Scaling laws for language encoding models in fMRI
Authors: Richard Antonello
Aditya Vaidya
Alexander Huth
Venue: NeurIPS 2023 poster (2023)
Keywords: Encoding Models
Language Models
Neuroscience
Scaling Laws
TL;DR: We describe the scaling laws that show that bigger language models can better predict brain activity.

Abstract: Representations from transformer-based unidirectional language models are known to be effective at predicting brain responses to natural language. However, most studies comparing language models to brains have used GPT-2 or similarly sized language models. Here we tested whether larger open-source models such as those from the OPT and LLaMA families are better at predicting brain responses recorded using fMRI. Mirroring scaling results from other contexts, we found that brain prediction performance scales logarithmically with model size from 125M to 30B parameter models, with ~15% increased encoding performance as measured by correlation with a held-out test set across 3 subjects. Similar log-linear behavior was observed when scaling the size of the fMRI training set. We also characterized scaling for acoustic encoding models that use HuBERT, WavLM, and Whisper, and we found comparable improvements with model size. A noise ceiling analysis of these large, high-performance encoding models showed that performance is nearing the theoretical maximum for brain areas such as the precuneus and higher auditory cortex. These results suggest that increasing scale in both models and data will yield incredibly effective models of language processing in the brain, enabling better scientific understanding as well as applications such as decoding.

Scaling laws for language encoding models in fMRI
Richard J. Antonello Department of Computer Science The University of Texas at Austin jjantonell o@utexas edu
Aditya R. Vaidya Department Computer Science
The University of Texas at Austin avaidya@utexas edu
Alexander G. Huth
Departments of Computer Science and Neuroscience The University of Texas at Austin huth@ca utexas. edu
Abstract
Representations from transformer- unidirectional language models are known to be effective at predicting brain responses to natural language. However, most studies comparing language models brains have used GPT-2 or similarly sized language models. Here we tested whether larger open-source models such as those from the OPT and LLaMA families are better at predicting brain responses recorded using IMRL. Mirroring scaling results from other contexts, found that brain prediction performance scales logarithmically with model size from 125M to 30B parameter models, with 155 increased encoding performance as measured by correlation with a held-out test set across 3 subjects. Similar logarithmic behavior was observed when scaling the size of the fMRI training set. We also characterized scaling for acoustic encoding models that use HuBERT, WavLM, and Whisper, and found comparable improvements with model size. A noise ceiling analysis of these large, perrforrrfe encoding models showed that performance is nearing the theoretical maximum for brain areas such the precuneus and higher auditory cortex. These results suggest that increasing scale in both models and data will yield incredibly effective models of language processing in the brain, enabling better scientific understanding as well as applications such as decoding.
Large language models have come to dominate the field of Al due to incredible capabilities that range from reasoning [1] to code generation [2] to even predicting how human brain would respond to language [3]. Rapid improvement in these abilities has largely been driven by scale: the most capable models today use nearly identical architectures early transformer language models [4], but have orders of magnitude more parameters and larger training data [5]. Overall, model capabilities-often measured as zero-shot performance across range of language tasks-tend to scale logarithmic with the number of model parameters [6, 7], suggesting that improvements will continue as model scale increases. Here we test whether these scaling "laws" hold for the task of modeling the human brain.
The human brain is the quintessential language processing system, but there still much to learn about how processes and represents language. One paradigm used for this purpose is the encoding model: given measured brain responses to natural language, construct a model that predicts those responses from the natural language stimulus [9-19]. If an encoding model is able to accurately predict brain responses across a range of new stimuli, then that model must use similar representations the brain. High-performing encoding models then be interpreted to gain insight into the brain's computations [20-22] or the function of different brain areas [1 [11, 23-25]. The highest performance currently offered by encoding models that based on large language models such as GPT-2 XL [26]. To build an encoding model, a language model is fed the same language stimuli that the
37th Conference on Neural Information Processing Systems (NcurIPS 2023).

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human subject is hearing or reading. The internal states at each layer of the language model are then extracted, yielding contextual embeddings that capture semantic and syntactic properties of the stimuli [27]. These embeddings are then entered into a linear regression model that predicts the human brain responses, often measured using functional magnetic resonance imaging (fMRT).
Though text-based language models are the norm, language encoding models have increasingly been trained with acoustic features derived from audio-based neural networks [28-34]. Models like
HuBERT [35] are able to derive phonetic, lexical, and semantic properties by learning from unlabeled waveforms or annotated transcripts [36]. Even when trained with human- coman-plausible amounts of training data, these models can be more effective than language models in predicting brain responses in low-level speech processing areas such as the auditory cortex [31]. While earlier works examined the utility of several self self-supervised audio models in brain encoding, newer models have since been released with substantially increased training data and speech recognition performance.
In this paper, we study whether encoding models for fMRI benefit from scaling neural network model parameters and datasets the same degree as other tasks. We show that using contextual embeddings from larger language models can increase the prediction performance of encoding models by 15% over smaller counterparts. Larger acoustic models improve similarly with model size, showing largest improvements in auditory cortex and in higher-level areas. Finally, encoding performance for both model types scales logarithmically with the amount of fMRI training data from each subject, demonstrating an increasing need for very large fMRI datasets. These new state-of of-the-art encoding models may enable a new frontier in the study of biological language comprehension and may provide deeper insight into the mechanisms that the brain uses to reason about and employ natural language.
2 Methods
2.1 Language models and speech audio models
Decoder-only transformer architectures have become dominant in recent years for language modeling [37]. For semantic encoding, we used representations from two families of large decoder-only Transformer language models, OPT [38] and LLaMA [39]. From the OPT family we used the pretrained 125 million, 1.3 billion, 13 billion, 30 billion, 66 billion, and 175 billion parameter models. From the LLaMA family, we used the pretrained 33 billion and 66 billion parameter models.
HuBERT and wav2vec 2.0 [35, 40] have been previously used to study auditory perception in the brain [29, 31, 33]. Both are trained to learn representations from unlabeled audio. WavLM [41] extends the HuBERT paradigm with data augmentation and also adds new data sources to increase the total training dataset size. Whisper [42] is family of encoder-decoder models that use 680,000 hours of weakly-labeled audio - an order of magnitude larger than previous datasets - to reach state-of-the-art speech recognition performance. In this work, we used the pretrained Base, Large, and X-I X-Large variants of HuBERT; the Base+ and Large variants of WavLM; and multilingual variants of the Tiny, Base, Small, Medium, and Large Whisper models.
Table shows the architecture details for all neural network models used in this work. 2.2
MRI data
We used publicly available functional magnetic resonance imaging (fMRI) data collected from 3 human subjects as they listened to 20 hours of English language podcast stories over Sensimetrics S14 headphones [43, 44]. Stories came from podcasts such as The Moth Radio Hour, Modern Love, and The Anthropocene Reviewed. Each 10-15 minute story was played during a separate sean. Subjects were not asked to make any responses, but simply to listen attentively to the stories. For encoding model training, each subject listened to roughly 95 different stories, giving 20 hours of data across 20 scanning sessions, or total of ~33,000 datapoints for each voxel across the whole brain. For model testing, the subjects listened to two test stories times each, and one test story 10 times, at a rate of I test story per session. These test responses were averaged across repetitions.
Details of the MRI methods can be found in the original publications [43, 44], but important points are summarized here. MRI data were collected on a 3T Siemens Skyra scanner at The University of Texas at Austin Biomedical Imaging Center using a 64-channel Siemens volume coil. Functional
scans were collected using a gradient echo EPI sequence with repetition time (TR) = 2.00 echo time (TE)= = 30.8 ms, flip angle = 71% multi-band factor (simultaneous multi-slice) 2, voxel size 2.6mm x 2.6mm x 2. 2.6mm (slice thickness = 2.6mm), matrix size 84x84, and field of view

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Table Model architecture summary.
LANGUAGE MODELS
AUDIO MODELS
Family
Layers
Width
Parameters
Family
Layers
Width
Parameters
12
768
125M
384
8M
24
2048
1.3B
512
21M
OPT [38]
40
5120
13B
Whisper [42]
12
768
88M
48
7168
30B
24
1024
307M
9216
66B
1280
637M
96
12288
175B
12
768
95M
60
6656
33B
HuBERT [35]
24
1024
317M
LLaMA [39]
80
8192
66B
48
1280
964M
12
768
95M
WavLM [41]
1024
317M
Whisper counts include only the encoder.
220 mm. Anatomical data were collected using Tl-weighted multi-echo MP-RAGE sequence with voxel size = Imm X Imm x Imm.
All subjects were healthy and had normal hearing. The experimental protocol used by [43, 44] was approved by the Institutional Review Board The University of Texas Austin. Written informed consent was obtained from all subjects.
In addition motion correction and coregistration [43], low frequency voxel response drift was identified using a 2nd order Savitzky- filter with a 120 second window and then subtracted from the signal. To avoid onset artifacts and poor detrending performance responses for training data were trimmed by removing 20 seconds (10 volumes) at the beginning and end of each sean, which removed the 10-second silent period and the first and last 10 seconds of each story. Test responses were trimmed by an additional 80 seconds (40 volumes) to account for an fMRI artifact (see Section 3.5). The response was scaled to have unit variance.
each end of the scan,
response for each voxel was subtracted and the remaining
2.3 Encoding model construction
We used the IMRI data estimate voxelwise brain encoding models for natural language using the intermediate hidden states of the various language and speech models discussed in Section 2.1. First, activations for each word in the stimulus text were extracted from each layer of each LM. In order to temporally align word times with TR times, we applied Lanczos interpolation together with finite impulse response model [43]. Previous hidden state extraction methods (e.g. [23]) involved extracting the hidden state at the last token of the final word from fresh context of fixed length of N tokens. This method requires N forward passes through the model in order to compute the hidden state for single word. As this is impractical for models over a certain size, we improved computational efficiency here using dynamically-ste were grown until they reached 512 tokens, then reset to new context of 256 tokens. More formally, the hidden state for token i, H (i) is defined as
context window. For given story, contexts
H(1) = [0 (X (250
i < 512
zio | 2256.))
i >>> 512
where ((j.)) is the context of the tokenized story X from the token at index j to the token at index and 0 is the function parameterized by the language model. This allowed hidden state extraction for most tokens to be completed with single forward pass per token, rather than forward passes as in previous methods. Differing tokenization schemes for handling whitespace across language models presented a challenge for consistent evaluation and were handled on rase-by-cat basis.
Unlike the analyzed language models, the audio models used are bi-directional, we must use fresh context to preserve the causality of the extracted features. We windowed the stimulus waveform with sliding window of size 16s and stride 100 ms before feeding it into model. At each layer,

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use the hidden state of the final token as the model's representation for the window. As Whisper follows an encoder-decoder architecture, we only use states from the encoder, since operates only on the waveform. We then downsample the features as before with Lanczos interpolation.
Let (S)) indicate a linearized ridge regression model that uses a temporally transformed version of the language model hidden states H (S) as predictors. The temporal transformation accounts for the lag in the hemodynamic response function [9, 45]. We use time delays of 2, 4, 6, and seconds of the representation to generate this temporal transformation. For each subject 8, voxel v, and language model layer h4s we fit a separate encoding model fh; to predict the BOLD response B from our embedded stimulus, i.e. B(a,,,h.) = SKj (H)( Encoding model performance for a given layer was computed the average voxelwise performance of that layer's 's hidden states across of all of cortex for all of our 3 subjects. For all figures with cortical flatmaps, we present the flatmap for one subject. Cortical flatmaps showing results for the other two subjects are shown in Section F of the supplement.
2.4 Stacked regression
A unified "optimized" encoding model combining the LLaMA language model and Whisper audio model was computed using an adaptation of the stacked regression approach from Lin et al. [46]. For every even-numbered non-embedding layer / in the Whisper model, as well as the 18th layer of the 33 billion LLaMA model, we held-out ~200 of the training data and built an encoding model using the remaining ~80% of the training data. This was repeated for each of 5 folds. The predictions of these encoding models on the 5 folds of held-out training data were concatenated to generate full
held-out predictions of the training data, fh: ( (1) After this cross validation procedure, we build
covariance matrix for each voxel and subject RR of the residuals such that
R
y
(1
Sha
(hh
where is the total number of time points and y is the ground truth BOLD response for voxel on subject We then optimize the quadratic problem min R "h such that Oh, > 0 and Ej= by with quadratic program solver [47] to get convex set of attributions ". which serve as weights for each feature space in the joint encoding model. This yields the final encoding model
go
0,8 20.8 Biyy Jh
(xz)
where k is the number of feature spaces. As a final step, we validate this stacked encoding model independently using a held-out validation set and build final encoding model that uses the stacked prediction for voxels where the stacked approach is significantly better on this validation set and uses the prediction from the 18th layer of LLaMA otherwise.
To determine which layers of the model are used model each voxel, we computed voxelwise attribution center-of-mass. For each of the ax:,, the center-of-mass attribution C(a":)) is computed
as
C(a
Σ
i0
i0
where m is the total number of Whisper layers used in the stacked attribution. This allows us to summarize whether the attributions are primarily weighted on the earlier later layers of the network for that voxel.
2.5
Noise ceiling computation
Data from brain recordings such as fMRT are inherently noisy, it is useful to distinguish response variance that could potentially be explained by some model from noise variance that cannot be explained. We estimated the amount of explainable variance, or noise ceiling, using the averaged responses from the test story with 10 repeats and the method of Schoppe et al. [48]. The maximum
correlation coefficient of the ideal encoding model is estimated as CC CCmaa
(v (1+ NP
SP

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Semantic
A % Correlation Q A Correlation
250
Mean
190
100
OFF OFT2160
16
10
109
189
10
100
10
16
Speech
Pefermnnce Jark
100
6.5
107
10'
Num. Parameters
Num. Stories
Normalized Layer Depth
Figure 1: Scaling laws of Semantic and Speech Audio Encoding Models -Fiures la and 1b show logarithmic scaling of semantic encoding model performance with number of parameters and number of stories. Figure Ic shows average voxelwise y2 for each layer of all tested models averaged across 3 subjects. Figures 1d, le, and If show analogous results for speech audio models. Error bars for Figures 1b and Ie denote standard across bootstraps. Error bars for Figures 1c and If denote SNR-normalized subject-axis standard error. y2 is computed as |r| r.
where N is the number of repeats of our test data, NP is the noise power unexplainable variance, and S is the signal power or the amount of variance that could in principle be explained by the ideal predictive model. Using these estimates, we can then extract normalized correlation coefficient CCnorm CCAba.
OCmea where CCabs is the mromenttmoment correlation coefficient of the model's predictions against the ground truth fMRI responses. In some voxels, random noise cause C'Cube > C'maas leading to CCrorm estimates greater than one. To regularize CCnorm estimates for noisy voxels set CCmaz values smaller than 0.25 0.25. The normalized correlations CCnorm are only used for the noise ceiling analysis Figure 3. All other reported correlations are uncorrected (CCabs). For brain map visualizations only show voxels with CC > 0.35.
2.6 Compute specifications
The generation of the encoding models presented in this paper required significant computational resources. Ridge regression was performed using compute nodes with 128 cores (2 AMD EPYC 7763 64-core processors) and 256GB of RAM. total, roughly 4,000 node-hours of compute was expended. Feature extraction from language and speech models was performed specialized GPU nodes that were the same as the sevviously-deseribnn compute nodes but with NVIDIA A100 40GB cards. Feature extraction required roughly 200 node-hours of compute these GPU nodes.
3 Results
3.1 Scaling laws for semantic encoding models
Encoding models were fit for each of three subjects using roughly 20 hours of fMRI training data. For the 125 million parameter OPT model we also encoding models using varying amounts of training data in order to study the effect of training data size on encoding model performance. To capture encoding model performance, we compute the average prediction performance across all voxels in the cortex of each subject.
Figure la shows the relationship between language model size, measured number of parameters, and encoding performance, measured as percent change in average prediction performance across all voxels in cortex relative to the smallest model. For consistent comparison, we only compare between the six model sizes from the OPT family. The layer that performed best for each model size was used. The result shows approximately logarithmic scaling of encoding performance with model size. For each order of magnitude increase in the number of parameters in the language, the encoding performance the average subject increases by roughly 4.4%. However, this logarithmic relationship (r 0.91) tapers off to plateau for models in excess of 30 billion model parameters.
5

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42921
Voxel 80037
Fw2775
PFC
PrCu
Prcu
Broca
Broca
AG
AG
Vaxel 15032
AC
Zocand baxitx
Voxel 25558
16
Encoding Performance
Figure 2: Large-scale encoding models Performance of an encoding model built using OPT-30B on 20 hours of training data from a single subject. Surrounding plots show model predictions (red) against the average response (dashed black) over 10 separate trials (gray) language test stimulus for selected voxels (Clockwise from bottom left: Well-predicted voxels from fusiform body area (FBA), Broca's 's area, precuneus, prefronnal cortex, and secondary auditory cortex.) Only voxels with CCmaz > 0.35 are shown. (PFC = prefrontal cortex, PrCu precuneus, AC auditory Dortex/Wernicker area, AG angular gyrus)
held-out natural
We hypothesize this is effect of the increased hidden state size that larger models possess, combined with limitations in our dataset size. Each encoding model was fit using the same 33,000 data points. As the models grow wider, the regression problem becomes more ill-conditioned. When FIR delays are added, models past the 30B parameter threshold have more hidden states than there are data points train the regression, which lowers encoding performance. Further analysis of the relationship between dataset size and model size is provided in Section E in the supplement.
Figure 1b shows the relationship between the number of training stories (roughly proportional to total training data) and encoding performance on OPT-125M (layer 9). Here we see a strong logarithmic relationship between training data size and encoding performance. Each time the number of training stories increases by an order of magnitude, the encoding performance of the average subject increases by 122%. This strong relationship (r 0.989) gives compelling support the usefulness of collecting "deep" datasets that focus on collecting greater amount of data from a few subjects rather than a smaller amount of data from many subjects.
Figure 1c shows the encoding performance for each layer of each LM. The LLaMA models are marginally better encoding than the OPT models, and also have different pattern, with peak performance in relatively early layers followed by slow decay. contrast, the OPT models have maximum performance with layers that roughly 3/4 into the model. This mirrors results in other GPT-like models [3, 49]. This divergence from the typical pattern may warrant further study into the underlying mechanisms that define these trendlines. We suspect that the larger training of the LLaMA models (1.4T tokens) over the OPT models (180B tokens) may explain its better encoding performance.
3.2 Scaling laws for speech audio encoding models
We trained encoding models of increasing sizes from three families of audio models: HuBERT, WavLM, and Whisper. Encoding models were using an identical procedure as with the LMs in Section 3.1 individually for three subjects, with roughly 20 hours of training data. We repeat the analyses from Section 3.1 on the audio models to examine the importance of model size and training dataset size encoding performance.

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Figure 1d shows how audio model size affects encoding performance. We use the Whisper model family for this analysis, since has the most models of different sizes. Again, the best performing layer for each size was used. As before, there is logarithmic relationship (r 0.991) between model size and encoding performance: performance for the average subject increases roughly 32.2% for every additional order of magnitude increase in model size. Though the scaling improvements are greater overall than with OPT, it should be noted that the smallest Whisper models are substantially smaller than the OPT models, and have lower baseline performance, which exaggerates the difference. Additionally, within auditory cortex, we observe that encoding performance does not plateau with model size (see Section B. suggesting that improvements in AC complemented by reductions in performance elsewhere
Figure 1e shows how additional training data improves the encoding performance of Whisper Large (636 million parameters, layer 30). As before, we fit separate encoding models on increasing amounts of training data. Additional training data for Whisper has an effect that is comparable to OPT: Encoding performance linearly related to log-dataset size (r 0.988), and increasing the training dataset by an order of magnitude increases performance by 144%.
Figure If shows the performance of each layer of every Whisper and WavLM model. For legibility, HuBERT results are omitted from this plot and are included in the supplement (Figure B.2). The upper-middle and uppermost layers of each model tend to have the best performance, aligning with previous results on acoustic encoding models [29, 3 31]. In contrast with WavLM, the Whisper models increase in performance with layer depth; this can likely be attributed to our choice of only using the encoder module from the network.
Voxelwise scaling laws, examining the relationships described in Figure 1 on per-voxel basis, can be found in Section A of the supplement.
3.3 Large-scale encoding models
After characterizing these scaling laws, we next visualized the performance of one of the top- performing semantic encoding models
Figure shows the encoding performance of the best OPT model, which uses the 33rd layer of OPT-30B, as measured on the test story with 10 repeats. For several voxels from different areas of cortex we show the encoding model predicted timecourse and ground truth BOLD response. We see strong prediction performance across cortex, with "classical" language regions like Broca's 's area and auditory cortex being well explained, as well as areas that are typically considered to be more "amodal" in nature, like prefrontal cortex. Voxelwise correlations for this subject are as high similar map showing the change in encoding performance from OPT- 125M (comparable to GPT models used in earlier papers) to OPT-30B is given in the supplemental material (see Figure C.1).
0.82. A
3.4 Noise ceiling analysis
We further investigated the degree to which encoding models can be improved past this point. To do this, we performed a noise ceiling analysis whereby for each voxel, we estimated its CCmaz (see Section 2.5). This gave us approximation of the degree to which an ideal encoding model could explain the response variance in each voxel. We then renormalized the correlations from Figure 2 to compute a normalized correlation coefficient CCnorm-
Figure 3a shows the room for improvement, or the difference between the correlation coefficients measured in Figure 2 and their C'maz. Voxels are yellow if there is significant room for improvement, and purple if the model for that voxel is already close to optimal. Regions that are typically believed to contain high-level representations of language such angular gyrus (AG) [50-52] still have the potential for substantial modeling improvement, while some areas in temporal cortex (near AC), prefrontal cortex (PFC), and the precuneus (PrCu) are nearly optimal. Figure 3b shows a histogram of absolute correlation coefficients (CCata), and Figure 3e shows the normalized correlations CCnorn-
"Keeping with the scaling results from Section 1, we chose to demonstrate this using the best model from the OPT family, however it should be noted that the best model from the LLaMA family is about 5% more performant measured by correlation. This LLaMA model is further explored in Section 3.6.
7

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PFC
MCC
RrCu
Broca
Eircca
-07
12 64
03
Norme Lred Cormicatio Conficlatt (OC..))
Figure 3: Noise Ceiling Analysis- - Figure 3a: A two channel flatmap showing which ROIs remain poorly explained by an encoding model built from the 33rd layer of ОPT30B. Voxels are less transparent if they have a higher idcalized encoding performance (CCmaa). Voxels are more yellow they have high room for improvement, defined the difference between the best possible encoding model and this model. Angular gyrus and some parts of prefrontal cortex are still poorly explained, while precuneus and higher auditory cortex are close to optimal. Figure 3b: A histogram of voxel correlations (CCabs). Figure 3c: A histogram of normalized voxel correlations (CCnorm)) (PFC prefrontal cortex, PrCu = precuneus, AC auditory cortex, AG angular gyrus)
3.5 Long context artifacts
Granting encoding models access to contexts as long as 512 tokens implicitly gives them access to the information that the fMRI scan has started recently. For instance, if the input context has only 64 tokens, this implies that the context is occurring at the 64th token in the story. In parallel, responses in some voxels tend to rise or fall gradually over the first minute of each scan (potentially due to underconstrained detrending at scan edges, MRI magnetization reaching steady state, neural adaptation). The combination of these two effects can have unintended effects on the fair evaluation of these models by artificially inflating measured performance, as encoding models are adept at capturing this early slow drift, We found that long context effects exist up to roughly 100 seconds into a story, so to mitigate this issue we simply exclude the first 100 seconds of predicted and actual responses from each test story when measuring encoding model prediction performance. Figure D.1 in the supplement gives a map of the effect of long-contex, artifacts measured encoding model performance. Long-context artifacts can inflate measured performance by up to 20%, but the effeets mostly localized areas typically associated with low-level speech processing such early auditory cortex. This effect is most prominent for encoding models using early LM layers and speech models, and tends to not be as significant for later LM layers.
3.6 Unifying semantic and speech encoding models with stacked regression
We used stacked regression (see Section 2.4) to augment our best semantic model with the Whisper speech model representations. Figure 4a shows the regions that benefit from this augmentation, blended with a flatmap showing the overall semantic encoding model performance. We observe that these benefits are highly localized to auditory cortex and mouth motor cortex. The butterfly plot in Figure 4b shows the effect on voxels modified by this augmentation. We see that the auditory cortex voxels that are best predicted by the semantic model are also those that are most improved by this augmentation. Figure 4c plots the center of mass of the attribution weights 2.a For voxels where the attribution weights favored the later layers of the Whisper model, the voxel is plotted in a brighter hue. We see that this attribution plot demonstrates a clear progression auditory information from primary AC to secondary AC coinciding with layer depth. Figure 4d shows the benefits of this stacked regression augmentation. see that the lion's share of the improvements happen primary AC and early secondary AC.
4 Discussion & conclusions
These results suggest the existence of two major effects on the capacity of encoding models to predict BOLD response given finite brain data. First, LM changes that correspond to downstream task
8

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1.00
LLaMA Layer 18 model
0.75
0.50
Attribution CoM
A Encoding Performance
-0.25
-022
Stacked Regression model
Figure 4: Stacked Regression Figure 4a: A flatmap shows which regions of cortex improve when augmenting semantic encoding model built from the 18th layer of LLLMA-33B with the layers of Whisper using stacked regression. Voxels used the stacked regression the stacked regression performed better on validation set. The effect is highly localized to auditory cortex. Figure 4b: A butterfly plot comparing the voxelwise encoding performance of the stacked regression encoding model to the baseline semantic model. Figure 4c: The center-of-mass of the stacked regression attributions, C(a=".) are visualized in auditory cortex. Figure 4d: The improvement in encoding performance of the stacked regression model over the baseline visualized auditory cortex.
performance improvement tend to also improve encoding performance, such as when moving from a LM trained on little data to one trained on more data. Second, increasing hidden state size while keeping other metrics fixed tends to lower encoding performance, as it worsens the conditioning of the encoding model regression problem without a corresponding benefit to model effectiveness. The conflict between these two effects has led to a scenario where the largest model is not necessarily best for predicting BOLD responses, as we have seen for both the OPT and LLaMA LMs where encoding model performance peaks at about 30B parameters. Rather, a careful balance must be struck between model size and model efficacy in order to maximize encoding performance. Audio models, on the other hand, have not yet seemed to reach this plateau.
What are the use cases for better encoding models? One promising application is the use of encoding models to supplement more classical experimentation techniques, as suggested by Jain et al. [20]. Higher encoding performance leads to more trustworthy model predictions and more accurate conclusions. Another use case of effective encoding models is language decoding, or predicting the language stimulus from the BOLD response. Recent work has shown that effective language decoding models can be built from encoding models by applying Bayesian techniques [45, 53), so it likely that the performance of such decoders will improve along with the performance of encoding models [33, 44J. Finally, improved encoding performance could enable fine- fine-grained control over voxel activation through stimulus generation, as demonstrated by Tuckute et al. [54].
Given our results, what can computational neuroscientists do to improve the performance of their own encoding models? One potential observation that deep datasets [43, 55-57] those that focus on collecting many samples from a few subjects, rather than a little data from many subjects are more useful for modelling brain activity. Encoding performance improvements scale well with both model size and dataset size, and large datasets will no doubt be necessary in producing useful encoding models. Another straightforward adjustment that can be performed is to simply use larger, more performant LMs for building encoding models. To the authors' knowledge, no other natural language encoding models paper at the time of this writing has used models larger than GPT-2 XI., which is 1.5B parameter model with performance far below the best 30B parameter models. This

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could be due to valid concerns that the amount of natural language brain data available is insufficient to train effective encoding models on such a scale. However, we found that even in low data cases, such as with as little as an hour's 's worth of data, encoding models built from larger models tend to outperform their smaller counterparts, as seen in Figure E. of the supplement. We have released code as well selected precomputed features, model weights, and model predictions generated for this paper. We hope this data release will encourage the use of more performant encoding models in natural language computational neuroscience.
Acknowledgements
The authors acknowledge and thank the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have significantly contributed to the research results reported within this paper. This work was funded by grants from the NIDCD and NSF (IROIDC020088- 001), the Burroughs- Werlloome Foundation, and a gift from Intel Inc. We thank Ruogu Lin, Leila Wehbe, and Javier Turek for their aid and thoughtful suggestions in assisting with this work.
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13


Reviews:
[{"review_id": "mW6KW8ZRf3", "reviewer": "Reviewer_dAos", "summary": "The authors of this paper delve into the investigation of the scaling law between the performance of predicting brain activity (measured using BOLD) and the number of parameters in large language models, coupled with the amount of training data for the linear readout for retrained LLM used in AI. This pursuit of exploring a log-linear scaling law relationship is an interesting and valuable. It holds promise in providing crucial information for paving a path forward in developing better functional models of brain activity, which could be instrumental in understanding brain computations. The technical dimensions of the paper are well-executed. The authors have displayed a solid grasp of the subject matter and have employed appropriate methodologies to carry out their research. However, I have some reservations about the validity of their claims concerning the non-saturation of the scaling law for the number of parameters in large models. Specifically, Figure 1, which is central to their argument, seems to present evidence contrary to their claim. They acknowledge a visible saturation but attribute this observation to memory limitations in the way they fit the linear readout (i.e. they select one layer). However, unless they successfully demonstrate that the saturation does not occur when a more sophisticated linear readout is utilized (for example, from all layers for larger models), it is not justified for them to assert that the predictive models demonstrate scaling as a function of parameter size. Thus, the authors need to refine their claims or provide additional analysis to convincingly demonstrate that the saturation effect they observed is truly an artifact of their methodological limitations, not an inherent feature of the models they are studying. Without such demonstrations, the claim about the non-saturation of the scaling law remains unsubstantiated. In conclusion, while the paper tackles an intriguing concept and showcases strong technical elements, the authors need to strengthen their assertions through concrete evidence or refinement of their conclusions. This additional effort will greatly enhance the paper's overall quality and the validity of their findings, adding substantial value to the body of knowledge in the field.", "questions": "The authors need to demonstrate using other linear readouts that there is not saturation of performance in the neural prediction task. ", "limitations": "yes ", "rating": 5, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The question of how far scaling deep learning models can continue to improve neural prediction is an important question in the quest to build more accurate models of the brain. ", "weaknesses": "More work is needed to demosncate that the current LM are not saturating the performance of the neural prediction task. This is very critical since the main contribution of this work is that even the largest LM do not saturate the performance. ", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ">More work is needed to demonstrate that the current LM are not saturating the performance of the neural prediction task. This is very critical since the main contribution of this work is that even the largest LM do not saturate the performance.\n\nThank you for your review and thoughtful comments. We agree that we did not adequately prove that the performance plateau after 30B parameters is a side-effect of the poor conditioning of the regression problem at that size, so we have performed an additional analysis to strengthen our argument. Doing a more sophisticated linear readout from multiple layers is currently out of reach, as this would be too costly to realistically train and would have even worse conditioning, with the number of features far exceeding the number of training points from our fMRI dataset. Instead, we performed an additional analysis regarding the relationship between data scaling and parameter scaling. Conditioning of the encoding regression problem depends on both the size of the dataset and the number of parameters: more data is good, more parameters is bad. If the problem with the large models is not poor conditioning, then we would expect dataset size to be less impactful than for smaller models. Conversely, if conditioning is the culprit, then we would expect the large models to show stronger data size scaling than the smaller models. Our analysis shows the latter: for larger language models performance scales more strongly with dataset size. Figure 1 of the rebuttal PDF shows a histogram with the distribution of voxelwise scaling laws (i.e. the slope of the log-linear relationship) across cortex for one subject, filtered by a minimum $cc_{max}$ (i.e. only in voxels with sufficient signal to model).\n\nWe see that the distribution is shifted to the right for the larger language model, showing that encoding models built from larger LMs on average benefit more from additional data. This makes sense, as large models are those that are most affected by poor conditioning.  As it seems unlikely that the representations from larger language models contain less information than those of smaller models, we suggest that the plateau we observe at 30B is mostly the result of limited dataset size. Given this result, we intend to refine and clarify the paper text, suggesting that it has to do mostly with data constraints and that with sufficient amounts of data, parameter scaling would likely continue to improve above 30B parameters.\n\nWe found this result by comparing data scaling between the 125M and 30B OPT models, which we had already fit. Ideally we would have also tested the 175B OPT model, but testing dataset scaling is computationally expensive and re-fitting those models is substantially beyond our compute budget.\n\nFurthermore, in responding to another reviewer, we recomputed Fig. 1c with a sum of $r^2$ metric (Figure 2 in the rebuttal PDF) and found that by using this metric, the model trained by OPT-175B is slightly better than the OPT-30B metric. The sum of $r^2$ metric favors increases in encoding performance in well-predicted voxels over poorly predicted voxels. As well-predicted voxels will be more resilient to poor conditioning, this result aligns with our conditioning argument as well.\nWe hope that this argument is satisfactory to you and allays your concerns.\n"}, {"review_id": "L8tbeCDadk", "reviewer": "Reviewer_jqqd", "summary": "Previous works have demonstrated that activations from Language Models fit, to some extent, brain activations in participants listening to audio texts.  Here, the authors examine how the fit is influenced by model size (number of parameters) and the training dataset size. \nThe main observation is that performance scales log-linearly with model size (until 30B parameters) and with fMRI training set size (from 1 to 100 stories).\n\n", "questions": "Figure 1 shows the increase in performance averaged _across the whole cortex_. Have you checked whether this profile is similar in different regions (e.g. auditory cortex, core language region, and higher-level regions like precuneus and medial prefrontal)? \n\nWere the (OPT) models of different sizes trained with the same language corpora (fixed size)?  \n\n ", "limitations": "The limitations were adequately discussed.", "rating": 8, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "The main originality of the work is to explore language models that are much bigger than the ones that had been used in previous works of this type (as well as recent, large, acoustic models). Not only does this represent a technical feat, but it also advances knowledge on the topic, as it was not clear if the representations constructed by larger models would necessarily converge towards more and more brain like representations when the models become bigger.  Data presented here show that there was still a lot of room for improvment from GPT-2 like models. \n\nThe raw performance of the best model (OPT-30B), presented in Fig.2 is quite impressive and, along with the analysis of the effect offmri training set  size, buttresses the authors' claim of the usefulness of using large within subject dataset.\n\nFig.3b which compares performance to estimated ceilings is very interesting theoretically as it suggest that the models model some regions better than others. \n\n\n\n", "weaknesses": "As the authors mention (at line 300), when models grow in size, the regression problem may become ill conditioned. Would there be any strategy to remedy this problem?  ", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your review and thoughtful comments. We have included responses to your questions below.\n\n> Weaknesses:\n>\n>As the authors mention (at line 300), when models grow in size, the regression problem may become ill conditioned. Would there be any strategy to remedy this problem?\n\nNaturally, poor conditioning is difficult to remedy algorithmically without relying on additional data as nothing will get around the fact that there is insufficient data to mathematically constrain the regression problem. Still, there may be alternative methods for enabling the continued scalability of encoding models without relying on unreasonably sized single-subject datasets. For example, instead of using ridge regression for the linear readout, one might consider using a bottlenecked neural network trained simultaneously on data from multiple subjects to assist in dimensionality reduction. This may help with regularization as it enables the model to learn a general, low-dimensional joint semantic representation that works well across many subjects. We believe that the possibility of jointly training language encoding models across subjects is worthy of additional study.\n\n>Questions:\n>\n>Figure 1 shows the increase in performance averaged across the whole cortex. Have you checked whether this profile is similar in different regions (e.g. auditory cortex, core language region, and higher-level regions like precuneus and medial prefrontal)?\n\nWe have, and appendix B gives some indication of the percentage scaling improvements for each voxel/ROI. We agree that this may not be fully addressed, however, and will include an additional flatmap showing the slope of the scaling law per voxel in the supplement (Figures 3 and 4 in the rebuttal).\n\n>Were the (OPT) models of different sizes trained with the same language corpora (fixed size)?\n\nYes, according to the original OPT paper, all models were trained with the same training set of 180B tokens. We will include a clarification of this detail in an appropriate place in the main text.\n"}, {"review_id": "cPFQGH6SAo", "reviewer": "Reviewer_fnMd", "summary": "The authors study how the scaling of large language models produce accurate features to predict human brain fMRI activity. They report scaling-like laws for fMRI encoding models – models with more parameters tend to more accurately predict fMRI activity (as measured with the Pearson correlation of the encoding model predictions and fMRI time series).", "questions": "For an ‘fMRI encoding model practitioner’, it would be helpful if there were concrete ‘recommendations’ for what models are most appropriate for language/audio modeling. For example – and this is a minor point – does it matter which layers one uses to produce the regression model features?\n\nIf possible, it would be interesting to see a surface map that shows which voxels/regions follow a scaling law for the audio v language models, respectively.\n\nHow dependent is the scaling law on computing the average (across voxels) for each of the maps per model?\n\nCan the authors also report R^2 for their encoding models benchmark?\n\nWhat does it mean (scientifically) that the model that best produces regression features for brain encoding models look nothing like the brain? Are there conclusions one should draw from this? Or is this just a coincidence?\n\nMight there be any correspondence between layers in an LLM and different brain regions?", "limitations": "The limitations are mostly in terms of the scientific utility of claiming that there are scaling laws for fMRI. I doubt the authors intend this interpretation, but the title seems to hint at the possibility that if one achieves enough scale with language models, one might be able to perfectly predict brain activity (and therefore model the brain). This seems implausible (and likely not intended), but some discussion around this would be helpful.\n", "rating": 7, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "I found the paper to be of general interest, and the methods to be sound. The paper suggests that there is a utility to using modern large ML models as producing features for fMRI encoding models.", "weaknesses": "It is hard to determine whether this result should be expected, and what to make of its scientific significance (beyond an engineering feat). On one hand, one would expect that models that are larger (and therefore better at modeling language/sound data) should produce more useful features for language/sound data. On the other hand, these large models process language/sound data in ways that are almost certainly distinct from how the brain processes information (e.g., the brain doesn’t appear to merely do next-word prediction). So what does one make of this discrepancy? Do the authors believe that the brain mimics the computational processing of these models? And what is the scientific significance of using a model – that presumably looks nothing like the brain – to build better models of the brain?\n\nHow valuable is using percent correlation change as a metric for how well the encoding models perform relative to, for example, R^2? Is it truly useful to benchmark or establish ‘scaling laws’ based on the average encoding performance across all fMRI voxels, rather than identify one or two key regions (or the variability across regions)? What might be interesting to evaluate is whether these scaling laws only apply to a subset of voxels/brain regions, since, presumably, how well a voxel/region follows a scaling law is likely dependent on how well a brain region’s function matches with the model type.\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your review and thoughtful comments. We have included responses to your questions below.\n\n>Weaknesses:\n>It is hard to determine whether this result should be expected, and what to make of its scientific significance ... So what does one make of this discrepancy? Do the authors believe that the brain mimics the computational processing of these models? And what is the scientific significance of using a model – that presumably looks nothing like the brain – to build better models of the brain?\n\nWe thank the reviewer for raising this point, as it is an important one. The suggestion that language models share fundamental commonalities with human brains is an ongoing discussion - see Schrimpf et. al., Goldstein et. al., and Caucheteux et. al., c.f. Antonello and Huth for more details. However, regardless of whether these models are mechanistically similar to the brain, they remain the most powerful fine-grained predictive models of biological language processing that have ever existed, and that alone gives them high scientific and practical value. While prediction should not be conflated with explanation, powerful predictive models of brain activity provide a uniquely useful pathway to eventual explanation. Sufficiently powerful encoding models can be used to simulate brain activity *in silico*, allowing for the rapid simultaneous testing of thousands of hypotheses that would be impossible to test *in vivo*. Furthermore, encoding models play an important role in Bayesian decoding techniques which have tremendous practical value – see Tang et al. 2023 for further discussion.\n\n> How valuable is using percent correlation change as a metric for how well the encoding models perform relative to, for example, R^2? Is it truly useful to benchmark or establish ‘scaling laws’ based on the average encoding performance across all fMRI voxels, rather than identify one or two key regions (or the variability across regions)? What might be interesting to evaluate is whether these scaling laws only apply to a subset of voxels/brain regions, since, presumably, how well a voxel/region follows a scaling law is likely dependent on how well a brain region’s function matches with the model type.\n\nAppendix B in the supplement gives a voxelwise breakdown of parameter scaling as a percentage improvement from our OPT-125M model to our OPT-30B model. As an additional analysis, we have now also generated flatmaps of the slopes of the individual voxelwise scaling laws for both data scaling and parameter scaling (see Figures 3 and 4 in the rebuttal PDF). We see that for data scaling, almost all voxels associated with language processing in cortex benefit from additional data. Scaling laws for parameters are a bit more complicated, but it seems that in general, areas that are typically associated with high-level language processing and cognition are those that benefit the most from increasing parameter size.\n\n>For an ‘fMRI encoding model practitioner’, it would be helpful if there were concrete ‘recommendations’ for what models are most appropriate for language/audio modeling. For example – and this is a minor point – does it matter which layers one uses to produce the regression model features?\n\nWe believe that this is addressed in the current draft – see Figures 1c and 1f which show which layers perform best in each model. We would recommend layer 18 from the LLaMA-30B model and layer 20 from WavLM-317M, as these layers perform well and can be computed with relative ease. In cases with larger amounts of data than we possess, we would suggest using representations from larger models. We will add an explicit mention of these suggestions in the final version. Pretrained weights of these models will be released as well in the camera-ready version.\n\n>If possible, it would be interesting to see a surface map that shows which voxels/regions follow a scaling law for the audio v language models, respectively.\n\nYes, we will include this in the supplement, and it has been attached to this rebuttal.\n\n>How dependent is the scaling law on computing the average (across voxels) for each of the maps per model?\n\nSome voxels scale more than others, but scaling is a brain-wide phenomenon that impacts nearly all language-selective brain regions positively. This is observable from the flatmaps mentioned above.\n\n>Can the authors also report $R^2$ for their encoding models benchmark?\n\nUnfortunately, these models were trained to optimize correlation and not $R^2$, so computing $R^2$ directly would not be meaningful. Retraining the models with the $R^2$ objective would fall outside our compute budget, but we will include a plot similar to Figure 1c showing the average $r^2$ across voxels, which bounds $R^2$ from above. This can be found in the rebuttal PDF (Figure 2). We will also be correcting a notational oversight and converting occasional mentions of $R$ to $r$.\n\n>What does it mean (scientifically) that the model that best produces regression features for brain encoding models look nothing like the brain? Are there conclusions one should draw from this? Or is this just a coincidence?\n\nWe would not describe it as a coincidence. It makes sense that two systems that can both engage with language in a high-level way will have shared information about that language. This does not entail that they are performing the same computations or are “learning” in the same way. Your question is part of a larger scientific debate about encoding models that extends beyond the scope of this particular paper.\n\n>Might there be any correspondence between layers in an LLM and different brain regions?\n\nFor language models we don’t find this to be the case. However, for audio models there does seem to be some correspondence, where earlier layers predict primary auditory cortex better and later layers predict higher-order auditory cortex better. This is shown in Figure 4c, with the center-of-mass attribution analysis in the stacked model.\n"}, {"review_id": "hbPMwSp3dK", "reviewer": "Reviewer_NDv4", "summary": "Researchers compared the effectiveness of larger open-source language models, such as those from the OPT and LLaMA families, in predicting brain responses recorded using fMRI. They found that brain prediction performance improves logarithmically with model size, with a 15% increase in encoding performance as model size increases. Similar improvements were observed when scaling the size of the fMRI training set. The study also explored the scaling of acoustic encoding models and found comparable improvements. The analysis suggests that increasing the scale of both models and data will lead to highly effective models of language processing in the brain, enabling better scientific understanding and applications such as decoding.", "questions": "- Wernicke's area is often paired and observed alongside Broca's area. Did the authors consider observing the Wernicke's area for both auditory and language encoding models?\n- In section 3.4 figure 3a, the \"room for improvement\" seems to be slightly more prominent in the right hemisphere. Please note that this observation is purely from the figure. Have the authors explored why this may be the case? \n- To observe the scaling laws in increasing data size, the authors withheld different amounts of the training data. Did the authors consider augmenting the data in other ways?", "limitations": "The authors adequately addressed the limitations of the paper. ", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- Presents a novel empirical observation of scaling laws for language and audio encoding models in fMRI. \n- They show log linear scaling in brain prediction, encoding performances in both language and acoustic domains. \n- They also show when scaling the size of the fMRI data, the performances increase log-linearly.", "weaknesses": "Most of my concerns are addressed in the questions section. \nOne concern I have is that the code is not publicly available. If the authors published the code it would be greatly appreciated. ", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your review and thoughtful comments. We have included responses to your questions below.\n\n>Weaknesses:\n>Most of my concerns are addressed in the questions section. One concern I have is that the code is not publicly available. If the authors published the code it would be greatly appreciated.\n\nWhile not currently available, we intend to include a link to code as well as pretrained encoding models that can be used to help replicate our results in the camera-ready version.\n\n>Questions:\n>Wernicke's area is often paired and observed alongside Broca's area. Did the authors consider observing the Wernicke's area for both auditory and language encoding models?\n\nThe area we have defined as “left auditory cortex” is also referred to as Wernicke’s area. We apologize for the confusion and will mention this in an appropriate place in the camera-ready version.\n\n>In section 3.4 figure 3a, the \"room for improvement\" seems to be slightly more prominent in the right hemisphere. Please note that this observation is purely from the figure. Have the authors explored why this may be the case?\n\nThis seems to be a subject-specific effect, as the other two subjects (presented in Appendix E) do not have the same lateralization. Given the small number of subjects, it is difficult to productively speculate on the reason for this.\n\n>To observe the scaling laws in increasing data size, the authors withheld different amounts of the training data. Did the authors consider augmenting the data in other ways?\n\nThere may be other ways of withholding data, such as based on its semantic content or original source, to analyze the effects on model performance, if that is what you mean by augmentation. However, we think such analyses would likely be beyond the intended scope of this work.\n"}, {"review_id": "JFCMQXLj6O", "reviewer": "Reviewer_Tsw4", "summary": "The authors evaluate the effect of LM scale (in terms of N parameters) and fMRI dataset size on the performance of downstream encoding models, trained to predict the activity of individual voxels across the brain as a function of the input those participants received during a scanning session. They explore both the OPT and LLaMa models as pure text based LMs and the HuBERT, WavLM, and Whisper models as acoustic models, across a number of sizes. The authors find that fMRI encoding performance can be improved linearly via logarithmic increases in model scale, up to ~30B for text-based models, and the asymptote has not yet been reached for acoustic models. Increases in the amount of fMRI data included per subject also yield dramatic improvements. They also attempt to characterize what additional encoding performance is yielded by the use of acoustic models over text-based ones and find improvements only in auditory areas but not in higher-level associative areas. Such results propose for increased focus on “deep” neuroscience data collection and scaling up the computational resources utilized for encoding analyses.", "questions": "General:\n\nAside from LM model size (N parameters) a crucial component in predicting LM performance is the size of the pretraining dataset (e.g., OPT’s 180B tokens vs. LLaMa’s 1.4T tokens). Given that the authors observe differences between the architecturally similar LLaMa and OPT model families, but these models differ substantially in pretraining dataset size, this is worth mentioning.\n\nRelatedly, for the combined analysis of the LLaMa and OPT models, a more unified axis along which to evaluate the encoding performance of these models might be their mean perplexity across the evaluated podcast stories dataset. I strongly encourage the authors to consider this visualization as a parallel to 1a. It is both likely to be informative, and also proposes a more functional view of the problem space. One would be unlikely to encourage the use of a larger but undertrained 30B model over a smaller 6B model trained on more data with lower perplexity for an fMRI encoding task, particularly due to the author-mentioned advantages of more compressed representations and suggestion that “a careful balance must be struck between model size and model efficacy in order to maximize encoding performance”.\n\nError bars:\n\nWhat do the error bars in figure 1b and 1e represent? (stdev, se, x% ci, etc.?)\n\nNo uncertainty quantification is included for any other figures. Given that “Encoding model performance for a given layer was computed as the average voxelwise performance of that layer’s hidden states across of all of cortex for all of our 3 subjects”, there would be a number of ways to include uncertainty quantification at this top level even without rerunning any models.\n\nMinor: \n\nincrease resolution of figures 1a,1b,1d,1e,3b,3c. \n", "limitations": "The limitations of the work are appropriately addressed.", "rating": 7, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "The work explores a novel and relevant axis for brain encoding analyses and is appropriately contextualized via discussion of related work. The submission is technically sound and most claims are well supported. The submission is clearly written and well organized. The results are relevant and important and will hopefully encourage a “scaling up” of neural encoding analyses.", "weaknesses": "The sole evaluation of LM scale as a function of N parameters is reductive and should be addressed. There is a lack or under-specification of uncertainty quantification. See below for more detailed comments.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful review and comments. We have included responses to your questions below.\n\n>Weaknesses:\n>The sole evaluation of LM scale as a function of N parameters is reductive and should be addressed. There is a lack or under-specification of uncertainty quantification. See below for more detailed comments.\n>Questions:\n>General:\n>Aside from LM model size (N parameters) a crucial component in predicting LM performance is the size of the pretraining dataset (e.g., OPT’s 180B tokens vs. LLaMa’s 1.4T tokens). Given that the authors observe differences between the architecturally similar LLaMa and OPT model families, but these models differ substantially in pretraining dataset size, this is worth mentioning.\n\nYou are correct, we should have included this detail. We will mention this in an appropriate place in the camera-ready version of this paper.\n\n>Relatedly, for the combined analysis of the LLaMa and OPT models, a more unified axis along which to evaluate the encoding performance of these models might be their mean perplexity across the evaluated podcast stories dataset. I strongly encourage the authors to consider this visualization as a parallel to 1a. It is both likely to be informative, and also proposes a more functional view of the problem space. One would be unlikely to encourage the use of a larger but undertrained 30B model over a smaller 6B model trained on more data with lower perplexity for an fMRI encoding task, particularly due to the author-mentioned advantages of more compressed representations and suggestion that “a careful balance must be struck between model size and model efficacy in order to maximize encoding performance”.\n\nTo address your concern, we have computed the mean perplexity across one of our test stories for all but our largest model (which we cannot rerun due to limitations in our computational budget). We would like to note that the perplexities are not directly comparable across the different model families as they employ different tokenization schemes. The table is included below and will be included in some form in the final version.\n\n| Model    | Perplexity |   |   |   |\n|----------|------------|---|---|---|\n| OPT-125M | 35.9191    |   |   |   |\n| OPT-1.3B |  22.4842    |   |   |   |\n| OPT-13B |   18.1750     |   |   |   |\n| OPT-30B |   17.3551     |   |   |   |\n| OPT-66B |   16.5627     |   |   |   |\n| LLaMA-30B | 10.2188     |   |   |   |\n| LLaMA-65B | 9.7363     |   |   |   |\n\n>Error bars:\n>What do the error bars in figure 1b and 1e represent? (stdev, se, x% ci, etc.?)\n\nWe apologize for the oversight. These error bars represent standard error. This will be clarified in the camera-ready version.\n\n>No uncertainty quantification is included for any other figures. Given that “Encoding model performance for a given layer was computed as the average voxelwise performance of that layer’s hidden states across of all of cortex for all of our 3 subjects”, there would be a number of ways to include uncertainty quantification at this top level even without rerunning any models.\n\nWe chose to omit error bars in Figure 1a and 1d as the only sources of uncertainty quantification would be along the voxel axis or the subject axis. Quantifying uncertainty along the voxel axis would be more misleading than helpful as some voxels are inherently less responsive to language. Quantifying uncertainty along the subject axis is also not necessary here as we plot the individual performance for each subject as well as the mean. Figure 2 similarly shows uncertainty estimation by plotting all individual time courses of the 10 test story repeats.  \n\nWe will add to the final camera-ready version SNR-normalized subject-axis uncertainty estimation to Figures 1c and 1f, which should give a sense of how the shape of the layerwise encoding performance curve varies from subject to subject. This uncertainty estimation can be seen in Figure 2 of the rebuttal PDF. We are happy to include additional uncertainty estimation in any other figure however we are unsure of where else that information would be beneficial or does not already exist.\n\n>Minor:\n>increase resolution of figures 1a,1b,1d,1e,3b,3c.\n\nApologies. We intend to revise this for the final camera-ready version.\n"}]

Author rebuttal:
Thank you to all our reviewers for their detailed and thoughtful feedback. For our general response, we are attaching a series of figures that were requested or that we believe resolves the outstanding concerns that each of you have voiced. The figures will each be included somewhere appropriate in the supplemental material of the final camera-ready version. Here are descriptions of the figures, in order:

Figure 1. A histogram of the relationship between data scaling and parameter scaling, meant to flesh our our argument surrounding the conditioning of our ridge regression past the 30B plateau we observe. We see that as model size increase, the average slope of voxelwise data scaling laws increase as well.

Figure 2. A recreation of Figure 1c using an average $r^2$ metric. We see that using this metric, the performance of the best layer in OPT-30B is slightly better than the performance of the best OPT-175B layer, which further supports our point about conditioning.

Figure 3. A flatmap of voxelwise data scaling laws. The redness of the voxel indicates the degree to which that voxel improves with additional data. 

Figure 4. A flatmap of voxelwise parameter scaling laws. The redness of the voxel indicates the degree to which that voxel improves with larger language models.

We have attempted to address specific points mentioned in your reviews in each of the reviewer-specific rebuttals. Thanks again for your feedback.


Meta-review: The 5 reviewers here have expressed support on this work and did endorse it for publication. Given the thorough reviews and later discussions I support the publication of this work at NeurIPS 2023.
Decision: Accept (poster)