TopoLM: brain-like spatio-functional organization in a topographic language model
Authors: Neil Rathi
Johannes Mehrer
Badr AlKhamissi
Taha Osama A Binhuraib
Nicholas Blauch
Martin Schrimpf
Venue: ICLR 2025 Oral (2025)
Keywords: language modeling
topography
fMRI
neuroscience
Primary area: applications to neuroscience & cognitive science
TL;DR: We develop a transformer language model with topographically organized units predicting brain-like spatio-functional organization.

Abstract: Neurons in the brain are spatially organized such that neighbors on tissue often exhibit similar response profiles. In the human language system, experimental studies have observed clusters for syntactic and semantic categories, but the mechanisms underlying this functional organization remain unclear. Here, building on work from the vision literature, we develop TopoLM, a transformer language model with an explicit two-dimensional spatial representation of model units. By combining a next-token prediction objective with a spatial smoothness loss, representations in this model assemble into clusters that correspond to semantically interpretable groupings of text and closely match the functional organization in the brain's language system. TopoLM successfully predicts the emergence of a spatially organized cortical language system as well as the organization of functional clusters selective for fine-grained linguistic features empirically observed in human cortex. Our results suggest that the functional organization of the human language system is driven by a unified spatial objective, and provide a functionally and spatially aligned model of language processing in the brain.Neurons in the brain are spatially organized such that neighbors on tissue often exhibit similar response profiles. In the human language system, experimental studies have observed clusters for syntactic and semantic categories, but the mechanisms underlying this functional organization remain unclear. Here, building on work from the vision literature, we develop TopoLM, a transformer language model with an explicit two-dimensional spatial representation of model units. By combining a next-token prediction objective with a spatial smoothness loss, representations in this model assemble into clusters that correspond to semantically interpretable groupings of text and closely match the functional organization in the brain's language system. TopoLM successfully predicts the emergence of a spatially organized cortical language system as well as the organization of functional clusters selective for fine-grained linguistic features empirically observed in human cortex. Our results suggest that the functional organization of the human language system is driven by a unified spatial objective, and provide a functionally and spatially aligned model of language processing in the brain.

Published as a conference paper at ICLR 2025
TOPOLM: BRAIN-LIKE SPATIO-FUNCTIONAL ORGANI- ZATION IN A TOPOGRAPHIC LANGUAGE MODEL
Neil Rathi', Johannes Mehrer 1, Badr AlKhamissi",
Taha Binhuraib Nicholas M. Blauch', Martin Schrimpfl./
EPFL, Stanford University, Georgia Institute of Technology, "Harvard University
ABSTRACT
Neurons in the brain are spatially organized such that neighbors on tissue often exhibit similar response profiles. In the human language system, experimental studies have observed clusters for syntactic and semantic categories, but the mech- anisms underlying this functional organization remain unclear. Here, building on work from the vision literature, we develop TopoLM, a transformer language model with an explicit wo--imensionnll spatial representation of model units. By combining next-token prediction objective with a spatial smoothness loss, rep- resentations in this model assemble into clusters that correspond semantically interpretable groupings of text and closely match the functional organization in the brain's 's language system. TopoLM successfully predicts the emergence of a spatially organized cortical language system as well as the organization of func- tional clusters selective for fine-grained linguistic features empirically observed human cortex. Our results suggest that the functional organization of the human language system is driven by a unified spatial objective, and provide a functionally and spatially aligned model of language processing in the brain.'
INTRODUCTION
Artificial neural network (ANN) models of language have recently been shown accurately predict neural activity the human language system (Schrimpf et al., 2021; Caucheteux & King, 2022; Goldstein et al., 2022). When presented with the same text input, the unit activity at internal layers of especially transformer- based models (Vaswani et al., 2017; Radford et al., 2019) is strikingly similar to the internal activity measured experimentally in human cortex. The most powerful models predict even close to 100% of the explainable variance of neural responses to sentences in some brain datasets (Schrimpf et al., 2021). However, while there a strong alignment to the brain's 's functional responses, crucial element of cortex is entirely lacking from today's 's language models: the spatial arrangement of neurons on the cortical surface.
In recent models of the visual system, the introduction of topography has led to ANNs that begin to match brain activity functionally as well as spatially (Lee et al., 2020; Margalit et al., 2024; Keller et al., 2021; Blauch et al., 2022: Lu et al., 2023). These models provide principle for understanding the development of spatial organization in the brain, in the form of minimizing wiring cost, such that neurons with similar response profiles tend to cluster together. These clusters resemble the spatio- functional organization the early cortex with orientation preferences such as pinwheels (Hubel & Wiesel, 1962; 1968; Maunsell & Newsome, 1987; Felleman & Van Essen, 1991), and in higher-level visual regions with nategory-selective regions such as face patches (Kanwisher et al., 1997; Haxby et al., 2001; Tsao et al., 2003; 2006; 2008; Freiwald et al., 2009).
The topography of the human language system on the other hand lacks a comprehensive compu- tational explanation. Neuroscience experiments suggest both macro-organization at the level of a distributed cortical network that selectively responds to linguistic processing (Fedorenko et al., 2010; 2011; 2024; Blank et al., 2014), as well as micro-organization into clusters that correspond
"Equal contribution by NR and JM. 'Corresoondenc:: Code available https: //gi thub.

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Figure 1: Building a topographic language model with brain-like spatio- organiza- tion. (a) To modifies the Transformer architecture with woo-dimensional spatial encoding at the output of each attention and MLP layer. This representation enables the use spatial cor- relation loss that encourages smooth response profiles in adjacent units. This spatial loss is jointly optimized with cross-entropy task loss during training. (b) At each forward pass, we randomly se- lect five neighborhoods in each layer (of which we here only show 3 for clearity) and compute the pairwise correlation of unit activations within each neighborhood. The spatial loss is computed by comparing these correlations the inverse distances between associated unit pairs, with the final loss averaged across units pairs and neighborhoods. Computing the loss on cortical neighborhoods an efficient approximation of the spatial loss. (c) We use a FWHM filter to simulate the fMRI sampling process such that simulated voxel's response ('IMRI-like signal") ') is composed of com- bination of responses from neighboring units (Kriegeskorte et al., 2010). We simulate the response Gaussian random variable, with FWHM 2.0 mm, assuming unit distances of 1.0 mm.
syntactic and semantic categories such verbs, nouns, and concrete words (Shapiro al., 2006; Moseley & Pulvermüller, 2014; Hauptman et al., 2024). What are the mechanisms underlying this fpatio-functional organization of the language system the brain?
Here, we develop MM neural network model for brain-like topographic language processing. TopoLM based on the transformer architecture but incorporates an explicit spatial arrangement of units. We train the model via combined task and spatial loss, which optimizes the model to per- form autoregressive language modeling while encouraging local correlation, similarly to a recent approach used in vision (Lee et al., 2020: Margalit et al., 2024). The spatio-functional organization that emerges in this model is semantically interpretable and aligned with clusters that have been observed experimentally in brain recordings. Comparing TopoL.M with non-topographic baseline model (i.e. one trained without spatial loss) on a series of benchmarks, we show that while Topol achieves slightly lower scores on some behavioral tasks (BLiMP), its performance on other down- stream tasks (GLUE) and on brain alignment benchmarks (using the Brain-Score platform) is on par with the nonttopographic control.
Importantly, this spatial loss, as the model is trained solely on naturalistic text without fitting to brain data. This work thus extends the principle of cortical response smoothness proposed in vision (Margalit et al., 2024) into the language system, providing a unified explanation for understanding the functional organization of cortex.
organization arises purely as a result of the combined task and
2 RELATED WORK
Topographic Vision Models. In contrast to the core human language system, the primate visual cortex shows a clear hierarchy of interconnected regions starting at the primary visual cortex (VI), passing V2 and V4, and reaching inferior temporal cortex (IT) which is thought to underlie rep- resentations of complex visual objects such as faces and scenes. Within V1, orientation-selective cortical patches (" ('hypercolumns') orientation of neurons rotates smoothly around a central point, covering all possible orientations (0 to 180 degrees). This structure is observed across species, including humans and non-human
spatially arranged in circular "pinwheels," where the preferred
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primates (Kaschube al., 2010). On more global level, early visual areas (V1, V2) show strong retinotopic organization where nearby stimuli in the visual field activate nearby locations in early visual regions (Engel et al., 1994; 1997; Tootell et al., 1998). While the strength of retinotopic organization strongly decreases, but remains detectable going to higher-level regions of the visual cortex (Larsson& & Heeger, 2006; Schwarzlose et al., 2008; Kravitz al., 2010; Groen al., 2022), the final stage of the ventral visual pathway, IT, shows clear categorical clustering into e.g. regions selective for faces or scenes (Kanwisher et al., 1997: Haxby al., 2001).
This spatial organization of the primate visual cortex has prompted work on topographic ANNs for vision. First approaches focused on the organization of inferotemporal cortex, restricting topo- graphic organization to later model layers (TDANN, Lee et al. 2020: ITN, Blauch et al. 2022; DNN- SOM, Zhang et al. 2021, Doshi Konkle 2023). Recent models are designed such that all layers are topographic and thus mimic topographic features across the visual cortex-for example, smoothly varying orientation preference maps forming pinwheels in model VI and seneeoor--sllcctio regions in model IT (AII-TNNs, Lu et al. 2023; new version of TDANN, Margalit al. 2024).
Our topographic language model belongs to the Topographic Deep Artificial Neural Network (TDANN) family of models (Lee et al., 2020; Margalit et al., 2024). Herein, central claim is that inducing a preference towards smoothness of cortical responses in the model provides a unifying principle for the development of topography in the brain. This smoothness optimization is applicd to all layers in the model and replicates functional organization in early (e.g. V1) and later (e.g. IT) regions of the visual cortex. The TDANN's spatial smoothness, as implemented with an additional loss term, is an indirect but efficient approach to minimizing local wiring-length, and can addition- ally help to minimize long-range connectivity which, in neuroscience terms, corresponds brain size and power consumption (Margalit et al., 2024).
Topographic Language Models. Comparatively little work has explored the idea of inducing topography in language models. In particular, the only topographic language model we are aware of is BinHuraib et al. (2024)'s Topoformer, which induces spatial organization onto a single-headed attention Transformer architecture using local connectivity constraints. This model arranges keys and queries on 2D grids, combined with locally connected layer in the attention mechanism as opposed to full connectivity.
Our approach primarily differs from Topoformer in that we use spatial smoothness loss term to drive the emergence of local correlations, similarly to Lee et al. (2020) and Margalit et al. (2024)'s TDANN vision models. In this sense, our model extends Margalit et al. (2024)'s unifying principle of functional organization from the visual cortex into the language system. TopoLM is thus able to benefit from full connectivity, rather than requiring local connectivity develop clustering. Because we apply this loss to the output of entire attention mechanism at each layer (as well as to the MLP), To can also benefit from multi-head attention, which empirically improves fits to neural data (AlKhamissi et al., 2024); this was not explored in (BinHuraib et al., 2024). Finally, our model also uses an autoregressive task loss, rather than masked autoencoder objective (as used in BinHuraib et al. (2024)), which has been shown to have higher performance on neural alignment benchmarks (e.g. Schrimpf et al., 2021).
3 MODEL DESIGN AND VISUALIZATION
Instead of the convolutional neural network architecture used in topographic vision models (Mar- galit et al., 2024), we use the Transformer architecture (Vaswani et al., 2017) which is dominant in language modeling. We augment the objective function with spatial correlation loss, in addition to the cross-entropy task loss. This loss function measures spatial smoothness, which serves as an efficiently computable proxy for neural wiring length: neurons located close one another should have similar response profiles-i.e i.e. their activations should be correlated (Lee et al., 2020).
To introduce notion of 'space' in the model, bijectively map the units of each attention layer and MIP to a square grid. We randomly permute these positions for each layer such that each layer has unique spatial encoding. On each forward pass, first compute the pairwise Pearson's
"Our goal is abstract away from foed-forward propagation as much possible, as the hierarchical orga- nization of the brain is quite different from that of language model. This random permutation prevents the
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correlation vector ry between unit activations the input batch for each layer &s (see Figure IB). If a layer has units, r is of dimension nCr(N,2). Then, the spatial loss for layer ls is given by
1 corr(r dx)), SL*
(1)
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where dı is vector of pairwise inverse distances between units, based on their spatial encoding, and corr is Pearson's r. This means that nearby units (i.e. high inverse distance) should have highly correlated activations the same inputs, and that distant units should be less correlated; this gives us a notion of spatial smoothness. We scale by a factor of 0.5 to ensure that SL E 1].
We compute this spatial loss for every attention and MLP layer in Transformer, prior normaliza- tion and addition into the residual stream. Rather than computing the spatial loss for the entire layer, as in Margalit et al. (2024) we approximate the loss using small neighborhoods, ensuring that the model optimizes for local, rather than global 'long-distance' constraints. For each batch of inputs, the model is then optimized subject to the loss criterion
L TT. Σ kElayers
ag
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where TL is the task loss and og is the relative weight of the spatial loss associated with layer k. This combined loss metric encourages the model to learn representations that are both spatially organized and useful (and, in the case of self-supervised cross-entropy task loss, task-general).
Model Specification and Training. In the below experiments, we utilize an adapted GPTl---malll style architecture (Radford et al., 2019). We use hidden dimension 784 such that we can evenly embed units in a 28 x 28 grid. The model has 12 Transformer blocks, each with 16 attention heads and a GELU activation function. We train our models on randomly sampled 10B-token subset of the Fine Web-Edu dataset. The task loss cross-entropy on next-word prediction. We use batch size 48 and block size 1024. For spatial loss, we set Org 2.5 across all layers* and operationalize the inverse distance vector with the gor norm. For each batch, we average the spatial loss across 5 randomly selected neighborhoods, each of fo radius 5. This allows us to compute loss more efficiently without significant performance drops.
We train both topographic model and non-topographic bascline, where as 0 and all other hy- perparameters remain the same. We trained both models with early stopping after three consecutive increases validation loss. At the end of training, the topographic model achieved validation task loss of 3.075 and spatial loss of 0.108 (summed across layers), while the non-topographic model achieved validation loss 2.966. Models trained for days 4xNVIDIA 80GB A100s.
In all below analyses, we compare TopoLM to BinHuraib et al. (2024)'s pre-trained Topoformer- BERT, BERT-style model (Devlin al., 2019) with local connectivity trained on the BookCorpus dataset (Zhu et al., 2015). Note critically that Topoformer-BER is a baseline, but not a control-it trained on a much smaller corpus, has only one attention head per layer, and is bidirectional.
model from exploiting the feed-forward nature of the Transformer. Without it, the model minimizes spatial loss by propagating the same spatial pattern through the network; Figure 12.
"This could be controlled for using many alternative methods, e.g. a Gaussian smoothing kernel. However, we choose use neighhorhood--evel approximations for simplicity.
*We chose this value after extensive hyperparameter search. In particular, lower values of a do not adequately encourage the development of topography, while greater values impede task performance and the development of meaningful representations.
After hyperparameter tuning, we optimize using AdamW with 31 0.9, 32 0.95 and learning rate 6 x 10 4 scheduled with warmup and cosine decay. We use weight decay 0, gradient clipping at 1.0, and do not use dropout. Neighborhood size and number of neighborhoods were also determined via hyperparameter search; note, however, that empirically observed little effect of neighborhood size and number of neighbor- hoods task performance on our topographic metrics.
'Topoformer- BERT has 16 layers, each with single attention head, with topographic constraints applied both at the output of each attention layer and after the key matrix product; we therefore compare Topol.M to outputs these levels. We refer BinHuraib al. (2024) for more details.
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(a) TopoLM: Individual Responses Across Language Selective Clusters
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Figure 2: Brain-like response profiles across the core language system. (a) Applying a functional localizer (Fedorenko al., 2010) we isolate the core language system of TopoLM, and find clear brain-like spatial organization (for brevity, we only show Transformer blocks 5-12 here). Response profile across individual language-selecnn selective clusters (shown in yellow) TopoLM are similar to one another, consistent with (b) the language system in human cortex (Fedorenko et al., 2024). (c) Across the entire core language system, TopoLM (blue) mostly matches the neural data (green), but not exactly; however, the non-topographic baseline model (orange) fails capture neural patterns as well.
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Readout Sampling. Due to the coarse spatial sampling in fMRI neuroimaging work, voxels con- tain the aggregated response of a large population of neurons (Kriegeskorte et al., 2010, Figure 1C). In all following analyses, we thus apply simulated version of fMRI readout sampling to model acti- vations, consisting of smoothing with a Gaussian kernel, to imitate the locally aggregated responses of fMRI voxels. Importantly, we do so before computing selectivity based these activations, and thus do not apply readout sampling to the functional selectivity maps directly. We set unit distance 1.0 mm and FWHM 2.0 mm.
4 SPATIO-FUNCTIONAL ORGANIZATION OF THE CORE LANGUAGE SYSTEM
Language processing in the brain engages a set of left-lateralized frontal and temporal brain regions. These areas are typically referred to as the "core language system' (Fedorenko et al., 2010) and respond selectively to linguistic input in contrast to non-linguistic stimuli (see Fedorenko et al., 2024, for an overview). Due to anatomical differences between individuals, the language system is defined via a functional localizer that contrasts syntactically and semantically valid sentences against a perceptually matched control, such as strings of nonwords (Fedorenko et al., 2011).
Within individuals, the core language system shows clear spatio-functional organization, wherein language selective neurons cluster together across multiple cortical lobes. Anatomically distinct subregions of this system exhibit highly consistent response profiles to stimuli. suggesting that the system operates as a network (e.g. Fedorenko et al., 2011: Tuckute et al., 2024) (Figure 2B).
Prior work on neural alignment in language models typically compares neural responses across the entire core language system of the brain to model activations. The topographic organization of our model enables us to test for the emergence of a brain-like spatially organized core language alignment between brain and model would mean that (1) distinct innguage-selectiv clusters emerge in the model, (2) these clusters all have consistent response profiles similar to consistent response profiles across sub-regions of the 'core language system' in humans 7, and (3) the response profiles match the activity profiles in the brain (sentences (unconnected words, jabberwocky) > nonwords; AlKhamissi et al., 2024).
system in silico. A successful
Methods. To isolate the core language system in TopoLM, we use the same localization stimuli as Fedorenko et al. (2010), which consists of set of 160 sentences and 160 strings of non-words, all 12 words each. After passing these through the model, at each attention and MLP layer we run a t-test across the activations of all layer units. We then define the core language system as all units that are significantly language-selective (p < 0.05 after correction for multiple comparison across all layers using the false-discoverr--att (FDR) (Benjamini & Hochberg, 1995)).
We then define iinguage-selectvvv clusters using an evolutionary clustering algorithm applied to each contrast map. In each layer, we begin with the most selective unit by (-value, and then repeatedly add the most selective neighboring unit to the cluster, until we hit a pre-determined p-value threshold associated with the unit's selectivity (here, (FDR) 0.05). We repeat this process, searching for new clusters until all units in the layer are exhausted. We discard clusters with fewer than 10 units.
Within each cluster, we measure responses to the same stimuli used in neuroscience experiments (Figure 2B, Fedorenko et al., 201 I): sentences (indexing syntactic and lexical information), uncon- nected (scrambled) words (lexical but not syntactic), Jabberwocky sentences which are well-formed sentences where content words are replaced by phonotactically plausible non- wondwords (syntactic but not lexical), and unconnected (scrambled) non-words (neither syntactic nor lexical). Note that these stimuli are distinct from those used for localization. We measure the model 'response" as the mean absolute activation across all units in a cluster.
Results. TopoLM exhibits clear brain-like spatial organization of the language network, such that (1) multiple Linguage-selective clusters emerge across the topographic tissue (Figure 2A and Fig- ure 8), (2) across most clusters, the response profiles are consistent with one another (Figure 9), and (3) response profiles mostly match the ones in the brain. The response profiles are not perfect match to the brain data-whi sentences have higher activations than Jabberwocky and nonword stimuli,
T"The language areas all show similar response profile (despite slight apparent differences, no region by condition interactions come out as reliable, even in well-powered studies." " Fedorenko al. (2024),

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Figure 3: Brain-like verb- and noun-selective clusters in TopoLM. (a) IMRI data from Hauptman et al. (2024) points to verb- (red) and noun-selective (blue) regions in the human cortex with strong clustering (Moran's = 0.96). (b) Quantification of clustering. Relative the brain (green dashed line), the non-topographic baseline shows limited clustering (orange). The topographic model shows moderate clustering at the unit level (light blue) and strong clustering when simulating fMRI sampling (dark blue). On stimuli from Moseley & Pulvermüller (2014) (fMRI data not available) we find qualitatively similar results. (c) Exemplary model maps (last MLP layer) showing the verb-/noun contrast (red-blue) in response to stimuli from Hauptman et al. (2024). The non-topographic baseline shows no clustering while the topographic model develops verb- and noun-selective clusters.
high clustering in
they do not have higher activation than unconnected words as in brain data. However, looking across the entire language selective network, the response profile of the non-topographic baseline model similarly fails to capture the neural response profile (Figure 2C), suggesting general shortcoming of the base transformer model, rather than weakness topography. We similarly find evidence for Linguage-selective clustering in Topoformer-BERT BERT (see Figure 13).
5 SPATIO-FUNCTIONA. ORGANIZATION OF SEMANTIC CLUSTERS
Beyond selectivity for language in general, experimental evidence supports the existence of cortical noun- and verb-selective clusters across human subjects during processing of verbal and nominal stimuli in auditory (Elli et al., 2019; Hauptman et al., 2024), visual (Moseley & Pulvermüller., 2014), and speech production (Shapiro et al., 2006) tasks. Here, we compare spatial activation patterns predicted by TopoLM to two groups of fMRI studies: Elli al. (2019)/ Hauptman et al. (2024), who use the same set of stimuli and the same experimental setup (Figure 3 and Appendix Figures 7 and 10), and Moseley & Pulvermüller (2014) (Figure 4). We evaluate Topol predictions quantitatively using Hauptman et al. (2024)'s IMRI data and perform qualitative evaluations where no neural data was available (Elli al., 2019; Moseley & Pulvermüller, 2014).
5.1 CLUSTERS SELECTIVE FOR VERBS AND NOUNS
Neuroimaging Study. Using fMRI data from Hauptman et al. (2024) ( (Appendix B), we find verb- and noun-selective clusters in the left hemisphere (Figure 3A and Appendix Figure 7), thus repli- cating their results. To quantify the 'degree' of clustering in these maps, use Moran's I with
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Figure 4: Verb- and noun-selectivity in response to concrete and abstract stimuli. (a) Using stimuli from Moseley & Pulvermüller (2014), we find verb-/noun-seelectve clusters (verb: red / noun: blue) emerging in TopoL.M for concrete (solid lines), but not for abstract words (dashed lines), thus replicating their results.
(b) We obtain strong verb-/noun-clustering when concrete words are used to compute the verb-/noun-contrast (light blue, solid lines), / = 0.80), but substantially lower clustering for abstract words (/ = 0.23, light blue, dashed lines, 1-test: p < 0.001). However, we when using the cootrppoga control (I = 0.11 vs. 0.12, f-test: p > 0.05, orange). Results do not change qualitatively when fMRI readout sampling is performed before computing contrasts and clustering (dark blue). In all the presented cases, spatial autocorrelation is computed on un-thresholded maps (for all layers, see Figure 11). Following neuroimaging conventions on defining category-selectee cortical clusters, we show model maps thresholded at p(FDR) < 0.05.
do not find evidence for such difference in verb-/noun-clusterii
Queen contiguity (i.e. fe0 radius, following the distance metric used train TopoLM), common measure of spatial autocorrelation, ranging from -1 to 1 (see Appendix A for details). The group level effects indicate strong clustering (I 0.96, p < 0.001).
Clustering in TopoLM To investigate whether similar verb- and noun-selective clusters emerge in TopoLM, we extracted the model activations in response to the same stimuli as Elli et al. (2019) and Hauptman al. (2024). We find that verb and noun-selective clustering emerges across layers in MM after contrasting activations to verb and noun stimuli (verb: red / noun: blue, Figure 3A, Figure 10). Similar to our analysis of the neuroimaging data, quantified this observation using Moran's T. The non-topographie baseline model yields a low degree of clustering (T = 0.11). Contrast maps in TopoLM show strong degree of clustering (1 0.48) which is further increased when applying iMRI-like readout sampling (1 = 0.81, Figure 3B). Applying the same sampling to the non-topoga model also increases clustering, but remains substantially less brain-like than the topographic model (I = 0.60, Appendix Figure 10).
Clustering in Topoformer-BERT. Applying the same procedure to Topoformer-Bal BERT, we find no evidence for noun-verb selective clustering, with few units coming out significant in the noun- verb contrast (10.61% of units; see Figure 13). However, we do find that, before thresholding for significance (p 0.05), the model does exhibit high degree of clustering competitive with TopoL. (Moran's / = 0.66 before sampling, 0.85 after sampling). In other words, though local connectivity constraint induces clustering in the model, these clusters do not match the paaiiofunctional organi- zation of the brain. This impression is confirmed by additional anaylsis using a variant of Moran's 's that only considers units with significant t-values (Figure 14).
5.2 CLUSTERS SELECTIVE FOR CONCRETE, BUT NOT ABSTRACT VERB-NOUN CONTRASTS
Neuroimaging Study. Moseley & Pulvermüller (2014) focus how cortical noun-verb selectiv- ity relates to semantics, in particular focusing on concreteness. Examining specific anatomically defined brain regions in fMRI, this study finds evidence for selectivity between concrete verbs and
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concrete nouns; yet, critically, there is no evidence for responses abstract words from the same categories. Here, we investigate whether TopoLM replicates these findings- both the existence of spatially organized noun-verb selectivity in response to concrete words and the nonexistence of this selectivity in response to abstract words (Figure 4).
Clustering in TopoLM. We presented the original experimental stimuli to TopoLM and computed contrasts between abstract and concrete verbs and nouns (see Appendix C for stimulus details). Rather than comparing response profiles in anatomically defined subregions as in Moseley & Pul- vermüller (2014) (since the model lacks defined 'anatomical' regions), we explore whether lexical class-selective clustering emerges between concrete and abstract words. Consistent with brain data, we find clustering of verb- and noun-sclective model umits in concrete stimuli, but find only very weak or no clustering for the same contrast in abstract stimuli. We quantified this impression us- ing again Moran's s Т: concrete words yield substantially higher verb-/noun-clustering than abstract words (7 0.8 vs. = 0.23 in unthresholded maps for TopoL.M, Figure 4, light blue). We obtain qualitatively similar results when simulating the IMRI sampling process before computing contrasts (Figure 4, dark blue). Additionally, we observed overall low degrees of clustering in non-topographie baseline models and no evidence for difference in the degree of clustering when concrete vs. abstract words were used for computing the werb-/noun-conraat (Figure 4, orange).
Clustering in Topoformer-BERT. We again apply the same procedure to Topoformer-Bal and find evidence for noun-verb selective clustering. with units coming out significant in the noun-verb contrast (see Figure 13). Again, before thresholding, we find high clustering (concrete- 0.60 before sampling, I 0.84 after; abstract-abstract: sampling, / 0.84 after); yet since none of these units come out significant, we fail to find evidence for brain-like spatio-fumt fantioffuntional organization in Topoformer- BeeRTorme-BBRRTTTT BERT (for details, see Figure 14).
concrete: Moran's
0.61 before
6 DOWNSTREAM PERFORMANCE AND BRAIN ALIGNMENT
Some topographic vision models sacrifice task performance for the sake of spatial organization, leading diminished utility as a model of brain function (Lee al., 2020). As control, we evaluate TopoLM's performance on linguistic knowledge (BLiMP), downstream task (GLUE), and brain alignment benchmarks (Brain-Score), compared to the non-topographic baseline model.
Benchmark Description and Methods. BLiMP (Warstadt et al., 2020) is a multi-task linguistic benchmark consisting of minimal pairs (acceptable / unacceptable) that probe knowledge of linguis- tie phenomena; Models are evaluated without fine-tuning. Brain-Score Language (Schrimpf al., 2021; 2020) is a set of benchmarks that measure how well models align with the human language system. We train a ridge regression model to predict brain activity from model representations, using the same stimuli as in the neuroimaging studies. Representations are taken from each transformer block with spatial loss (attention and MLP). For both models, we select the output layer with the best alignment across datasets. The final score is the Pearson correlation between actual and pre- dicted brain activity, averaged over 10 vross-validation folds and over four recordigg datasets (Blank et al., 2014 4; Fedorenko et al., 2016; Pereira et al., 2018: Tuckute al., 2024, Appendix D). GLUE (Wang et al., 2018) is a multi-task benchmark for downstream performance on tasks like entailment and sentiment analysis. We fine-tune models for each task. During fine-tuning, we use the same weighted combination of task loss (cross-entropy or MCC) and spatial correlation loss with = 2.5. We set batch size 64, dropout 0.1, and learning rate 2 x 10 10-5; all other hyperparameters are the same as during pretraining. We use early stopping after 3 successive increases in validation loss, keeping the checkpoint before this increase.
Results. We find that introducing spatial correlation loss does not strongly affect task performance or brain alignment (Table 1). On BLiMP, we find slight decreases in performance between TopoLM and the non-topographic baseline across all subtasks, with a 5 point average decrease overall. On Brain-Score, we find 2 point average decrease overall, with TopoLM ourperforming the non- topographic baseline on some subtasks (see Appendix D, Figure 6). On GLUE, across most subtasks see increase in performance from TopoLM compared to the baseline model, with 3 point average increase overall. We hypothesize this increase might be due the spatial loss term serving as additional regularization against overfitting.

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Model
BLiMP
GLUE
Brain-Score
TopoLM
0.71
0.68
0.78
Non-topo
0.76
0.65
0.80
Table 1: Results from evaluation of TopoLM and a non-topographic baseline ("non-topo") on BLiMP, GLUE, and Brain-Score The baseline model outperforms TopoLM on BLiMP (5 pts) and Brain-Score (2 pts), but TopoLM outperforms the non-topographic control on GLUE (3 pts).
7 DISCUSSION
Here, we presented a new topographic Transformer language model based on spatial smoothness constraint and showed that it predicts key patterns of spatio-functional organization from the neu- roimaging literature. We demonstrated that TopoLM has a spatially organized core language system exhibiting brain-like uniformity of response profiles across clusters. TopoLM also shows brain- like noun-verb selective clusters, specific to concrete over abstract words. This spatial correspondence the human brain comes at virtually no cost to performance or functional brain alignment.
Spatial smoothness principle. TopoLM is in the TDANN family of models. Margalit et al. (2024) originally posited the loss term underlying TDANN models as a unifying account of the develop- ment of spatio-fund funicionna organization in the visual cortex. TopoLM successfully extends the corre- sponding spatial loss to the domain of language neuroscience, and thus provides evidence that this principle of spatial smoothness indeed generalizes across cortex.
Comparison with Sopoformer-BRRT. We also observe evidence for spatial organization with noun-verb contrasts in TopoLM, but not BinHuraib al. (2024)'s Serfformer-BRRT However, Fedorenko et al. (2010)'s stimuli do reveal spatially organized language network in Topoformer- BERT. This asymmetry likely in part because the model induces topography only in the attention layers, which primarily track relationships between tokens: while Fedorenko et al. (2010)'s 's stimuli consists of entire sentences, the noun-verb contrast stimuli are one or two word items.
However, it's important to note that-while this comparison is useful baseline- primary goal to ask whether the TDANN spatial smoothness principle generalizes to language, not build topographic language model that "improves" on certain benchmarks. Topoformer asks similar question using a different guiding principle (local connectivity), but these models do not necessarily "compete" with one another: indeed, TopoLM's spatial smoothness and Topoformer's 's explicit local connectivity are both closely related to the principle wiring length minimization.
Limitations.
TopoLM a feed-forward model of linguistic processing with multiple layers. Since the topographic maps are specific to each layer, there is as such no coherent tissue across the entire system in the the brain. This also limits eventual modeling of 'BMI' tissue perturbations, such as since the spread of current ends at one topographic map (out of several).
Model-guided experiments. Since TopoLM is stimulus-computable can used to discover new candidates for spatial clustering in linguistic processing. For instance, the automatic identi- fication of clusters emerging from model activations in response to extensive textual input could inform the selection of optimal stimuli for further neuroimaging experiments. Given that the model successfully predicted spatio-functional organization three existing brain datasets, it is likely that additional predictions derived from this approach would be informative.
Taken together, our results suggest that the spatial smoothness principle leads to topographic orga- nization consistent with the spatio-functional organization of linguistic processing in the brain.
ACKNOWLEDGMENTS
We thank Miriam Hauptman and Marina Bedny for providing fMRI data and for useful discussion. We also thank Greta Tuckute, members of the EPFL NeuroAl lab, and members of the Stanford CLiMB Lab for helpful feedback. Neil Rathi supported by Summer@ Commer@@PPP. EPFL Fellowship.
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A MORAN'S I AND SPATIAL AUTOCORRELATION
We use Moran's / to estimate the degree of clustering in TopoLM layer maps and in surface-based IMRI data. Moran's / given by
N j== -
1 N
Li=1
Ei=1 (2, x)²
where is the number of units (e.g. fMRI vertices or model units), 2; is the value at position i, 7 is the mean of all 3;, and Way is weight indicating the spatial relationship between units at positions i and j such that Wij = if two points are 'neighbors' and wii = 0 otherwise (see below on how this is defined).
Moran's / ranges from -1 to 1. Positive values indicate spatial clustering, where similar map val- ues (e.g., high-high or low-low) tend group together; negative values indicate spatial dispersion, where dissimilar map values (c.g., high-low) are neighbors; and a value close to 0 indicates no au- tocorrelation, i.c. random distribution. In our data, we do not see significantly negative values of I, as spatial dispersion is systematic non-random pattern not encouraged by topography.
Application to TM layer maps. To quantify the degree of clustering in TopoLM maps (fig- ures 3, 4), apply Moran's using 'Queen' contiguity (i.e. an 8o0 radius). Queen contiguity a measure commonly used in geospatial statistics, where each model unit is considered to be a neighbor if it shares any boundary (edges or corners) with another model unit of the same layer. This method allows for more inclusive neighborhood structure than 'Rook' contiguity, which only considers edge-sharing neighbors.
Application to (MRI vertices. We analyzad fMRI data from the left hemisphere of 22 sighted subjects from Hauptman et al. (2024). The functional and structural data were pre-processed by Hauptman et al. (2024) and provided as GIfTI files. These files contain the cortical surface repre- sentation with 32,492 vertices (GIfTI format, Human Connectome Project benchmark) spanning the left hemisphere. To quantify the spatial autocorrelation in the fMRI data (fig. 3), we define wij such that each vertex is considered to have six direct neighbors, reflecting the surface mesh struc- ture where each vertex connects to six surrounding vertices based on their adjacency on the cortical surface.
Independent of the input modality (model layer units, fMRI vertices) Moran's / was always applied to un- un-thresholded maps. This is because thresholding map before applying Moran's s I would artificially inflate the estimate of spatial autocorrelation, as it results in contiguous patches of values.
B HAUPTMAN ET AL. (2024): DESIGN AND FMRI PROCESSING
IMRI Processing. Both Elli et al. (2019) and Hauptman et al. (2024) are based on IMRI recordings in response to the same task and stimuli similarity judgments of auditorily presented words and both investigate the relationship between sensory input and conceptual representations in the human cortex. Elli et al. (2019) (n 13) provide evidence suggesting that lexico-semantic information about verbs and nouns is represented in partially non-overlapping cortical networks (Figure 1A in Elli et al. (2019)). The data from Hauptman et al. (2024) are available at OPENICPSR.
Hauptman et al. (2024) presented the same auditory stimuli 21 congenitally blind and 22 sighted subjects and investigated how neural representations of sensory concepts develop independent of sensory experience; here, we only include data from the 22 sighted subjects our analysis. Similarly to Elli et al. (2019), Hauptman et al. (2024) find distinct verb- and noun noun-selective regions (c.g. Figure 3A Hauptman et al. (2024); Figure 7 below). For scanning parameters, and details on the fMRI preprocessing pipeline, see Hauptman et al. (2024).
Experimental Design. In each 2-second trial, subjects assessed the similarity of two auditorily presented words from the same verb or noun subcategory (e.g., bird or mammal for nouns, light
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Figure 5: Brain-Score brain aligmment performance (linear predictivity). We tested TopoLM and the non-topographic control on Brain-Scont language using linear predictivity to estimate align- ment. TMpoLM outperforms the control in Blank2014 and Tuckete2024, but performs slightly worse at Pereira2018 8 and Fedorenko2016 (f-test performed for each benchmark separately: < 0.05). For each benchmark, we sampled from cross- valssvvali loops to compute the bootstrapped 95% confidence intervals (black bars). When results are averaged across the 4 benchmarks (last panel "Brain-Score",, we don't find evidence for significant difference between TopoLM and its control (t-test: p > 0.05).
or sound for verbs). Four trials, all using stimuli from the same subcategory, form mini-block, followed by 10-second baseline condition. This yielded total of 288 pairs of nouns and 288 pairs of verbs?.
To evaluate each vertex's selectivity for mini-block, we ran general linear model with one pre- dictor per mini-block. Contrasting verb and noun mini-blocks produced t-value for each vertex, indicating selectivity toward verbs vs. nouns. As in Hauptman et al. (2024), we based our analy- sis on data from the left hemisphere, which is more involved in language processing (Frost, 1999; Szaflarski et al., 2006); this is standard in work language neuroscience.
C MOSELEY & PULVERMÜLLER (2014): EXPERIMENTAL DESIGN.
In each trial, 18 participants from Moseley & Pulvermüller (2014) silently read single word from one of four categories: abstract nouns (e.g. clue, guide). concrete nouns (e.g. rice, goose), abstract verbs (e.g. heal, dwell). and concrete verbs (e.g. knit, poke). In total, there were 40 stimuli in each category for total of 160 words. For additional information on the experimental design and neuroimaging parameters, please see Moseley & Pulvermüller (2014).
D BRAIN-SCORE LANGUAGE DATASETS AND PERFORMANCE
Blank et al. (2014) This dataset consists of fMRI signals recorded from 12 functional regions of interest (IROIs), offering a lower resolution than the dataset used by Pereira al. (2018). Five par- ticipants listened to eight naturalistic stories, adapted from fairy tales and short stories (Futrell et al., 2018). Each story lasted approximately five minutes, containing around 165 sentences, providing significantly longer context compared to other neuroimaging datasets.
Fedorenko et al. (2016) This dataset captures ECoG signals from five participants as they read sentences consisting of eight words, presented one word time for either 450 or 700 ms. Follow- ing Schrimpf et al. (2021), we focus on 52 out of 80 sentences presented to all participants.
'aah pair was presented with verbs in the infinitive (with 'to') and nouns in the definite (with 'the'). Removing these determiners when feeding stimuli through the model results in visually more distinct selectivity clusters; Figure 10.
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Pereira2018
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non-topograge graaphiccc
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Figure Brain-Score brain alignment performance (RSA). We tested TopoLM and the non- topographic control on Brain-Score language using representational similarity analysis (RSA) to estimate alignment. TopoLM outperforms the control in Pereira2018, but performs worse at Blank2014 and Fedorenko2016 (t-test performed for each benchmark separately: p < 0.05). For each benchmark, we sampled from 10 cross-validation loops to compute the bootstrapped 95% confidence intervals (black bars). When results averaged across the 3 benchmarks (last panel "Brain-Score",, we find evidence for a significant difference between TopoLM and its control (t- test: p > 0.05). However, this result needs be interpreted with caution it is dominated by the results from Fedorenko2016 which only show very large absolute values, because the underlying data used for normalization very noisy, i.c. the noise ceiling is very low.
Pereira et al. (2018) This dataset contains fMRI activations (BOLD responses) recorded as par- ticipants read short passages, with each sentence displayed for four seconds. It consists of two experiments: the first with nine participants reading 384 sentences, and the second with six partici- pants reading 243 sentences. Each experiment covered 24 topics. Results reported the average alignment across both experiments, normalized using cross cuoss-tubect consistency estimates.
Tuckute al. (2024) This dataset used assess the distributional robustness of language mod- els. Five participants read 1,000 six-word sentences, each presented for two seconds. BOLD sponses from language network voxels were averaged both within and across participants, providing overall response for each sentence. The stimuli span wide linguistic range, allowing for diverse model-brain comparisons. Randomized sentence order and averaging across participants reduce temporal autocorrelation effects, making this dataset particularly challenging for model evaluation due to the linguistic diversity.
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SUPPLEMENTARY FIGURES
ventral
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Figure 7: Verb/noun-cluster across the human cortex. Re-analyzing data from Hauptman et al. (2024), we replicated their main findings in that we found gerb-/noun-selecttin clusters (red vs. blue) across the left hemisphere. We here show group-level results of all sighted subjects at p(FDR) < 0.05.
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TopoLM language selectivity
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Figure 8: Core language system. Using stimuli from Fedorenko et al. (2010), we create contrast maps reflecting language-selectivity for each unit of a given layer (language-selective cluster in yellow). We here show maps for TopoLM with (right columm, dark blue) without (center column, light blue) simulating the fMRI readout sampling process. Using a cluster growing algorithm we identify language-selective clusters. For comparison, we also show the language-selectivity maps from the non-topographic control (left column, orange frames).
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Figure Consistent response profiles across language-selective clusters in TopoLM, Us- ing stimuli from Fedorenko et al. (2024), we extract response profiles to 4 linguistic categories across language-selective clusters. Importantly, the observed response profiles are consistent across Iinguage-selective clusters. For brevity, here, only show clusters with more than 100 units.
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Figure 10: Verb-noun clusters across TopoLM layers in response stimuli from Hauptman et al. 2024. Complementing Figure 3, here, we show autocorrelation estimates (Moran's 1) for both To and its non-topographic control with and without FWHM filtering to simulate the fMRT sampling process (upper panel) and the associated verb-noun contrast maps (verb: red / noun: blue) for layers (columns 1-4). When the stimuli are presented without 'to" or "the" to accompany verbs and nouns, respectively, the verb-noun clustering becomes more prominent (columns 5-6).
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stimulus presentation Moseley 2014]
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Figure 11: Verb-noun clusters across TopoLM layers in response to stimuli from Moseley et al. 2014. Complementing Figure 4, here, we show autocorrelation estimates (Moran's Z) for both TopoLM and its non-topographic control with and without FWHM filtering to simulate the fMRI sampling process (upper panel) and the associated verb-noun contrast maps for 5 layers. Autocorre- lation estimates based the verb-noun contrast maps (verb: red noun: blue).
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Figure 12:
Verb-noun clusters in a TopoLM without randomly permuted positions. As de- trained an equivalent model without first randomly permuting the spatial
scribed in Footnote encoding of each layer. We evaluate this model on the stimuli from Hauptman et al. (2024) and Moseley & Pulvermüller (2014). We see that the spatial activation pattern propagates through the entire network, the model no longer has to learn unique spatial maps for each layer in order to minimize spatial loss. Verb and noun clusters shown in red and blue respectively.
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Figure 13: Topoformer-BERG Evaluations. Contrast maps (with fMRI-like readout sampling) for Topo (BinHuraib et al., 2024) on stimuli from Fedorenko et al. (2010), Hauptman et al. (2024), and Moseley Pulvermüller (2014). We plot contrasted activations after multiplication by the key matrix and after the entire attention layer, this is where local connectivity is applied. We note that few units come out significant for the stimuli from Hauptman et al. (2024) and Moseley & Pulvermüller (2014); however, identify some clusters in Fedorenko et al. (2010)'s language localization task.
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Figure 14: TopoLM comparison of clustering with baseline model. We compared TopoLM to an additional baseline model (Topoformer BERT,, BinHuraib et al. (2024)) with regard to clustering. Most t-values across contrasts multiple datasets (Hauptman et al. (2024); Moseley & Pulvermülllrr (2014)) are not significant in Topoformer BERT (after applying FDR correction as has been done in TopoLM).. Thus, we estimated autocorrelation using variant of Moran's I only considering "is- lands" of units with significant t-values for given contrast (and averaging across islands while not considering island size to obtain a single estimate per map). We computed "Islands Moran's for both TopoLM and Topoformer BERT. A) Using this metric, we find strong clustering in TopoLM (Island's Moran's 0.52 without simulated fMRI sampling, and Island's Moran's = 0.83 with sampling). numbers matching our results when computing Standard Moran's simulated iMRI sampling, 0.85 with sampling). In contrast, we observe patterns of dispersion neither clear dispersion. nor autocorrelation in Topoformer BERT (Island's Moran's -0.51 without simulated IMRI sampling, and Island's Moran's -0. with sampling). B-E) With the exception of one contrast (see panel E), TopoLM results based data from Moseley & Pulvermüller (2014) using Islands Moran's 's qualitatively match the results obtained by using Standard Moran's I. In contrast, in Topoformer BERT autocorrelation using Islands Moran's cannot be computed for the contrasts in Moseley & Pulvermüller (2014) as t-values underlying the contrast maps are not significant. F) Legend.
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Reviews:
[{"review_id": "ZAJ16Ua3tQ", "reviewer": "Reviewer_3QeR", "summary": "This work introduces TopoLM, a transformer language model incorporating information about the spatial arrangement of the units to model brain-like activity in the processing of language. In particular, the spatial information is integrated by adding a spatial smoothing term to the classical autoregressive loss of decoder-only transformers. By performing functional localization experiments, the authors identify clusters of artificial neurons in TopoLM whose activations are language-selective. The authors highlight the similarity between TopoLM clusters of activations and response in the brain by conducting experiments on verb-noun and concrete-abstract selectivity.", "questions": "Some further experiments and discussions could further strengthen the work:\n- How does the choice of randomly permuting positions at each layer influence the representations? It would be extremely interesting to consider different types of mapping between spatial positions at successive layers.\n- The authors stress the role of considering architectures with multi-head self-attention. Is this type of architecture expected to better model human neural activity? \n- In the NLP community, it has been observed a hierarchical organization of syntactic and semantic information in hidden layers of deep learning models (e.g. Belinkov, ACL, 2017; Manning, PNAS, 2019). Do the TopoLM clusters of activation exhibit some level of hierarchy through the layers of the model?\n- In case it is feasible, comparing TopoLM representations/clusters also to Topoformer would further strengthen the quality of experiments.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "The authors contextualized and described with clarity the strategy introduced to incorporate spatial information of activations in transformers for natural language processing. Both the training details and experiments are very well explained and organized.\n\nThe work, inspired by previous efforts in vision models, introduces for the first time (to the reviewer knowledge) explicit spatial information in the loss of transformers trained on natural language.", "weaknesses": "Given the strong inspiration from human neural activity studies of the work, the work would benefit from more extended discussion and analyses related to some architectural choices (e.g. random permutation of spatial position between layers and role of multi-head attention).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "dY0lHLJiRT", "reviewer": "Reviewer_TBeb", "summary": "The study introduces TopoLM, a model based on the transformer architecture, aimed at exploring the spatial functional organization of human language systems. This model optimizes autoregressive language modeling by incorporating two-dimensional spatial encoding, along with task and spatial loss, which encourages response smoothness among adjacent units. Experiments demonstrate that the spatial functional organization generated by TopoLM closely aligns with the neuronal clusters found in the brain's language system. Although TopoLM scores slightly lower on certain behavioral tasks compared to non-topological baselines, its performance is comparable on other downstream tasks and brain alignment benchmarks. This indicates that TopoLM successfully captures the topological structure involved in language processing when trained on natural text, providing new insights into the functional organization of language systems.", "questions": "Could you elaborate on the specific architectural choices made in TopoLM?  For instance, what motivated the selection of particular layers or activation functions, and how do these choices contribute to the model's performance compared to traditional language models?\n\nCan you provide more insight into the training process for TopoLM?  Specifically, what datasets were used, and what were the criteria for their selection?  Additionally, how did you address potential issues like overfitting during training?\n\nIn your discussion of the biological implications of TopoLM, could you provide references or data from neuroimaging studies that support the connection between the topological aspects you incorporate and the way the human brain processes language?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "TopoLM introduces a novel approach to understanding the spatial organization of language processing in the human brain.  By integrating two-dimensional spatial encoding into a transformer architecture, the model effectively captures the topological structure of language, which has not been extensively explored in existing literature.  This innovative perspective opens new avenues for research in language modeling and cognitive neuroscience.  Meanwhile, this research has significant implications for both artificial intelligence and neuroscience.  By aligning computational models more closely with the biological structures of the brain, TopoLM paves the way for more effective natural language processing applications.  Furthermore, it contributes to a deeper understanding of the neural mechanisms underlying language, potentially informing both theoretical frameworks and practical applications in cognitive science and related fields.", "weaknesses": "While the paper presents a promising theoretical framework, the empirical evaluation of TopoLM is somewhat limited.  The experiments primarily focus on a small set of tasks, which may not fully capture the model's robustness across diverse linguistic contexts.  Meanwhile, this paper does not sufficiently explore or compare TopoLM with other existing topological models in language processing.  Including a comparative analysis with relevant models could strengthen the argument for TopoLM's effectiveness and novelty.  Highlighting specific improvements or unique aspects of TopoLM in relation to these models would enhance the discussion around its contributions to the field.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "DevF8uxIxw", "reviewer": "Reviewer_U3qv", "summary": "The paper presents a language model whose training objective is based on a joint loss function: the standard next-word prediction loss and an additional spatial regularization term, which enforces a constraint where adjacent neurons exhibit more similar activation profiles than those of more distant neurons. The primary contributions of the paper are: (1) demonstrating that such a model can be successfully trained, resulting in an increase in local spatial correlations, (2) showing that its performance on standard benchmarks is comparable to models trained without the spatial regularization, and (3) providing evidence that the learned representations exhibit some degree of isomorphism with neural representations. For example, certain spatial clusters show stronger activation in response to well-formed sentences compared to nonsensical ones, and there appears to be a distinction between cluster-responses to nouns and verbs.", "questions": "1.  I did not understand the argument about smoothing reducing wiring length. From my understanding, the TDANN network, even after training with the spatial regularization, retains the same dimensionality (weight matrix) as a non-spatial network. What then is the basis for the claim that this minimizes wiring length? (This refers to p. 3: “The TDANN’s spatial smoothness, as implemented with an additional loss term, is an indirect but efficient approach to minimizing local wiring-length.”) Additionally, from a functional perspective, in vision, hierarchical processing may reduce the need for long-range connectivity, as much processing occurs in localized circuits (even though reciprocal connections still exist). But in language processing, long-range connectivity seems essential. For instance, world knowledge can immediately influence lexical processing, and predictions can impact activity in primary and secondary auditory cortices, indicating that long-range connections are necessary in this domain.\n\n2. page 6, the statement that a successful alignment between brain and model is accompanied by “these clusters have consistent response profiles”; the meaning of this phrase was unclear.\n\n3. The analysis is focusing on univariate methods, where preference for sentence or word class is identified by differences in single-unit activation. But it is well known that the brain also represents information using multivariate (population) codes. What if a set of units, each of which shows similar activation for two classes of linguistic stimuli, can still be used to decode stimulus class through a population code?  From the perspective of the current work, these units will be defined as being outside the identified ‘selectivity’ clusters (and hence not considered ‘core’ to language). However, to the extent that a linear probe indicates that this population-code contains relevant information, there is no a priori reason to exclude them as being less relevant, essential or core to language.  For example, the null effect reported for sentences vs. unconnected words (p.6; results section) could still be consistent with the possibility that this set of units can differentiate between the two classes if a classifier trained and tested on their activations using linear probing. In short, the authors should better motivate why the operationalize ‘centrality’ to language based on univariate tests rather than population codes. \n\n4. For the benchmarks (p. 9) it seemed that fine-tuning involved retraining the entire model, rather than freezing the trained model, using it as feature extractor, and using a linear head for classification.  To evaluate the quality of features produced (rather than the model’s capacity to learn a new task) it would be useful to treat TopoLM and the control architecture as feature extractors, and apply the same procedure for learning a new task.\n\nReferences\n\nZhu, J., Evtimova, K., Chen, Y., Shwartz-Ziv, R., & LeCun, Y. (2023). Variance-covariance regularization improves representation learning. arXiv preprint arXiv:2306.13292.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper addresses a novel and important issue. There has been little work on training LLMs with topography constraints.  Successful training opens the door to interesting analyses, and potentially more flexible approaches for supervised learning of model-to-brain alignment. The writing is clear, and the analyses are interesting in that the authors apply well established statistical approaches used in the human neuroimaging literature to the model itself.", "weaknesses": "**P.S  following the discussion period: I believe the more critical perspective that was adopted by the authors during the review process improves the soundness of the paper. I have modified my evaluation.**\n\n1. The spatial loss term is a key element in the work and should be better motivated. \n1a. As phrased in the paper, the loss term constrains neurons that are closer to each other (according to a predefined spatial arrangement) to have more strongly  correlated activation profiles than those farther apart. However, this introduces a global, long-range constraint, because activation profiles of neurons that are far apart are not independent, but constrained to differ. To enforce a strictly local connectivity constraint, the authors could have employed a formulation that emulates Gaussian smoothing or another local averaging kernel, which would only consider the immediate neighborhood of each neuron. Reading the authors' motivation for the spatial regularization term on page 3, I expected a local spatial smoothing constraint rather than the more global constraint that was implemented. They write: \"This loss function measures spatial smoothness, which serves as an efficiently computable proxy for neural wiring length: neurons located close to one another should have similar response profiles—i.e., their activations should be correlated (Lee et al., 2020)\". In practice, for computational efficiency, the authors do not transform an entire layer to a grid-topology, but select 5 smaller areas; however, the point still holds.\n\n1.b In addition, the spatial-loss term introduces certain computational characteristics that should be considered in greater depth. Given its properties, it may encourage learning of decorrelated features, which could be advantageous for downstream transfer learning and fine-tuning.  In fact, this principle is used in a regularization technique introduced by Zhu et al (2023; https://arxiv.org/abs/2306.13292) to learn a potentially richer feature set. On the other hand, the spatial regularization term also pushes in the opposite direction: it enforces strong correlations between nearby units, potentially reducing the model’s effective capacity. In the extreme case, it can force two adjacent units to have almost identical activation patterns. This could limit the model’s ability to learn distinct features, which is a fundamental goal in neural network training. The authors briefly touch on this issue in the results section (p. 9), where they mention that the spatial regularization may help prevent overfitting, but this point asks for a more thorough treatment. \n\n2. The effects of the spatial loss on neuron-to-neuron similarity should be quantitatively evaluated\nIt is not clear how and whether TopoLM training changes the covariance structure of neural firing. It is important to rule out the possibility that non topographic models produce similar unit-to-unit correlation patterns compared to TopoLM. Otherwise, it would mean that training with spatial loss is not necessary for obtaining the resulting covariance structure.  This could be done by computing, for each neuron, a histogram of correlation values and averaging these histograms across all neurons.  If both TopoLM and standard models produce similar correlation distributions, it would suggest that typical neural networks naturally develop a graded connectivity structure similar to what TopoLM enforces, but this structure may manifest in a shuffled form in the absence of an explicit spatial arrangement.\n\n3. Some of the spatial results appear determined or constrained by the training objective and other procedures. \nThe finding that training produces stronger spatial smoothness and clustering seems to me to be a direct consequence of the spatial constraint in the training objective, which inherently encourages the formation of locally correlated clusters with weak correlations between remote clusters. Essentially, it implements a result similar to spatial data smoothing. Similarly, the fact that a simulation of fMRI readout-sampling (which applies further local averaging of unit activations) produces an even smoother data map is expected, as this is a direct result of the averaging imposed by the readout kernel.  Consequently, these properties do not emerge organically from the model’s spatial-loss training or fmri-like sampling, but instead reflect the successful implementation of the externally imposed constraints and workflow.  Because of this, the documentation of spatial clusters in statistical analyses is not surprising. For example, the authors write (p. 7) that “Contrasting model activations to verb and noun stimuli yields clear verb- and noun-selective clusters across layers in our topographic model”, but given the smoothing constraint applied, it would be very likely that the results would manifest in the form of clusters, as nearby units are constrained to be non-independent.  If these results are rephrased to be presented as a validation or sanity check that would make sense, but currently they are phrased as if they are a novel result. \n\n4. Some of the language-activation results appear dependent on the definition of language regions\nThe authors define a language system in TopoLM as the set of units that respond more strongly to grammatically valid sentences than to strings of non-words, which is analogous to the use of a functional localizer task in fMRI studies.  Then, for the network units identified by this condition, they evaluate responses to well-formed sentences and different types of language and language-like stimuli including strings of scrambled non-words or stings of phonotactically plausible non-words (jabberwocky sentences).  However, the aforementioned test used to define the localizer is not entirely independent of the subsequent evaluations. While it does not fully determine them, the localizer identifies units that are likely sensitive to word meaning and syntactic relationships, which are properties not found in the other stimulus types. Therefore, it is not entirely surprising that in the areas identified by the localizer, the strongest responses were to sentences, as compared to unconnected words, non-words, or Jabberwocky sentences.\n\nIt would have been more convincing if these results were found without the use of a localizer, using the spatial distribution alone: if the local clusters formed in the network are functionally meaningful, it would be important to see what information is encoded in those clusters.  If the strongest clusters naturally show a gradient of responses (e.g., from sentences to unconnected non-words), this would suggest that such distinctions are inherently emphasized during learning. Clusters can be identified via regional homogeneity (as done for fMRI) by computing correlation in response profiles across neurons.\n\nThe last two points also bear on the author’s ultimate conclusion, where they write, “Our results suggest that the functional organization of the human language system is driven by a unified spatial objective..”  I don’t think this follows from the results,  because I don’t see a basis for the analogy between the explicit spatial objective implemented in the paper (which produces some of the results) and those factors that ultimately lead to local correlations in the brain. Specifically, in the brain it is probably *unlikely* that there exists an objective that constraints nearby areas to fire similarly. This more likely emerges from cytoarchitecture constraints which produce different gradients of correlation (sometimes within the same neural population; https://pmc.ncbi.nlm.nih.gov/articles/PMC3412441/). \n\n5. General comment: I do not see a general weakness in the fact that benchmarks are not consistently improved by TopoLM. But what is lacking are more clear statements about whether TopLM develops different representations than non-Topo architectures.  This can be quantified by comparing representation-dissimilarity matrices, CCA, CKA or other methods for quantifying similarity of representations.  Of course, a comparison of these against RDMs computed from brain areas could also be helpful.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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:

Decision: Accept (Oral)