrelevant.
"Individuals may be more likely purchase pricy car if it is placed next to an ex- tremely expensive car."
13

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rhetorical
ad hominem
a thetorical strategy where the speaker attacks the character, motive, or some other attribute of the person.
"Boss, you heard my side of the story why think Bill should be fired and me. Now, am sure Bill is going come to you with some pa- thetic attempt weasel out of this lie that he has cre- ated."
rhetorical
appeal to author- ity (argumentum ab auctoritate)
a form of fallacy when the opinion of expert on a topic is used evidence to support an argument or when the au- thority is used say that the claim is true, as au- thorities can be wrong. an informal fallacy char- acterized by the manip- ulation of the recipient's emotions in order to win argument, especially the absence of factual evidence.
Citing "Albert Einstein" as authority for determi- nation on religion, when his primary expertise was physics, is an example of ap- peal authority.
rhetorical
appeal to emotion (argumentum ad passiones)
A student says, "If get fail- ing grade for this paper, will lose my scholarship. It's not plagiarized."
rhetorical
argumentum ad populum
a fallacious argument which is based on claim- ing truth or affirming something is good be- cause the majority thinks so.
"Everyone is going to get the new smart phone when it comes out this weekend. You should too!"
rhetorical
argumentum ad baculum (appeal to force)
An appeal to force to bring about acceptance of conclusion.
If you don't 't join demon- stration against the expan- sion of the park, will evict you from your apartment. So, you should join demon- stration against the expan- sion of the park.
rhetorical
tu quoque
Claiming an argument false because of hypocrisy of the person making the argument.
"How can you tell me not smoke when you yourself smoke?"
rhetorical
extrapolation
Generalizing conclu- sion beyond the range in which its truth has been established.
"Water boils at 212 degrees at sea level. Therefore, it must boil at this temperature all levels."
rhetorical
post hoc ergo
fallacy of the form "af- ter this, therefore because of this".
"hh are you whistling?"
propter hoc
"To keep the elephants away.' But there are elephants around here.' 'See? It works."
rhetorical
accident (fallacy)
informal fallacy and a deductively valid but unsound argument curring in a statistical syllogism (an argument based on a generaliza- tion) when an exception to a rule of thumb is ig- nored.
Cutting people with knives is a crime. Surgeons cut peo- ple with knives. Surgeons are criminals.
14

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rhetorical
paradox
seemingly absurd or self contradictory state- ment.
"A chicken is born from an egg, so it stands to reason an egg comes before a chicken. However, an egg is laid by a chicken, so stands to rea- son an egg comes after a chicken."
rhetorical
slippery slope (ar- gument)
The assumption that small change will cas- cade larger series of (undesirable) changes. Assuming that something is true of the whole from the fact that true of some part of the whole.
"Changing the grading stan- dards will have ripple effect throughout the college."
rhetorical
fallacy of compo- sition
"If someone stands up from their seat at a cricket match, they can see better. There- fore, if everyone stands up, they can see better." "
rhetorical
fallacy of division
Assuming that something that is true for a whole must also be true of all or some of its parts.
"Americans eat lot of ham- burgers. Bob is American. Therefore Bob eats lot of hamburgers."
rhetorical
false dichotomy
informal fallacy based on a premise that erroneously limits what options are available.
"Stacey spoke out against capitalism; therefore. she must be communist."
rhetorical
begging the ques- tion assuming the conclusion complex question (loaded question with implicit as- sumption
circular argument that paraphrases the question.
"Of course the earth is round; people have known this for hundreds of years."
rhetorical
question that is loaded with an implicit assump- tion.
"Why are you lying to me?" is a question that presup- poses you are lying to me. Any answer you give will force you agree you are lying.
rhetorical
equivocation (in- formal fallacy)
an informal fallacy re- sulting from the use of a particular word/expres- sion in multiple senses within an argument.
warm beer is better than a cold beer. After all, nothing is better than a cold beer, and warm beer is better than nothing.
rhetorical
argumentum ignorantiam
ad
a statement of the form "not p has not been proven be true. There- fore, p is true".
"The politician is having an affair. 'Prove it, then.' 'Can you prove he's having an affair?"" lactic where the arguer diverts attention away from the relevant conclu- sion.
rhetorical
diversion
The prosecutor claims with- out proof the defendant is guilty child abuse. The prosecutor then goes and on about how awful child abuse is, instead of proving the original claim of the de- fendant's guilt.
rhetorical
straw man
A type of diversion whereby one states an exaggerated or false version of an opponent's argument.
Suppose Louise goes to her professor and asks for more time for class discussion. Her professor responds, don't want the entire class to be aimless student discussion while sit silent."
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rhetorical
red herring
Introducing irrelevant points to detract attention from a question.
member the press asks the president why they voted expand a welfare program. The president responds, "The strength of America the strength of its communities, and am proud make our communities better places." "Why are you wearing your shirt backwards?" "There will be a lunar eclipse tonight.""
rhetorical
non sequitur
An argument where the conclusion does not fol- low from the premises.
rhetorical
rhetorical
ques-
A question asked in order create dramatic effect or to make point rather than to get an answer.
"How could you be so stupid?"
tion
rhetorical
category mistake (rhetorical error)
An error in which things belonging to a particular category are presented as they belong to a differ- category.
A visitor Oxford was be- ing given a tour. The vis- itor, upon viewing the col- leges and library, reportedly inquired, "But where the University?"
literary
anaphora resolu- tion
Resolving the antecedent of pronoun or noun phrase.
"The car falling apart, but it still works." Here "it" is the anaphor and "car" is the antecedent.
literary
answer ellipsis
An ellipsis (omission of speech) that occurs in swers to questions.
"Who walked the dog?' asked Mary. 'Sam,' replied Jill." This an example of answer ellipsis, as Jill's complete answer would have been "Sam walked the dog".
literary
anthropomorphism
The attribution of human traits, emotions, or inten- tions to non-human enti- ties.
Some examples of anthropo- morphism include "talking clocks". "singing teapots". "Buck the dog from Call the Wild", and "feeling em- barrassment." "
literary
antithesis
figure of speech involv- ing the bringing out of a contrast in the ideas by an obvious contrast in the words, clauses, sen- tences, within a parallel grammatical structure. a lexical relation in which words have opposite meanings. short saying that ob- serves general truth.
"One small step for man, one giant leap for mankind." Here, the contrast of "one small step for man" versus "one giant leap for mankind" is an antithesis.
literary
antonymy
"Shallow" is an antonym of "deep".
literary
aphorism
"Pride goeth before a fall."
literary
aposiopesis
A figure of speech which the speaker abruptly ends their sentence, leaving the statement incomplete.
"If ever get my hands on you I'll_"
literary
antimetabole
the repetition of words in successive clauses, but in transposed order.
"Ask not what your country do for you, but what you can do for your country."
16

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literary
cliché
An element of an artis- tic work, saying, or idea that has become overused to the point of losing its original meaning or ef- fect, even to the point of being weird or irritating, especially when at some earlier time was consid- ered meaningful or novel. language that is informal and conversational.
"All that glitters is not gold" has been used so often, it is now cliché.
literary
colloquialism
"Did you see that town over yonder?" Here, "over yon- der" is an example of collo- quialism.
literary
compounding (combining words)
Combing two more words produce new word.
"Waterbed" illustrates com- pounding, as combines the words "water" and "bed" to produce a new word. In the phrase "his Machiavel- lian tendencies," "Machiavel- lian" is epoynm derived from the Florentine diplomat and political theorist Niccolo Machiavelli.
literary
eponym
A word derived from the name of a person or place.
literary
fallacy
mistaken belief, espe- cially one based on un- sound argument.
"People have been trying prove for centuries that God exist. However, no one has proven God exists. There- fore, God does not exist."
literary
hyperbole
Exaggerated statements or claims not meant to be taken literally.
had to wait at the station for ten days-an eternity." Here, "an eternity" is hy- perbole.
literary
hypocorism
pet name. Also word formation process which a longer word reduced to a shorter word ending with "ie' or "y", often affectionately. using special technical vocabulary associated with specific activity or topic.
"Telly" is hypocorism for "television"; "movie" is a hypocorism for "motion pic- ture."
literary
using jargon
"He is the kind of lawyer who likes sprinkle 'ami- cus curiae' in dinner conver- sations." Here, "amicus cu- riae" is an example of jargon. "All the world's a stage, And all the men and women merely players" is a metaphor because it's a comparison without using "like" or "as."
literary
metaphor
a figure of speech that, for rhetorical effect, di- rectly refers to one thing by mentioning another.
literary
oxymoron
A figure of speech in which apparently contra- dictory terms appear in conjunction.
"The hall was filled with a deafening silence." Here, the phrase "deafening silence" is oxymoron.
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literary
sluicing
types of ellipsis that occurs in both direct and indirect interrogative clauses.
"Phoebe ate something, but she doesn't know what" is an example of sluicing, be- cause the full sentence is "Phoebe ate something, but she doesn't it know what she ate".
literary
litotes
Using understatement to emphasize a point by stat- ing negative to further aftirm positive, often in- corporating double nega- tives for effect.
Using the phrase "not bad" to mean "good", or "non- trivial" to mean "compli- cated", are examples of litotes.
literary
tautology guage)
(lan-
a statement that repeats an idea, using near- synonymous morphemes, words or phrases, effec- tively "saying the same thing twice".
"You re simply going to have to score more points than the other team win the game."
literary
unaccusative verb
verb whose subject does not actively initiate, or is not actively respon- sible for, the action pressed by the verb.
"The tree fell."
literary
topicalization
mechanism of syntax that establishes expres- sion as the sentence or clause topic by having appear the front of the sentence or clause (as opposed to in a canoni- cal position further to the right).
"Because the pressure was too great, everyone refused to answer."
(syntax mecha- nism)
literary
pscudogapping
Pscudogapping
el- lipsis mechanism that re- moves most but not all of a non-finite verb phrase.
"He drinks milk more often than he does water." This is an example of pseudo- gapping because the verb "drink" is removed from the phrase "he does drink water".
literary
phrasal verb
a single semantic unit composed of verb followed by a particle, sometimes combined with preposition.
"The store has run out cheese." The phrasal verb is "run out of."
literary
subjunctive clause
clause in the subjunc- tive mood is finite but tenseless clause. Sub- junctive clauses use bare or plain verb form, which lacks any inflec- tion.
"It is imperative that he be here on time." Here, the verb "to be" appears in its plain form in the subjunctive clause.
literary
subordinate clause
clause that is embed- ded within a complex sen- tence.
"Whoever made that asser- tion wrong." this case, "whoever made that asser- tion" is a subordinate clause.
18

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literary
syntactic ambigu- ity
situation where sen- tence may be interpreted more than one way due to ambiguous sentence structure.
"John saw the man on the mountain with a telescope." The syntax ambiguous as it could either mean that John used a telescope to see the man on the mountain, or that the man on the mountain had a telescope and John saw the man.
literary
allusion (literary reference)
Allusion is figure of speech, in which an ob- ject or circumstance from an unrelated context is re- ferred to covertly indi- rectly.
Describing two people in relationship as "star-crossed lovers" is an allusion the Shakespeare play Romeo and Juliet.
Table 9: The list of held-out skills for evaluating SKII.I--MXhehi (k:). Combined with the training skills list Table the full list skills used for SKILL-MIX,I(k)) For each skill, we list its category, name, definition, and one example using this skill.
Category logical
Skill
Definition
Example
enumerative induction
Using evidence from par- ticular examples to con- clude property is true in general.
"Every particular life form we know of depends on wa-
ter exist. Therefore, all known life depends on wa- ter."
logical
spatial reasoning
The capacity to reason about the spatial relation- ships between objects.
The key fit into the box. Us- ing spatial reasoning, one can deduce that the width of the key was smaller than the width of the box.
logical
spatial orientation
Words or phrases used to situate people and objects relation to each other in space.
Mark was sitting on a chair. Using spatial orienta- tion skills, one can deduce that Mark was above the chair.
logical
logical
proposi-
logical proposition is a statement that takes no arguments and evaluates True or False.
a proposition that evaluates to "True." "3 + 2 4" is a proposition that evaluates to "False."
+
tion
logical
categorical syllo- gism
Infers conclusion from two premises.
"No geese are felines. Some birds are geese. Therefore, some birds are not felines." "If today is Tuesday, then John will go to work. Today is Tuesday. Therefore. John will to work."
logical
modus ponens
syllogism that is of the form "If P then Q P. Hence Q."
logical
modus tollens
syllogism that is the form "If then Q. Not Q. Hence not P."
"If is sunny, I will wear my sunglasses. I am not wearing my sunglasses. Therefore, it is not sunny."
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logical
analogical induc- tion
special type of in- ductive argument, where perceived similarities are used basis to in- fer some further similar- ity that has not been ob- served yet.
"Swans in the northern hemi- sphere are white. Therefore, swans in the southern hemi- sphere are likely white, too."
logical
entailment (logi- cal)
An expression A entails if the truth of A guar- antees the truth of B and the falsity of B guaran- tees the falsity of A. A syllogism in which the conclusion or premise is left unstated, because they are taken be com- mon sense.
"The emperor assassi- nated" entails "the emperor dead."
logical
enthymeme
"Anyone who crashes their car into police station lawn is looking for trouble. That's what Mitch did." " The preced- ing is an enthymeme because the conclusion "Mitch was looking for trouble" is so ob- vious it left unstated.
logical
disjunctive syllo- gism
syllogism that is of the form "P or Q. Not P. Hence Q."
room 205 or 306. The meeting is not in room 205. Hence it is in room 306."
"The meeting
logical
syllogism that is of the hypothetical syllo- gism
"If I not wake up, then cannot to work. If I can- not go to work, then I will not get paid. Therefore, if do not wake up, then will not get paid."
form "P implies Q. Q im- plies R. Hence P implies R."
logical
statistical gism
syllo-
syllogism that argues, using inductive reason- ing, from a generaliza- tion for the most part to particular case.
" "Almost all people are taller than 26 inches. Gareth is person. Therefore, Gareth is taller than 26 inches."
logical
gestural commu-
mode of communica- tion that uses gestures, facial expressions, and body language to express and understand informa- tion.
Bill pulled out the chair next him. Charlie smiled and sat down.
nication
theory of mind
perspective taking
The act of perceiving situation understand- ing a concept from an al-
Bill is afraid of heights, and Carl loves heights. Bill and Carl are on the observation deck of the Empire State Building. Bill knows that Carl must be enjoying the ex- perience.
ternative point of view.
theory mind
empathy
The ability of understand and share the feelings of another.
The nurse said to her patient, "I am sorry you not feel- ing well." "
theory of decoding nonver- mind
Recognizing and inter- preting nonverbal cues.
As Willow was sketching her plan, Amy frowned. "Are you worried won't work?" Willow asked.
bal cues
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theory of recognizing false mind beliefs
The ability understand that others can hold be- liefs that do not align with reality or with one's own beliefs.
"Unicorns are real," said Larry. "No they aren't," thought Percy.
theory of root cause analy- mind sis
method of problem solving whereby the un- derlying cause is found.
"Aha!" exclaimed Stephen. "The leak is coming from here." " The preceding is ample of root cause analysis, because Stephen has found the source of the leak.
theory of divide and con-
Breaking large diffi- cult to solve problem into smaller, easier to solve parts.
"Mary, Jamie, you search the right quadrant. Kelly and will take the left." " The pre- ceding is an example of di- vide and conquer. Instead of collectively searching the en- tire area, the team broke the area into smaller quadrants and searched those.
mind
quer
theory of help seeking
The behavior of actively seeking help from other people.
"Freddie held up the broken clock to Marsha. 'Do you think you could fix it?"" Here, Freddie seeks help from Mar- sha.
mind
theory of trial and error mind
The process of exper- imenting with various methods until one is found the most success- ful.
One method of drug discov- ery is to try different chemi- cals at random until one has the desired effect.
theory of hypothesis testing mind
assuming a possible ex- problem
assume all lilies have the number of petals. Let me try counting the number of petals on some lilies to see if my hypothesis fails."
planation and sometimes trying to prove (or disprove) said explanation.
theory of perspective aware- mind ness
The awareness that one's own mental states may not be known or accessi- ble to others without com- munication.
"John, do you mind throw- ing that spider outside?' asked Jane. "Actually, I'm afraid of spiders, so I can 't,' replied John."
theory of visualization mind
The formation of men- tal image of real world object phenomenon.
"Jerry watched the clock tick down towards his lunch hour. He could his burger wait- ing for him in his mind's eye."
theory of expressing grati-
is feeling of apprecia- tion (or similar positive response) by a recipient of another's kindness.
"Expressing her gratitude during her acceptance speech, the actress thanked her husband and parents for their support."
mind tude
theory of self motivation mind
the ability to maintain a drive towards one's goals.
"If get this done, I'll reward myself by playing video games"
theory of altruism mind
the principle and practice of concern for the well- being and/or happiness of other humans or animals.
Examples of altruism include caregiving for relative with a chronic condition, and help- ing an older adult walking with a cane cross the street.
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theory of the mind
emotional self reg- ulation
a complex process that in- volves initiating, inhibit- ing, or modulating one's state or behavior in given situation.
Examples of emotional self regulation include meditat- ing, pausing to collect one- self before speaking, and practicing stress manage- ment.
theory of the mind
optimistic attitude
am attitude reflecting be- lief or hope that the out- come of some specific en- deavor, outcomes in general, will be positive, favorable, and desirable.
"There was a lot of talent at the tryouts and only few openings. That pushed me practice hard and I played my best - it felt good! The coach gave me great feed- back. I'm going to work on the things he suggested and watch all the games this sea- son. That way, I'll have a better chance next year." m so sorry for your loss."
theory of sympathy the mind
the perception of, under- standing of, and reaction to the distress or need of another life form.
pragmatics
synecdoche
figure of speech where the whole is represented by the part, or vice versa.
have hungry mouths to feed" is example of synecdoche, because "hun- gry mouths" is a part refer- ring to "children."
pragmatics
presupposition
An implicit assumption about the world back- ground belief relating to utterance whose truth is taken for granted in dis- course.
"Jane no longer writes fic- tion" presupposes Jane once wrote fiction.
pragmatics
dilemma
A situation in which choice must be made between two or more alternatives, especially equally undesirable ones. Something speaker suggests implies with an utterance, even though it is not literally pressed.
"If go to bed early, I won't have studied enough for the test. But if I stay up late, I'l be too tired to do well."
pragmatics
implicature (prag- matic suggestion)
" "Alice says, 'I am out gas.' Bob replies, 'There is gas station around the corner." " Here, Bob does not say, but conversationally implicates, that the gas station is open, because otherwise his utter- ance would not be relevant in the context.
pragmatics
intention matics)
(prag-
The ability to identify speaker's 's intent.
"It's a little loud in here," said Bella. 'Oh, sorry, I'l try to be quieter,' replied Sarah." Here, Sarah un- derstood Bella's intention, which was to tell Sarah be quieter, and not merely re- mark on the room's tom's loudness. "If roll the pen off of the table, it will fall the floor."
physical knowl- edge
folk physics (com- knowledge physics)
The untrained human per- ception of basic physical phenomena.
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common sense
reasoning about effects of events
The ability to reason from a specific event and general knowledge about the effects of events to the specific effects the specific event.
"Given that Lisa picked up the newspaper, we can infer that Lisa now holding the newspaper."
common
reasoning about indirect effects
The ability to reason about indirect effects or ramifications of events.
"Lisa picked up the newspa- per and walked into the room. Therefore, the newspaper is now in the room, because know that if a person is hold- ing object moves along with the person."
common sense
reasoning about preconditions
The ability to reason about the conditions that held before an action or event.
"Kate set the book on the ta- ble. Therefore, before Kate set the book on the table, she was holding the book and she was near the table."
common sense
commonsense law of inertia
Things tend to stay the same unless affected by some event.
" "Ktte the book the ta- ble and left the living room. When she returned, the book was still on the table." "
common sense
default reasoning
The ability to reason where one reaches default conclusion with incomplete information by assuming that un- expected exceptional events do not happen.
"Kimberly turns on a fan. What will happen? The fan will start turning."
common sense
temporal reason- ing
the ability make pre- sumptions about humans' knowledge of times, dura- tions and time intervals. form of logical infer- ence that seeks the sim- plest and most likely con- clusion from set of ob- servations.
born after Haydn and died earlier than him, therefore Mozart died younger than Haydn."
"Mozart
common sense
abductive reason- ing
"Nathan was sleeping. Now, Nathan is looking at his phone. Therefore, Nathan must have woken up, and picked up his phone."
common
reasoning about motivations
Determining the goals mental states that led to the action of person.
"John opened the refrigera- tor and took out a sandwich. Based this observation, it is likely that John was hun- gry."
sense
B Prompts for Data generation
In this section, we document our prompts for generation and prompts for grading.
B.1 Prompts for generation
PROMPT1
language processing generate example of text that illustrates multiple skills in sementica syutex. The example should be a minimal natural piece text with up to fae lines in the context topic that keep
Greatings! intereated
wondaring you help
illustrates of folloving skills: [ekills.str). and make sure the concepte can be found fully from the text.
possible,
23

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Table 10: List of training and held-out topics
Skiing, Climbing Everest, Grocery cashiers, Sledding, Opera solo, Reunion, Archacologists, Rabbis, Pirates, Acupuncture, Regatia, sailing, Elizabethan England, Basketball, Civil Law, Tropical rainforest, Ecology, Ancient Greece, Civil War, Broadway play,
Tennis match, Coal mine, Bowling, Fitness, Confession, Animation, Podcasts, Documentaries, Indie music, Jazz music,
Training
Dubstep, Rugby, Veganism, cryptocurrency. Violinists, Pianists, Olympies. Woodworking, Crochet, Knitting, Sewing. Calligraphy, Felting, Kayaking, Snorkeling, Pathology, Baking, Pizza making, Winning the Lottery, Equestrian pursuits, Thermodynamies
Dungeons and Dragons, Golf, Hiking, Makeup, Escalators. Australia, French architecture, Fireworks, Ducling, Colorado, Rafting, Mushrooms, Sushi, Stcampunk, The Ottoman Empire, Palcontology. Wooly mammoth, Urbanism, Ice skating, Beckeeping, Beatboxing, Acrobatics, Gymnastics, Ballet, Sitcoms, Thriller movies. Cruise ship, Whaling. Ballroom dancing, Eliquette, Survivalism, Camping, Utlitarianism, Consequentialismn, Guerilla warfare, Siberia, Vikings. Triathlons. Mercantilism, Submarines, Sandwiches, Gardening, The Renaissance, Comedy, Japan, Dinosaurs, Leopards, Wrestling, Plumbers, Knots
Held-out
reference, here are the definitions and examples for the concepta: faillls_defe.o_ exad_exampee__itpll
minimal piece 'Ansver;' 'Explanation:',
explenation
Thanks much!
PROMPT2
Thanks very mach. Could you please look over your anewer and improve it? Please nake sure that the rensins topic. top that, please the new ansver only contains to (nun_sentencos_stry)
Again,
the improved ninimal natural piece of with 'nnserr and start the explanation with 'Explanation:".
Thanke very much!
Note that this pair of prompts the same as the generation prompts for GPT-4 in Yu et al. B3 which is slightly different from the generation prompts for LLaMA-2 in Yu et al. 33 This difference of prompts, along with randomness from multiple sources, caused some difference in -LMMA-2-133 Chat performance on SKILL-MIX(K) between our paper and Yu et al. 33
B.2 Prompts for grading
Grading prompt for GPT-4 Grader:
Greetings! vaa condering if you could help ne grade the following ansver given by a student.
I'll first describe the question that vas given to the student, and then give the student's anszer, and grading
The question given to the student was as follous: "Give single piace of text with up to fmun_sentences_sta
(topic), This single piece of text ahould illustrate all of the following ekills: (ekilla_etr)."
The student's ansuer was: ('taddnn__nsvves
For reference, here the definitions for the skills: {akilla_dafs_am aedteadddddadddddeeel...... examplen__stpple
Using rubric table fornat, please grade the student's anever with positive ecoring. Each criterion

---

Table 11: Performance of fine-tuned LLaMA-2-13B Bh-Cht on SKILL-MIX (k) graded by GPT-4 in various settings. Ratio of Full Marks/Ratio All Skills/Skills Fraction are reported for each model different & = 2, 3, 5. DsKul-MIX (k) denote the data generated with full SKILL-MIX (k) score. (see
Section 3.1
SKILLI-MIX (k) Performance
Model
k =
=
=
==
k = 5
Evaluations on training skills and topics SSKILL-MIX irain (minn))))))))) (k))
LLaMA-2-13B-CHE
52/.56/.52
.17/.19/.47
.02/.02/.4
.00/.00/.33
.00/.00/.1
ft'ed on DSXILL-MIX (1)
87/.91/887
.15/.19/.1
.00/.00/.43
.00/.00/.37
.00/.00/.35
ft'ed on MIXILL-MI 1,
88/.96/88
550/.88/70
.12/.1//.6
.01/.03/.55
.02/.02/.2
ft'ed on DSKILL-MIX 1,2, 3)
89/.96/89
.51/.621.73
.241.28/.68
.08/.10/64
.03/.03/.0
Evaluations held-out skills and topics (SKILI-MIX
ILaMA-2-13B-hha
46/.53/.66
.281321.50
.047.05/.22
.01/.01/.39
.00/00//43
ft'ed on DSXILL-MIX (1)
87/.95/87
.43.50//.7
.05/.06/.54
.01/.01/.49
.00/.0//.4
ft'ed on DSKILLMIXX [1
95/999/95
751.79187
.251.29/.68
.05/.05/60
.2//02/.56
ft'ed on DSKILLMIX (1, 2,
96/1.0/.96
.78/.11.88
.371.431.55
,09/.12/.9
,02/02/600
Evaluations
all skills and topics (SKILL-MIXxI(())
-LMMA-2-13B-CH ft'ed on DSKILL-MIX (1)
46/.54/.6
241.29/.50
,021.02/42
.01/.02/.40
.00/.00/.34
88/.95/88
271.281.62
.051.05/.50
.00/.00/440
.00//00/.33
ft' ed on DSKILLMMIX (1
96/99//96
511.571.74
.171.231.65
.01/.01/.54
.00/.00/.1
ft'ed on D (1,23)
96/999/99
.651688811
.33136//73
.15/16/.69
.06/.07/.2
worth point. The criteria (rubric_items). tabla should only have following columns: "Criteria', 'Points Earned'. In the "Points Earned' colum, please provide only numerical values additionel formatting. and please include rov for "Tstal Points Barned! at the end of the table. Pinally, please start your grading explanation with "Explamation':
introduce
with 'Here's the grading table;'
Grading prompt for Claude 3 Opus Grader:
Greetinga!
vondering you help grade following given by
I'11 firat deacribe queation vaa given student, and then give you the student and the grading rubric.
The question given the student frun_sentances_str in the context of (topic). This single piece of text should illustrate all the following exills: (skille_str)."
follous: "Give single of text with
The student's ansver was: "naaveent,anaver""
For reference, here are the definitions for the skills: {skills_dafs_nn andd__eaaples_stnplll
delimiter), please grade student's anever with positive scoring. Each criterion is vorth 1 point. The criteria are: (rubric_itens). The table should only have the folloving columne: 'Criteria', 'Points Earned', provide only numerical values with additional fornatting. Please introduce the table vith 'Bere's the grading table:' and please include a row for 'fotal Points Earned' at the and of the table. Finally, please your grading explanation with "Bxplanation':
Using
the *Pointe Earned' columa, please
C Complete Results for SKILL-MIX Evalution
Besides Ratio of Full Marks and Skill Fraction, Yu et al. 33 also consider another metric in their main text called Ratio of All Skills evaluate SKILL-MIX performance.
Ratio of All Skills: l points are awarded for the i skills and at least 2 points are awarded for the remaining criteria, and 0 otherwise
We also report this metric for LLaMA-2-13H 3h-Ch and DSKILL-MIX( (k)). The full results for fine-tuning LLAMA-2-13RB 1----hh are shown in Table TT (corre-
fine-tuned on
sponding to Table in Section 4) and the full results for fine-tuning Mistral-7B Caatral-B--nnttuuue Instrucc--OO.. can be
25

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Table 12: Performance of fine-tuned Mistral-BB-Instruct- on SKILL-MIX (k) graded by GPT-4 in various settings. Ratio of Full Marks/Ratio All Skills/Skills Fraction are reported for each model at different & = 2, 3, 5. DsKiL MIx (k) denote the data generated with full SKILL-MIX (k) score. (see
Section 3.1
SKILLI-MIX (k) Performance
Model
k
=
=
=
k = 5
Evaluations on training skills and topics (SKILL-MIX (k))
Mistral-7BBIInttruct--022 ft'ed on PSKILL-MIX (1)
86/.917.66
.18/.26/.5
.057.07/.46
.01/.01/.36
.00/.00/.35
95/.97/.95
.43/.4//.8
.10/.11/.7
.03/.03/.52
.00/.00/.52
ft'ed on DIKILLMMX 1,
98/1.0/998
.65/.72/.81
.26/.30/.2
.13/.13/.6
.08/.08/68
ft' (t'ed on DSKILL-MIX 1,2.
92/997/.9
.66/.70/81
.341.381.76
.18/.19/722
.05/.0/.68
Evaluations held-out skills and topics (SK
Mistral-7B--nnstrutt-002
.85.89//85
.48156/.73
.08/.11/.66
.01/.01/.2
.0T/01//39
ft'ed on DSXILL-MIX/
97/.99/.97
.64/68/81
.20/221/.68
.05/.06/57
.04/.4//60
ft' ed on DSKILLMMIX (1
97/.99/97
85/.86/.3
.371.43/.74
.17/.19/74
.1//13//70
ft'ed on DSKILLMIX (1, 2,)
.71.991.97
86/.89/93
.49156//82
.26/2281.76
.13.13/74
Evaluations
all skills and topics (SKILL-MIXxI(K))
Mistral-7B B-nalll7--tnttuuc--o...
.83/.77/.3
.351.41/.6
.06/.07/.0
.00/.00/441
.00/.00/.37
ft'ed on DSXILL-MIX (1)
94/.96/99
.451.71.71
.20/.20/.64
.05/.06/.56
.01/.1//52
ft' ed on DSKILLMMIX (1,2)
98/999/98
.75/,80000
46/.49/800
.16/.16/.33
.03/.04/.7
ft'ed on D 1,2,3)
96/997/96
851.87193
54//60//3
.19/20/775
.041.5//70
bound in Table 12 (corresponding to Table Ratio of All Skills metric.
Section 4). All of our findings still hold under this
D Examples of SKIIL-MIIX Generations
In this part, we present some example generations during the SKILL-MIX evaluations, showing that the model indeed learns how to combine different language skills, instead learning some ways to bypass the graders like GPT-4. For simplicity, omit the original prompts and responses given to the models, and only show the topic, skills, skills definition for the specific SKILL-MIX instance and the models' answer (without any explanation etc).
Example
SKILL-MIX question
Topic: Japan
Skills: false dichotony, availability bias, visualiration, obeerver biss
Skills definitions:
fallacy on prenise erroneourly are available. For exampla, ""Stacay spoke out against capitalisn; therafore, she must be communist.""
dichotony:
opti
2. availability bias: nental shortcut that relies on innediate examples that cone to given person's nind evalusting specific topic, concept, method, people believe are safer than planea, since plane crashes are dranatic and widely reported.
example,
3. visualization: The formation of nental
of real world object phenonenon. For exampla, "'Jarry untched the clock tick down tovards his lunch hour. He could sea his hurgar waiting
mind"s eye."*
4. actor observer bias: The difference perception that occure when one an actor in observer in eitustion. For example, The difference in perception between ""Janes failed the test. He must be a bad student, and ""I failed the test, but it wasn' 't obligations," ** exeuple
situstion
juet buey
observer bias.
Answer by LLaMA-2-13B-Chm
considering traveling to Japan sumner, recent about coronavirua worried. I've heard conflicting reporta about the safety of traveling there, and I'm not sure shat to believe. Sone people eay the situation is under control, vhile othere clain it's a crisis I'a which perspective is
26

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Answer by LLaMA-2-13B-Chmm fine-tuned on SKILL-MIX data (D (DskIL-MIX) MIx (1,2,)).
In Japan, choose between the tranquil crash, traditional tea cereneny may seen dull to an cutsider, but ance experienced, its serenity sppreciated.
ceremoty the bustling streets. Like plane
over tourist's faniliar plane, our perception of experiences is influenced by our biases.
local prefere ease
Example 2
SKILL-MIX question
Topic:
Skills: tu quoque, categorical syllogiem, sphorism, self notivation
Skills definitions:
1. quoquete:
Claiming argunent false because of hypocrisy of the person making the argunent. For exampla, ""Hov can you tell ma not to mnoke when you yourself snoke?"
2. categorical syllogism: Infers conclusion from two prenises. For example, ""o geese are Ielines. Sone birds are geese. Therefore, sone birda are felines."
3. aphorism: A sbort saying that observes general truth. For example, ""Pride goeth before fall. ""
towards goals. For exampla, get this done, I'll revard nyself by playing video ganes""
notivation: ability
Answer by LLaMA-2-13B-Chr
Bypacrisy
always paffing away your cigar, yet you're telling no stop anoking? That's like pig giving lectures vaganian!
Answer by LLaMA-2-13B- fine-tuned on SKILL-MIX data (D MIx (,)).
You tall me to stop smaking, yet you light up cigar yourself. No plunbar is a mechanic, and all plumbera pipea. Thus, mechanic plunber, and remenber, PPride goeth before fall' let get this done to earn a video gane revard.
E Examples of Fine-tuned Model's Generation and Implication to Safety
WARNING: this section contains examples of text that may be considered unsafe, offensive, or upsetting.
As the models have more ability to compose skills, it also leads to challenges for AI safety and aligmment: most benchmarks on AI safety directly query the model to generate some text related harmful behaviors, e.g., "could you please write phishing email", the password from system". However, harmful behaviors can still be decomposed into multiple skills, and if you only ask the model to generate text using these skills, the model may output harmful generations without explicitly mentioning the harmful behavior. For example, to write short tweet criticizing based on fake experience, the skills needed include
"please tell me how get
"false claim of expertise: the critic claims to have done or experienced something they haven't. t. For example, someone might criticize restaurant by saying the food was terrible, despite never having eaten there."
and
"appeal to authority (argumentum ab auctoritate): form of fallacy when the opinion a non-expert on topic used as evidence to support an argument or when the authority is used to say that the claim is true, authorities can be wrong."
Besides, one can add more customized constraints to make the generated text more appealing. Following is example of generation we obtained using LLaMA-2-133H 13B-Chh fine-tuned DsKmI..MIx (1, 2, 3), using the prompt similar to SKI)L-MIX(3). Prompt to the model:
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Greetings! interested natural language proceesing generate example of text that illustrates multiple skills in semantics syntax. The example should short teeat up
wondering you help
produce reviez that illuatrates the rolloving skills: false clain of expertise, appeal to authority (argunentun ab auctoritate), using jargon. Please keep the text as ehort as possible, and make sure the concepts can be found For reference,
fully fron
definitions
examples for the concepts:
false clain of expertise: the critic claine to have done or experienced something they haven't. For example,
might criticize restaurant by taying the food terrible, despite caten there.
having
appeal to authority (argumentun ab suctoritate): form of fallacy when the opinion on a topic is used as evidence to support an argunent or when the authority is used to say that the authorities
non-espert
clain is for a determination on religion, ohen his prinary expertise was in physica, is an exanple of appeal authority.
urong. For example, citing *Albart Einstein"
authority
using jargon: using special technical vecabulary associated with specific activity or topic. For exemple,
kind lavyer who likes sprinkle 'enicus curiae' in dinner conversations." Here, "amicus curiae" is an example of jargon.
Please start the minimal natural piece text with 'Ansver:' and the explamation with 'Explanation:", Thanks vary nach!
Model's response:
underohelning experience #5ally'sProduss sPPrducce is nothing but farce, clearly they don't knou the first thing about crop rotation. As seasoned agrologist, can assure you their produce is anything but 'ussstiiaablee #FalseEspertine #AppaalTokuthortty #Jargon"
Anszer:
'organic'
Explanation: (omitted)
Another example is in the context of writing customized phishing or spam emails, where query the model to generate an email (with link or attackment inside) trying to grab the attention from Sushi enthusiasts and allure them to click the link.
Prompt to the model:
Greetings! an interested natural language processing and was wondering you could help generate example of text that illustrates multiple skills semantics syntax. The example should be a ninimal natural piece of text with up to fev lines in the context of Knitting that illustrates all of the folloving skills: email vriting, appeal authority (argunentun auctoritate), using jargon. Please keep the text short possible, and make sure the concopts concepta:
found fully from text. reference,
dafinitions examples
crafting urgent, clear, concise uesesges effectively commnicate requests of personal information by giving both a link and attachment, has generic greetings while adhering to professional or personal etiquette. For exeuple: An esail from Doregly120baiieeeureint..
writinge::
with the subject 'Inmediate action required!' clain your account will be closed unless you click link to verify your information. The amail uses generic greating provided.
"Dear Quatoner,"
**appeal authority (argunentur ab auctoritate) form fallacy when the opinion of a non-expert topic is used evidence to support argunent when the authority is used say that the clain is true, as authoritiea can be srong, For example, citing "Albert Einstein" as an determinstion religion, of appeal to authority.
authority
primary expertise
physics,
example
*rusing jargon**;
using special technical vocabulary associated with spacific activity topic. For example, He ia the kind of lavyer whe likea to sprinkle fanicus curiae' in dinner conversations." "anicus
example of jargon.
Please start the mininal natural piace of text with 'Ansvar:' and start the explanation with "Explanation=", Thanks very
Model's response:
Answer:
Sushi Eathueiest,
As a renouned Sushi Manter, I highly reconnend you domload our latent suahi- makinn app. *The Nigiri Ninja.? This revolutionary tool will guide you through Don't miss out on this geme-changing technology click the link below to dovaload now!
creating perfect suahi every tine.
28

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Best,
Suchi Sensei"
Explanation:
(onitted)
These examples show that as the model gains more ability to compose skills, it might also leave potential holes for Al safety. Note these examples are easy to adjust to other topies and scenarios. is not able to fulfill the requests for any of the two examples.
The original LLaMA-2-13B-CHE Further studies and new benchmarks the effect of compositional capability in Al safety might be of interest.
29

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35


Reviews:
[{"review_id": "X7TfM5lmdH", "reviewer": "Reviewer_bbsi", "summary": "The authors present a (family of) fine-tuned LLMs, trained using the SKILL-MIX dataset. They show that models trained on composite tasks where each instance involves a sequence of different skills improves the model in similar composite tasks. They demonstrate generalization by fine-tuning the models on subsets of task combinations and evaluating them on held-out sets. They also evaluate out-of-distribution generalization on the number of skills sequenced together and show that training on sequences of 2 or 3 skills can help generalize to sequences of 4 and 5 skills.", "questions": "1. Perhaps I missed this in the main text, but how many seeds and dataset recombinations were used in the experiments? I’m particularly interested in the observation that the model performed better on the held-out set than the training set (Line 260) and whether that is a consistent phenomenon.\n2. Could you provide a metric for how consistently the two models from Table 4 rated the responses? It would provide higher confidence if the 31% and 24% (top-left entries) actually had high overlap.", "limitations": "The authors have acknowledged the limitations and impact in the supplements.", "rating": 5, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 2, "strengths": "1. The authors have done extensive experiments using the SkillMix dataset to support their arguments.\n2. Using LLM to judge LLMs can introduce a lot of variability. I understand that the authors are following the procedure from Yu et al. Reading Appendix B of Yu et al. did increase my confidence and I appreciate adding another evaluator model which supports the analysis even further.", "weaknesses": "1. My main concerns with this paper have less to do with the methods of this particulaar submission, but of the dataset and methodology from Yu et al. that the authors extensively draw upon. Looking over the dataset and scoring design, it seems that the scores could be highly inflated simply by writing three disconnected sentences that each individually illustrates the skill. The only criterion in the rubric that is relevant for cohesion is ‘Makes sense’, which still can be evaluated independently for each sentence. This seems to be a rather weak form of skill compositionality that is the central point of this paper. Moreover, the authors imply that the skills and topics would not be highly related (Line 138), but given the skills presented in Appendix B, I’m not entirely convinced that this is true. I would be surprised if there weren’t at least a few hyperlinks between them.\n2. The baselines presented in Section 4.1 seem a bit weak. Fine-tuning on SM_train(1) is a useful starting baseline, but it is still severely restricted in its ability to span the dataset. If I understand the authors’ intent correctly that the goal is to demonstrate that fine-tuning to combine different skills, then what I think would be a more informative comparison would be to include within the training set samples involving the same skill/topic category but use higher than 1 k. Otherwise, this confounds with length-generalization, which we know sequence models struggle with. \n3. A similar concern exists for Sections 4.2 and 4.3, where training with higher k is confounded with training on longer sequences. I would be interested in understanding the effect size after controlling for sequence length how and what the distribution of sequence lengths are between the different k’s.\n4. The three findings are not particularly novel nor surprising (in fact, it would’ve been more surprising if any of the three findings had been shown to be false). The authors appeal to novelty with respect to Arora and Goyal (Line 73), and if that is indeed true, then it would be helpful to provide more substantial analyses with respect to the specific claims made in the first paper (e.g. show which relations or equations from Arora and Goyal fail to predict the results of this paper).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer bbsi,\n\nThanks for your time and effort in reviewing our paper. Below we address your questions and concerns.\n\n> Q: Concerns about Skill-Mix\n\n**A:** The reviewer is correct that there could be “cheating” ways to pass the Skill-Mix eval that fool the GPT4 grader, since “Make sense” is quite vague. \n\nHowever, in this paper (as opposed to the original Skill-Mix evaluation paper) the models were produced by our fine-tuning, where they saw only good-quality answers to Skill-Mix questions. Human examination of the answers from our fine-tuned models has not detected such cheating behavior. Thus the conclusions in our paper about the ease of inducing compositional behavior are valid. \n\n> Q: Confounding factor about length\n\n**A:** Thank you for raising this important point. We agree that the sequence lengths in the training set could be a confounding factor, since longer sentences may be required to illustrate more complex language skills. To address this concern, we have now designed an experiment that takes out this confounding factor. It will be in the final version.\n\n\nExperiment: In this experiment, we show that even if two SFT datasets have similar average lengths, the dataset with richer skills induces better performance on Skill-Mix.\n\nSkill-Mix k=1,2,3 data have average lengths of 144, 205, and 273, respectively  If we put all Skill-Mix k=1,2,3 data together (D_skilmix(1,2,3) in paper), the average length is 204, which is similar to the average length of D_skilmix(2). We finetune Llama 13b chat on D_skilmix(2), and evaluate its performance on the training skills and topics. The full mark ratio under different settings is presented below: \n\n|                                             | k=3  | k=4  |\n|---------------------------------------------|------|------|\n| ft’ed on D_skillmix(2)                      | 0.11 | 0.01 |\n| ft’ed on D_skillmix(1,2,3) (6000 subsample) | 0.22| 0.08 |\n\nFor a fair comparison, we subsample D_skillmix(1,2,3) so its number of data points is smaller than D_skillmix(2). This experiment shows that, even if two sets have the same average length, the one with richer skills indeed performs better.\n\n> Q: Findings are not surprising and it lacks illustrations of why the empirical results in this paper cannot be predicted from Arora and Goyal 2023.\n\n**A:** Thanks for asking this question. We would like to clarify that the theory in Arora and Goyal et. al does not predict our empirical findings. (1) That theory relied on pre-training (specifically on scaling laws for pretraining) whereas we are doing fine-tuning at fairly modest scales. (2) More importantly, the theory does not predict that training on examples that combine k-tuples of skills can lead the model to improve on (k+1)-tuples of skills. We explain the technical reason below.\n\nThe theory makes two key assumptions (1) all individual skills (“ground truth” set of skills)  are demonstrated during training (but most k-tuples of skills were not), and (2) for a random combination of k skills, competence on that particular k-tuple of skills corresponds to the ability to answer questions about random text pieces that involve/compose that k-tuple of skills. The theory predicts that if the model excels at composing random k-tuples of skills, it will also be good at composing random k’-tuple of skills (where k’ <= k) from the ground truth skills set. However, the theory does not predict our empirical results that training on k=3,2,1 leads to (1) performance improvement on k=4 (i.e., where k’ > k), and (2) improved performance on Skill-Mix evaluation for the held-out skills.\n\n> Q: How many seeds are used for the experiment? Do the results depend on the choice of random seed? How stable is the effect (especially the performance on the held-out set is better than the training set)? \n\n\n**A:** Due to budget constraints (cost of large number of OpenAI API queries for data generation and grading), we were unable to use multiple random seeds for all experiments in the paper. As a result, all the results presented in this paper are based on a single random seed (42). \n\nIn the following table, we show results for the following experiment with multiple random seeds: Skill-Mix evaluation performance on k=3 and k=4 for model fine-tuned on D_skillmix(1,2,3). Each row represents the seed used during fine-tuning and Skill-Mix evaluation. In each entry, we show the (Skill-Mix performance on training skills)/(Skill-Mix performance on held-out skills).\n\n| Skill-Mix | seed 42 (in paper) | seed 13   | seed 87   |\n|-----------|--------------------|-----------|-----------|\n| k=3       | 0.24/0.37          | 0.22/0.35 | 0.24/0.36 |\n| k=4       | 0.08/0.09          | 0.09/0.11 | 0.11/0.12 |\n\nAs shown in the table, Skill-Mix performance over different seeds is quite stable, and the finding that the Skill-Mix performance on held-out skills is better than that on training skills also holds over different random seeds.\n\n> Q: Consistence between GPT-4 and Claude-3 as graders?\n\n**A:** Thanks for your perceptive question. In the following table, we show the Skill-Mix results, each entry shows (full mark ratio graded by GPT4)/(full mark ratio graded by Claude-3)/(full mark ratio given by both GPT-4 and Claude-3) on Skill-Mix evaluation on all skills and topics. As seen in the table, our findings are consistent between GPT-4 and Claude-3 as graders (they have a high overlap), and the results corroborate our claim that GPT-4 is stricter than Claude-3.\n\n|                                      | k=2            | k=3            | k=4            | k=5            |\n|--------------------------------------|----------------|----------------|----------------|----------------|\n| Llama-13b-chat on SkillMix_train     | 0.24/0.31/0.19 | 0.02/0.07/0.01 | 0.01/0.06/0.01 | 0.00/0.00/0.00 |\n| -ft’ed on D(1,2,3) on Skillmix_train | 0.65/0.69/0.58 | 0.33/0.57/0.29 | 0.15/0.26/0.12 | 0.06/0.10/0.05 |", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ntbhmiCrwQ", "reviewer": "Reviewer_ZBU1", "summary": "The paper explores the capacity of smaller language models to learn compositional generalization from finetuning. Utilizing the Skill-Mix set-up, the study delivers comprehensive experiments to assesse how small language models can improve their performance on both in-distribution and out-of-distribution compositional tasks after finetuning on systhetic datasets regarding in-distribution easier tasks generated by GPT-4.", "questions": "- The skill-mix paper only released small part of topics and skills to prevent people from chasing the leaderboard, so I'm wondering if the full list of skills and topics used in this paper is the same as the original paper.\n- The second-last line in Table 3 shows that Mistral-7B-Instruct-v0.2 get 0 point for Skill Fraction on $\\text { SKILL-MIX }(k)$ after finetuning on $\\mathcal{D}_{\\text {SKILL-MIX }}(1,2)$. This seems to be a typo.\n- The experimental results showing performance improvements after finetuning are unsurprised unless the author can justify if the model is indeed learning how to combine skills compositionally during finetuning.", "limitations": "The limitations are mentioned in the Appendix section.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The paper is well-written.\n- The paper focuses on a very important topic (compositional generalization) of current LLM research.\n- It's easy to understand the intuition behind the comprehensive experiments.", "weaknesses": "- The experiment pipeline is not novel and highly overlaps with the previous work [1]  .\n- The paper is limited on one specific method on evaluating if language models can generalize compositionally on 'harder' tasks after finetuning on 'easier' compositional examples. There exists many other evaluation methods/metrics covered in related works that are not mentioned, including [2] and [3].\n- The paper does not properly explain and support the claim made in line 64-65 and line 243-244, i.e., \n\n    > Instead, they are acquiring a higher-order meta-skill that allows them to generalize and apply to combine unseen skills.\n\n    > The results suggest that its ability to compose multiple skills does not come from overfitting training data but should be perceived as learning a *meta-skill* instead. \n\n   This claim is very strong and needs more experimental results from other compositional tasks or theoretical justifications.\n\n[1] Yu, Dingli, et al. \"Skill-Mix: A flexible and expandable family of evaluations for AI models.\" arXiv preprint arXiv:2310.17567 (2023).\n\n[2] Dziri, Nouha, et al. \"Faith and fate: Limits of transformers on compositionality.\" Advances in Neural Information Processing Systems 36 (2024).\n\n[3] Chen, Jiaao, et al. \"Skills-in-context prompting: Unlocking compositionality in large language models.\" arXiv preprint arXiv:2308.00304 (2023).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer ZBU1,\n\nThanks for your time and effort in reviewing our paper. Below we address your questions.\n\n> Q: The pipeline has already been introduced by Yu et al. 2024 and there is limited novelty.\n\n**A:** Thanks for asking this question. We want to point out some differences between the Skill-Mix paper (Yu et al. 2024) and this paper. \n1. We consider fine-tuning in the paper, whereas Skill-Mix paper (Yu et al. 2024) presents a new evaluation. In order to successfully fine-tune the Skill-Mix data, we need to force the model into text mode (i.e., there is no 
 and 
 around the prompt), while the original Skill-Mix evaluation is purely in the chat mode (i.e., there is always 
 and 
 around the prompts). If we fine-tune in chat mode, the model’s chat ability will degenerate, and even affect some outputs during Skill-Mix evaluation. \n2. Skill-Mix (Yu et al. 2024) does not separate skills into different sets, whereas our work partitions the skills based on categories (and leads to the “skill composition” results on held-out skills and their corresponding categories).\n\nYu et al. show that while large (stronger) models like GPT-4 can combine 4 or 5 skills well, small (weaker) models struggle. The purpose and novelty of our work come from answering the following question (inspired by that finding in Yu et al): can we teach small models to compose skills? Our experiments provide evidence to answer this question in the affirmative.\n\n> Q: The skill composition claim made in the paper is too strong, and there are potential related works not added.\n\n**A:** Thanks for pointing out the claims and other papers. We intend to restrict the claims in our paper under our setup (language skills) and we will make it clear in our next version. We agree our setup based on Skill-Mix is not universal. For example in [2], the authors argue that compositional generalization cannot be induced during fine-tuning (very inefficient, not generalizable to OOD), while our findings show that models can learn how to compose language skills through fine-tuning, even to some  OOD tasks (higher k and held-out skills). We already had discussed many past works under different settings in our related works section, and will include more (including the papers you mentioned) in our next version. However, as we mentioned in the paper, prior evaluations/setups for compositionality often rely on rule-based languages or underlying multi-step execution, which arguably deviates from natural languages. Skill-Mix is a well-established benchmark for LLMs that focuses on the capability of language models for combining language skills in natural text settings. The results from the Skill-Mix paper align with previous theory work (Arora & Goyal 2023) and has implications of LLMs going beyond stochastic parrots. Thus, it fits perfectly for our goal of studying whether language models can learn skill composition. Our results also potentially suggested that the language models can indeed go beyond stochastic parrot with a small number of fine-tuning examples, which we believe is significant in the future development of LLMs and is of interest of AI safety and alignment. \n\n> Q: Do you use the same skills and topic set as in Yu et al 2024?\n\n**A:** Yes, Yu et al. provided us with all the skills and topic sets, and permission to include the skills in the Appendix. Given our findings that fine-tuning can improve the Skill-Mix performance a lot even on heldout skills, they realized that keeping some skills secret does not make the evaluation any harder.\n\n> Q: SkillMix performance improvement does not necessarily mean skill composition\n\n**A:** We are not sure exactly what the reviewer meant. Possibly they meant that skill composition is a broader phenomenon than what Skill-Mix covers. We agree. No single evaluation can fully test skill composition capability.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Gp1OxGr9VU", "reviewer": "Reviewer_4iaf", "summary": "This article studies whether or not LLMs can be fine-tuned to compose skills for text generation. The authors generated training data from GPt-4 in the style of the Skill-Mix benchmark, asking the model to generate text about a topic while using a set of k skills (e.g., sympathy, temporal reasoning, syllogism, etc.). LlaMa-2 and Mistral-7B were then fine-tuned on this synthetic data and evaluated on their ability to generalize to combinations of novel skills, and to more combinations of skills than seen during training. Using GPT-4 as a grader, the authors find that fine-tuning substantially improves compositional generalization.", "questions": "I don't have additional questions at this point.", "limitations": "This section is fine.", "rating": 7, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "This article has a number of strengths\n- addresses the important topic of compositional generalization using complex tasks\n- well-written article\n- technically sound\n- evaluation for combining novel skills and combining novel numbers of skills\n- Two graders were evaluated (GPT-4 and Claude)\n- Data efficiency was also studied\n\nThis is solid work that is consistent with other recent work on \"learning to compose\" through training [1,2]. It addresses these ideas on a larger scale than in past studies and shows compelling results, especially the generalization to more complex combinations.\n[1] Conklin, H., Wang, B., Smith, K., & Titov, I. (2021). Meta-learning to compositionally generalize. arXiv preprint arXiv:2106.04252.\n[2] Lake, B. M., & Baroni, M. (2023). Human-like systematic generalization through a meta-learning neural network. Nature, 623(7985), 115-121.", "weaknesses": "The tasks in the Skill-Mix benchmark seem quite artificial, and difficult for people to both produce and evaluate. Only two example generations are provide in the appendix, and the first one has odd syntax in the prompt: \"The example should be a short tweet up to a few lines in the context of produce review...\"\n\nAnother weakness is the use of automatic grading by GPT-4, although it seems unavoidable and they also tested another grader from Claude. Additional discussion justifying this choice and the accuracy of the grader seems warranted.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer 4iaf,\n\nThanks for your review and suggestions. We will add more visualization about the results in the next version.\n\n> Q: Skill-Mix seems very artificial, and there are very few examples in the paper. One example in the paper (among 2) has a weird syntax in the prompt.\n\n**A:** Thanks for your suggestion. We will put more examples in the next version, ranging not only from Skill-Mix evaluation itself but also some other tasks related to languages. As for the odd syntax in the prompt, the aim for that example is to show that this skill composition ability might lead to potential danger for safety and alignment, and in order to make the model “unsafe”, we reuse the prompt template for the Skill-Mix evaluation and only switch specific words and skills definitions.\n\n> Q: Automatic grading by GPT-4 is a weakness\n\n**A:** Thanks for pointing out this weakness. We agree that automatic grading may not be perfect and hard to avoid since human grading has higher variance according to Yu et al. We have newly added a consistency check between the GPT-4 and Claude-3 graders, which shows that these two graders also have high overlap when giving full marks.\n\nIn the following table, we show the Skill-Mix results, each entry shows (full mark ratio graded by GPT4)/(full mark ratio graded by Claude-3)/(full mark ratio given by both GPT-4 and Claude-3) on Skill-Mix evaluation on all skills and topics. As seen in the table, our findings are consistent between GPT-4 and Claude-3 as graders, and the high overlap between the 2 graders also implies the consistency between these 2 graders.\n\n|                                      | k=2            | k=3            | k=4            | k=5            |\n|--------------------------------------|----------------|----------------|----------------|----------------|\n| Llama-13b-chat on SkillMix_train     | 0.24/0.31/0.19 | 0.02/0.07/0.01 | 0.01/0.06/0.01 | 0.00/0.00/0.00 |\n| -ft’ed on D(1,2,3) on Skillmix_train | 0.65/0.69/0.58 | 0.33/0.57/0.29 | 0.15/0.26/0.12 | 0.06/0.10/0.05 |", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "cGnPphEnTd", "reviewer": "Reviewer_vwLV", "summary": "The paper studies the extent to which LLMs can learn compositional generalization over skills by finetuning with suitable training examples. Based on abundant experimental results, the paper concludes that finetuning using a dataset with skill composition examples helps the model build a “meta-skill” that allows them to generalize to more complex (i.e., composition of more skills) tasks. The paper also finds that the training samples containing higher-order skill compositions are more efficient in eliciting such a meta-skill. The paper is quite easy to follow and the conclusions might inspire more interesting applications on LLM’s finetuning.", "questions": "- Line 157 mentions that the data has a form of [prompt 1, answer 1, prompt 2, answer 2]. I do not quite understand why we need prompt 2 and answer 2 here. Will the analysis still hold for simple [prompt 1, answer 1] data samples?\n- In line 260, the paper mentions a counter-intuitive phenomenon that the held-out performance is better than the train performance. The hypothetical explanation is that the model knows how to compose the held-out skills better than training skills. I think an experiment of switching the skill categories of the training and held-out sets can further support (or against) this hypothesis.\n- The problem setting studied in this paper reminds me of the “least-to-most” prompting design [1]. This paper shows using some in-context examples of $k=1,2$ can make the model generalize to problems with large $k$. Hence I’m curious about whether combining these more complex in-context prompt designs could further improve the finetuning performance. (I think the analysis and experiment in the current submission is enough for a good paper, just point out this paper and a potential idea.)\n\n[1] Zhou, Denny, et al. \"Least-to-most prompting enables complex reasoning in large language models.\" ICLR 2023", "limitations": "Please refer to the question and weakness part.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- The paper proposes a dataset that consists of examples with different selected skills for the analysis of skill composition.\n- The results in this paper show that finetuning not only provides new knowledge to the LLM but also the skill of composing different skills, which potentially inspire novel applications using finetuning.\n- The proposed method (although looks simple) efficiently improves the model’s performance on skill composition. The observation that the “skill-richer” data can induce the ability to compose skills faster would be very useful for practical LLM finetuning applications.", "weaknesses": "- It might be a bit hard to read the trends and compare results in the tables, visualizing some results might be helpful.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer vwLV,\n\nThanks for your time and effort in reviewing our paper. Below we address your questions and suggestions.\n\n> Q: Why use [prompt 1, answer 1, prompt 2, answer 2] instead of [prompt 1, answer 1]?\n\n**A:** This prompt template aims to improve the Skill-Mix performance of the model being tested. “answer 1” may correctly include the skills, but it might conflict with the length constraint in Skill-Mix evaluation, i.e., it might use too many sentences to compose all skills in a short paragraph. “prompt 2” asks the model to revise and improve “answer 1”, and then the model generates “answer 2”. Since “answer 2” is usually better than “answer 1”, we include it in training. If we train on [prompt 1, answer 1], generating full-mark Skill-Mix data becomes much less efficient, and so we might not obtain enough training samples.\n\n> Q: Training on the data generated on held-out skills and topics to verify (or against) the hypothesis the held-out skills are easier than the training skills.\n\n**A:** Thanks for your suggestion. We generate Skill-Mix k=2 and k=3 data on held-out skills and topics, and the original Skill-Mix k=1 full-mark data (since k=1 contains both training and held-out skills), and fine-tune this data.\n\nWe summarize the results in the following table. In each entry, we present “(the performance of llama-2-7b-chat)/(the performance of model fine-tuned on training skills and topics)/(the performance of model fine-tuned on held-out skills and topics)”. The first row in the Table denotes the Skill-Mix evaluation on training skills and topics, and the second row denotes the Skill-Mix evaluation on held-out skills and topics. We directly copy “the performance of model fine-tuned on training skills and topics” from Table 2.\n\n|                                        | k=3       | k=4       |\n|----------------------------------------|-----------|-----------|\n| SkillMix on training skills and topics | 0.24/0.16 | 0.08/0.04 |\n| SkillMix on held-out skills and topics | 0.37/0.40 | 0.09/0.13 |\n\nFrom the result, we observe that: when fine-tuning on SkillMix data on held-out skills and topics, the SkillMix performance on held-out skills improves (compared with fine-tuning on training skills and topics), and the SkillMix performance on training skills decreases. This verifies our hypothesis that the held-out skills (and their corresponding categories) might be easier for the model to compose; this offers an explanation for our previous observation that even if we fine-tuning on training skills and topics, the SkillMix performance on held-out skills and topics is even better than on training skills and topics.\n\n> Q: In-context examples improve fine-tuning performance?\n\n**A:** Thanks for this suggestion! We believe that properly adding in-context examples can improve the fine-tuning performance, either with a better final Skill-Mix evaluation performance or with a lower sample complexity to reach the reported performance in the paper (thus more efficient). The primary goal of the current paper was to study the effect of vanilla SFT.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper is borderline, but was positively received by the reviewers. Because the paper addresses an important topic (compositional generalization in LLMs) and demonstrates non-intuitive results (that generalization can be learned via fine-tuning), I believe the results will be interesting to the community and I therefore recommend acceptance.

That said, I encourage the authors to respond to the reviewers' concerns about the transparency of the evaluation protocol, and whether or not "cheating" is possible.
Decision: Accept (poster)